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Differing roles of disorder

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Title:
Differing roles of disorder Non-Fermi-Liquid behavior in UCu5-xNix and curie temperature enhancement in UCu2Si2-xGex
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Mixson, Daniel J., II
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x, 195 leaves : ill. ; 29 cm.

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Magnetization ( jstor )
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Thesis (Ph. D.)--University of Florida, 2005.
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Includes bibliographical references.
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by Daniel J. Mixson II.

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DIFFERING ROLES OF DISORDER:
NON-FERMI-LIQUID BEHAVIOR IN UCus-,Nix
AND CURIE TEMPERATURE ENHANCEMENT IN UCu2Si2-.Ge.













By
DANIEL J. MIXSON II


A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL
OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT
OF THE REQUIREMENTS FOR THE DEGREE OF
DOCTOR OF PHILOSOPHY
UNIVERSITY OF FLORIDA


2005































This work is dedicated to my Lord and Savior Jesus Christ. I can do all things
through Christ which strengthens me.-Philippians 4:13















ACKNOWLEDGMENTS

The Lord has placed a lot of special people in my life. Thus, the thoroughness

of the acknowledgments may exceed that of the actual dissertation. I will attempt

to thank everyone in the order in which they were introduced into my life.

My first thank you goes to my parents, Dan and Judy Mixson, for their love

which includes discipline and support. My sister, Venessa, has been very supportive

of all my undertakings. I also want to thank all four of my grandparents who

played and are continuing to play a major role in my life: Jim and Sue Mixson;

Marion and Winonah Pettit.

I need to recognize my high school physics teacher, Mr. Dan Pate, who served

as a mentor to me during my last two years of high school. His inspiration and

encouragement were indispensable.

A broad thank you goes to my undergraduate institution, Mississippi State

University. The academics were good, but the life lessons I learned hopefully will

never be forgotten.

The majority of these acknowledgments are directed to people affiliated with

the Department of Physics at the University of Florida (UF). First, I want to

thank the two graduate coordinators in the Department of Physics during my

time at Florida: Dr. John Yelton and Dr. Mark Meisel. Also, special thanks go

to the Department of Physics Student Services personnel who were affiliated with

graduate student affairs: Mrs. Susan Rizzo and Mrs. Darlene Latimer. I also want

to thank all the faculty who were instructors in the graduate classes I took: Dr.

Pierre Sikivie, Dr. Richard Woodard, Dr. Charles Thorn, Dr. James Fry, Dr.




iii


**>









Charles Hopper, Dr. Fred Sharifi, Dr. James Dufty, Dr. Alan Dorsey, Dr. David
Tanner, Dr. Robert Coldwell, Dr. Andrey Korytov, and Dr. F. Eugene Dunnam.
I also want to acknowledge the personnel/professors I served under during my
"instructor" years: Mr. Greg Martin, Mr. Ray Thomas, Dr. Robert DeSerio, Dr.
Dmitrii Maslov, Dr. John Klauder, Dr. Gary Ihas, and Dr. Andrew Rinzler.
The most influential professor upon my physics career at UF has to be Dr.
Greg Stewart. I want to thank him for allowing me to work in his lab these past
four years. I especially want to thank him for funding me these past two years
[with money from a Department of Energy (DOE) grant] and for allowing me to go
to Los Alamos National Laboratory (LANL) during the Summer of 2004.
There are many people affiliated with Dr. Stewart's lab that have influenced
my research career. First, special thanks go to Dr. Jungsoo Kim for showing me
the "ins and outs" of the lab. I am indebted to the following people who were/are
affiliated with Dr. Stewart's lab: Mr. Josh Alwood, Mr. Patrick Watts, Mr. Adam
Bograd, Mr. Michael Swick, Mr. Tim Jones, and Mr. Don Burnette. I would
also like to acknowledge Dr. Bohdan Andraka and members of his group I have
interacted with in some form: Dr. Richard Pietri and Mr. Costel Rotundu.
I would also like to recognize Mr. Ju-Hyun Park of Dr. Meisel's lab. His
extensive knowledge was very useful for magnetization measurements I took.
I want to thank the following personnel who help make up part of the infras-
tructure in the Department of Physics at UF and who have been more than willing
to assist me: Mrs. Janet Germay, Mr. Pete Axson, Mr. Marc Link, Mr. Edward
Storch, Mr. Bill Malphurs, Mr. John Mocko, Mr. Greg Bennett, Mr. Jay Horton,
Mr. John Graham, Mr. Greg Labbe, Mr. Bryan Allen, and Mr. Brent Nelson.
I am very grateful to the following five members of my dissertation committee
who have taken time out of their busy schedules to serve: Dr. Greg Stewart (chair),









Dr. Bohdan Andraka, Dr. Pradeep Kumar, Dr. Dinesh Shah, and Dr. David

Tanner.
The following people helped me broaden my knowledge of condensed matter
physics at LANL in the Summer of 2004: Dr. John Sarrao, Dr. Eric Bauer, Dr.

Veronika Fritzsch, Mr. Jason Leonard, Dr. Mike Hundley, and Dr. Joe Thompson.

Finally, I would like to recognize people around the world I have had the
chance to collaborate with on the UCus-aNia and UCu2Si2_-Gea systems. Special
thanks go to Dr. E.-W. Scheidt and Prof. W. Scherer at the University of Augs-
burg for their low temperature measurements on the specific heat of the UCu5-asNia
system with a dilution refrigerator. Also, I would like to thank Drs. T. Murphy
and E. Palm at the National High Magnetic Field Laboratory (NHMFL) in Talla-
hassee, FL, for their low temperature resistivity measurements on the UCus-.Nia
system. Also, I would like to thank Prof. A.H. Castro Neto (Boston University)
for his communication on the Griffiths phase disorder model and in trying to help
me understand how the model applies to the UCu_5-,Nia system. Lastly, I am very

grateful to Dr. M.B. Silva Neto and Prof. A.H. Castro Neto for their theoretical
efforts on the UCu2Si2-zGe_ system.

















TABLE OF CONTENTS


ACKNOWLEDGMENTS ..... .. ....................

LIST OF TABLES ... .... ............. .... ..... .

LIST OF FIGURES ................................

ABSTRACT ........ ... ........................

CHAPTER


1 INTRODUCTION .........

1.1 NFL Behavior in UCus-.Ni,
1.1.1 UCus-.Pd ......


1.1.2 UCus-rNi.


1.2 Curie Temperature Enhancement in UCu2Si2-zGe_.

2 THEORY ...........................

2.1 Non-Fermi-Liquid Theory .............
2.1.1 Introduction ..................
2.1.2 Fermi-Liquids .................
2.1.3 Non-Fermi-liquids ..............
2.2 Curie Temperature Enhancement Theory ......


3 EXPERIMENTAL TECHNIQUES ....................

3.1 Arc-M elting ..............................
3.2 X-Ray Diffraction/Lattice Parameter Determination from X-Ray
D iffraction . .
3.3 Magnetic Susceptibility ........................
3.3.1 DC Magnetic Susceptibility .................
3.3.2 AC Magnetic Susceptibility .................
3.4 Cryogenics ...............................
3.5 Probes . . .
3.6 DC Resistivity .............................
3.7 Specific Heat ..............................


page

iii


. 1


.. 23


--


......oo.......
..............
..............


.









CHAPTER
4 UCus-,Ni, RESULTS AND DISCUSSION ................ 74

4.1 Lattice Parameter Values for UCus-sNia ............. 74
4.2 DC Electrical Resistivity Results for UCus5-Ni3 .......... 79
4.2.1 DC Electrical Resistivity Discussion for UCus-Ni 79
4.3 Magnetization Results for UCus-.Nia ............... 85
4.3.1 Magnetization Discussion for UCus5-Ni. .......... 86
4.4 AC Magnetic Susceptibility Results for UCu5-,Ni ........ 89
4.4.1 AC Magnetic Susceptibility Discussion for UCus5-Ni, 89
4.5 DC Magnetic Susceptibility Results for UCu5-sNis ... 92
4.5.1 DC Magnetic Susceptibility Discussion for UCus-.Ni2 95
4.6 UCus-,Ni2 Specific Heat Results . 102
4.6.1 UCu5-.Nia Specific Heat Discussion ............ 114
5 UCu2Si2-.Ge, RESULTS AND DISCUSSION .............. 136
5.1 UCu2Si2-_Ge. Results ....................... 139
5.2 UCu2Si2-.GeB Discussion ...................... 142
5.2.1 Tc Enhancement ...................... 142
5.2.2 Resistivity displaying electrons in the ballistic or diffusive
regime ........................... 143
6 CONCLUSIONS AND FUTURE WORK ................. 157
6.1 UCus5-Nia Conclusions ........................ 157
6.2 Future Work Derived from UCus5-Ni, Results ........... 159
6.3 UCu2Si2-_Gez Conclusions ..................... 163
6.4 UCu2Si2-,Ge_ Future Work .................... 164
APPENDIX ..................................... 166
A LATTICE PARAMETER GRAPHS ................... 166

B MAGNETORESISTANCE GRAPHS ................... 169

C UCus-5Ni, MAGNETIC SUSCEPTIBILITY GRAPHS .......... 172
D UCu5sNi, SPECIFIC HEAT GRAPHS .................. 177
REFERENCES ................................... 185
BIOGRAPHICAL SKETCH .............................. 195














LIST OF TABLES
Table page
4-1 Lattice parameter values for the nine UCus5-Ni, compounds ...... 126

4-2 The low temperature resistivity results for UCu5s-zNi_ samples. 127
4-3 The low temperature resistivity results for UCus5-Nix samples. 128
4-4 Magnetization data for UCus5_Nia annealed 14 days at 750C. 129
4-5 AC susceptibility results for select UCus5-Nia samples. 130
4-6 DC magnetic susceptibility results for annealed UCu5-sNi.. .. 131
4-7 Fit results for UCus-_Nis dc susceptibility data at 1 kG and 1 T. 132
4-8 Fit results for UCus-aNia dc susceptibility data at 2 T and 3 T. 133
4-9 Fit results for UCu5-zNi. dc susceptibility data at 4 T. 134

4-10 Specific heat results for annealed UCu5-aNi, samples. ... 135
5-1 Magnetic susceptibility and resistivity results for unannealed
UCu2Si2-zGe_ samples (I) ........................ 153
5-2 Magnetic susceptibility and resistivity results for unannealed
UCu2Si2-,Ge_ samples (II). . .. 154
5-3 Magnetic susceptibility and resistivity results for annealed
UCu2Si2-Gea samples (I) ........................ 155
5-4 Magnetic susceptibility and resistivity results for annealed
UCu2Si2-zGe_ samples (II). . .. 156














LIST OF FIGURES
Figure page

1-1 The conventional unit cell for the AuBe5 crystal structure ....... 3
1-2 The unit cell for the tetragonal ThCr2Si2 crystal structure. .. 18
2-1 The Doniach phase diagram taken from Ref. [21]. ... 35
2-2 The Griffiths phase diagram taken from Ref. [21]. .... 41
2-3 Curie temperature predictions by Silva Neto and Castro Neto. 45
3-1 Cross-section of a helium 3 probe. . ... 58
3-2 Schematic diagram outlining the thermal relaxation method. .. 64

3-3 An overhead and bottom view of the mounted sample platform. 65
4-1 Lattice parameter values for unannealed UCu5s-_Ni, compounds. 75
4-2 Lattice parameter values for annealed UCu5s_.Nia compounds. 76
4-3 Low temperature normalized resistivity for UCus5-Nia samples. 80
4-4 Magnetization for UCus-zNi, samples annealed 14 days at 750*C. 87
4-5 AC susceptibility data for annealed UCu4.5Nio.5 .. 90

4-6 DC susceptibility for annealed UCu4Ni in different magnetic fields. 93
4-7 Low temperature dc susceptibility for annealed UCus-..Ni, samples. 94

4-8 Semilog plot of dc magnetic susceptibility for UCu4Ni ..... 99
4-9 Log-log plot of dc magnetic susceptibility for UCu4Ni. ... 100
4-10 Specific heat for eight annealed UCus-.Ni, samples. ... 103
4-11 UCus5-Ni, specific heat results on a semilog plot. ... 105
4-12 UCus-zNia specific heat results on a log-log plot. ... 106
4-13 Specific heat of UCu4.1Nio.9 in 0, 3, and 6 T. .. 108
4-14 Specific heat of UCu3.9Ni1.1 in 0, 3, and 6 T. .. 109
4-15 Specific heat of UCu3.sNi1.2 in 0, 3, and 6 T. .. 110









4-16 Specific heat of UCu4Ni in 0, 2, 3, and 6 T.


4-17 Specific heat of UCu3.95Nii.o5 in 0, 2, 3, and 6 T. ... 112

4-18 Phase diagram for UCus-,Nix and UCus-.Pd. .. 115

4-19 Specific heat data at 6 T for UCus-5Ni, samples. .... 124

5-1 Tc determination for annealed UCu2Ge2. ... 138

5-2 Resistivity versus temperature for UCu2SiGe. .. 140

5-3 Tc phase diagram for UCu2Si2_-Ge . ... 144

5-4 The reciprocal RRR values for annealed UCu2Si2-_Gex ........ 146
5-5 Phase diagram for unannealed UIrl-aPt.Al system. ... 152

6-1 DC magnetic susceptibility results for UCu5_-Co. .... 162


A-1 Theoretical and experimental x-ray diffraction patterns for annealed
U Cu4N i . . .
A-2 Lattice parameter values versus corresponding error function values
for annealed UCu4Ni ...........................
B-1 Low temperature magnetoresistance measurements of annealed
U Cu4N i . . .
B-2 Low temperature magnetoresistance measurements of annealed
UCus.95Ni.o5. .. .. .. .. .. .. .
C-1 Semilog and log-log plots of UCu4.1Nio.9 dc susceptibility. .

C-2 Semilog and log-log plots of UCu3.95Nil.05 dc susceptibility. .

C-3 Semilog and log-log plots of UCu.Ni1.1 dc susceptibility. .

C-4 Semilog and log-log plots of UCus.8Nil.2 dc susceptibility. .
D-1 The determination of TNde for annealed UCu4.4Ni0.6 ..........

D-2 Specific heat of annealed UCu4Ni in 6 and 13 T. .
D-3 Specific heat of UCu4Ni in 13 T with Castro Neto-Jones fit. .
D-4 UCu4.1Nio.9 specific heat data in 3 T and 6 T on a log-log plot. .

D-5 UCu4Ni specific heat data in 2 T and 3 T on a log-log plot. .

D-6 UCu3.95Nil.05 specific heat data in 2 T on a log-log plot. .

D-7 UCus.8Nil.2 specific heat data in 3 T on a log-log plot. .


167


168


170


171

173

174

175

176
178

179
180
181

182
183

184














Abstract of Dissertation Presented to the Graduate School
of the University of Florida in Partial Fulfillment of the
Requirements for the Degree of Doctor of Philosophy
DIFFERING ROLES OF DISORDER:
NON-FERMI-LIQUID BEHAVIOR IN UCus_-Ni.
AND CURIE TEMPERATURE ENHANCEMENT IN UCu2Si2-.Ge.

By
Daniel J. Mixson II
May 2005
Chair: Gregory R. Stewart
Major Department: Physics
Disorder may be created by the substitution of one element for another where
the elements are found on the periodic chart of elements. One compound that has
structural disorder is UCus5-Nix where the transition element, copper, is replaced
with another transition element, nickel. Another compound that has disorder
is UCu2Si2-TGeq, where silicon atoms are substituted with isovalent germanium
elements. The disorder in these two compounds leads to interesting physics at low
temperatures.

UCu5 is antiferromagnetic at around 16 K; however, the antiferromagnetism
may be suppressed by doping nickel atoms onto the copper sites in the unit cell.
The antiferromagnetic transition is suppressed to zero for the UCu4Ni compound,
leading to non-Fermi-liquid (NFL) behavior due to a quantum critical point.
Multiple UCus5-Nia compounds with small changes in the stoichiometry are
synthesized around UCu4Ni in order to investigate if the cause of NFL behavior
crosses over from a quantum critical point to rare strongly coupled magnetic
clusters in a Griffiths phase scenario. The investigation is carried out by performing









the following measurements on UCus5-Nia compounds: 1) x-ray diffraction;
2) direct current (dc) magnetic susceptibility as a function of temperature in
various magnetic fields; 3) alternating current (ac) susceptibility; 4) magnetization
measurements as a function of magnetic fields; 5) low temperature dc resistivity;
and 6) low temperature specific heat in zero and applied magnetic fields (up to 13
T).

UCu2Ge2 and UCu2Si2 are ferromagnets with ferromagnetic ordering temper-
atures, TcuH, occurring at around 108.5 K and 102.5 K respectively. Various com-
pounds lying between the two aforementioned ferromagnets on the UCu2Si2-zGe,
phase diagram were synthesized in order to test theoretical predictions made
concerning the nonmonotonic behavior of Tcurie as a function of the amount of
structural disorder. The nonmonotonic behavior was confirmed by measuring
the dc magnetic susceptibility. As the amount of disorder is varied, the electron
scattering crosses over from a ballistic regime for no structural disorder to a dif-
fusive regime when disorder is present. This crossover is proven by dc resistivity
measurements.














CHAPTER 1
INTRODUCTION
The chemical substitution of one element for another element has been a
longstanding practice in the condensed matter physics community. In fact, the first
system published that claimed non-Fermi-liquid (NFL) behavior [i.e., deviations
occurred from Fermi liquid behavior: at low temperatures, p (the resistivity) = po
+ AT2, x (magnetic susceptibility) and C/T (specific heat divided by temperature)
approach a constant value as T -* 0 K] was Yi-UsPd3 by Seaman et al. [136].
This NFL behavior in Yi-U..UaPd3 was attributed to disorder created by the
chemical substitution of yttrium atoms for uranium atoms [93]. Another such alloy
that displays NFL behavior at low temperatures due to disorder is UCus-sPd,.
The characteristics of the UCus-_Pd, system will be discussed and the motivation
behind the study of the isostructural UCus5-Ni, system will be clarified.
A second part of this dissertation concerns the ferromagnetic behavior of the
ternary UCu2Si2-zGez compounds. The driving force behind these compounds
is disorder, specifically the silicon/germanium sublattice disorder introduced by
substituting (or doping) germanium atoms onto silicon atom sites in the unit cell
(the fundamental "building block" of any crystal structure). Silva Neto and Castro
Neto have made theoretical predictions that this sublattice disorder combined
with thermal and quantum fluctuations will enhance Curie temperature values in
quantum ferromagnets [137]. A discussion of why the UCu2Si2-.Ge, system was
chosen to test the theory will be carried out.









1.1 NFL Behavior in UCus-,Ni.
1.1.1 UCu5-,Pd.

UCus-5Pd, was the first system to display NFL behavior with no dilution of
the f-atom (i.e., the uranium atom) site [143]. UCu5 is an antiferromagnet with a
Neel temperature, TN, around 15 K [104]. The palladium (Pd) atoms are doped
onto the copper (Cu) atom sites and this suppresses the antiferromagnetic ordering
temperature. Andraka and Stewart reported that doping the Cu sites with Pd
suppressed the antiferromagnetism at x z 0.75 and that UCu4Pd displayed NFL
behavior with a power law divergence in the specific heat (C/T ~ T-0-32 for 1-
10 K) and a linear dependence in the resistivity (p = Po a T for 0.3 to 10 K, with
Po = 375 pA2 cm and a = 6.3 Aj cm K-1) [4]. More recent measurements down to
lower temperatures have shown that UCu4Pd orders antiferromagnetically below
TN = 190 milliKelvin (mK) while UCu3.9Pd1. shows no ordering temperature
down to the lowest measurable temperature [77].
UCu5 crystallizes in the AuBe5 structure with the beryllium sublattice
possessing two inequivalent beryllium sites. A schematic drawing of the AuBe5
crystal structure is shown in Fig. 1-1 on page 3 [27]. The AuBe5 structure is cubic
with twenty-four atoms occupying a unit cell. So, for UCus, there are four uranium
(U) atoms and twenty Cu atoms. The U atoms occupy the face-centered cubic
(fcc) sites (denoted 4a). The Cu atoms are divided up among sixteen smaller sites
(called 16e sites) and four larger sites (called 4c sites). When the Cu atoms are
replaced by Pd atoms in UCu5s-.Pda compounds and since Pd atoms are larger
than Cu atoms, one might expect an ordered model for the UCu4Pd sample: the
U atoms would occupy the 4a sites, the Pd atoms would occupy the 4c sites, and
the Cu atoms would occupy the 16e sites. Some compounds do exhibit this ordered
arrangement in the AuBe5 structure: AgErCu4 [145] and ErMnNi4 [43]. Despite
claims by Chau et al. using a high-intensity powder diffractometer that UCu4Pd








































Figure 1-1: The conventional unit cell for the cubic AuBe5 crystal structure. The
4a sites are located on the edges of the cube and in the center of each square face.
The 4c and 16e sites are crystallographically inequivalent sites with the 4c site
larger than the 16e site. The drawing is taken from the paper by Chau et al. [27].









is chemically ordered [27], Pd/Cu disorder does exist on the 4c and 16e sites with
experimental evidence coming from MacLaughlin et al. using magnetic resonance
measurements [93], Booth et al. using extended x-ray-absorption fine-structure
(EXAFS) [15], and Weber et al. using unannealed and annealed UCus5-Pd, lattice
parameter values [160]. MacLaughlin et al. found that muons are relaxed rapidly
in UCu4Pd and this rapid relaxation comes from a large disorder effect. Booth
et al. revealed that for the unannealed UCu4Pd, 24 3% of the Pd occupies the
majority sites (the 16e sites) instead of all the Pd occupying the minority 4c sites.
Then, Weber et al. found that annealing UCu4Pd decreased the lattice parameters
compared to unannealed UCu4Pd. These results from the lattice parameters
indicate that Pd atoms are rearranged from the 16e to the 4c sites. However, Booth
et al. performed EXAFS measurements on annealed UCu4Pd samples made by
Weber et al. and still found that 19% of the Pd is located on the 16e sites [16].
Clearly, UCu4Pd shows Cu/Pd disorder on the Cu sublattices.
The disorder in UCu5-,Pd4 leads to unique low temperature properties in
the specific heat, especially for the UCu4Pd compound. Andraka and Stewart
proposed, based upon their results, that UCu4Pd lies near the suppression of a
second order phase transition, TN = 0 [4]. This quantum critical point (QCP) (i.e.,
TN = 0) was thought to be the source of NFL behavior for the thermodynamic
properties at finite temperatures. As mentioned earlier, power law behavior was
found between 1 and 10 K while the lowest temperature C/T data fell under the
power law curve by as much as 16% at 0.34 K [4]. Then Scheidt et al. extended
the specific heat measurements down to lower temperatures and found that for
unannealed UCu4Pd, the specific heat data leveled off at around 0.2 K [130]. The
specific heat of unannealed UCu4Pd showed logarithmic temperature dependence
over a decade of temperature (0.2 K to 2 K) in agreement with the work of
Vollmer et al. [156]. However, there is disagreement concerning the behavior









below 200 mK. Scheidt et al. measured ac susceptibility as a function of frequency
and found a peak at ~ 0.24 K at 95.5 Hz that shifted to 0.27 K at 995 Hz. This
large shift in the ac susceptibility peak with frequency was strong evidence for
superparamagnetism associated with spin clusters [105]. This magnetism at lowest
temperatures was consistent with the theoretical efforts of Castro Neto et al. [20]
in which the formation of magnetic clusters (i.e., Griffiths phase behavior [57])
in highly correlated systems is caused by disorder that leads to competition
between the Kondo and Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction.
In addition, unpublished results by Dr. Jungsoo Kim that measured the specific
heat of UCu4Pd in various magnetic fields showed a magnetic field induced peak,
a feature that is indicative of a possible Griffiths phase disorder description. On
the other hand, Vollmer et al. concluded that below 0.2 K, there is spin-glass
freezing of the U magnetic moments in UCu4Pd. Different interpretations have
continued to carry on. K6rner et al. then stated that UCu4Pd is antiferromagnetic
with TN = 190 mK and simultaneously shows evidence of spin glass behavior
below TN from specific heat and ac susceptibility measurements [77]. Then
Weber et al. performed experiments on annealed samples of UCu4Pd [160]. Not
only did they perform lattice parameter measurements as stated earlier, but
also specific heat data at low temperatures were taken. Annealing the UCu4Pd
sample for 14 days at 750 C suppressed the antiferromagnetic transition with
no hint of the transition down to the lowest measured temperature of 80 mK.
Also, the logarithmic temperature dependence of the specific heat now covered
more than two decades of temperature starting from 80 mK. This expansion of
the logarithmic temperature dependence suggested that crystallographic order
could be an alternative tuning parameter for NFL behavior besides pressure [14],
doping [5], or magnetic field [61]. This logarithmic temperature dependence also
suggests that the Kondo disorder model (consisting of a broad distribution P(TK)









of Kondo temperatures, TK, which extends down to very low temperatures [11,
99]) could be a plausible explanation for the NFL behavior in UCu4Pd [11].
Another interpretation based upon C/T ; log T concerns ordered systems near a
QCP [143]. Unfortunately, these major theories (Griffiths phase, ordered systems,
Kondo disorder model are discussed in greater detail in the "Theory" chapter)
based upon the specific heat data have gaps in their interpretation. For example,
the specific heat data in annealed UCu4Pd are not consistent with the theoretically
predicted power-law behavior, C/T oc T-1+', for the Griffiths phase model [160]
while ordered systems (e.g., UBe13) near a QCP do not show a magnetic field
induced peak in C/T [143]. The Kondo disorder model is not a valid interpretation
based upon resistivity data discussed below.
The dc electrical resistivity for UCus-sPd, has been measured by several
groups. The first electrical resistivity measurements for UCu4Pd were reported
by Andraka and Stewart [4]. For temperatures lower than 10 K, the UCu4Pd
resistivity was approximately linear in T: p w Po (1 T/To) where Po 375 p cm
and To = 60 K. This linear temperature dependence of p gave experimental
evidence for a non-Fermi-liquid ground state. Chau and Maple then measured
the electrical resistivity for unannealed UCus-,Pd. with concentrations ranging
from x = 0 to x = 1.5 [26]. They found that p(T) increases monotonically with
decreasing T and does not display a peak or downturn at low temperatures.
Experimental evidence also proved that the resistivity of the Pd-substituted
samples increases with increasing Pd concentration. Specifically, Chau and Maple
fit the electrical resistivity data for UCu4Pd to p po (1 T/To) below 10 K and
found Po = 258 Ap cm and To = 63 K, numbers that are comparable to Andraka
and Stewart's results. This linear dependence in the resistivity suggested that
the NFL behavior in UCu4Pd may be explained by a Kondo disorder model. The
results of Weber et al. seem to suggest otherwise [160]. First, annealing UCu4Pd









samples drops the residual resistivity, po, by a factor of about 2.5. Then, the
linear temperature dependence that was reported previously for the unannealed
samples disappears with annealing. The resistivity of the annealed samples has a
Kondo-like minimum around 35 K. However, the resistivity of the 14-day UCu4Pd
annealed sample for 2 K < T < 8 K may be described by a Fermi-liquid expansion
p pr = AT2 + BT4 where pr = 141.5 I cm, A = -0.024 pQ cm K-2, and B = -
0.00013 p4 cm K-4 [160]. Weber et al. note that the sign of A in the expansion
above is unusual for f moments forming a Kondo lattice. Thus, Weber et al.
conclude that the Kondo disorder model is not applicable for annealed UCu4Pd and
suggest it is not the origin for NFL behavior in unannealed UCu4Pd either.
The third major measurement performed on UCus-zPd. samples concerns
dc magnetic susceptibility measurements. Andraka and Stewart reported that dc
magnetic susceptibility of UCu4Pd could be approximated by T-6 at low fields
(100 G) from 10 K down to 1.8 K [4]. This x temperature dependence is consistent,
although coincidental with an overcompensated four-channel magnetic Kondo
model [129]. It will be noted here (although not important to one of the two
subjects of this dissertation) that a spin glass freezing temperature of 2 K was
measured for the UCu3Pd2 composition [4]. Chau and Maple then measured the dc
magnetic susceptibility for UCus-.sPd, and were able to fit the low temperature X
data for UCu4Pd to x(T) = Xoln(T/To) for 2 K < T < 10 K [26]. Plus, Chau and
Maple state that above x = 1.5, the UCus5-Pda system exhibits spin-glass freezing.
They also mention that for the low temperature x data, it is difficult to distinguish
between a logarithmic and a weak-power-law temperature dependence [26]. Vollmer
et al. then measured the magnetic susceptibility down to 0.08 K for UCu4Pd [156].
The low temperature x data according to Vollmer et al. suggest a spin-glass
transition around 0.2 K due to the splitting between zero-field cooled magnetization
and field-cooled magnetization. K6rner et al. confirmed the evidence of spin









glass behavior below the antiferromagnetic transition temperature for unannealed
UCu4Pd by dc-susceptibility measurements [77].
All of these interesting results from the specific heat, resistivity, ac susceptibil-
ity, and dc susceptibility prove no current theoretical model is able to explain all
the current elements of the experimental data [16]. New theories are being devel-
oped to try to explain all the different data such as a Kondo/quantum spin-glass
critical point [56]. These results have also led researchers to further explore the role
of disorder in the UCu5s-Pd, system, especially for UCu4Pd.
Expanding upon their research on unannealed UCu4Pd [15], Booth et al. made
EXAFS measurements on UCu4Pd as a function of annealing time [16]. Their
results show that the main effect of annealing is to decrease the fraction of Pd
atoms on the nominally Cu 16e sites, confirming the conclusions reached by Weber
et al. concerning annealing upon UCu4Pd [160]. Booth et al. also conclude that
disorder must be included in any complete microscopic theory of NFL properties in
the UCus-5Pd, system.
MacLaughlin et al. performed magnetic resonance measurements upon the
UCu5rPda system and also concluded that structural disorder is a major factor
in NFL behavior. The longitudinal-field muon spin rotation (pSR) relaxation
measurements on UCus-_Pd. at low fields reveal a wide distribution of muon
relaxation rates and divergences in the frequency dependence of spin correlation
functions [93]. Interestingly, the divergences seem to be due to slow dynamics
associated with quantum spin-glass behavior, rather than quantum criticality
as in a uniform system (such as CeNi2Ge2 [68, 140], YbRh2Si2 [151], and doped
alloys that include CeCus.gAuo.1 [158, 157, 3] and Ce(Rul_.Rh,)2Si2 where
x 0.5 [164, 165]) because of the observed strong inhomogeneity in the muon
relaxation rate, and the strong and frequency-dependent low-frequency fluctuation.
In conclusion, the disorder in the UCus5-Pd, system, especially in UCu4Pd, has led









to considerable interest from researchers and a search to look for compounds in the
AuBe5 cubic structure that possesses sublattice disorder.
When searching for compounds that crystallize in the AuBe5 structure and
that display possibly the same behavior as UCus-_Pdx, two factors should be
taken into consideration. The first factor concerns the substitution of transition
metals for Cu using UCu5 as the starting point. For example, the substitution
of Au for Cu (i.e., UCus5-Aua) leads to an initial increase in TN up to x = 2,
but TN decreases above x = 2 [150] while the substitution of Ag for Cu does not
show the same rapid suppression of magnetic ordering as UCus5-Pd, does [117].
Also, the substitution of Ag or Au for Cu did not result in any NFL behavior.
Chau and Maple point out that the Au and Ag atoms have a completely filled
d-electron shell and the same valence as Cu [26]. There could be a correlation
between substituting atoms with the same valence and lack of NFL behavior since
Pd atoms have a partially filled d shell and a different valence. Since the complete
subshell configuration atoms with d10 show no NFL behavior, this might possibly
extend to the half filled subshell configuration atoms with d5 due to their stability
(or lower total energy). The second factor concerns how much of a dopant atom
may be substituted in the UCu5 cubic cell. For example, when x approaches 2.4 for
the UCus5-Pd, system, a mixture of cubic and hexagonal phases appears and may
run until x = 5 [26]. The supposition concerning the secondary hexagonal phase
may be related to studies that showed the hexagonal CaCu5 type structure may
exist with atomic radii ratios (Ca site/Cu site) ranging from 1.29 to 1.61 and that
below this range, cubic AuBes-type compounds are formed [42, 19]. A possibility is
that the hybridization between the Pd and Cu atoms reduces the apparent radii of
those atoms and thus the atomic radii ratio of some U/Cu-Pd atoms (maybe the
ratio between nearest atoms) now lies above 1.29 while other ratios are below 1.29.
Thus, the mixture of cubic and hexagonal crystal phases.









It has been known that uranium forms the cubic AuBe5 structure only
with Ni, Cu, and Pt atoms [150]. The UCu5 has been well chronicled with its
antiferromagnetic ordering around 15 K [101, 1041. In addition, UCus undergoes
another phase transition around 1 K (in the electrical resistivity and magnetic
measurements) and this was the first example of such a distinct enhancement
effect that occurs in a magnetically ordered material [117, 115]. Then, Chau and
Maple doped UCu5 with Pt and found a region in the phase diagram where the low
temperature physical properties exhibit NFL behavior [26]. This then leaves UCu5
to be doped with Ni since Ni has the same valence as Pd and Pt and the d-electron

shell is not full or half-full. The main difference between the dopant atoms nickel
and palladium is that the replacement Ni atoms are smaller than the Cu atoms
as opposed to the larger Pd atoms replacing Cu atoms. Sublattice order for x ~ 1
should not occur in UCu5-aNi, as happened in UCus5,Pd2. Thus, the answer to
the question of any NFL behavior in UCu5s-Ni2 as TN --+ 0 being due to disorder
or quantum critical behavior should be better differentiable.
1.1.2 UCus-.Ni,

The first part of this section will review in chronological order previous works
performed on the UCus-5.Ni2 system. The surname of the first author and the
publication year will serve as the title for each work's review. One will see that the
majority of the literature has mainly centered around UCu4Ni, possibly in hopes of
searching for interesting behavior as found in UCu4Pd.
1.1.2.1 van Daal 1975

The first work performed on the UCus5-Ni, system was done by van Daal
et al. who measured lattice constants for 0 < x < 5 along with the susceptibility,
specific heat, electrical resistivity, and absolute Seebeck coefficients as a function
of temperature [153]. The susceptibility reveals that UNi5 has a U41 (tetravalent)
state while on the Cu-rich end of the system (especially for 0 < x < 1), the









uranium ions are mixed tetravalent and trivalent (U+). van Daal et al. suggest
that this mixed valency is possibly the source of the anomalies observed in the
Cu-rich compounds (0 < x < 1): an extra increase of the lattice constants, an
extremely high electronic specific heat, a resistivity varying in the paramagnetic
range in proportion to logo10 T at high temperatures and to 1 (T/T*)2 at low
temperatures and being extremely sensitive to deviations from stoichiometry, and a
Seebeck coefficient showing large negative peaks at low temperature [153].

1.1.2.2 Chakravarthy 1991

Chakravarthy et al. performed neutron diffraction measurements on Cu-rich
compounds, in particular, x = 0.0, 0.2, and 0.5 [22]. The conclusions made are
that UCu5 is an itinerant magnet involving a strong hybridization of 5f electrons
with the conduction electrons. For UCu4.gNio.2, the suppression of long-range
magnetic order (LRO) by small substitution of Cu by Ni indicates the enhancement
of the interaction of 5f electrons with the conduction electrons [22]. However, TN
is not significantly affected (12 K for x = 0.2). Thus, the band structure may
be responsible for the LRO [159]. The third composition, UCu4.sNio.5, did not
show LRO down to 1.5 K and the authors suggested that the suppression of the
ordered magnetic moment of the U ion causes the LRO to disappear in the x = 0.5
system [22].
1.1.2.3 L6pez de la Torre 1998

L6pez de la Torre et al. made electrical resistivity and magnetic susceptibility
measurements down to 0.4 K for UCu4.5Nio.5 and UCu4Ni samples [891. For
UCu4.5Nio.5, the magnetic susceptibility displays an irreversibility below a broad
maximum for a zero-fiell cooled (ZFC) and field-cooled (FC) regime and the
maximum is the "freezing temperature" for a spin glass at about 6 K. For UCu4Ni,
the magnetic susceptibility shows no spin glass or magnetic order feature down to
0.4 K. No saturation in the magnetic susceptibility is apparent at low temperatures









and an asymptotic T1/2 dependence describes quite accurately the magnetic
susceptibility from 0.4 K to 2.5 K [89]. The electrical resistivity measurements for
UCu4Ni showed that all samples had linear temperature dependence from 0.4 K to
~ 30-40 K. Also, annealing did not change the low temperature electrical resistivity
properties significantly; however, the electrical resistivity values did show a large
sample dependence. The authors raise the question of whether or not this NFL
behavior is attributable to a two-channel Kondo effect [136], a quantum phase
transition at T = 0 [5, 158], or disorder (specifically Kondo disorder) [39].
1.1.2.4 L6pez de la Torre 2000
L6pez de la Torre et al. try to address the previous question by applying
the Kondo disorder model to the magnetic, electrical, and thermal properties of
UCu4Ni [90]. The claim is that the existence of two nonequivalent copper sites in
the AuBes cubic structure is the origin of the crystallographic disorder resulting
in a distribution of Kondo temperatures [11, 15]. The phenomenological Kondo
disorder model given by Bernal et al. [11] was used to describe the magnetic
susceptibility data in a 1 T field and the fit described the data over two decades of
temperature. L6pez de la Torre et al. and van Daal et al. both agree that UCu4Ni
is in a mixed valence state between U3+ (J = 3/2 where J is the effective angular
momentum) and U4+ (J = 1). The electronic specific heat measurements for the
UCu4Ni sample show typical NFL log10 T dependence from 0.9 K to 9 K [90].
A comparison between the experimental specific heat results and a calculation
made using a distribution of Kondo temperatures (similar to Graf et al. [55])
and applying the resonant-level model for the specific heat of a single Kondo
impurity [135] show pretty good agreement from about 1 K to 10 K [90]. L6pez de
la Torre et al. observed an upturn in the specific heat around 0.9 K and they think
the origin may be some form of spin-glass-like freezing at temperatures below their
experimental limit (0.4 K). The upturn in the specific heat may also be related to









the inflection in the magnetic susceptibility around 1 K [90]. The conclusion by
L6pez de la Torre et al. is that the Kondo disorder model could play a significant
role in the NFL behavior reported in UCu4Ni.
1.1.2.5 L6pez de la Torre 2003

L6pez de la Torre et al. made electrical resistivity measurements of UCu4.75Nio.25
and UCu4Ni over a wide temperature range (0.4 800 K) [88]. In summary, the
high-temperature electrical properties of UCu4Ni and UCu4.75Nio.25 were explained
in terms of single-impurity Kondo behavior. The interesting part of this paper
concerns the high values of the electrical resistivities (p(0) ~ 440 pI cm and p is
usually well above 100 /M cm over the entire experimental temperature range).
The rather poor electrical conductivity would indicate that the electronic mean
free path is close to the interatomic distance and kF f is of the order unity where
f is the mean free path. This class of strongly correlated electron systems that
approaches the Ioffe-Regel limit for the metallic state includes high-Tc supercon-
ductors, fullerenes, and ferromagnetic perovskites (e.g., SrRuO3), which all have
properties suggesting some sort of NFL behavior [1541. In the results part of this
dissertation, these reported high electrical resistivity values will be revisited.
1.1.2.6 Present Work

One reason for studying the UCu5-zNia system concerns the fact that the
Kondo disorder model may not be the best explanation for the NFL behavior
present in the experimental data. For example, a quantum critical point (QCP)
may also be a possibility since the antiferromagnetic temperature (a second
order phase transition) is suppressed to zero and the QCP has a large influence
on the measured properties at finite temperatures [143]. However, some recent
research on the isostructural UCus-xPdx system has suggested that theories that
limit the cause of NFL behavior to just one phenomena such as disorder or a
quantum critical point may not be the best explanation. In fact, theories that









combine quantum critical points with disorder may explain all the different data
of systems such as UCus-xPdx and UCu5-_Ni. [16]. One such model in which
the magnetic ordering temperature, Tord,, has been suppressed via doping based
on the effects of the accompanying disorder is the Griffiths phase disorder model.
In the Griffiths phase model, disorder leads to tunneling between closely spaced
energy levels in rare strongly coupled magnetic clusters [21]. The Griffiths phase
model depends on the strong magnetic fluctuations produced "near" a QCP. The
Griffiths phase model predicts that X and C/T follow a power law temperature
dependence, T-1+A [20]. One of the unique features of the Griffiths phase model is
that once a crossover magnetic field is determined (from magnetization versus field
measurements), a magnetic field around the crossover field induces a peak in C/T
at low temperatures (C/T z (H2+^/2/T3-A/2) exp(-_eff.H/kBT)) and the induced
peak broadens and moves to higher temperatures for higher fields. Two systems in
which the NFL behavior may be explained by the Griffiths phase model and that
demonstrate field induced peaks are Cel-aThaRhSb [74] and Cel-zLa.RhIn5 [73].
The field induced peak is unique to the Griffiths phase model. This should not
be confused with the peaks in magnetic fields for the multichannel Kondo prob-
lem [132]. There are distinct differences. First, the Griffiths phase model predicts
that for zero magnetic field, the specific heat (C) follows T^ behavior as mentioned
earlier. In contrast, the specific heat for a Kondo system like CrCu [149] shows
a peak in zero magnetic field. The peak in the specific heat for a Kondo system
shifts towards higher temperatures and the height of the peak also grows as the
magnetic field is increased. The Griffiths phase explanation differs since, although
the field induced peak moves up in temperature, it broadens and decreases in size
with increasing field.









For the present work, eight different UCu5-,Ni, compounds were produced
with x ranging from 0.6 to 1.2. The reason for such a large variation in the concen-
trations is to explore whether or not clear distinctions may be made concerning the
cause of NFL behavior at different concentrations. In fact, small variant concentra-
tions (i.e., x = 1.05, 1.1, and 1.2) have been made near UCu4Ni, the concentration
where TN is approximately zero. A possible crossover concentration level might be
found where one concentration's NFL behavior may be explained by a QCP while
increasing the Ni concentration by 5% could cause the NFL behavior to be due to
another model, like a disorder model. Also, the Griffiths phase model is predicated
upon strong magnetic fluctuations "near" a QCP; it would be interesting to see
if "near" could be quantified in terms of the Ni concentrations. The only system
investigated by small variations of doping around the QCP was UCus-5Pdx, where
the quantum critical concentration was x w 1 as discussed earlier. The problem
with UCus5-Pda was the preferential sublattice ordering of the larger Pd atoms
on the minority 4c site (in the AuBe5 structure) occurring in UCu4Pd as discussed
previously [16]. In fact, MacLaughlin et al. concluded that there were still signs
of disorder on annealed UCu4Pd [93]. The UCus-5Ni_ system should not have
to contend with a preferential sublattice ordering since the Ni atoms are smaller
than the Cu atoms. Thus, the smaller Ni atoms will be distributed at slightly less
than the 25% level on the majority 16e sites (i.e., the physically smaller Be site
in the AuBe5 structure) for UCu4Ni, with some small fraction in the energetically
more unfavorable larger 4c sites. This conclusion will be discussed when the lattice
parameter values are presented in the "UCu5-a.Ni, Results and Discussion" chap-
ter. Thus, all concentrations around UCu4Ni should have a significant amount of
disorder present.









In addition to the lattice parameters for all eight concentrations being re-
ported, direct current (dc) resistivity, magnetization as a function of field, al-
ternating current (ac) susceptibility down to 2 K, direct current (dc) magnetic
susceptibility down to 2 K, and heat capacity in zero field along with heat ca-
pacity in magnetic fields for concentrations around the QCP composition will be
reported in the "UCus-,Ni, Results and Discussion" chapter. To date, a complete
and thorough characterization of the UCus-sNia system around the QCP has
not been reported in the literature. The measurements reported here will try to
answer if clear distinctions can be made about the sources of NFL behavior (i.e.,
quantum criticality and disorder) at various Ni concentrations around the QCP
(i.e., UCu4Ni). Also, the measurements will try to clarify the role of Griffiths phase
model for NFL behavior in the UCus-xNix system. An attempt to determine the
concentration range for which the Griffiths phase model applies will be made.

1.2 Curie Temperature Enhancement in UCu2Si2-,Ge,
A Curie temperature, Tc, enhancement as a function of disorder was pre-
dicted by Silva Neto and Castro Neto [137]. The fundamental idea behind this
enhancement effect concerns electrons scattering from the localized moments and
acting as a heat bath for the spin dynamics. Then, the dissipation that arises from
the electronic diffusion in the case of structurally disordered ferromagnets is what
affects the Curie temperature.
The study of ferromagnetism in disordered alloys has received renewed
interest in recent years due to the development of Gal_-MnAs [114, 110, 112]
and In_-..MnaAs [113] as ferromagnetic semiconductors (with x ; 1-10%). In fact,
there are now reports of ferromagnetism (some at room temperatures and above) in
several magnetically doped semiconductors [36], e.g., GaMnP [146], GaMnN [125],
GeMn [118], GaMnSb [29]. However, the observed ferromagnetism in dilute
magnetic semiconductor (DMS) systems like GaMnAs is not just associated with









disorder created by the random positions of the magnetic dopants, but also the
thermal fluctuations of magnetic moments along with impurity band and discrete
lattice effects playing an integral part if the magnetic coupling can be assumed to
be a simple local exchange coupling between local impurity moments and carrier
spins [36]. Thus, trying to isolate the effects of disorder on the ferromagnetism in a
DMS to test the proposed theory by Silva Neto and Castro Neto is impossible due
to the aforementioned complexities in a DMS.
The choice of a ferromagnetic material to test the theory of Silva Neto and
Castro Neto depends upon being able to test the effect of structural disorder on the
ferromagnetic properties without introducing sundry complications [138]. De Long
et al. investigated over 100 metallic Ce and U compounds to look for trends in the
occurrence of ferromagnetism and to consider parameters such as the closest f-atom
separation notatedd by d) [37]. For example, Hill observed that f-state magnetic
order did not occur for d < dH, where dH 3.4 or 3.5 A, the respective "Hill
limits" for f-state localization in Ce- and U-based materials [65]. Thus, when trying
to induce structural disorder upon the selected compound, it is important not to
inadvertently change the f-atom separation because it would be very difficult then
to distinguish the change in Tc between structural disorder and f atom separation.
De Long et al. also mention that hybridization of f-levels with non-f conduction
states has an effect upon the ferromagnetism [37]. This pretty much rules out any
binary ferromagnetic compounds since doping on one of the two atoms not only
would create structural disorder, but also the doping would affect the hybridization.
The two ferromagnets, UCu2Si2 and UCu2Ge2, meet the conditions outlined
above. UCu2Si2 is a ferromagnet at 103 K (with an antiferromagnetic transition
right above at 107 K) [37] while UCu2Ge2 is a ferromagnet at 107 K (with a
controversial antiferromagnetic transition at around 43 K [78, 47]) [37]. UCu2Ge2
and UCu2Si2 are isostructural, crystallizing in the ThCr2Si2 structure [28]. The









ThCr2Si2 structure is shown in Fig. 1-2 on page 18. In Fig. 1-2, one can see



















Figure 1-2: The unit cell for the tetragonal ThCr2Si2 crystal structure. The c-axis
is up in this diagram, running parallel to the longest dimension of the unit cell.
The ThCr2Si2 is layered with Th-Si-Cr2-Si-Th planes stacked along the c axis. This
diagram was taken from the paper by Welter et al. [161].

that for the UCu2(Si, Ge)2 compounds, the U atoms replace the Th atoms, the
Cu atoms (the transition metal, T) replace the Cr atoms, and the Ge atoms
replace the Si atoms for UCu2Ge2. The shading in Fig. 1-2 also highlights the
tetraderal coordination of the Si (or Ge) around the T ion with small T-Si (Ge)
distances: 2.40 A for UCu2Si2 and 2.42 A for UCu2Ge2 [28). The smallest distance
between two neighboring U atoms is well above the Hill limit for a U-compound
(3.5 A): 3.98 A for UCu2Si2 and 4.05 A for UCu2Ge2 [37]. It was decided that the
structural disorder could be intentionally created by doping Ge onto the Si site in
UCu2Si2 and that 9 compounds with differing Ge concentration levels (x = 0, 0.2,
0.4, 0.6, 1, 1.4, 1.6, 1.8, and 2) would be arc-melted to investigate whether or not
nonmonotonic behavior exists for Tc as predicted by Silva Neto and Castro Neto.









The replacement of Si atoms with Ge atoms should not affect the magnetic
sublattice in the UCu2Si2_-Gez compounds. The structural disorder .will occur on
the p orbitals deep within the isovalent Si and Ge atoms. The structural disorder
will affect the conduction band due to the complex p-d hybridization between the
T ion and Si/Ge as seen in Fig. 1-2. Thus, the strong hybridization between the
T ions and the U ions should not be directly affected by this intentional structural
disorder. This is in agreement with the neutron diffraction and magnetization
measurements of Chehnicki et al. that gave no magnetic moment on a copper
ion [28]. In fact, the explanation by Chelmicki et al. for why the T ion does
not carry a magnetic moment originates from the coordination of a T ion by
silicon/germanium atoms. Four silicon atoms are located at the comers of a
flattened tetrahedron around each T ion as shown in the shaded part of Fig. 1-2
on page 18. The short T-Si/Ge distances amount to less than the sum of atomic
radii of T and Si/Ge [28]. Thus, the overlap (or hybridization) of electronic shells
and electron density transfer from the 3p shell of the silicon/germanium to the 3d
shell of the Cu ion in UCu2Si2-zGe, compounds is what probably vanquishes the
magnetic moment on the Cu ion. M6ssbauer studies on isostructural NpFe2Si2 [109]
and REFe2Si2 (where RE is a rare earth element) intermetallics [51, 108] show that
the T ion does not carry a magnetic moment. The information by Chehnicki et
al. justifies that the Si/Ge exchange creating sublattice disorder will not affect the
long-range magnetic ordering of uranium moments in UCu2Si2-sGe2.
The effective magnetic moments and the isotropic RKKY mechanism de-
termined by Chehnicki et al. were used by Dr.s Silva Neto and Castro Neto to
calculate the nonmonotonic dependence of Tc [137]. The effective magnetic mo-
ment, pieff., for UCu2Si2 was determined to be 3.58 Bohr magnetons (~B) from the
inverse susceptibility versus temperature curve using the Curie-Weiss law [28]. The









3.58/B value is the exact value calculated for a free ion configuration of U4+ as-
suming 3I-4 as a ground state. The Peff. value for the U ion in UCu2Ge2 is 2.40pJB.
Possible reasons for why the effective moment is lower in UCu2Ge2 are crystal
field effects or magnetic moment compensation [138]. The magnetic interactions
of the U ions may be explained by an isotropic RKKY model, in agreement with
neutron diffraction and magnetization data [28]. This model was also successful
in explaining the magnetic interactions in isostructural UPd2Si2, URh2Si%, and
UPd2Ge2 [122]. The details of using this isotropic RKKY mechanism will be
discussed in the "Theory" chapter of this dissertation.
One important point that cannot be emphasized enough concerns the Si/Ge
sublattice disorder that is intentionally created and differs from other alloying
experiments on the UCu2Si2 and UCu2Ge2 compounds. Since Si and Ge are
isovalent, the carrier density is not changed. In contrast, the carrier density
changes in the UNi2-_CuaGe2 system along with the magnetic sublattice since
the hybridization between the U and Cu ions is altered by the substitution of the
Ni atoms. Also studies done on the UNi2-a.CuzGe2 system [82, 79] show that the
ferromagnetic phase only exists for 1.20 < x < 2 in the UNi2-aCu3Ge2 magnetic
phase diagram. In fact, for x > 0.75 (i.e., the samples closest to pure UCu2Ge2),
there is a ferromagnetic-to-commensurate crossover. For example, for x = 0.95,
a To value of 110 K was observed in ac-susceptibility measurements while at
94 K, the sample underwent another transition to an antiferromagnetic phase [79].
Kuznietz et al. even state that the transition metal sublattices determine the
type of ordering on the uranium sublattice in the UM2X2 (where M = Co, Ni,
Cu and X = Si, Ge) systems [79]. For the UCu2Si2 side of the phase diagram,
neutron-diffraction results by Kuznietz et al. upon UNio.aoCul.moSi2 show that
, 93% of the sample volume orders antiferromagnetically while the other 7%
orders ferromagnetically [81]. It should be clear from the examples above that









it would be very difficult to individually distinguish the effects on Tc between
the disorder acting on the transition metal's conduction electrons and disorder
altering the magnetic sublattice. Thus, familiarity and acknowledgment concerning
the tremendous amount of work on the magnetism of UCu2Si2 [63, 128, 96]
and UCu2Ge2 [23, 102, 45, 148] is revealed, e.g., UCo2_-CuzGe2 [80, 41] and

Ul-aYaCu2Si2 [64, 62]. However, despite all this research, this UCu2Si2-aGez
is unique because it is the first project to try and isolate the effects of disorder
upon Tc by creating structural disorder at the Si/Ge site (i.e., the 4e site of the
ThCr2Si2 crystal structure).
A final factor in determining the Tc enhancement for UCu2Si2-aGea con-
cerns minor changes in the stoichiometry of the UCu2Si2-aGea system. Particular
attention to the stoichiometry in the UCu2Si2-aGea compounds is paid in the "Ex-
perimental Techniques" chapter and the "UCu2Si2-zGe, Results and Discussion"
chapter. Kuznietz et al. point out that small deviations from stoichiometry on the
copper sublattice alters the number of conduction electrons [79]. The effect of small
stoichiometry changes upon the magnetic properties is closely monitored since
predictions by Silva Neto and Castro Neto originate from conduction electrons on
the Cu sublattice scattering from the localized U spins [137] as discussed earlier.
In fact, multiple samples with the same Si/Ge concentration are synthesized in
order to compare the stoichiometry differences to the experimentally determined
Tc values.
The low temperature resistivity on the UCu2Si2-_Gea compounds is also
measured. Low temperature resistivity predictions for the scattering of conduction
electrons from localized spin fluctuations have the resistivity varying as T2 as
observed in dilute Pd-Ni alloys [131] and dilute Ir-Fe alloys [70]. This Fermi-liquid
like resistivity behavior is expected for the UCu2Si2-_Gea compounds. Also, the
resistivity measurements are expected to provide insight into the type of dissipation







22

occurring from the scatter of the conduction electrons. The two main sources
of dissipation are Landau damping for clean magnets and electronic diffusion
for structurally disordered magnets [137]. The electrons in the Landau damping
case have a longer mean free path than the electrons in the diffusive case. Thus,
the resistivity for the Landau damping electrons (i.e., the ballistic electrons) is
expected to be smaller than the diffusive electrons.














CHAPTER 2
THEORY
2.1 Non-Fermi-Liquid Theory
2.1.1 Introduction

The discovery of the electron in 1897 by J.J. Thomson has led to many theo-
ries concerning the behavior of electrons in metals. In 1900, P. Drude formulated
his theory of metallic conduction by using a slightly modified method of the kinetic
theory of a neutral dilute gas. Unfortunately, the Drude model was not accurate in
predicting many physical properties, such as the specific heat of a metal. A quarter
of a century passed until Sommerfeld's model solved the problem by using the
Pauli exclusion principle's requirement that the electronic velocity distribution is
the quantum Fermi-Dirac distribution instead of the classical Maxwell-Boltzmann
distribution. After the passing of another quarter century or so, L.D. Landau intro-
duced his Fermi-liquid theory that was able to explain many physical properties in
metals such as Cu and Al. All of the previous models made use of an independent
electron approximation or free electron model.
As one comes to present day, complex metals have Been discovered where
at low temperatures, the electron-electron interactions cannot be simply ignored
or slightly modified with respect to the free electron case. The strong electronic
correlations lead to non-Fermi-liquid behavior. In fact, non-Fermi-liquid behavior
has been observed in metals with disorder, such as UCus-a.Pda [4]. The theory will
begin with some of Landau's arguments for Fermi-liquid theory and then explore
some of the theories characterizing non-Fermi-liquid behavior.









2.1.2 Fermi-Liquids

In 1957, L.D. Landau proposed his Fermi-liquid theory. The original intent
of the theory was to explain the liquid state of the isotope of helium of mass
number 3 [7]. However, Fermi-liquid theory is now being applied to the theory of
electron-electron interactions in metals.
Landau's Fermi-liquid theory has two main points. First, the electrons that
are within kBT of the Fermi energy and that do have interactions with each other
do not ruin the success of the independent electron picture in explaining low-
energy metallic properties. Secondly, single electrons are not just being considered
anymore, but rather quasiparticles (or quasielectrons). These quasiparticles share
many of the properties of non-interacting electrons, but quasiparticles are like
electrons that have been perturbed from their non-interacting state by means of
interaction [134].

Instead of going through a quantitative analysis as Landau did to obtain
respective thermodynamic and transport properties [83, 84, 85] of a Fermi liquid,
a qualitative analysis is more appropriate for this dissertation. The quasiparticles
that are of most importance are those that are within kBT of the Fermi surface
as stated above. Most quasiparticles in metals are so far buried down below
the Fermi surface that they are unable to obtain the required energy needed to
reach an unoccupied quantum state. Thus, only quasiparticles within kBT of the
Fermi surface can contribute kB to the specific heat and the specific heat grows
linearly with temperature. Likewise, only quasiparticles within IBB (where B is
an external magnetic field) of the Fermi surface can magnetize with a magnetic
moment proportional to pAB leading to a temperature independent magnetic
susceptibility [134]. If the temperature is above absolute zero, then some energy
levels above the Fermi energy will be occupied within a range of kBT of the Fermi
surface. Therefore, the scattering rate for the quasiparticles near the Fermi surface









is proportional to T2. Since the resistivity is proportional to the scattering rate, the
low temperature resistivity goes like T2.
2.1.3 Non-Fermi-liquids

In 1991, Seaman et al. discovered low-temperature measurements of specific
heat, magnetic susceptibility, and electrical resistivity on the Yi-.,UPd3 system
that were contradictory to Landau's Fermi-liquid theory [136]. Specifically, the
compound Yo.8Uo.2Pd3 displayed a linear low temperature behavior in its resistivity
and a logarithmic relationship in its low temperature heat capacity for over a
decade of temperature in both. To date, over fifty systems have been discovered
that do not obey Landau's Fermi liquid theory [143].
Since the discovery of Yo.8Uo.2Pd3 displaying this non-Fermi-liquid (NFL)
behavior, there has been considerable interest in explaining this NFL behavior
by condensed matter theoreticians. The various theories are segregated into three
general categories: 1) multichannel Kondo models; 2) models where the magnetic
phase boundary lies near 0 K (i.e., the quantum critical point); and 3) models
based on disorder. A synopsis of the various theories will be given while particular
attention will be paid to models that are applicable to UCus5-Niz.
2.1.3.1 Multichannel Kondo Model

The multichannel Kondo effect is based upon single-impurity physics. The
multichannel Kondo effect is described by a quantum impurity spin S that is
coupled antiferromagnetically to n degenerate channels of spin- conduction
electrons [1]. The so-called Kondo lattice Hamiltonian is derived from the Anderson
Hamiltonian to describe the single-impurity multichannel Kondo model [143]:

HK = Ek kamW + J E S a 'teakme, (2.1)
k,m,u k,k',m,^,o,

where ek is the conduction-electron dispersion relation, at and am, are creation
and annihilation operators on electrons with momentum k and spin projection









m, J is the antiferromagnetic coupling constant between the localized impurity
spins and the conduction electrons, S is the localized spin impurity, and o,,' are
the Pauli spin matrices. Three distinct cases arrive from the above Hamiltonian
between the n channels (or flavors) of the conduction electrons and the impurity
spin S [143]:
1. If n = 2S, the conduction-electron channels fully screen the impurity
spin channels and a singlet ground state arises. This leads to Fermi-liquid
behavior as described above.
2. If n < 2S, the conduction-electron channels only partially screen the impurity
spin channels and no singlet ground state exists. The result is a new effective
Kondo effect with a net spin S' = S n/2 [25]. The ground state is Fermi-
liquid-like and mirrors the model of Coqblin and Schrieffer [30] (n = 1, S >
1/2).
3. If n > 2S, the local spin is "overcompensated" yielding a critical ground
state with a non-Fermi-liquid excitation spectrum [75]. The result of this
overcompensation is power-law or logarithmic behavior in measured physical
quantities like magnetization, resistivity, and specific heat as the temperature
and external field approach zero.
The third case is particularly interesting since the low temperature dependence
of the magnetic susceptibility, specific heat, and resistivity depend upon the
number of channels of conduction electrons, n, and the impurity spin S. For
example, if n = 2 ("two-channel") and S = 1/2, then the low temperature, zero-
field magnetic susceptibility and specific heat divided by temperature, C/T, go
approximately like log (T/TK) [132]. Such logarithmic temperature dependence has
been observed in systems such as Yi-.UPd3 [136] and Thl-.UzPd2Al3 [34, 38].
Also, the low temperature resistivity at zero-field behaves like Po AVT [91].
Unfortunately, this low-temperature resistivity has not been observed in many NFL









systems. The reason may be that the low-temperature resistivity predictions were
made in the dilute impurity limit while the NFL behavior in systems crops up more
in the concentrated limit.
Cox and Zawadowski [32] have addressed this concentrated limit. It is a special
case of the multichannel Kondo effect that has a quadrupolar origin. The NFL
behavior in this model results from an effective exchange interaction between
pseudospins and the electric quadrupole moment of the groundstate [25]. However,
no system has met the strict requirements required by this quadrupolar Kondo
effect.

The multichannel Kondo model portrays NFL behavior as single-ion in
nature [21]. This means that each impurity moment is treated independently and
concentrated systems might not be of single-ion character since no interaction
between the impurities is taken into effect.
2.1.3.2 Quantum Critical Point

The second general theoretical category describing non-Fermi-liquid behavior
is quantum critical point models. The quantum critical point theories arise from
the critical phenomena that occur at or near a zero temperature phase transition.
Classically, a phase transition would occur at a nonzero temperature and temper-
ature would be the control parameter. The temperature parameter would control
the thermal fluctuations and if the thermal fluctuations have characteristic energies
(hw*, where w* is the frequency associated with the fluctuations) much less than

kBTc (where Tc is the critical temperature of a phase transition), then the fluc-
tuations may be described by classical statistics [25]. However, in 1976, Hertz [60]
considered the case when the critical temperature is at T = 0. The fluctuations
would have zero thermal energies. Thus, quantum mechanical fluctuations would
arise that could not be controlled by temperature. These fluctuations may be con-
trolled by chemical substitution, external pressure, or magnetic field. An example









of pressure control is CePd2Si2 where a pressure of ~ 28 kbar suppresses antiferro-
magnetism, induces superconductivity at 0.43 K, and shows NFL behavior in the
electrical resistivity (p(T) oc T12) [58]. The idea is that one of the aforementioned
control parameters "tune" a system from an ordered ground state to a non-ordered
state crossing a quantum critical point [143]. The assumption is that at low enough
temperatures, the system's behavior will be dictated by quantum effects despite
not being able to measure thermodynamic properties at T = 0 [139]. At these
low temperatures, non-Fermi-liquid behavior appears at or near a quantum critical
point since usually a magnetic phase transition is suppressed. The quantum critical
point theory is relevant to the UCus5-Nix system because doping UCu5 with Ni
suppresses the long range antiferromagnetic order and TN&I approaches zero.
As mentioned above, measurements at T = 0 cannot be performed. Thus,
in order to confirm whether or not the NFL behavior is due to a quantum critical
point, one must analyze scaling behavior [152] (either for temperature or frequency)
on finite-temperature properties and compare to predictions made by several
different models. A synopsis of each model with key points is provided below.
The first theoretical model was developed by Tsvelik and Reizer [152]. This
theory matched the low-temperature thermodynamics measured in Uo.2Yo.sPd3 and
UCu3.5Pd.s5 [136, 5, 4]. The theoretical model states that the two previous systems
are on the verge of a phase transition that occurs at zero temperature and results
in a domination by collective bosonic modes. The model also matched the correct
scaling analysis of the low-temperature properties [4]:

magnetization: M = ~f(



specific heat : (HT) (0,T)
T T gT( +)









where 7 = 0.25 0.3; # + 7 = 1.2 1.3; (the model predicted a scaling dimension
of 4/3) and f and g are nonsingular scaling functions. Along with the above
scaling analysis, the specific heat has a logarithmic divergence and the dc magnetic
susceptibility has a divergent form (T-7) at low temperatures.
A second theoretical model investigating quantum critical phenomena was
developed by Hertz [60] and Millis [97]. A major assumption is made to integrate
out the fermions (i.e., the conduction electrons) and thus the problem is reduced
to the study of an effective bosonic theory describing fluctuations of the ordering
field [97]. Results depend crucially upon the value of d + z, where d is the spatial
dimension and z the dynamic exponent (z=2 for the antiferromagnet and z=3
for the ferromagnet) of the T = 0 transition [60]. All of the cases considered
except for the two-dimensional antiferromagnet have an effective dimension, (d+z),
greater than their upper critical dimension [60]. Hyperscaling (which is used to
derive the scaling analysis mentioned in the previous paragraph) has been shown
not to apply to systems above their upper critical dimension [17, 121]. Phase
diagrams with crossover temperature relationships between various regions have
been obtained for different cases (e.g., two spatial dimensions and dimensions larger
than two [97]). None of the derived relationships for measured properties in this
model are applicable to the UCu5s-Nia system.
A third theoretical model investigating quantum critical phenomena was
developed by Moriya and Takimoto [103] and it involves spin fluctuations in heavy
electron systems around their antiferromagnetic instability. This idea is particularly
applicable to the UCus5-Nia system since the heavy electron system UCus has
its Niel temperature suppressed by Ni doping. This theory is based on exchange-
enhanced spin fluctuations playing a major role in displaying various anomalous
properties around the magnetic phase boundary. Moriya and Takimoto addressed
the problem of coupling among the different modes of spin fluctuations in heavy









electron systems [103]. Their answer was to take a phenomenological point of view
by using a sum rule for the local spin fluctuations valid in the strong correlation
limit:

SLO + SLT = +L2

where SLo is the mean square local amplitude of the zero point, SLT is the mean
square local amplitude of the thermal spin fluctuations, and SL is the amplitude
of the local spin density that takes a constant value. The sum rule is then used to
calculate the reduced inverse staggered susceptibility in the low temperature limit,
yo, for a nearly antiferromagnetic metal:

1
Yo = 2TAXQ(0)

where TA is a characteristic energy parameter and XQ(O) is the local dynamical
susceptibility for the antiferromagnetic wave vector Q. This expression has the
same form as in the self-consistent renormalization (SCR) theory for weak itinerant
antiferromagnetism [103]. The parameter yo goes to zero as the magnetic instability
is approached; in fact, at the critical boundary, yo equals zero [103]. Thus, the
value of yo gives a prediction for the proximity to the magnetic instability [143].
The value of yo is obtained by fitting the specific heat and electrical resistivity
data.
Moriya and Takimoto made predictions for the specific heat and electrical
resistivity due to the spin fluctuations. When yo = 0, the specific heat takes a finite
value, 70, and starts to decrease with increasing temperature proportionally to
T1/2. Immediately after the square root behavior, the specific heat shows a negative

logarithmic behavior in a certain range of temperature (over about 60% of a decade
in temperature above the 7o ATO5 behavior [143]). Interestingly, as one gets
further from the phase boundary (i.e., yo 0), Fermi-liquid behavior arises and the
range of linear specific heat increases with increasing yo. The electrical resistivity









at the critical boundary is proportional to T3/2 at low temperatures and as the

temperature increases, there is a certain range where the resistivity is almost linear
in T. The electrical resistivity is similar to the specific heat in that as one moves
further away from the antiferromagnetic critical boundary, there exists a normal
Fermi-liquid behavior at low temperatures. Physically, the interpretation of the
departure from the T1/2 behavior to the logarithmic dependence in the specific
heat and crossover from the T3/2 behavior to the linear dependence in the electrical
resistivity is that at the lowest temperatures, the coupling among the different
modes of the spin fluctuations is small in magnitude; however, as the temperature
increases, the coupling also increases [143]. Application of Moriya and Takimoto's

theory will be discussed later on.
Several other theoretical models exist describing quantum critical phenomena.
However, in the interest of relevance to this dissertation, one should be directed to
Dr. Stewart's review article [143] for a complete summary of all theoretical models
pertaining to the quantum critical point.

2.1.3.3 Disorder

The third theoretical category describing non-Fermi-liquid behavior concerns
models based on a disorder. These models originate from the multichannel Kondo
model. It was previously discussed that when the conduction-electron channels
are sufficient to compensate the impurity spin, then Fermi-liquid behavior occurs.
TK is the Kondo temperature below which the conduction electrons fully screen
the local impurity spin for S = 1/2 and n = 1 (the number of conduction-electron

bands). The disorder model has been proposed to reduce TK to lower temperatures
for some of the magnetic impurities and thus, some of the long-range magnetic
order survives leading to non-Fermi-liquid behavior. The Kondo temperature, TK,
is given as follows [76]:

kBTK epF exp-1/N(O)J









where EF is the Fermi energy, N(O) is the density of states at the Fermi energy,
and J is the exchange constant between the local moment and conduction-electron.
Mathematically, if disorder could increase N(O), J, or both, then the Kondo
temperature could be lowered below the average TK. Thus, if the temperature were
at average TK, then not all magnetic impurity spins would be compensated for and
the uncompensated spins would lead to NFL behavior.
The first disorder driven model was constructed from the work of Dobrosavl-
jevic et al. [39] and Bhatt and Fisher [12]. Then, Bernal et al. [11] used this
"Kondo disorder" model to explain the large inhomogeneous nuclear magnetic
resonance (NMR) linewidths they observed in UCus5_Pda. The large linewidths
reflected a broad distribution of local uranium spin static susceptibilities that were
considered to be due to a probability distribution, P(TK), of Kondo temperatures.
The distribution of Kondo temperatures was assumed to be due to disorder. The
uniform magnetic susceptibility, x(H,T) M(H,T)/H, was thought of as the aver-
age of x(H, T;TK) over P(TK) and fits on x(H,T) were used to obtain parameters
characterizing P(TK). The NMR linewidths, which come from the distribution of
Knight shifts and measure directly the width of the distribution P(X) of X, were
found to agree well with the Kondo disorder model and no further fitting of P(TK)
was required. The temperature and field dependence of the specific heat agreed
well with the Kondo disorder model.
The Kondo disorder model was extended further by Miranda et al. [98, 100,
991, who focused on non-Fermi-liquid behavior due to the interaction between
disorder and strong electron-electron correlations. Their theory sums up as a
small amount of disorder playing a major role in the low-temperature logarithmic
divergence in magnetic susceptibility and specific heat along with the linear
behavior in the low temperature resistivity [25].









Not only was the multichannel Kondo model mixed with disorder, but
also spin fluctuations near a quantum critical point were mixed with disorder.
Rosch [126] explained that the reason why the resistivity varies as TI where a is
between 1 and 1.5 for various systems [68, 95, 53] is due to the interplay between
quantum-critical antiferromagnetic spin fluctuations and impurity scattering in
a conventional Fermi-liquid. In other words, the dependence of the exponent de-
pended on sample quality. The disorder in a sample was quantified by taking the
inverse of the residual resistivity ratio: R(T--0)/R(T-+300 K).
The most relevant disorder model to UCu5-sNi, involves a model proposed
by Castro Neto et al. [21, 20]. The model by Castro Neto et al. takes place in a
disordered environment and features the competition between the Kondo effect
and Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction (i.e., magnetic ordering)
as represented by the Hamiltonian in Eq. 2.1. The problem with studying this
competition is the fact that both the RKKY interaction and the Kondo effect have
origins on the same magnetic coupling between spins and electrons [21]. However,
perturbation theory may be used to treat the RKKY interaction since the RKKY
interaction depends on electronic states on the Fermi-surface and states embedded
inside the Fermi-surface while the Kondo effect just affects the Fermi surface. The
RKKY interaction leads to an order of the magnetic moments while the Kondo
coupling leads to the destruction of long-range order in a magnetically ordered
system.
In the model by Castro Neto et al., disorder also affects the magnetic order
in these systems. For a ligand system (e.g., UCus5-Nix, the metallic Cu atoms
are replaced by Ni atoms), if the metallic atoms are replaced with smaller metallic
atoms (as is the case for UCus-5Nis), then the difference in size between the metal-
lic atoms leads to a local lattice contraction which modifies the local hybridization
matrix elements [21]. Large local effects in the system can occur because the local









hybridization matrix elements are exponentially sensitive to the overlap between
different angular momentum orbitals. Also, the local value of the exchange constant
between the conduction electrons and the localized moments, J in Eq. 2.1, changes
due to the change in the local hybridization matrix elements.
Castro Neto et al. disagree with the interpretations of the Doniach argu-
ment [40] which are based on homogeneous changes in the exchange constants
between conduction electrons and magnetic moments. It is true that when the
local exchange constant, J(i), is below a critical value Jc, the RKKY energy scale
is larger than the Kondo temperature as shown in Fig. 2-1 on page 35. However,
Castro Neto and Jones argue that since disorder is present in the system, the mo-
ment can locally order with its environment as the system is cooled down [21]. The
Doniach argument differs because it is based on a global change in the exchange
constant, J, instead of just a local change. Doniach's picture predicts a change
in the exchange constant over the entire lattice and the ordering temperature in
Fig. 2-1 vanishes at a quantum critical point where the system goes from ordered
state to fully Kondo compensated state [21]. The picture by Castro Neto and Jones
represents a quantum percolation problem where moments are compensated due to
local effects and that a local change in a coupling constant does not immediately
imply a change of the "average coupling" constant. Thus, even if chemical substi-
tution occurs on a non-magnetic site, individual moments will be compensated for
magnetically due to the distribution of exchange constants in the presence of disor-
der [21]. At some critical doping concentration, long-range magnetic order will be
suppressed and the system will enter a paramagnetic phase. However, since Castro
Neto and Jones argue that the situation is a percolation problem, the paramagnetic
phase can still contain clusters of atoms in a relatively ordered state.
The alloying of a metallic atom with a different metallic atom is what leads
to this percolation problem. In this percolation problem, the interest lies in the




















J


-.4
RKKY Mono

Figure 2-1: The Doniach phase diagram taken from Ref. [21]. The thick dashed
line is the Kondo temperature, TK EFe-/N(o)J. The thin dashed line is the
RKKY temperature, TRKKY oc [N(0)J]2. The continuous line that equals zero at Jc
is the ordering temperature, TN.









paramagnetic phase or when p > pc, where p is a percolation parameter (related
to the density of quenched moments) and pc is the percolation threshold of the
lattice. When p > pc, then there are only finite clusters of magnetic moments
(i.e., magnetic atoms) which are more coupled than the average [21]. Castro Neto
and Jones assumed that these clusters do not have strong interactions amongst
themselves and that to a first approximation, they can be thought of as isolated
and permeated by a paramagnetic matrix. Castro Neto and Jones termed the
behavior of a cluster of N atoms in the presence of a paramagnetic environment as
the N-impurity-cluster Kondo effect.
The N-impurity-cluster Kondo effect involves a cluster of N magnetic moments
close to a quantum critical point (due to the presence of disorder). If N is large,
then the magnetic cluster may be considered as a large magnetic grain. The
ground state is either a full ferromagnet or antiferromagnet. The ground state of
the cluster has to be at least doubly degenerate due to time-reversal symmetry
and the cluster can fluctuate quantum mechanically (i.e., tunnel) between the
two degenerate states in the absence of an applied magnetic field [21]. Since
the magnetic clusters can tunnel in the presence of a metallic environment, this
produces dissipation (due to particle-hole excitations in the conduction band [21]).
Castro Neto and Jones show that the sources for tunneling depend upon
the symmetry of the system. To summarize, if the magnetic cluster has XYZ
symmetry or very low spin isotropy and Nc is the threshold limit of spins in
a given cluster above which the Kondo effect ceases to occur, then NC is the
maximum number of magnetic moments that can still tunnel due to the anisotropy
in the RKKY interaction. If N > Nc, then there is no Kondo effect and the
tunneling ceases along with cluster motion due to freezing. The other case involves
XXZ or Heisenberg symmetry. For this case, the only source of tunneling is the
Kondo effect. This Kondo effect is due to the dissipative dynamics of states [21].









Dissipation is vital in this case because it allows tunneling to vanish for a finite
number of spins given by Nc.
As mentioned above, tunneling and dissipation are created when a set of
magnetic impurities interacts through a conduction band. Castro Neto and Jones
also show that three different energy scales are created in the mean-field-like
picture: the ordering temperature, the tunneling energy, and the damping energy
[21]. Castro Neto and Jones explored how these different energy scales would affect
the Kondo lattice. If the previous example of a ligand system having its metallic
atom replaced by a smaller atom is used again, then the lattice locally contracts
resulting in local matrix elements that have exponentially large values and the
local exchange parameter may be much larger than the average exchange in the
lattice [21]. The calculations by Castro Neto and Jones reveal that this problem is
equivalent to an anisotropic d+1 classical Ising model with long-range interactions
in the imaginary-time direction, and short-range interactions in the space direction.
The solution to this problem involves extending the quantum droplet model of Thill
and Huse [147] in the context of insulating magnets. In the paramagnetic phase,
the quantum droplets are the magnetic clusters. A distribution of the energy scales
(or cluster Kondo temperatures) is fixed by the percolation theory mentioned above
and this distribution arises from a distribution of cluster sizes. The behavior of this
statistical problem reveals that as the critical number of spins, Nc, is finite, the
distribution for the energy levels diverges logarithmically; however, as Nc -* oo,
there is a crossover in the problem to a power-law distribution for the energy
levels. Now that the distribution of the energy scales has been obtained, the actual
physical properties of these magnetic clusters were calculated by Castro Neto and
Jones.

Castro Neto and Jones considered two distinct domains of temperature for the
physical properties: T < T* and T > T* where T* is a crossover temperature. The









crossover temperature values depend upon the source of tunneling. For example,
if the source is RKKY interaction, then the critical number of magnetic clusters
for which tunneling ceases is very large and the crossover temperature is effectively
zero [21]. For the case where the Kondo effect is the source of tunneling, then the
crossover temperature is on the order of magnitude of about 0.5 K for a ligand
system [21].
The asymptotic behavior of the magnetic susceptibility and specific heat is
considered for temperatures less than the crossover temperature. Interestingly,
there are no analytic expressions for the magnetic susceptibility and specific
heat of a Kondo system [31]. For T < T*, tunneling ceases and the tunnel
splitting is zero. The spin cluster motion is frozen and dissipation dominates the
spin dynamics. This leads to a divergent behavior in the susceptibility at low
temperatures [21]:
1
(T) K Tln(W/T) (2.2)
where W s EF, the Fermi energy. Similarly, the specific heat diverges for extremely
low temperatures [21]:
1
(T) oc T (W/T) (2.3)

Unfortunately, the measurement of temperatures below the crossover temperature
is physically impossible except for a few rare earth cases [21].
The temperature range above the crossover temperature and below the average
RKKY interaction energy gives rise to physical properties that are indicative
of quantum Griffiths-McCoy singularities in a paramagnetic phase [57]. For
temperatures above the crossover temperature, a power-law behavior is present
for the magnetic susceptibility [21]: x(T) oc T-'+A, where A < 1. In the high
temperature limit, the susceptibility goes like normal Curie behavior: x(T) oc 1/T.
Likewise, power-law behavior is present in the specific heat: Cv(T) oc T-'+A, with
A < 1. The lambda values above do not have to be the same, contrary to an earlier









work [20]. Castro Neto and Jones caution that the temperature above the crossover
temperature should not exceed the order of the ordering temperature of the pure
system because the magnetic clusters will decompose.
Castro Neto and Jones also consider physical quantities with the application of
an external magnetic field, H, and in the temperature regime above the crossover
temperature. The response functions are calculated by knowledge of the dynamical
exponent in the Griffiths-McCoy phase. The first physical quantity to be considered
is the magnetization and Castro-Neto and Jones observed that the magnetization
has a scaling form
M(H, T) = f, (, (2.4)

where fA(x,y) is a simple scaling function and w0 is the attempt frequency of the
cluster. The focus will be on the case of wo > T, EH (where EH is the magnetic
energy of the cluster that is proportional to H); thus, the scaling function above
will just be dependent on H/T. If T > EH (i.e., the low-field limit), then Castro
Neto and Jones calculated the scaling function to be fA(x,0) 1 when x -- 0.
The magnetization has a linear dependence with the magnetic field at constant
temperature or the magnetization diverges at low temperatures like TA-1 for
A < 1 at constant magnetic field. If EH > T, then the high-field limit has
the magnetization scaling like H' and the susceptibility (x = dM/dH) goes like
HA-1 [211. The following conclusion may be drawn about the scaling function:
fA(x,0) ; xA-1 asx -+ o0. One important note that will be further explored
in the "UCus-.Ni. Results and Discussion" chapter is that the lambda in the
high-field magnetization should equal the lambda determined from the low-field,
low-temperature magnetic susceptibility.









Castro Neto and Jones also calculate low-temperature limits in the context of
specific heat. Their calculations yield a scaling form

Cv(H, T) = T^ gx (2.5)

where gA(x,y) is a scaling function. Just like the magnetization case, the scal-
ing function will only be dependent upon one variable, gX (x, 0), since it is as-
sumed wo > EH, T. For low fields, the specific-heat coefficient, Uvv(H, T)/T,
diverges at low temperatures like TA-1. The scaling function behavior is then
g9(x, 0) --+ 1 for x --+ 0. In the case of high fields, the dominant behavior is a little
more complicated:

Cvv(H, T) oc 2A/2 exp (2.6)

The scaling behavior is g9(x, 0) --* e-x x2+A/2 asx -- oo. The more complicated
scaling behavior is from a Schottky anomaly due to the high magnetic field [21].
The scaling behavior for the magnetization and specific heat is summarized in
Fig. 2-2 on page 41 (taken from Ref. [21]).
In concluding this theory of Griffiths-McCoy singularities in the paramag-
netic region close to the quantum critical point for magnetic orders of U and
Ce intermetallics, Castro Neto and Jones have made predictions for the behav-
ior of the imaginary part of the average frequency dependent susceptibility, the
nonlinear magnetic susceptibility, the Knight shift measurement in NMR, and
neutron scattering [21]. All the behaviors at low temperatures are based upon the
quantum-mechanical response of magnetic clusters. Experiment has shown that
these magnetic clusters may be the source of NFL behavior in Cel-,LaRhIn5 [73]
and Cel-,ThRhSb [74].

2.2 Curie Temperature Enhancement Theory
The enhancement (i.e., the unexpected nonmonotonicity) of the Curie tem-
perature, Tc, was predicted by Silva Neto and Castro Neto [137]. Silva Neto and



















gf(H/T


*)~1
)~ ^/"--


g,(H/T)~(H/T) 'r"'e-1"

f,(H/T)~(H/T)'


Figure 2-2: The Griffiths phase diagram taken from Ref. [21]. T-H phase diagram
showing the behavior of the scaling functions for magnetization, fx(H/T), and spe-
cific heat, gA(H/T). The T ~ H line is the crossover behavior between the high and
low field limits. r is the average RKKY interaction in the system and above F, the
magnetic cluster does not exist.









Castro Neto believe that their study in the realm of quantum ferromagnets is
applicable to a wide class of systems:
1. heavy-fermion compounds such as URu2-,RezSi2 [35] and Thi-aUaCu2Si2 [87];
2. dilute magnetic semiconductors such as Gai_-MnaAs [111];
3. ferromagnetic dichalcogenides such as CeTe2 [69];
4. manganites such as Lal-aSr.MnO3 [67]; and
5. two-dimensional electron systems in the quantum Hall regime [10].
The Curie temperature enhancement theory starts from the premise that local
moments couple directly to an itinerant electron liquid and this premise can be
expressed mathematically by the Hamiltonian [137]

H = -J Si. S + JK E Si c 0,o'a o, ci,,j + He (2.7)
(ij) i,o,oa
where J is a Heisenberg exchange between localized spins Si (total spin S), JK is
an exchange coupling between localized spins and conduction electrons, c!,. (ci,,)
is the creation (annihilation) electron operator, V are the Pauli matrices, and He
describes the conduction electrons. Silva Neto and Castro Neto find for the case
of a metallic system described by the Hamiltonian in Eq. 2.7 that dissipation (due
to disorder) results from electrons scattering off localized moments and acting
as a heat bath for the spin dynamics. The two main sources of dissipation are
Landau damping in the case of clean magnets and electronic diffusion in the case of
structurally disordered magnets [49, 44]. The effects of dissipation upon Tc will be
discussed.
To begin their study of the dissipative problem, Silva Neto and Castro Neto
considered an action of the form [124]

So(n) =/ dr /ddx MoA(n) orn + 6 (Vn)2 (2.8)









where /3 = 1/T, n is a N-component vector that represents the local magnetization,
pO is the spin-stiffness, and Mo is the magnetization density in the ground state.
The reason for showing this action is that the first term of the expansion inside the
integral is a topological term (the kinematical Berry phase [123, 59]) described by
the vector potential A of a Dirac monopole at the origin of spin space. This term
signals the presence of localized moments [137]. This term is the main difference
between the action of Silva Neto and Castro Neto and the action used by Hertz
in his famous study of itinerant quantum critical phenomena [60]. Hertz did not
include such a topological term. The topological term, along with dissipation, plays
a vital role in the behavior of the Curie temperature [137].
Silva Neto and Castro Neto determined the effects of dissipation upon the
Curie temperature. The phase diagram of the dissipative problem is determined
by applying the momentum shell renormalization group and large-N analysis
to the partition function of the system [137]. The dissipation depends upon the
conduction electron dynamics as mentioned previously: Landau damping for a
clean system and electronic diffusion for a dirty system. Silva Neto and Castro
Neto show that if the Curie temperature is a function of dissipation, then the Curie
temperature decreases faster for Landau damping than for electronic diffusion.
The physical interpretation is that the ballistic electrons (from Landau damping)
have an infinite mean free path and strongly scatter from the localized magnetic
moments in the "cleaner" system. This strong scattering leads to a large amount
of thermal and quantum fluctuations in the system. In the other case, the diffusive
electrons (from electronic diffusion) have a finite mean free path and do not
increase the thermal and quantum fluctuations as much. Interestingly, Silva Neto
and Castro Neto predict about a 1% increase for the Curie temperature of a dirty
system with a small amount of dissipation compared to the Curie temperature of a
dirty system without dissipation (i.e., no disorder). No increase is expected for the









Curie temperature of a clean system with a small amount of dissipation compared
to a clean system without any dissipation. The increase of the magnetism due to
diffusion appears to be important in the 2D MOSFET problem also [24]. One final
note concerning the Curie temperature enhancement involves the importance of the
topological term in the competition between the dissipative and topological terms.
If a diffusive system has no topological term, then Tc is rapidly suppressed and
a slight increase in Tc is not predicted. To summarize the behavior of the Curie
temperature between the ballistic/diffusive electrons and the existent/non-existent
topological term, a figure taken from Silva Neto and Castro Neto is provided on
page 45 [137].
Resistivity measurements should provide insight into whether or not a system
is in the ballistic or diffusive case. Silva Neto and Castro Neto state that ballistic
electrons have an infinite mean free path while diffusive electrons have a finite
mean free path. Thus, b > d where t(b,d) represent the (ballistic, diffusive)
electrons respectively. Since the resistivity, p, is inversely proportional to the mean
free path [7], then one would expect the resistivity for a diffusive system to be
larger than the resistivity for a ballistic system. Thus, not only will magnetic
susceptibility measurements be performed on UCu2Si2-sGe, compounds, but also
resistivity measurements.
In summary, disorder along with the competition between the RKKY in-
teraction and the Kondo effect may lead to NFL behavior in UCus5-Nia due to
magnetic clusters. On the other hand, disorder may lead to electronic diffusion in
ferromagnetic UCu2Si2-_Ge: and possible Curie temperature enhancement.


























0.95 .. :..?'^,, "-



-2- 2
0.85


0.1 02 03 0.4 05 0.6 0.7 0.8 0.9




Figure 2-3: Curie temperature predictions by Silva Neto and Castro Neto. The
Curie temperature Tc(qo)/Tc(m0 = 0) as a function of dissipation, N. S is the to-
tal spin. If 6 = 1, then the dissipation is in the ballistic (clean) regime while 6 = 2
gives the diffusive (dirty) regime. The bare topological constant is represented by
Co and as Co -- 0, then the topological term disappears.














CHAPTER 3
EXPERIMENTAL TECHNIQUES
All alloys in this dissertation were created by an arc-melting technique. In or-
der to accurately categorize a system or compound, several experimental techniques
must be employed. The first experimental technique is x-ray diffraction which
confirms whether or not the compound formed into the correct crystal structure.
The x-ray pattern is also used to determine the lattice parameter values of the
fundamental "building block" of the compound, the unit cell. After confirmation
of the correct crystal structure, many techniques are used to determine the correct
thermodynamic and transport properties of the particular sample. These tech-
niques (in no particular order) include direct current (dc) magnetic susceptibility,
alternating current (ac) magnetic susceptibility, dc resistivity, and heat capacity
measurements. All techniques and measurements previously mentioned will be
described in further detail below.

3.1 Arc-Melting
The UCu5-.sNia and UCu2Si2-_Gex systems had their own unique preparation
procedures. The general idea behind the arc-melting process will be discussed first,
followed by the preparation of the UCus-5Ni, system and UCu2Si2-.Gea.
The arc-melting process is based upon a large amount of current (with low
voltage) passing through a tungsten electrode and producing an electric arc in Ar
gas that runs from the tungsten tip down to a water cooled copper hearth inside a
vacuum-tight chamber. Arc-melting is ideal for melting constituent elements with
high melting points together. This dc apparatus melts the elements together in a
zirconium-gettered argon atmosphere. The arc strikes the zirconium first because
zirconium has a high absorption rate for certain residual gas components like









oxygen. The argon atmosphere is used because argon is an inert gas and the argon
helps raise the pressure inside the vacuum chamber so that the electric arc may
be struck. Whenever melting elements together with significantly different melting
points, the general principle is to melt the element with the lower melting point
first and then draw the higher melting point elements into the molten element. In
this respect, the mass loss of the lower melting point element is minimized. This
arc-melting process is very similar to tungsten inert gas (TIG) welding.
The arc-melting of the UCus5-Nix involves the melting of three constituent
elements. The uranium and nickel have similar melting points and vapor pressures.
The copper has the lowest melting point and the highest vapor pressure. Thus,
excess copper (~ 0.5% of the total Cu mass) was added to each UCus5-Nia
sample to account for the copper loss. Each UCu5s-Nia sample was arc-melted
three to four times. After each melt, the sample bead was flipped over to insure
homogeneity.
The effort involved in the arc-melting of the UCu2Si2-_Ge_ compounds was
a bit more intensive. The dilemma in arc-melting the UCu2Si2-.Ge, compounds
came from the explosive nature of melting two semiconductors together, Si and
Ge, along with the electric arc thermally shocking the formed UCu2Si2-_Gez
lattice. Two techniques were employed to solve these problems. First, the U, Si,
and Ge constituent elements were melted together first and then subsequently
melted together a minimum of at least six times. Second, the copper element was
then melted into the U, Si, and Ge bead. All elements were melted together a
minimum of six times to insure homogeneity. The second technique was employed
on all arc-melts after the initial one. Instead of moving the electric arc directly
from the zirconium bead to the UCu2Si2-,Ge, bead (this tended to blow apart
the UCu2Si2-zGez bead), the electric arc was moved very slowly towards the
UCu2Si2-zGe, bead. Thus, the arc's convection and radiant heat would melt the









UCu2Si2-aGe, bead and, before the arc was directly over the UCu2Si2-zGe, bead,
the bead would be molten. These techniques were used in the production of all
UCu2Si2_-..Ge compounds.
Excess mass amounts of Cu, Si, and Ge were added before arc-melting. U
has a very high melting point and low vapor pressure, so the mass loss of U was
assumed to be negligible. Cu and Ge had almost identical melting points and vapor
pressures, so the mass loss of Cu and Ge was assumed to be equal. The melting
point of Si is about 50% higher than the melting points of Cu and Ge; thus, it was
assumed that the mass loss of Si would be about half the mass loss of Cu or Ge.
The assumptions above were taken into account so that the appropriate extra
masses could be added before arc-melting. Since a minimum of 12 arc-melts (as
discussed previously) were performed on each UCu2Si2-..Ge, sample, all melts
would "blow away" approximately 1.5% of the total Ge mass present, 0.50% of the
total Cu mass, and about 5% of the total Si mass for compounds on the Ge rich
side. Arc-melting compounds on the Si rich side would result in a loss of about 2%
of the total Si mass, 5% of the total Ge mass, and 1% of the total Cu mass. Thus,
depending on which UCu2Si2-,Ge. compound was being synthesized, excess Cu,
Ge, and Si was added according to the above conditions.
One final technique that is related to sample preparation and arc-melting
is the process of annealing. The purpose of annealing is to eliminate as much
disorder as possible. All UCus5-Ni_ and UCu2Si2-a.Gez compounds were annealed.
Annealing involves pieces of sample being wrapped in tantalum foil and the
wrapped sample is sealed in a quartz tube under vacuum. The samples are placed
in ovens for an experimentally determined time such that the mass loss remains
acceptably small (< 0.5% of the total mass) while the order of the crystal lattice is
improved. The order in the lattice may be checked by x-ray diffraction.









3.2 X-Ray Diffraction/Lattice Parameter Determination from X-Ray Diffraction

Lattice parameter values can play an important part in determining the site
occupation of atoms in a crystal structure along with the lattice values telling
the story of whether or not the lattice expands or contracts upon the doping of
a certain element. For example, the UCus5-Pds system, which crystallizes in the
face-centered cubic (fcc) AuBe5 structure, shows that Pd substitution initially goes
onto the larger Be I site until about x = 0.8 and for x > 0.8, the Pd atoms also
start to occupy the smaller Be II sites also. This was seen not only in muon spin
rotation (pSR) [92] and extended x-ray-absorption fine-structure (EXAFS) [15]
measurements, but also by a change in slope of the lattice parameter values at
x m 0.8 [77].
The present study is similar to those on the UCus-5Pdz system. Instead of
doping larger (relative to the Cu atom) Pd atoms on the Cu sites, smaller Ni atoms
will be doped on the Cu sites. The knowledge of the lattice parameter values at
different Ni concentrations is imperative to gain insight on which copper site the Ni
atoms are found (i.e., the Be I or Be II site).
Lattice parameters are calculated from x-ray diffraction patterns. X-ray
diffraction was run on a Phillips XRD 3720 machine at the Major Analytical In-
strumentation Center (MAIC) on the University of Florida campus. The complete
x-ray diffraction process is described elsewhere [119].

The particular machine on which the x-rays were generated used two different
wavelengths of radiation [copper Kal = 1.54056 Angstrom (A) and copper
Ka2 = 1.54439 Angstrom (A)]. Also, the intensity of the a, beam was twice
as great as the a2 beam. This made resolving two distinct peaks at a particular
crystallographic plane sometimes quite difficult since the ai peak would conceal the
a2 peak.









The typical x-ray pattern was generated with a 20 (degrees) domain from
200 to 1200 in 0.020 steps where 20 is the total angle by which the incident X-
radiation beam is deflected by a lattice plane. Almost all measurements had a one
second step time where the detector on the x-ray machine moved continuously
through a 0.020 interval in one second. The reason for such a long total scan time
(~- 90 minutes) was to obtain good resolution around the high angle x-ray peaks
(> 800).
The Phillips XRD 3720 machine operation was controlled with a computer
interface. Once the x-ray process was complete, the computer would generate a
list of peaks from the x-ray pattern. The computer found the peaks at a respective
20 value by finding the minimum of the 2nd derivative of the peak (i.e., where the
change in the slope on the x-ray pattern is least).
Once the peaks along with their particular 20 values are found via the com-
puter, lattice parameter determination may begin in earnest. The easiest way
to explain the lattice parameter calculation [107] is by using an example. The
UCu5s-Nix system will be the example. Since the UCus-5 Ni, system forms in
the cubic AuBe5 crystal structure, this system has very high symmetry and the
perpendicular distance between two parallel lattice planes, d, may be written in
terms of the Miller indices (hkl) of the plane [119]:

d(hkl) = h2k2 12 (3.1)
h" + k2 +12

where lattice parameter value, a, is the side of the cubic crystal one is calculating
and the Miller indices are defined as the coordinates of the shortest reciprocal
lattice vector normal to a lattice plane, with respect to a specified set of primitive
reciprocal lattice vectors (e.g., a plane with Miller indices h,k,l is normal to the
reciprocal lattice vector hb1 + kb2 + lbs) [7].









The inter-plane distance, d, is related to half the total angle by which the
incident X-radiation beam is deflected, 0, by the well known Bragg condition [7]:

nA = 2d sin0 (3.2)

where n is a positive integer and A is the wavelength of the incident radiation

beam. If one combines Eq. 3.1 and Eq. 3.2 and assumes that n = 1, then 'a' may

be written in terms of A, 0, and (hkl):

A h2 + k2 + 12
a = 2sin (3.3)

The values obtained from Eq. 3.3 will be the ordinate values for the graphical

extrapolation method. The reason 'a' cannot be obtained directly from Eq. 3.3 is

that Eq. 3.3 would require 0 to equal 900 and 20 would be 180, which is physically

impossible for the XRD machine. If 20 were 1800, this would mean that the

source and detector of the XRD machine were located at the same position. The

detector and source at the same position on the XRD machine is not possible. The

maximum achievable 20 angle by the XRD machine is 1400. This justifies why an

extrapolation method is needed to obtain 'a'.

The abscissa values used in the graphical extrapolation method take into

account some possible sources of error. The function to be used for the x-axis

values is advocated by Nelson and Riley [107]: 1 (cos2 0/0 + cos2 0/ sin 0). This
functional form takes into account possible errors caused by absorption and

divergence of the x-ray beam.

Before the 'a' values can be graphed against the functional x-axis form, it has

to be determined what (hkl) values correspond with peaks in the x-ray pattern.

Thus, a particular 0 value may be linked with a set of (hkl) values. Since it is

known that UCus-5Nix crystallizes in the AuBe5 structure [153], a theoretical

crystal pattern can be calculated with known information [33, 155] such as a lattice









parameter constant (in this case, used the known UCu5 value: 7.043 A [155]), space
group number (216 for UCu5 structure), and atomic positions in the unit cell. This
information was used by the PowderCell computer program to provide a theoretical
pattern which included peaks with known (hkl) values. A visual inspection between
the theoretical patterns and the experimental patterns of the UCus5-Nix system

could link peaks with particular (hkl) values as shown in Fig. A-1 on page 167 for
UCu4Ni annealed 14 days at 7500C. A list was generated with (hkl) values and
corresponding 20 values.
Once the (hkl) values and corresponding 20 values are obtained, the 'a'
values and x-axis values may be obtained from Eq. 3.3 and the Nelson-Riley error
function respectively. A graph plotting the 'a' values versus the corresponding
error function values for annealed UCu4Ni is shown in Fig. A-2 on page 168. The
values when plotted should show that the extrapolation line has a negative slope.
The reason behind this negative slope is because all the sources of error lead to
high values of 0 and so to low values of the lattice parameters [119]. It should be
stressed here that it is very important to have as many (hkl) values with 200 values
greater than 800 as possible. The importance comes from the fact that 0 values
close to 900 give Nelson-Riley functional values close to zero, insuring that the
extent of extrapolation is not large [119].
The graphical extrapolation method is an excellent technique for determining
lattice parameter values on a highly symmetric system such as UCus5-Nia. The
error in the lattice parameter values as will be seen later for the unannealed
and short term annealed UCus5_Ni. compounds is on the order of 10-3 A. This
error may be improved upon by running a cubic Silicon standard along with the
respective experimental compound or by running the Silicon standard alone to
determine the offset in the XRD machine. The latter process was done for this









dissertation. The determination of lattice parameter values has been facilitated
greatly by the advent of computers with software such as Jade.
3.3 Magnetic Susceptibility

Magnetic susceptibility measurements were used to measure the low tem-
perature magnetization of the UCus5-Nix and UCu2Si2-_Ge, samples. The
susceptibility measurements were taken with two superconducting quantum in-
terference devices (SQUIDs): an MPMS-5S [can measure with a magnetic field
from 0 to 5 Tesla(T)] and an MPMS XL (measures up to 7 T) machine, both made
by Quantum Design. Both machines could take magnetization measurements in
the temperature range from 2 K to 300 K. The MPMS XL machine only had the
capability to measure dc magnetic susceptibility while the MPMS-5S machine
could measure both ac and dc magnetic susceptibility. Alternating current and dc
magnetic susceptibility measurements will be discussed below.
3.3.1 DC Magnetic Susceptibility

Direct current magnetic susceptibilities are usually made in 1 kiloGauss (kG)

magnetic fields. If the signal of the sample is comparable to the signal of the
addenda (i.e., the plastic straw that holds the sample), then a 1 T magnetic field
may be used so that the sample's signal is dominant over all other signals.
Direct current magnetic susceptibility measurements are based upon the
principles of Lenz's Law. The sample is magnetized by a 1 kG magnetic field and
the magnetic moment as a function of temperature of the sample is measured [94].
The magnetic susceptibility is determined by the following ratio: x = M/H. The
magnetic moment is measured by induction techniques. The inductive measure-
ments are done by moving the sample relative to a set of superconducting pickup
coils and the SQUID instruments measure the current induced in superconducting
pickup coils. The sample is typically moved 4 cm through the superconducting









pickup coils while 48 data points are taken during the sample's movement to pro-

duce the magnetization curves. The sample is moved through the coils four times
and the average of the four measurements is reported for a particular temperature.

Not only is the dc magnetization measured at various temperatures in a
constant magnetic field, but also the dc magnetization is measured in different

magnetic fields at a constant temperature. The magnetization versus field curves

are typically generated at the lowest possible temperature (2 K). The MPMS XL is
a particularly good machine for this type of measurement since it has a secondary

impedance line that can maintain low temperatures continuously over an extended

period of time (on the order of about 12 hours).
3.3.2 AC Magnetic Susceptibility

Unlike dc magnetic susceptibility measurements where the sample moment is
constant during measurement time, ac magnetic susceptibility measurements for
the MPMS-5S machine use a small ac drive magnetic field that is superimposed
on the dc magnetic field, causing a time-dependent moment in the sample. Alter-

nating current measurements do not require sample motion (as for the dc case)
since the field of the time-dependent moment induces a current in the supercon-
ducting pickup coils. The measurements are usually made in a narrow frequency
band, the fundamental frequency of the ac drive magnetic field. The ac suscepti-

bility measurements in this dissertation were made at three different frequencies:

9.5 Hertz (Hz), 95 Hz, and 950 Hz. These three frequencies stayed within the

frequency range of the MPMS-5S machine and avoided any integer multiples of the
frequency of a common electrical outlet (60 Hz).
Alternating current magnetic susceptibility measurements yield two quantities:
the magnitude of the susceptibility, X, and the phase shift, 0 (relative to the ac
drive magnetic field). This phase shift comes from the fact that the magnetiza-

tion of the sample may lag behind the ac drive magnetic field [94]. In terms of









complex notation, the ac susceptibility measurements provide an in-phase, or real,

component X' and an out-of-phase, or imaginary, component X". The ac magnetic
susceptibility measurements on certain UCu5-aNix samples were used to determine
the antiferromagnetic phase transition temperature, TN&d, for each compound.

A peak in the real component of the ac magnetic susceptibility indicated the

antiferromagnetic phase transition.

3.4 Cryogenics
The remaining two experimental techniques, dc resistivity and heat capacity,
are primarily measured in a temperature range from 300 milliKelvin (mK) to about
10 K. In order to achieve such low temperatures, one must make use of liquid
nitrogen and liquid helium.

The probe that is used to measure either low temperature resistivity or specific

heat is first cooled down to the boiling point of liquid nitrogen (, 77.4 K [54]).
The probe is then quickly lifted out of the liquid nitrogen and placed in a Dewar, a
vacuum insulated flask. The Dewar is then filled with liquid helium, which boils at
4.2 K. After a couple of hours, the inside of the probe is cooled down to 4.2 K.

Helium 4 can be cooled to below its boiling temperature by reducing the
pressure inside the Dewar to below atmospheric pressure. In fact, using the

combination of a large vacuum pump and blower, a pumped bath of liquid helium 4

can cool a probe down to about 1.1 K. If liquid helium 4 is cooled below its
transition temperature, or "lambda point" (, 2.17 K [54]), then the helium 4 starts

to become a superfluid helium 4 that behaves as if it had no viscosity, i.e., it can
flow through tiny holes. Also, the superfluid helium 4 has no entropy and it flows
into a heated area to cool that area and restore the uniform mixture of normal
and superfluid helium 4. This last physical property of superfluid helium 4 allows

the temperature of the probe to be stable enough such that resistivity or specific

heat may be measured. A full dewar of helium 4 in the lab that has a vacuum









pump/blower attached to it can maintain a low temperature of 1.1 K for about 12
to 16 hours.

In order to achieve a temperature lower than about 1.1 K, helium 3 needs to
be used. Helium 3 boils at 3.2 K [at 1 atmospheric pressure (atm)] [54]. Helium 3

is inserted as a gas into the probe and due to its rarity, helium 3 is trapped inside

the probe so that it may be reused. Once the probe is cooled down to 1.1 K with
the superfluid helium 4, the helium 3 gas is condensed by coming into contact
with the 1.1 K probe and the helium 3 collects in the helium 3 pot. The low
temperatures down around 300 mK are achieved by reducing the vapor pressure

of the collected liquid helium 3 by using the internal sorption pump (i.e., charcoal

on the end of a long rod) [66]. The sorption pump is "turned on" by lowering
the charcoal into the vicinity of the helium 3 pot. This cools down the "warmed"
charcoal to below 20 K since the charcoal was initially at the top of the probe. The

helium 3 liquid is pumped on by the sorption pump while the sample (connected to

the helium 3 pot via a weak thermal link) is cooled down to around 300 mK. The

probe can stay down at such a low temperature for about three to four hours until
all the liquid helium 3 evaporates. The sorption pump is then turned off by raising

the charcoal in the probe so that it is above 20 K (i.e., above the 4He level in the
dewar) which desorbs the helium 3 gas and allows the helium 3 gas condensation

cycle to start over again.

3.5 Probes
In the above discussion concerning cryogenics, the generic term probe has
been used. In reality, two kinds of probes were used in the lab. One probe had a
helium 4 pot which did not require the entire Dewar to be vacuum pumped upon.
The second type of probe had no helium pot and pumping upon the Dewar was

imperative to achieve a temperature around 1.1 K.









A probe with a helium 4 pot has its cross section inside the vacuum can

shown in Fig. 3-1 on page 58 [71]. The vacuum can is mounted on the flange's

probe with a brass taper joint seal that is lightly coated with silicone high vacuum

grease, preventing the superfluid helium 4 to penetrate. The sample platform at the

bottom is connected to a copper block and a thermally conducting grease is used

so that the temperature gradient between the copper block and sample platform is

minimal. The other side of the copper block is connected to a helium 3 pot with a

brass thermal link and large diameter Cu wires (not shown in Fig. 3-1) run from

the copper block to the helium 3 pot for improved thermal conductivity These

connections allow the sample platform to reach low temperatures of 300 mK once

the sorption pump is turned on by lowering the charcoal inside the pumping line for

the helium 3 pot in Fig. 3-1.

Once the helium 3 cryostat in Fig. 3-1 on page 58 is placed in a Dewar and

allowed to reach normal liquid helium temperature (~ 4.2 K), the helium 4 pot

may be pumped upon, which allows the helium 3 gas to condense. As the probe is

cooling down inside the Dewar, a line connecting the helium 4 pot and the helium 4

bath inside the Dewar is open so that the helium 4 pot may be filled with liquid

helium 4. Once the probe cools down to around 4.2 K, the temperature is lowered

further by closing the capillary linking the helium 4 pot and the helium 4 bath

with a needle valve and then connecting an external vacuum pump to the pumping

line connected to the helium 4 pot. Thus, the liquid helium 4 inside the helium 4

pot is just pumped on instead of the entire helium 4 bath inside the Dewar. The

germanium thermometer close to the sample platform in Fig. 3-1 registers a low
temperature of about 1.6 K after the helium 4 pot has been pumped on for ~ 20-30

minutes.

The other important aspect to the helium 3 probe concerns the wiring for the

electronics to measure DC resistivity and specific heat. The wires come from the




















Pumping Line
for 4He Pot



















Brass Thermal Link-



Germanium Thermometer

Sample Platform-


-coal sorb trap

.Pumping Line for Vacuum Can
and Tube for Wires
Needle Valve
-Copper Heat Sink
Capillary Connecting
4He Pot and 'He Bath


He Pot


Block Heater


Heat Sinking Pins


-Heat Sinking Copper Block


Figure 3-1: Cross-section of a helium 3 probe. This simplified cross-section con-
tains a helium 4 pot. Such a probe is able to achieve a low temperature around
300 mK.









top of the probe and run down the pumping line for the vacuum can in Fig. 3-1.
The wires from the top of the probe are soldered to the copper block above the
helium 4 pot. The copper block is in temperature equilibrium with the Dewar's
helium 4 bath by the copper heat sink in Fig. 3-1. The wires on the top copper

block in Fig. 3-1 are then usually connected to the copper block right above the

sample platform by more wires wrapped around the helium 3 and helium 4 pots
and secured to these pots with General Electric (GE) varnish 7031 (a good thermal

conductor). The reason for the wires not running from the top of the probe directly
to the copper block above the sample platform concerns the amount of heat that
would be transferred from the top of the probe which is at room temperature. The

intermediate copper block connections allow the heat flow to be minimized.

The actual wires that are used in the helium 3 probe are either #40 gauge
copper or #40 gauge manganin wires. Either type of wire is insulated and requires
friction (from sandpaper or an eraser) to remove the insulation. The difference
between copper and manganin wires is that manganin wire is about 30 times more

electrically resistive than copper wire [71]. The higher electrical resistivity of the

manganin wires is associated with less heat being transferred from the top of the
probe. Thus, manganin wires should be used for low current loads while copper
wires are used for high current loads. The wiring in the probe is composed of pairs
of the same type of wiring twisted around each other so that the electrical noise is
reduced.

The probe without the helium 4 pot has the exact same configuration as in
Fig. 3-1 except for the helium 4 pot and the pumping line for the liquid helium 4.
The Dewar itself may be thought of as the helium 4 pot for the case of the probe
without the helium 4 pot.









3.6 DC Resistivity
Direct current electrical resistivity is based upon an equation derived from the
Drude model for electrical conduction [7]:

AR
P= T (3.4)

where p is the electrical resistivity that is being solved for, A is the cross sectional

area of the resistivity bar being measured, and L is the distance between the
voltage wires. The electrical resistivity was measured using a standard four wire
technique that is discussed below.
The first part of the four wire technique involves making resistivity bars. The
standard way of making resistivity bars involved cutting the particular sample
with a diamond saw. The diamond saw could cut resistivity bars with rectangular
cross sectional areas that had dimensions on the order of thirty thousandths of an
inch. Another way to produce resistivity bars that avoids possible microcracks in
the bars is the "sucker" method. The sucker method is done while arc-melting.
The idea behind the sucker method is that while the arc has a sample in its

molten state, a pressure difference between the arc-melter chamber and an external
chamber on the sucker apparatus has enough force to push down the molten sample
into a square cross sectional copper area. The copper area is water cooled, so the
molten sample should quench as a square resistivity bar ideally. A sucker produced
resistivity bar on a UCu4Ni sample will be discussed later on in this dissertation.
Once the resistivity bars are made, four platinum wires need to be attached
to each bar. The platinum wires have a diameter of 0.002 inches and a purity of
99.95%. There are two methods to attach these platinum wires to a resistivity
bar. One method is to use EPO-TEK H31LV silver epoxy to "glue" the platinum
wires onto the resistivity bar. The only problem with this method is that extra
resistance is added to the measurement with the resistance of the silver epoxy









and possible oxide barriers on the surface of the sample. The second method of

attachment was used in this dissertation. It involved spot welding the four wires

onto the resistivity bar. Spot welding minimized the contact resistance. The

four wires should be spot welded on the same face of the resistivity bar with two

wires on one end of the bar and the other two wires on the opposite end. The

two outside platinum wires are the current leads while the two inside platinum

wires are the voltage leads. The resistivity bar is then attached to a piece of non-

electrically conducting compensated silicon with GE varnish 7031. The varnish

is a good thermal conductor and a poor electrical conductor. The four platinum

wires are attached to the silicon base with silver epoxy and there is some slack in

the platinum wire between the resistivity bar and silver epoxy to account for the

contraction at low temperatures. The silicon base is attached to a low temperature

probe with a thermally conducting grease such as Apiezon N grease.

The low temperature resistivity measurements gather the resistance of

the sample at a particular temperature. The resistance in Eq. 3.4 is then used

to calculate the resistivity. One can see from Eq. 3.4 that in order for larger

resistance measurements (hence, larger voltage measurements from Ohm's Law),

one should maximize the distance between the voltage leads, L, and minimize the

cross sectional area of the resistivity bar, A. This helps reduce the scatter in the

resistance measurements (another apparatus that would help reduce the scatter is

an ac resistance bridge).

The resistance measurements are automated. An HP 9000/300 series computer

controls the current sources and voltmeters taking the measurements. The scatter
in the resistivity measurements is reduced two ways. One way is to measure the

resistivity in one current direction and then reverse the current to measure the re-

sistivity in the opposite direction. The average of these two absolute values should

eliminate any (e.g., thermoelectric) offset in the voltmeter taking measurements.









A second procedure should eliminate the effect of any drift in the voltmeter. The
computer is programmed with an external and internal loop while taking resistance
measurements. The internal loop reverses the polarity of the current as described
above while the external loop dictates how may times the internal loop should be
performed. The external loop averages the measurements taken by the internal
loop. Most resistivity measurements in this dissertation had an external loop value
of 10 and an internal loop value of 5.

3.7 Specific Heat
Specific heat is the quantity of heat needed to raise a unit mass of sample by
a unit degree of temperature while keeping the property x (in this dissertation,
pressure, p) constant during the rise of temperature:

C = lim. (3.5)
dT--0 dW

Before 1968, the above definition was used in a technique called the adiabatic
method [141] to measure specific heat. The adiabatic method added a pulse of
power (dQ) to a sample and the temperature rise (dT) in the sample was noted.
A couple of drawbacks to the adiabatic method are the large sample size needed
to minimize the effects of stray heat leaks and the thermal isolation of the sample
from its surroundings [71].
In 1968, Sullivan and Seidel published their ac heat capacity technique [144].
The ac method measures small samples that makes use of a commercially available
lock-in amplifier. The strength of this technique is its ability to detect very small
changes in heat capacity [141]. However, a drawback to this ac temperature
calorimetry is in measuring the absolute value of the specific heat of a sample. This
ac method usually provides only a relative measurement of the specific heat [71].
The specific heat technique used in this dissertation is the thermal relaxation
method [9]. The thermal relaxation method was constructed from the solution of a









one-dimensional heat-flow equation with appropriate boundary conditions [9]:

P = A + C(T)T-, (3.6)

where P is the power put into the sample, A is the cross sectional area of the wire
linking the sample platform to the copper block, K is the linking wire's thermal
conductivity and the heat flows along the z-axis. The solution for C in Eq. 3.6 is
C = KT1 where T1 is the time constant of

T = To + ATe-1t/' (3.7)

with AT = T To and To is the copper block temperature.

The answer above is interpreted by Fig. 3-2 on page 64. In Fig. 3-2, the
sample along with all the addenda on the sapphire (A1203) platform is heated a
small AT above the copper block temperature To, by means of power, P, flowing
through the platform heater. Once the power is turned off on the heater, the
temperature of the sample and platform decay exponentially as in Eq. 3.7 with
time constant, rl, through the linking wires. The time constant, rI, is determined
using computer analysis of the temperature decay. By knowing the thermal
conductance, K, of the linking wires, one may determine the total heat capacity of
the sample and platform. If the addenda are known as in Fig. 3-2, then one may
determine the heat capacity of the sample by subtracting the addenda from the
total heat capacity. All components of the addenda will be discussed in detail later
on. It should be said that the rise in temperature, AT, should be small enough
so that Tr does not change appreciably between To and To + AT [141]. When
performing low temperature specific heat measurements, AT was usually around
4%. The absolute accuracy of the thermal relaxation method to measure specific
heat is estimated to be 5% [71], which is verified by measuring the known specific
heat of a high purity standard, e.g., Pt or Au.









P





To + AT CTotal =
Csample + -



LAT


/


- Sample
- Sapphire
- Ge Chip
Thermometer
- Silver Epoxy
- 1/3 of Au-Cu Wires
- Thermal Grease


Four Au-Cu Wires




Copper Ring
Heat Reservoir


Figure 3-2: Schematic diagram outlining the thermal relaxation method. The ther-
mal relaxation method is used for the specific heat measurements. The addenda
is composed of the sapphire, the germanium chip thermometer, EPO-TEK H31LV
silver epoxy, 1/3 of the linking wires, and thermal grease. The linking wires are the
four Au-Cu wires connecting the sample platform to the copper block.



















block post


Au-Cu


Solder for Au (solid circle)
(44% In, 42% Sn, 14% Cd)


Au-Cu
Wires


sapphire


Figure 3-3: An overhead and bottom view of the mounted sample platform. (a.)
The thermal epoxy used was a two component Stycast 1266 epoxy. The copper
block post connects the copper ring to the copper block as shown in Figure 3-1.
The Au-Cu wires connecting the sample platform to the copper ring are Au with
7% Cu to provide the correct magnitude for the thermal link.
(b.) The evaporated 7% Ti and 93% Cr heater is a thin continuous film on the
bottom of the sapphire disk. The Ge chip thermometer is linked to the silver epoxy
with Au-Cu wires.


(b.)









In Fig. 3-3, two views of the sample platform are shown. The Au-Cu wires
that were used in this dissertation were Au-7% Cu wires. These wires steady the
platform on the sapphire and serve as electrical contacts and thermal links to
the copper ring (hence the copper block). The thermal conductance of the wires

depends on several factors. The first factor has been mentioned indirectly, the

composition of elements making up the wires. For example, Au-1% Cu wires have
a thermal conductance seven times that of Au-7% Cu, while Cu-2% Be has a
thermal conductance five times less than Au-7% Cu. The second factor that varies
the thermal conductance in the wires is the diameter of the wire. The specific
heat measurements in this dissertation used 0.003 inch (in.) diameter Au-7% Cu
wires. The thermal conductance of the 0.003 in. diameter wires is nine times
that of the 0.001 in. diameter wires [141]. The reasoning behind choosing the
0.003 in. diameter wires is that 0.001 in. diameter wires are a little too fragile
while inserting or removing the sample onto or off of the sample platform.
The Au-7% Cu wires are attached to the copper ring in part (a.) of Fig. 3-3
with special solder (44% In, 42% Sn, 14% Cd) on a silver pad. The silver pad
is electrically insulated from the copper ring with a thermal epoxy (in this case,

Stycast 1266 epoxy); however, the thermal epoxy is a good thermal conductor. The
reason for using the special solder is that regular solder (composed of Pb and Sn)
will dissolve the Au-Cu wires.
The sample itself is mounted on the "rough" side of a smaller sapphire disk.
The flat part of a sample (for improved thermal conductivity) is attached to the
sapphire disk with GE 7031 varnish. Then, the "smooth" side of the sapphire with
the sample is mounted on the 3/8 in. sapphire disk in part (a.) of Fig. 3-3 with
thermally conductive grease (in this case, Wakefield grease) [9]. Both sapphire
disks are pressed firmly together to allow for a continuous and even distribution
of thermally conductive grease between the disks. Before each measurement, both









sapphire disks have to have the grease cleaned off of them with trichloroethane.
The mass of all components (sample, GE 7031, sapphire, and grease) has to be

known for accurate specific heat values.

The platform heater in part (b.) of Fig. 3-3 is composed of a thin film
of 7% Ti and 93% Cr on the "rough side" of the 3/8 in. sapphire disk. This
platform heater is created by evaporating a Tio.07Cro.93 sample onto the sapphire
disk with evaporator instrumentation. The resistance of this platform heater is
around 300 Ohms (12) [71] and the resistance remains fairly constant with varying
temperatures.

The doped germanium chip thermometer (commercially obtained from
Cryocal or Lakeshore Cryotronics) in part (b.) of Fig. 3-3 is used for the sample
platform thermometer. The reason for using doped germanium was that its
resistance is a rapid function of temperature [141]. This sensitivity is vital for
the thermal relaxation method since the increase in the platform temperature at
each data point is not very large (~ 4%). The calibration of the germanium chip
thermometer's resistance versus temperature will be discussed later on.
The key to an accurate measurement of a sample's specific heat is the proper
subtraction of all components (i.e., the addenda) involved in the thermal re-
laxation method. As mentioned previously, some of the addenda are listed in
Fig. 3-2 on page 64. The sapphire disks that serve as the sample platform have
high thermal conductivity (about 1 Watt cm-1 K-1 at T = 4 K) and low spe-
cific heat (2 pJ gram-1 K-1 at T = 2 K and OD w 1035 K) [48]. The platform
heater in part (b.) of Fig. 3-3 that is composed of Cro.07Tio.93, which has a
mass < 0.01 mg, is assumed to have a negligible contribution to the specific heat
of the addenda [71]. The other component on the bottom of the sample platform
next to the platform heater is the germanium resistance thermometer that has a
specific heat value of 0.018 pJ/K at 2 K with a mass of 3.8 mg [71]. The leads









attached by the factory to the germanium resistance thermometer are connected to
the Au-7% Cu wires by means of H31LV silver epoxy. The silver epoxy is a source
of addenda contribution. For example, a mass of 0.63 mg of silver epoxy has a
specific heat value of 0.12 jJ/K at T = 2 K [71]. The GE7031 varnish and Wake-
field grease also add to the addenda. At T = 2 K, the Wakefield grease has a heat
capacity of 0.16 1pJ/K for a mass of 0.12 mg [71]. The final component of the ad-
denda concerns the Au-7% Cu wires. The diameter of the Cu wires not only has to
be known (0.003 in.), but also the length of the four wires (each wire was 0.25 in.
long) as shown in part (a.) of Fig. 3-3 on page 65. Bachmann et al. determined
that 1/3 of the Au-7% Cu wire's heat capacity should be included as addendum [9].
At T = 2 K, the amount of addenda for 1.5 mg of Au-7% Cu wires is 0.044 AJ/K.
The addenda contribution from the Au-7% Cu wire rises rapidly with temperature
due to the low Debye temperature of the wires (OD ~ 165 K [141]). The tempera-
ture range (0.3 K to 8 K) at which the specific heat was measured for samples in
this dissertation avoided too large an addenda contribution from the Au-7% Cu
wires. The computer programming language, HPBASIC, used temperature depen-
dent and mass dependent polynomial fits for each addenda contribution mentioned
above in order to provide a realtime subtraction for the heat capacity measured at
a particular temperature. A standard piece of gold was measured using the thermal
relaxation method and it was found that if all the aforementioned addenda was not
subtracted off, then the specific heat of gold at 2 K would be about 10% too high
from its reported standard value (~ 5.001 mJmole-1 K-1 [13]) [71].

Once the cryostat with all of its components is assembled, the cryostat parts
mentioned above need to be interfaced with instrumentation (i.e., voltmeters and
current sources) that is controlled by an HP 9000/300 series computer. The block
thermometer (i.e., a resistor) is hooked to a voltmeter and current source so that
resistance (i.e., temperature) values may be obtained. The block heater (usually









made up of a bundle of manganin wire) which controls the temperature of the

block thermometer, the copper ring, and the sample platform is connected to a

current source so that Joule heating may raise the low temperature of the bottom

of the cryostat. The platform heater that provides the small temperature rise to

the sample platform is also connected to a current source. The final component

concerns the germanium chip platform thermometer whose resistance is very

sensitive to small temperature changes. The platform thermometer is half of one

arm of an ac Wheatstone bridge. The other half of the arm is connected to a

variable resistor (i.e., a resistance box). The other arms of the ac Wheatstone

bridge consist of two known resistors (each resistor is 90 ku). The platform

thermometer has a lock-in amplifier connected across it to provide a source of ac

excitation current and to serve as a null detector [9]. The ac excitation current

is limited by the self heating of the platform thermometer. The other reason for

using the lock-in amplifier is to increase the signal-to-noise ratio [141] by filtering

out noise at other than the measurement frequency (~ 2700 Hz) [71]. The lock-in

amplifier is connected to the HP 9000/300 series computer through an analog-

digital converter. The converter digitizes the signal from the ac Wheatstone bridge

for the computer during specific heat measurements.

Before actual specific heat values are measured, proper calibration of the ger-

manium chip thermometer has to be performed. The ac Wheatstone bridge is used

to measure the platform thermometer resistance at a known block temperature on

the bottom of the cryostat [116]. The reciprocal of the platform temperature, T,

is then fitted to a polynomial as a function of the natural logarithm of platform
thermometer resistance, R:

= Ai (ln R)' (3.8)
i=0










where n = 4 was used in the calibration. Equation 3.8 is then used (by the HP

9000/300 series computer) to interpolate the platform thermometer temperature

value using the resistance value experimentally found.

The final calibration concerns measuring the thermal conductivity, K, of the

four Au-7% Cu wires in Fig. 3-3 on page 65. The thermal conductivity, K, may

be written in terms of the power, P, supplied across the platform heater and the

associated temperature rise, AT, in the platform thermometer:


P = KAT. (3.9)

If one starts from a base temperature, To, on the copper ring and the sample

platform in part (a.) of Fig. 3-3, then a small amount of known current is sup-

plied through the platform heater and the corresponding voltage drop across the

heater is measured in order to determine the power, P. The platform thermometer

resistance is determined before and after the power is supplied to the heater so

that To and AT are known from the germanium platform thermometer calibration

discussed previously. The thermal conductance of the Au-Cu wires is then deter-

mined using Eq. 3.9 at a temperature of To + AT/2. The thermal conductance

of the wires divided by temperature, K/T, may be written as a power series of just

temperature or the natural logarithm of temperature
n n
= AiT' (or) = B(ln T)' (3.10)
i=0 i=O
where n = 4 was usually used by the HP 9000/300 series computer to find an

interpolated conductance value at a particular temperature. The advantage of the

second form in Eq. 3.10 is that the same conductance equation may be used over a

larger temperature range (30 mK to 10 K) while the first form is usually split into

a low temperature equation and a high temperature equation where 1.3 K is the

approximate dividing temperature.









The calibrated thermal conductivity equation is then checked by either
measuring pure palladium, platinum, gold, or copper and comparing to known
standard specific heat values of the aforementioned elements [13]. The standard
sample used in this dissertation that was measured to check the conductance values

was pure platinum (99.9985% purity).

A problem that has to be taken into account when measuring specific heat
values by the thermal relaxation method is known as the "T2 effect." The T2
effect is the thermal lag between the sample and the platform [141]. The T2 effect
comes from large thermal resistance, poor conductivity of the sample, or of the
sample-platform contact and throws the temperature decay off from its exponential
shape [71]. A couple of procedures exist to account for this T2 effect. First, the
temperature decay curve should be composed of the sum of two exponential curves
like

T(t) = To + A exp (- + Bexp ( (3.11)

where T is the temperature, To is the baseline temperature, t is time, Tr is the time
constant of the sample and addenda, T2 is the second time constant that throws the

exponential decay off, and the coefficients A and B are determined by a graphical
fit using the HP 9000/300 series computer. The second procedure for improving the
T2 effect concerns the lock-in amplifier. The signal integration time should be set
to less than T1/40 for a better T2 correction. Not only is the T2 effect less smeared,
but also a transient, which causes rounding of the exponential decay curve near the
beginning, is eliminated.

When the actual specific heat measurements are taken, a program developed
by Dr. Bohdan Andraka on the HP 9000/300 series computer controls the mea-
surements. Once all known addenda masses are entered into the computer, the
computer first prompts the user for the base temperature, T, at which both the









block thermometer and platform thermometer are stabilized. The base tempera-

ture, T, is determined by varying the resistance in the ac Wheatstone bridge to

match the resistance of the platform thermometer using the lock-in amplifier as

the null detector. The experimentally determined resistance is then entered into

the computer so that the platform thermometer temperature is interpolated from

the calibrated germanium platform thermometer resistance. The computer also
"communicates" with the current source and voltmeter to determine the resistance

of the block thermometer and hence the temperature of the block thermometer

using a calibration curve. The computer then asks for the amount of current to

supply to the platform heater such that the temperature rise, AT, is about 4%

higher than T. Since the time constants that were dealt with in this dissertation

were usually under ten seconds, the new platform temperature usually became

stable in under one minute. The variable resistor was then changed to determine

the new, higher platform temperature. After the higher platform temperature was

determined, the resistance box was manually turned to the average of the two

determined resistance values with the current to the platform heater still on. The

computer then would perform one sweep to determine the temperature decay curve.

This sweep entailed the computer turning off the current to the platform heater

and then signal averaging 4000 points from the output of the lock-in amplifier for
the platform temperature decay curve. The platform temperature decays down to

the base temperature. The 4000 points are plotted on a semilogarithmic graph (the
distance from the decay curve to the base temperature is plotted on the graph)

and a least squares fit is used to determine the time constant value. Multiple

sweeps may be performed automatically by the computer and signal averaged to
improve the signal-to-noise ratio. Also, the computer allows the user the option of

taking into account the r2 effect. After the time constant value is determined, the

computer outputs the correct specific heat value of the sample after subtracting









off the addenda contributions. Then, more current is supplied to the block heater
such that the next specific heat value may be determined at a higher temperature.
A couple of systematic errors one needs to be aware of that might show up as
oscillations in the base temperature concerns changes in block heater current (due
to electrical pickup) and fluctuations in the surrounding liquid helium bath [9].

Specific heat measurements were also performed in magnetic fields (2 -
13 T) for this dissertation. The thermal conductance of the Au-7% Cu wires
has to be corrected depending upon the amount of magnetic field used. The
thermal conductance of the Au-7% Cu wires decreases approximately linearly
such that at 12 T, the thermal conductance of the Au-7% Cu wires is 3% less
than the 0 T thermal conductance values [120]. Also, calibration curves have
to be reconfigured for the block thermometer. A block thermometer calibration
curve has to be constructed for every magnetic field using a field correction
according to Naughton et al. [106]. Some drawbacks to measuring in magnetic
fields are that the germanium platform thermometer has a large magnetoresistance
p(18 T)/p(0 T) 5.6 at 4.2 K [141] and a noise problem in magnetic fields [71].
The ease of specific heat measurements has been facilitated by advancements
in technology. In fact, Quantum Design sells an automated specific heat measure-
ment system that uses thermal relaxation calorimetry and is named the physical
property measurement system (PPMS) [86]. It will be mentioned here that a cou-
ple of UCu2Si2-_zGea samples in this dissertation had their heat capacity values
measured on a PPMS at LANL.















CHAPTER 4
UCu5-_Nix RESULTS AND DISCUSSION
Nine UCus5-Nix compounds were arc-melted and annealed as described in

the "Experimental Techniques" chapter. The nine compositions were x = 0.5,

0.6, 0.75, 0.8, 0.9, 1.0, 1.05, 1.1, and 1.2. The "full spectrum" of measurements

was performed upon the UCu5sNix system. The following sections contain
lattice parameter measurements, dc electrical resistivity measurements, ac and dc

magnetization measurements, and specific heat measurements (in zero magnetic

field and various magnetic fields). The development of the NFL behavior in the

UCus5-Nix system will be investigated through the perspective of the Griffiths-

phase disorder model. All tables in this chapter are found at the end of the chapter
beginning on page 126.

4.1 Lattice Parameter Values for UCus-,Ni,

The lattice parameter values for the nine cubic UCus5-Nix compounds are
found in Table 4-1 on page 126. The unannealed and annealed (for 14 days at

7500C) samples that had their lattice parameter values reported came from the
same arc-melted bead. The arc-melted bead was cut in half with a diamond wheel

saw and half the bead was used as an unannealed sample while the other half was

annealed. All lattice parameters were determined using the graphical extrapolation

method described in the preceding "Experimental Techniques" chapter.

The unannealed and annealed lattice parameter values are shown graphically
in Fig.s 4-1 and 4-2. The unannealed UCu5_-Nix compounds show no signs of
a change in the slope of the lattice parameter value versus Ni concentration as

occurred in UCus-,Pd, [160]. Annealing the UCus5-Ni, compounds also shows

that there is no existence of preferential occupation by Cu or Ni as occurred with




















7.05-

7.04-

7.03-

7.02-
E
2 7.01-

0 7.00-

C 6.99-

6.98-


6.97-


I I I I I I I


UCu.Nix
unannealed


6.96 1 1 1 1 1--
0.0 0.2 0.4 0.6 0.8 1.0 1.2
x Ni concentration


Figure 4-1: Lattice parameter values for unannealed UCus_-Ni_ compounds. The
best fit line is for the nine experimentally determined lattice parameters in this
dissertation (represented by hollow squares while the vertical lines are the corre-
sponding error bars). The equation for the best fit line is as follows: a = 7.04521 -
0.06233 x. The UCu5 value (represented by a hollow circle) is taken from litera-
ture [18] and it was an unannealed sample.




















7.04-

7.03-

7.02 -

7.01-

7.00-

6.99- UCu Ni

6.98- annealed 14 days 750C

6.97-

0.0 0.2 0.4 0.6 0.8 1.0 1.2
x Ni concentration



Figure 4-2: Lattice parameter values for annealed UCu5s-Nix compounds. The
best fit line is for the nine experimentally determined lattice parameters in this
dissertation (represented by hollow squares while the vertical lines are the corre-
sponding error bars). The equation for the best fit line is as follows: a = 7.03348 -
0.05171 x. The UCu5 value (represented by a hollow circle) is taken from litera-
ture [181 and it was an unannealed sample.









Pd in UCus5-Pd, [143]. In fact, the annealing just sharpens the Vegard's law

behavior (i.e., the linear behavior of the lattice parameters as a function of Ni

doping since all compounds form in the same crystal structure). The difference
in the goodness of fits (i.e., the standard deviations) between the best fit lines for

unannealed (larger standard deviation) and annealed UCu5_-Nia lattice parameters
is greater than a factor of two (the best fit lines are seen in Fig.s 4-1 and 4-2).
Virtually all nine of the experimentally determined lattice parameters for annealed

UCus5-Ni, lie along (within their error bars) a straight line in Fig. 4-2.
Not only do the lattice parameters as a function of annealing show no change

in the order of the UCus_-Nix samples, but also high angle x-ray diffraction lines
provide insight into the order. The (7 3 1) diffraction line occurs at ~ 115.90
on an x-ray diffraction scan as seen in Fig. A-1 on page 167. The line width for
the (7 3 1) peak is the same for the unannealed UCus5-Ni, compounds and the

UCus5-Nia compounds annealed at 7500C for 14 days. Thus, short term annealing

does not increase the order of the UCus5-Nix compounds, contrary to what was
observed for UCus-_Pd, [160].

The lattice parameters' results also allow one to make a few comments
regarding the occupation of atomic positions in the cubic unit cell. In order to
get a visual representation of the discussion that follows, one may want to refer
back to the conventional AuBe5 crystal structure in Fig. 1-1 on page 3 of the

"Introduction" chapter. The lattice parameter results show that the 4a sites in
Fig. 1-1 are occupied by the U atoms as occurred in UCu5_-Pda. The larger

minority sites inside the unit cell (i.e., the 4c site) are basically occupied by the
larger Cu atoms (relative to the Ni atoms) while the smaller majority sites (the 16e
sites) inside the unit cell have approximately 25% of the Ni concentration located

at one of the four sites in the unit cell. A small percentage of the Ni concentration

does occupy the 4c sites even for the annealed cases. The exact amount would









have to be determined by pSR and EXAFS measurements as was done for the
UCu5sPd. system [15, 93]. This is in stark contrast to UCu5s-Pd- where the
Pd atoms (larger than the Cu atoms) show preferential sublattice ordering as
discussed earlier [143]. To summarize, the 4c sites inside the unit cell for annealed
UCu4Pd have a > 80% occupation by the Pd atoms while the 16e sites have a
less than 5% occupation by Pd [16]. Thus, the partial order present (along with
disorder) in the UCus5-Pdx system is not a concern in the UCus5-Nia system. The
lattice parameters in Fig.s 4-1 and 4-2 reveal this. The UCus5_Nix system has a
higher degree of disorder than the UCus5-Pdx system with the Ni atoms having
a much greater percentage of occupation at the 16e sites as compared to the Pd
atoms (~ 25% versus < 5%). The lattice parameter results also show that clear
distinctions can be made concerning the roles of quantum criticality and disorder in
the NFL behavior of UCus-5Nix without the worry of partial order as occurred in
UCus-_Pd,.
The lattice parameter values are used to determine the smallest U-U separa-
tion in the lattice. If one goes back to Fig. 1-1 on page 3 in the "Introduction"
chapter, one may determine that the smallest U-U distance is ~ 0.707a (the short-
est distance is a straight line from a corner 4a site to a nearest face-centered 4a site
in Fig. 1-1) where 'a' is the calculated lattice parameter of a particular UCus_5Nix
sample. The smallest lattice parameter value is for unannealed UCu3.8Nil.2 where
a = 6.97107 A in Table 4-1. Therefore, the smallest U-U separation is ~ 4.93 A.
This is not close to the Hill limit of 3.5 A [65] where if the distance of nearest U-U
separation, du-u, is less than 3.5 A, then the f-electron orbitals of uranium in
a lattice will overlap with those of the neighboring U ions and produce itinerant
f-electron behavior (i.e., non-magnetic ordering). If du-u > 3.5 A, then uranium
f electrons (barring strong hybridization effects) are localized and magnetic [143].
As one will see in the specific heat section of this chapter, UCus.8Nil.2 does not









display magnetic ordering down to ~ 0.3 K. Thus, there is significant f-electron
hybridization with the d-electron orbitals of Cu and Ni in the UCus_5Nix samples

since none of the samples in this dissertation have du-v < 3.5 A. This is consistent
with the conclusions drawn by Chakravarthy et al. that said hybridization was

responsible for the suppression of the long range magnetic order in UCus5_Nix [22].

4.2 DC Electrical Resistivity Results for UCus5-Nix
The low temperature resistivity results for the select UCus5-Ni. samples
that were measured are shown in Tables 4-2 and 4-3. All but two samples were
measured down to ~ 0.3 K (using helium 3 gas as described in the "Experimental
Techniques" chapter). The other two samples (UCu4Ni and UCu3.95Nil.05, both
annealed 14 days at 7500C) had their resistivity measured down to 0.060 K using

a dilution refrigerator at the NHMFL in Tallahassee, FL. A graph summarizing

the resistivity for annealed (14 days 750C) UCus-zNix samples in the range
0.9 < x < 1.2 along with unannealed x = 0.75 is shown in Fig. 4-3.
4.2.1 DC Electrical Resistivity Discussion for UCus_-Ni.

The UCus_5Ni. results in Tables 4-2 and 4-3 show large, varying residual
resistivity, Po, values. This was expected since previous literature values for

UCu4Ni were sample dependent with po ranging from 400 to 800 pf cm [89]. A
UCu4Ni resistivity bar was produced using the "sucker" method discussed in the
"Experimental Techniques" chapter to investigate whether or not microcracks in
the sample were the cause for the large po values. An example of microcracks being
the cause of large po values is U2Co2Sn where an arc-melted U2Co2Sn resistivity
bar gave po = 800 jf cm [72] while a "sucker" produced resistivity bar gave

po = 60 p2 cm [143]. Thus, the sucker method for U2Co2Sn avoided microcracks
and the po values were reduced by a factor of ~ 13. Yet, the quenched UCu4Ni
resistivity bar (i.e., the sucker method) in Table 4-2 (page 127) is only ~ 30%
lower than the arc-melted, unannealed UCu4Ni resistivity bar. Thus, microcracks















UCuKNix
annealed 14 days 7500C


1.14

1.12

1.10

1.08

1.06

1.04

1.02

1.00


T (K)


Figure 4-3: Low temperature normalized resistivity for UCus-_Ni, samples. The
UCus5_Ni, samples were annealed 14 days at 7500C and have Ni concentrations be-
tween 0.9 and 1.2. Also, the resistivity for unannealed UCu4.25Nio.75 is plotted. The
inset shows the extreme low temperature resistivity values for annealed UCu4Ni,
UCu3.95Ni1.05, and UCu3.gNil.1. The graph legend also applies for the inset. The
solid lines in the inset are high temperature best fit power law lines (that yield
minimum X2 values) showing that the UCu4Ni p data begin to deviate from the
high temperature fit line around 0.992 K while the UCu3.95Ni.0o and UCua3.Nii.1
p data deviate from the lines beginning at 0.834 K and 0.821 K, respectively. The
absolute accuracy of all p data is ~ 5%.









do not appear to be the major cause for the large po values in the UCu5s-Nix
samples.
One column in Tables 4-2 and 4-3 that may provide insight into the cause of
the behavior of the resistivity for UCu5_-Nix samples is the RRR (i.e., the residual
resistivity ratio) column. If one compares the RRR values of the UCu5-_Nia
samples (annealed 14 days 7500C) for 0.9 < x < 1.2, one sees a monotonic increase
in RRR as the Ni concentration increases. This trend may be irrelevant since
the RRR values for all short term annealed (i.e., 14 days at 750C) UCus_-Ni.
samples is below 1.0. In Rosch's theoretical work on the interplay of disorder and
spin fluctuations near a QCP [126], he defined a parameter x that was a measure
of the impurity scattering. 1/x is equivalent to RRR [143] and this means that
all UCu5_,Nix samples have an x value greater than 1. Rosch stated that x = 0
is a perfectly ordered sample while x > 0.1 is rather disordered [126]. Thus, all

UCus5_Ni. samples that were annealed for 14 days at 750C are significantly
disordered according to their RRR values.
An investigation of the data in Tables 4-2 and 4-3 (on pages 127 and 128)

and the short term annealed data shown graphically in Fig. 4-3 do not indicate
any significant changes brought about by annealing as occurred in UCu4Pd [160].
Annealing UCu4Pd reduced the residual resistivity by a factor of 2.5 [160] and the

A value (with appropriate units) in the power law form (Po + ATh) was reduced
by a factor of ~ 10 (-6.3 to -0.6 [143]). Also, a large change in the qualitative
behavior of the resistivity curve was brought about by annealing UCu4Pd. In the
temperature region between 2 K and 8 K, the annealed UCu4Pd resistivity data
was fit with a Fermi-liquid expansion p Pr = AT2 + BT4 while the unannealed

UCu4Pd resistivity data showed NFL behavior with p Pr oc T [160]. The
UCu_5-Nix equivalent to UCu4Pd, UCu4Ni, does not show a significant reduction
in its po value with annealing (only about a 17% decrease). Also, the A values in









the temperature regions of 2 K and 10 K, and 2 K and 12 K for unannealed and

annealed 14 days 750C UCu4Ni do not show a significant difference as occurred in

UCu4Pd (-5.52 for unannealed UCu4Ni and -5.03 for annealed UCu4Ni). It is not
just the UCu4Ni sample that shows this lack of significant change. A perusal of all

UCus5_Nix samples in Tables 4-2 and 4-3 shows that short term annealing causes
no significant changes.

Despite the extreme sample dependence of the UCus5-Ni, system which

makes any trends in po as a function of Ni concentration enigmatic, a few trends

in the short term annealed UCus5_Ni. samples may be observed in Tables 4-

2 and 4-3. First, the absolute values of A for the low temperature fit regions

decrease monotonically as the Ni concentration is increased for the short term

annealed UCu5-_Ni. samples with A = -93.0 IM cm K-0.224 for x = 0.9 and

A = -3.85 p2 cm K-0743 for x = 1.1. The "high" temperature fit forms show

that the resistivity values for 0.9 < x < 1.2 decrease just above a linear rate

with UCU3.gNil.2 decreasing at a rate almost equal to 1 (0.996). Interestingly,

Fig. 4-3 on page 80 shows that unannealed UCu4.25Ni0.75 unannealedd x = 0.75

and x = 0.80 have very similar low temperature curvatures) has upward curvature

over its entire measured temperature range. Yet, this upward curvature present

in unannealed x = 0.75 is not apparent until below 2 K for short term annealed

x = 0.9. This upward curvature is quite apparent for short term annealed x = 1.0

and x = 1.05 at the lowest measurable temperatures. However, the upward

curvature gets less steep with increasing Ni concentration and this is seen in the

inset in Fig. 4-3. The "high" temperature fit lines in the inset do not deviate as

quickly for x = 1.1 and x = 1.05 as occurred for x = 1.0. In fact, this upward

curvature disappears for x = 1.2. The cause of this upward curvature is unknown

and remains an open ended question. This upward curvature in the resistivity









has also been seen in annealed (14 days at 750C) UCu4Pd below 1 K [160] and
annealed (7 days at 9000C) UCu4Ni [88].
Figure 4-3, along with Tables 4-2 and 4-3 raise some interesting points
concerning the UCus-aNix resistivity. First, the resistivity of UCu4.25Nio.75 does
not show an antiferromagnetic phase transition at around 1.9 K as was seen in the
specific heat (and will be discussed in the specific heat section below). The most
interesting point concerns a comparison of the resistivity results of two 8 week
850C annealed UCu4Ni samples. The first sample is a UCu4Ni (production date
of 2-27-03 in Table 4-2) resistivity bar that was annealed for 8 weeks at 850C
after the resistivity was measured for the bar when it was unannealed. The po
value decreases by a factor of 20 and the RRR value is ~ 3.18 (very close to the
RRR value of 2.5 for annealed UCu4Pd [160]). Also, a similar result was obtained
for a UCu3.95Nii.o5 (7-14-03) resistivity bar that had its resistivity measured when

it was an unannealed bar and then was annealed at 850C for 8 weeks. The only
preparation difference between the UCu4Ni entries (in Tables 4-2 and 4-3) that
were annealed for 8 weeks at 850C was that the (2-27-03) entry (RRR ~ 3.18)
had its dimensions sanded really well before annealing so that the spot welded Pt
wires were not incorporated into the sample during annealing. The second sample
in Table 4-3 is a (10-13-03) entry (RRR ~ 0.313) for UCu4Ni that had its bar cut
from the arc-melted bead after the bead had been annealed for 8 weeks at 8500C
with no sanding of the resistivity bar dimensions. These minor differences led to
significant changes in the resistivity behavior.
The sanding of the resistivity bar was not the cause of the significant change
in the resistivity behavior because the long term annealed UCu4Ni sample (prod.
date: 4-13-04 in Table 4-3) was sanded and cleaned right before the Pt wires were
attached while the long term annealed UCu3.95Ni.o05 sample (prod. date: 4-14-04)
was not sanded before attaching Pt leads. Both samples show similar resistivity









behavior and have almost identical RRR values that are below 1. A couple of
possible explanations for the strange resistivity behavior have been formulated.
One explanation concerns the possibility of a copper oxide layer forming during
the 8 week annealing process and that the resistivity of a copper oxide layer

was measured for the resistivity bars that were not sanded. A second possible
explanation comes from Dr. Bohdan Andraka pertaining to small Cu "islands"
possibly existing in the UCus5-Ni, samples and that just pure Cu is present in
the grain boundaries. Thus, the Pt wires were possibly attached to pure Cu with
some impurities mixed in and the resistivity of a sample similar to the classical
examples of a Kondo system (i.e., diluted alloys of Fe and Cr in Cu [162]) were
measured. Magnetoresistance measurements need to be performed on the same
eight week annealed bars (that showed such odd resistivity behavior) in order to
test the validity of this theory.
Magnetoresistance measurements were taken on the short term (14 days at
7500C) annealed UCu4Ni (2-27-03) and UCu3.95Ni.o5 (7-14-03) samples. The
results are shown in Fig.s B-1 and B-2 of Appendix B. The results in both graphs
were taken by Dr. Jungsoo Kim at the NHMFL. The magnetoresistance low
temperature results show that for UCu3.95Ni.o05, the approximate po values in
zero field and in a 13 T field only have about a 2.6% difference between them
(~ 929 pM cm in 0 T and ~ 905 Ma cm in 13 T). Similarly, the results for UCu4Ni
show that when a 13 T field is applied, the po value is only reduced by about
2.8% (~ 797 ~Q cm in 0 T and ~ 775 Mp cm in 13 T). These magnetoresistance
measurements suggest that the origin of the large po values in the UCus_-Ni,
samples is not of an electronic nature. One last interesting point that is fairly well
seen in both figures of Appendix B is that the upward curvature in the temperature
dependence of the graphs in zero field flattens out with the application of magnetic
field and the temperature dependence remains fairly constant for fields higher than









4 T. Quantitatively, best fit lines (of the power law form po + AT') were fit to each
magnetic field data set in Fig.s B-1 and B-2. The a values obtained for UCu4Ni in

0 T, 4 T, and 13 T fields were 0.432, 0.794, and 0.762 respectively. The a values for

UCu3.95Nil.05 in 0 T, 4 T, and 13 T fields were 0.269, 0.722, and 0.711 respectively.
The physical reason for these magnetoresistance results is at present unexplained.
A final question that needs to be answered concerning these UCus5-Nix
resistivity results is whether or not the short term annealed resistivity provides

insight into the inherent properties of UCus5_Nia, i.e., does quantum criticality or
disorder dominate the behavior in the critical concentration of x = 1.0 (as will also

be discussed in the specific heat section)? The answer is no since the short term

annealing results for UCu4Ni do not vary significantly from the unannealed results
for UCu4Ni as seen in Table 4-2. The resistivity results for UCu4Ni are similar to

the resistivity results for unannealed UCu4Pd [160]. There was a drastic change
in the transport properties, e.g., resistivity, of UCu4Pd after annealing as has
been documented earlier. Thus, the unannealed UCu4Pd gave no insight into the

intrinsic disordered NFL behavior. Likewise, the resistivity for short term annealed

UCu4Ni (or any short term annealed UCus5-Nix sample) may not be connected
to its intrinsic NFL behavior. The resistivity results for the short term annealed
UCu5sNix samples are most likely stemming from an extrinsic effect that arises
from the disorder present in these samples.

4.3 Magnetization Results for UCus_-Nix

The magnetization results for the short term annealed UCus5-Nix samples
around the critical concentration, x = 1.0, are shown in Table 4-4 on page 129 and
Fig. 4-4 on page 87. The numerical information in Table 4-4 is shown graphically
in Fig. 4-4. Figure 4-4 shows the excellent agreement between the fit lines and the
data while the goodness of fits (the standard deviation and the X2 values) in Ta-
ble 4-4 confirm the excellent agreement. The reason for the low field magnetization









being fit to a linear form, M ~ H, and the high field magnetization being fit to a
power law form, M ~ HA, is to investigate whether or not the NFL behavior in the
UCu5-sNia system may be fit to the Griffiths phase disorder model [21].
4.3.1 Magnetization Discussion for UCu5-_Nix

A couple of trends are readily seen in Fig. 4-4 and Table 4-4. First, the
field range over which the linear magnetization form fits is widened as the Ni
concentration goes from 0.8 to 1.2. The slope of the linear form fit decreases

monotonically with increasing Ni concentration. Likewise, the constant in the front
of the field term for the power law fit decreases monotonically with increasing
Ni concentration. Also, the exponent value, A, in the power law form increases
monotonically for 0.9 < x < 1.2. In fact, the high field magnetization power
law form (for UCu3.sNil.2) is very close to a linear form with A = 0.953 (for
0.9 T < H < 7 T). Also, the unphysical constant offsets in the power law form
(M = A' + B' H^) and linear fit form (M = A + B H) for all Ni concentrations
listed in Table 4-4 are recognized. These offsets also show a trend as they get less
negative with increasing Ni concentration.

The Griffiths phase disorder model of Castro Neto and Jones [21] makes clear
predictions concerning such magnetization data shown here. As mentioned earlier,
the Griffiths phase disorder model predicts that the magnetization should exhibit

low field behavior (M ~ H) that crosses over to high field behavior (M ~ H^)
at some crossover magnetic field, Hcrossover. In other words, the magnetic spin
clusters should show some saturation behavior at higher magnetic fields when the
Griffiths phase disappears. This is evident in Table 4-4, especially around the
critical concentration of 1.0. The short term annealed UCu3.95Nil.0o sample has
a little higher A value (0.860) than the A values of Ceo.sTh0.2RhSb (0.686 [74])
and Ceo.o5Lao.95RhIn5 (0.41 [73]), two known samples that fit predictions made
by the Griffiths phase disorder model. Also, the magnetization results for samples

















UCu Ni
annealed 14 days 750C


10000 20000 30000 40000 50000 60000 70000
H (Gauss)


Figure 4-4: Magnetization for UCus-5Nix samples annealed 14 days at 7500C. The
magnetization versus field measurements were taken at a constant temperature
(2 K). The inset shows where the low field linear form (M ~ H) deviates from the
data for each sample while the primary graph shows the excellent fit of the high
field power law form (M ~ HA) to the data.









above the critical concentration (e.g., x = 1.2) do not saturate as quickly as those
samples adjacent to x = 1.0 in the phase diagram. This may suggest that the Ni
concentration range is limited for which the Griffiths phase model applies. The
dc magnetic susceptibility results and the specific heat results are intertwined

to the magnetization results in the Griffiths phase model since the A value from
the magnetization power law form should match the low temperature magnetic
susceptibility exponent, X oc T-'1+, and the exponent in the magnetic field
induced peak form in the specific heat, C/T ~ (H2+A/2/T3-A/2)e-effH/kBT, for
H > Hcrosoer, where HIrosoer is determined from the magnetization data.

Since saturation is present in the magnetization data, it is recognized that
the magnetization and susceptibility of the UCu_5-Nix samples may be fit with
the Kondo disorder model [143]. However, as will be discussed below in the
specific heat section, it is believed that the Kondo disorder model does not apply
to UCu5_-Ni_ in light of the fact that the Kondo impurity model, with its four
fit parameters, was unable to fit the specific heat data in a magnetic field of
isostructural UCus5-Pd. [11] and in fact does not reproduce the peak in C(H)
observed for UCus-_Ni,.

Finally, the method (as described in the inset of Fig. 4-4) of determining

Hro,,o from the magnetization data seems rather arbitrary. There was no
clear procedure in the literature for describing how Ho,,,e was determined for

Ceo.o5Lao.s9RhIn5 (z 0.8 T [73]) and Ceo.sTh0.2RhSb ( 1 T [74]). It was attempted
in this UCus5-Ni. study that if the Griffiths phase disorder model applied to

UCu5-_Ni,, then the rare strongly coupled magnetic clusters (responsible for the
NFL behavior) might possibly show hysteresis at each sample's respective Hcrosaoer-
Thus, the zero field cooled (ZFC) magnetization at T = 2 K was measured from
0 to 7 T and immediately afterwards, the field cooled (FC) magnetization was
measured from 7 to 0 T. This procedure was performed on three of the short term




Full Text

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DIFFERJNG ROLES OF DISORDER: NON-FERMI-LIQUID BEHAVIOR IN UCus-xNix AND CURJE TEMPERATURE ENHANCEMENT IN UCu2Si2-xGex By DANIEL J. MIXSON II A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORJDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY UNIVERSITY OF FLORJDA 2005

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This work is dedicated to my Lord and Savior Jesus Christ. / can do all things through Christ which strengthens me.-Philippians ,4:13

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ACKNOWLEDGMENTS The Lord has placed a lot of special people in my life. Thus, the thoroughness of the acknowledgments may exceed that of the actual dissertation. I will attempt to thank everyone in the order in which they were introduced into my life. My first thank you goes to my parents, Dan and Judy Mixson, for their love which includes discipline and support. My sister, Venessa, has been very supportive of all my undertakings. I also want to thank all four of my grandparents who played and are continuing to play a major role in my life: Jim and Sue Mixson; Marion and Winonah Pettit. I need to recognize my high school physics teacher, Mr. Dan Pate, who served as a mentor to me during my last two years of high school. His inspiration and encouragement were indispensable. A broad thank you goes to my undergraduate institution, Mississippi State University. The academics were good, but the life lessons I learned hopefully will never be forgotten. The majority of these acknowledgments are directed to people affiliated with the Department of Physics at the University of Florida (UF). First, I want to thank the two graduate coordinators in the Department of Physics during my time at Florida: Dr. John Yelton and Dr. Mark Meisel. Also, special thanks go to the Department of Physics Student Services personnel who were affiliated with graduate student affairs: Mrs. Susan Rizzo and Mrs. Darlene Latimer. I also want to thank all the faculty who were instructors in the graduate classes I took: Dr. Pierre Sikivie, Dr. Richard Woodard, Dr. Charles Thorn, Dr. James Fry, Dr. iii

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Charles Hopper, Dr. Fred Sharifi, Dr. James Dufty, Dr. Alan Dorsey, Dr. David Tanner, Dr. Robert Coldwell, Dr. Andrey Korytov, and Dr. F. Eugene Dunnam. I also want to acknowledge the personnel/professors I served under during my "instructor" years: Mr. Greg Martin, Mr. Ray Thomas, Dr. Robert DeSerio, Dr. Dmitrii Maslov, Dr. John Klauder, Dr. Gary Ihas, and Dr. Andrew Rinzler. The most influential professor upon my physics career at UF has to be Dr. Greg Stewart. I want to thank him for allowing me to work in his lab these past four years. I especially want to thank him for funding me these past two years [with money from a Department of Energy (DOE) grant] and for allowing me to go to Los Alamos National Laboratory (LANL) during the Summer of 2004. There are many people affiliated with Dr. Stewart's lab that have influenced my research career. First, special thanks go to Dr. Jungsoo Kim for showing me the "ins and outs" of the lab. I am indebted to the following people who were/are affiliated with Dr. Stewart's lab: Mr. Josh Alwood, Mr. Patrick Watts, Mr. Adam Bograd, Mr. Michael Swick, Mr. Tim Jones, and Mr. Don Burnette. I would also like to acknowledge Dr. Bohdan Andraka and members of his group I have interacted with in some form: Dr. Richard Pietri and Mr. Castel Rotundu. I would also like to recognize Mr. Ju-Hyun Park of Dr Meisel's lab. His extensive knowledge was very useful for magnetization measurements I took. I want to thank the following personnel who help make up part of the infras tructure in the Department of Physics at UF and who have been more than willing to assist me: Mrs. Janet Germay, Mr. Pete Axson, Mr. Marc Link, Mr. Edward Storch, Mr. Bill Malphurs, Mr. John Macko, Mr. Greg Bennett, Mr. Jay Horton, Mr. John Graham, Mr. Greg Labbe, Mr. Bryan Allen, and Mr. Brent Nelson. I am very grateful to the following five members of my dissertation committee who have taken time out of their busy schedules to serve: Dr. Greg Stewart (chair), iv

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Dr. Bohdan Andraka, Dr . Pradeep Kumar, Dr. Dinesh Shah, and Dr. David Tanner. The following people helped me broaden my knowledge of condensed matter physics at LANL in the Summer of 2004: Dr. John Sarrao, Dr. Eric Bauer, Dr. Veronika Fritzsch, Mr. Jason Leonard, Dr. Mike Hundley, and Dr. Joe Thompson. Finally, I would like to recognize people around the world I have had the chance to collaborate with on the UCus-xNix and UCu2Si2-xGex systems. Special thanks go to Dr. E.-W. Scheidt and Prof. W. Scherer at the University of Augs burg for their low temperature measurements on the specific heat of the UCus-xNix system with a dilution refrigerator. Also, I would like to thank Drs. T. Murphy and E. Palm at the National High Magnetic Field Laboratory (NHMFL) in Talla hassee, FL, for their low temperature resistivity measurements on the UCus-xNix system. Also, I would like to thank Prof. A.H. Castro Neto (Boston University) for his communication on the Griffiths phase disorder model and in trying to help me understand how the model applies to the UCus-xNix system. Lastly, I am very grateful to Dr. M.B. Silva Neto and Prof. A.H. Castro Neto for their theoretical efforts on the UCu2Si2-xGex system. V

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TABLE OF CONTENTS ACKNOWLEDGMENTS LIST OF TABLES iii viii ix xi LIST OF FIGURES ABSTRACT CHAPTER 1 INTRODUCTION 1.1 NFL Behavior in UCus-xNix 1.1.1 UCus-xPdx ........... 1.1.2 UCus-xNix ........... 1.2 Curie Temperature Enhancement in UCu2Si2-xGex 1 2 2 10 16 2 THEORY ............ 23 23 23 24 25 40 2.1 Non-Fermi-Liquid Theory 2.1.1 Introduction ... 2.1.2 Fermi-Liquids . 2.1.3 Non-Fermi-liquids 2.2 Curie Temperature Enhancement Theory 3 EXPERIMENTAL TECHNIQUES ........ 46 3.1 Arc-Melting . . . . . . . . . 46 3.2 X-Ray Diffraction/Lattice Parameter Determination from X-Ray Diffraction . . . . . . . . . . . 49 3.3 Magnetic Susceptibility . . . . . . . . . 53 3.3.1 DC Magnetic Susceptibility 53 3.3.2 AC Magnetic Susceptibility 54 3.4 Cryogenics . 55 3.5 Probes . . . . 56 3.6 DC Resistivity . . 60 3. 7 Specific Heat . . 62 vi

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CHAPTER 4 UCus-xNix RESULTS AND DISCUSSION 74 4.1 Lattice Parameter Values for UCus-:i:Ni:i: . . 74 4.2 DC Electrical Resistivity Results for UCus-:i:Nix 79 4.2.1 DC Electrical Resistivity Discussion for UCus-:i:Ni:i: 79 4.3 Magnetization Results for UCus-:i:Ni:i: . . . . 85 4.3.1 Magnetization Discussion for UCus-:i:Nix . . . 86 4.4 AC Magnetic Susceptibility Results for UCus-:i:Nix . . 89 4.4.1 AC Magnetic Susceptibility Discussion for UCus-:i:Nix 89 4.5 DC Magnetic Susceptibility Results for UCus-:i:Ni:i: . . 92 4.5.1 DC Magnetic Susceptibility Discussion for UCus-:i:Ni:i: 95 4.6 UCus-:i:Ni:i: Specific Heat Results . . 102 4.6.1 UCus -:i:Nix Specific Heat Discussion 114 5 UCu2Si2-:i:Ge:i: RESULTS AND DISCUSSION 136 5.1 UCu2Sia-:i:Ge:i: Results . 139 5.2 UCu2Si2-:i:Ge:i: Discussion . . . . 142 5.2.1 Tc Enhancement . . . . 142 5 2.2 Resistivity displaying electrons in the ballistic or diffusive regime .......... 6 CONCLUSIONS AND FUTURE WORK ...... 6 1 UCus-:i:Ni:i: Conclusions ............ 6.2 Future Work Derived from UCus-:i:Ni x Results 6.3 UCu2Si2-:i:Ge:i: Conclusions 6 4 UCu2Si2-:i:Ge:i: Future Work APPENDCT ............... A LATTICE PARAMETER GRAPHS B MAGNETORESISTANCE GRAPHS. C UCus-xNix MAGNETIC SUSCEPTIBILITY GRAPHS. D UCus-xNix SPECIFIC HEAT GRAPHS REFERENCES ....... BIOGRAPHICAL SKETCH vii 143 157 157 159 163 164 166 166 169 172 177 185 195

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LIST OF TABLES Table 4 1 Lattice parameter values for the nine UCu5_xNix compounds. 126 4-2 The low temperature resistivity results for UCus-xNix samples. 127 4-3 The low temperature resistivity results for UCus-xNix samples. 128 4-4 Magnetization data for UCus-xNix annealed 14 days at 750C. 129 4 5 AC susceptibility results for select UCu5_xNix samples. . 130 4--6 DC magnetic susceptibility results for annealed UCu5_xNix. 131 4-7 Fit results for UCus-xNix de susceptibility data at 1 kG and 1 T .. 132 4 8 Fit results for UCus-xNix de susceptibility data at 2 T and 3 T. 133 4-9 Fit results for UCus-xNix de susceptibility data at 4 T. 134 4-10 Specific heat results for annealed UCu5_xNix samples. 135 5-1 Magnetic susceptibility and resistivity results for unannealed UCu2Si2-xGex samples (I). . . . . . . . . . . . 153 5-2 Magnetic susceptibility and resistivity results for unannealed UCu2Si2-xGex samples (II). . . . . . . . . . . 154 5-3 Magnetic susceptibility and resistivity results for annealed UCu2Si2-xGex samples (I). . . . . . . . . . . . 155 5-4 Magnetic susceptibility and resistivity results for annealed UCu2Si2-xGex samples (II). . . . . . . . . . . . 156 viii

PAGE 9

LIST OF FIGURES Figure 1 1 The conventional unit cell for the AuBe5 crystal structure. 3 1-2 The unit cell for the tetragonal ThCr2Si2 crystal structure. 18 2 1 The Doniach phase diagram taken from Ref. [21]. 35 2 2 The Griffiths phase diagram taken from Ref. [21]. 41 I 2 3 Curie temperature predictions by Silva Neto and Castro Neto. 45 3-1 Cross-section of a helium 3 probe. . . . . . . . 58 3-2 Schematic diagram outlining the thermal relaxation method. 64 3 3 An overhead and bottom view of the mounted sample platform. 65 4-1 Lattice parameter values for unannealed UCus-:z:Ni:z: compounds. 75 4 2 Lattice parameter values for annealed UCus-:z:Ni:z: compounds. 76 4 3 Low temperature normalized resistivity for UCus-:z:Ni:z: samples. 80 4-4 Magnetization for UCus -:z:Ni:z: samples annealed 14 days at 750C. 87 4-5 AC susceptibility data for annealed UCu4 5Nio.5 . . . . . 90 4-6 DC susceptibility for annealed UCu4Ni in different magnetic fields. 93 4 7 Low temperature de susceptibility for annealed UCus-:z:Ni:z: samples. 94 4-8 Semilog plot of de magnetic susceptibility for UCu4Ni. 99 4 9 Log-log plot of de magnetic susceptibility for UCu4Ni. 100 4 -10 Specific heat for eight annealed UCus-:z:Ni:z: samples. 103 4 -11 UCus -:z:Ni:z: specific heat results on a semilog plot. 105 4 -12 UCus-:z:Ni:z: specific heat results on a log-log plot 106 4 -13 Specific heat of UCu4.1Ni0 9 in 0, 3 and 6 T. 108 4 -14 Sp ec ific heat of UCu3 9Niu in 0 3 and 6 T. 109 4 -15 Specific heat of UCu3 8Ni1.2 in 0 3 and 6 T 110 ix

PAGE 10

4-16 Specific heat of UCu 4 Ni in 0, 2, 3, and 6 T. . . 4-17 Specific heat of UCua.95Ni1.os in 0, 2, 3, and 6 T .. 4-18 Phase diagram for UCus-xNix and UCus-xPdx. 4-19 Specific heat data at 6 T for UCus-xNix samples. 5-1 Tc determination for annealed UCu 2 Ge 2 .... 5-2 Resistivity versus temperature for UCu 2 SiGe. 5-3 Tc phase diagram for UCu2Si2-xGex ..... 5-4 The reciprocal RRR values for annealed UCu2Si2-xGex. 5-5 Phase diagram for unannealed Ulr1_xPtxAl system. 6-1 DC magnetic susceptibility results for UCus-xCox .. A-1 Theoretical and experimental x-ray diffraction patterns for annealed 111 112 115 124 138 140 144 146 152 162 UCu4Ni. . . . . . . . . . . . . . . . . 167 A 2 Lattice parameter values versus corresponding error function values for annealed UCu 4Ni. . . . . . . . . . . . . 168 B 1 Low temperature magnetoresistance measurements of annealed UCu 4Ni. . . . . . . . . . . . . . . . . 170 B 2 Low temperature magnetoresistance measurements of annealed UCua.9sNi1,05. . . . . . . . . . . . 171 C-1 Semilog and log-log plots of UCu4_1Nio.9 de susceptibility. 173 C 2 Semilog and log-log plots of UCu3_95Ni1.os de susceptibility. 174 C-3 Semilog and log-log plots of UCu 3 9Niu de susceptibility. 175 C-4 Semilog and log-log plots of UCu 3 .8Ni1.2 de susceptibility. 176 D 1 The determination of TN~el for annealed UCuuNio.6178 D-2 Specific heat of annealed UCu4Ni in 6 and 13 T. . 179 D 3 Specific heat of UCu4Ni in 13 T with Castro Net~Jones fit. 180 D-4 UCu4.1Nio.9 specific heat data in 3 T and 6 Ton a log-log plot. 181 D 5 UCu 4 Ni specific heat data in 2 T and 3 Ton a log-log plot. 182 D-6 UCua.9sNi1.os specific heat data in 2 Ton a log-log plot. 183 D-7 UCua.aNi1.2 specific heat data in 3 Ton a log-log plot. 184 X

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Abstract of Dissertation Presented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy DIFFERING ROLES OF DISORDER: NON-FERMI-LIQUID BEHAVIOR IN UCus-xNix AND CURIE TEMPERATURE ENHANCEMENT IN UCu2Si2-xGex Chair: Gregory R. Stewart Major Department: Physics By Daniel J. Mixson II May 2005 Disorder may be created by the substitution of one element for another where the elements are found on the periodic chart of elements. One compound that has structural disorder is UCu5_xNix where the transition element, copper, is replaced with another transition element, nickel. Another compound that has disorder is UCu 2 Si 2 -xGex where silicon atoms are substituted with isovalent germanium elements. The disorder in these two compounds leads to interesting physics at low temperatures. UCu5 is antiferromagnetic at around 16 K; however, the antiferromagnetism may be suppressed by doping nickel atoms onto the copper sites in the unit cell. The antiferromagnetic transition is suppressed to zero for the UCu4Ni compound leading to non-Fermi-liquid (NFL) behavior due to a quantum critical point. Multiple UCus-xNix compounds with small changes in the stoichiometry are synthesized around UCu4Ni in order to investigate if the cause of NFL behavior crosses over from a quantum critical point to rare strongly coupled magnetic clusters in a Griffiths phase scenario. The investigation is carried out by performing

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the following measurements on UCu5_xNix compounds: 1) x-ray diffraction; 2) direct current (de) magnetic susceptibility as a function of temperature in various magnetic fields; 3) alternating current (ac) susceptibility; 4) magnetization measurements as a function of magnetic fields; 5) low temperature de resistivity; and 6) low temperature specific heat in zero and applied magnetic fields ( up to 13 T). UCu2Ge2 and UCu2Si2 are ferromagnets with ferromagnetic ordering temper atures, Tcurie, occurring at around 108.5 Kand 102.5 K respectively. Various com pounds lying between the two aforementioned ferromagnets on the UCu 2Sh-xGex phase diagram were synthesized in order to test theoretical predictions made concerning the nonmonotonic behavior of T Curie as a function of the amount of structural disorder. The nonmonotonic behavior was confirmed by measuring the de magnetic susceptibility. As the amount of disorder is varied, the electron scattering crosses over from a ballistic regime for no structural disorder to a dif fusive regime when disorder is present. This crossover is proven by de resistivity measurements.

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CHAPTER 1 INTRODUCTION The chemical substitution of one element for another element has been a longstanding practice in the condensed matter physics community. In fact, the first system published that claimed non-Fermi-liquid (NFL) behavior [i.e., deviations occurred from Fermi liquid behavior: at low temperatures, p (the resistivity) = Po + AT2 x (magnetic susceptibility) and C/T (specific heat divided by temperature) approach a constant value as T-+ 0 K] was Yi-xU:i:Pd3 by Seaman et al. [136]. This NFL behavior in Yi-xU:i:Pd 3 was attributed to disorder created by the chemical substitution of yttrium atoms for uranium atoms [93]. Another such alloy that displays NFL behavior at low temperatures due to disorder is UCus-:i:Pdx. The characteristics of the UCus-:i:Pdx system will be discussed and the motivation behind the study of the isostructural UCus-xNix system will be clarified. A second part of this dissertation concerns the ferromagnetic behavior of the ternary UCu2Si2_:i:Gex compounds The driving force behind these compounds is disorder, specifically the silicon/germanium sublattice disorder introduced by substituting ( or doping) germanium atoms onto silicon atom sites in the unit cell (the fundamental "building block" of any crystal structure). Silva Neto and Castro Neto have made theoretical predictions that this sublattice disorder combined with thermal and quantum fluctuations will enhance Curie temperature values in quantum ferromagnets [137]. A discussion of why the UCu2Si2_:i:Gex system was chosen to test the theory will be carried out. 1

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2 1.1 NFL Behavior in UCus-xNix 1.1.1 UCus-xPdx UCus-xPdx was the first system to display NFL behavior with no dilution of the /-atom (i.e., the uranium atom) site (143]. UCu5 is an antiferromagnet with a Neel temperature, TN, around 15 K (104]. The palladium (Pd) atoms are doped onto the copper (Cu) atom sites and this suppresses the antiferromagnetic ordering temperature. Andraka and Stewart reported that doping the Cu sites with Pd suppressed the antiferromagnetism at x 0. 75 and that UCu 4Pd displayed NFL behavior with a power law divergence in the specific heat ( C /T ,..., T -0 32 for 1-10 K) and a linear dependence in the resistivity (p = p0 -a T for 0.3 to 10 K, with Po= 375 fl. cm and a= 6.3 fl. cm K-1 ) (4]. More recent measurements down to lower temperatures have shown that UCu 4Pd orders antiferromagnetically below TN= 190 milliKelvin (mK) while UCu3 9Pd1.1 shows no ordering temperature down to the lowest measurable temperature (77]. UCu5 crystallizes in the AuBe5 structure with the beryllium sublattice possessing two inequivalent beryllium sites A schematic drawing of the AuBe5 crystal structure is shown in Fig 1-1 on page 3 [27]. The AuBe5 structure is cubic with twenty-four atoms occupying a unit cell. So, for UCu5 there are four uranium (U) atoms and twenty Cu atoms. The U atoms occupy the face-centered cubi c (fee) sites (denoted 4a). The Cu atoms are divided up among sixteen smaller sites (called 16e sites) and four larger sites (called 4c sites). When the Cu atoms are replaced by Pd atoms in UCus-xPdx compounds and since Pd atoms are larger than Cu atoms one might e xpect an ord e red model for the UCu4Pd sampl e : the U atoms would occupy the 4a sites the Pd atoms would occupy the 4c sites, and the Cu atoms would occupy the 16e sites. Some compounds do exhibit this ordered arrangement in the AuBe5 structure: AgErCu 4 [145] and ErMnNi 4 (43]. Despit e claims by Chau et al. using a high-intensity powder diffractometer that UCu4Pd

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Figure 1 -1: The conventional unit cell for the cubic AuBe5 crystal structure. The 4a sites are located on the edges of the cube and in the center of each square face. The 4c and 16e sites are crystallographically inequivalent sites with the 4c site larger than the 16e site. The drawing is taken from the paper by Chau et al. [27). 3

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4 is chemically ordered (27], Pd/Cu disorder does exist on the 4c and 16e sites with experimental evidence coming from MacLaughlin et al. using magnetic resonance measurements (93], Booth et al. using extended x-ray-absorption fine-structure (EXAFS) (15], and Weber et al. using unannealed and annealed UCus-xPdx lattice parameter values (160]. MacLaughlin et al. found that muons are relaxed rapidly in UC114Pd and this rapid relaxation comes from a large disorder effect. Booth et al. revealed that for the unannealed UCu4Pd, 24 3% of the Pd occupies the majority sites ( the 16e sites) instead of all the Pd occupying the minority 4c sites. Then, Weber et al. found that annealing UCu4Pd decreased the lattice parameters compared to unannealed UCu4Pd. These results from the lattice parameters indicate that Pd atoms are rearranged from the 16e to the 4c sites. However, Booth et al. performed EXAFS measurements on annealed UCu4Pd samples made by Weber et al. and still found that 19% of the Pd is located on the 16e sites (16]. Clearly, UCu4Pd shows Cu/Pd disorder on the Cu sublattices. The disorder in UCus-xPdx leads to unique low temperature properties in the specific heat, especially for the UCu4Pd compound. Andraka and Stewart proposed, based upon their results, that UCu4Pd lies near the suppression of a second order phase transition, TN = 0 (4]. This quantum critical point (QCP) (i.e. TN = 0) was thought to be the source of NFL behavior for the thermodynamic properties at finite temperatures. As mentioned earlier, power law behavior was found between 1 and 10 K while the lowest temperature C /T data fell under the power law curve by as much as 16% at 0.34 K [4]. Then Scheidt et al. extended the specific heat measurements down to lower temperatures and found that for unannealed UCu4Pd, the specific heat data leveled off at around 0.2 K (130]. The specific heat of unannealed UCu4Pd showed logarithmic temperature dependence over a decade of temperature (0.2 K to 2 K) in agreement with the work of Vollmer et al. [156]. However, there is disagreement concerning the behavior

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below 200 mK. Scheidt et al. measured ac susceptibility as a function of frequency and found a peak at ,..., 0.24 K at 95.5 Hz that shifted to 0.27 K at 995 Hz. This large shift in the ac susceptibility peak with frequency was strong evidence for superparamagnetism associated with spin clusters (105]. This magnetism at lowest temperatures was consistent with the theoretical efforts of Castro Neto et al. (20] in which the formation of magnetic clusters (i.e., Griffiths phase behavior (57]) in highly correlated systems is caused by disorder that leads to competition between the Kondo and Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction. In addition, unpublished results by Dr. Jungsoo Kim that measured the specific heat of UCu 4Pd in various magnetic fields showed a magnetic field induced peak, a feature that is indicative of a possible Griffiths phase disorder description. On the other hand, Vollmer et al. concluded that below 0.2 K, there is spin-glass freezing of the U magnetic moments in UCu 4Pd. Different interpretations have continued to carry on. Korner et al. then stated that UCu 4Pd is antiferromagnetic with TN = 190 mK and simultaneously shows evidence of spin glass behavior below TN from specific heat and ac susceptibility measurements (77]. Then Weber et al. performed experiments on annealed samples of UCu 4Pd (160]. Not only did they perform lattice parameter measurements as stated earlier, but also specific heat data at low temperatures were taken. Annealing the UCu4Pd sample for 14 days at 750 C suppressed the antiferromagnetic transition with no hint of the transition down to the lowest measured temperature of 80 mK. Also, the logarithmic temperature dependence of the specific heat now covered more than two decades of temperature starting from 80 mK. This expansion of the logarithmic temperature dependence suggested that crystallographic order could be an alternative tuning parameter for NFL behavior besides pressure (14], doping (5], or magnetic field (61]. This logarithmic temperature dependence also suggests that the Kondo disorder model (consisting of a broad distribution P(TK) 5

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6 of Kondo temperatures, TK, which extends down to very low temperatures [11, 99]) could be a plausible explanation for the NFL behavior in UCu4Pd [11]. Another interpretation based upon C/T log T concerns ordered systems near a QCP [143]. Unfortunately, these major theories (Griffiths phase, ordered systems, Kondo disorder model are discussed in greater detail in the "Theory" chapter) based upon the specific heat data have gaps in their interpretation. For example, the specific heat data in annealed UCu 4Pd are not consistent with the theoretically predicted power-law behavior, C/T ex: T-1+\ for the Griffiths phase model [160] while ordered systems (e.g., UBe13 ) near a QCP do not show a magnetic field induced peak in C/T [143]. The Kondo disorder model is not a valid interpretation based upon resistivity data discussed below. The de electrical resistivity for UCus-xPdx has been measured by several groups. The first electrical resistivity measurements for UCu 4Pd were reported by Andraka and Stewart [4]. For temperatures lower than 10 K, the UCu4Pd resistivity was approximately linear in T: p p0 (1 T /To) where Po 375 O. cm and To = 60 K. This linear temperature dependence of p gave experimental evidence for a non-Fermi-liquid ground state. Chau and Maple then measured the electrical resistivity for unannealed UCu5_xPdx with concentrations ranging from x = 0 to x = 1.5 [26]. They found that p(T) increases monotonically with decreasing T and does not display a peak or downturn at low temperatures. Experimental evidence also proved that the resistivity of the Pd-substituted samples increases with increasing Pd concentration. Specifically, Chau and Maple fit the electrical resistivity data for UCu 4Pd top~ p0 (1 T/T0 ) below 10 Kand found Po = 258 O. cm and TO = 63 K, numbers that are comparable to Andraka and Stewart's results. This linear dependence in the resistivity suggested that the NFL behavior in UCu 4Pd may be explained by a Kondo disorder model. The results of Weber et al. seem to suggest otherwise [160]. First, annealing UCu4Pd

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7 samples drops the residual resistivity, p0 by a factor of about 2.5. Then, the linear temperature dependence that was reported previously for the unannealed samples disappears with annealing. The resistivity of the annealed samples has a Konderlike minimum around 35 K. However, the resistivity of the 14-day UCu4Pd annealed sample for 2 K T 8 K may be described by a Fermi-liquid expansion p Pr = AT2 + BT4 where Pr = 141.5 O. cm, A = -0.024 O. cm K-2 and B = -0.00013 O. cm K-4 (160]. Weber et al. note that the sign of A in the expansion above is unusual for / moments forming a Kondo lattice. Thus, Weber et al. conclude that the Kondo disorder model is not applicable for annealed UCu4Pd and suggest it is not the origin for NFL behavior in unannealed UCu4Pd either The third major measurement performed on UCus-xPdx samples concerns de magnetic susceptibility measurements. Andraka and Stewart reported that de magnetic susceptibility of UCu4Pd could be approximated by T-6 at low fields (100 G) from 10 K down to 1.8 K (4]. This x temperature dependence is consistent, although coincidental with an overcompensated four-channel magnetic Kondo model (129]. It will be noted here (although not important to one of the two subjects of this dissertation) that a spin glass freezing temperature of 2 K was measured for the UCu3Pd2 composition (4]. Chau and Maple then measured the de magnetic susceptibility for UCus-xPdx and were able to fit the low temperature x data for UCu4Pd to x(T) = Xo ln(T /To) for 2 K < T < 10 K (26]. Plus, Chau and Maple state that above x = 1.5, the UCus-xPdx system exhibits spin-glass freezing. They also mention that for the low temperature x data, it is difficult to distinguish between a logarithmic and a weak-power law temperature dependence (26]. Vollmer et al. then measured the magnetic susceptibility down to 0.08 K for UCu4Pd (156]. The low temperature x data according to Vollmer et al. suggest a spin-glass transition around 0.2 K due to the splitting between zererfield cooled magnetization and field-cooled magnetization. Korner et al. confirmed the evidence of spin

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glass behavior below the antiferromagnetic transition temperature for unannealed UCu 4Pd by de-susceptibility measurements [77]. 8 All of these interesting results from the specific heat, resistivity, ac susceptibil ity, and de susceptibility prove no current theoretical model is able to explain all the current elements of the experimental data [16]. New theories are being devel oped to try to explain all the different data such as a Kondo/ quantum spin-glass critical point [56]. These results have also led researchers to further explore the role of disorder in the UCu5_xPdx system, especially for UCu4Pd Expanding upon their research on unannealed UCu 4Pd [15], Booth et al. made EXAFS measurements on UCu 4Pd as a function of annealing time [16]. Their results show that the main effect of annealing is to decrease the fraction of Pd atoms on the nominally Cu 16e sites, confirming the conclusions reached by Weber et al. concerning annealing upon UCu 4Pd [160]. Booth et al. also conclude that disorder must be included in any complete microscopic theory of NFL properties in the UCus-xPdx system. MacLaughlin et al. performed magnetic resonance measurements upon the UCus-xPdx system and also concluded that structural disorder is a major factor in NFL behavior. The longitudinal-field muon spin rotation (SR) relaxation measurements on UCu5_xPdx at low fields reveal a wide distribution of muon relaxation rates and divergences in the frequency dependence of spin correlation functions [93]. Interestingly, the divergences seem to be due to slow dynamics associated with quantum spin-glass behavior, rather than quantum criticality as in a uniform system (such as CeNi2Ge2 [68, 140], YbRh2Si2 [151], and doped alloys that include CeCu5 9At1o.1 [158, 157, 3] and Ce(Ru1-xRhxhSh where x 0.5 [164, 165]) because of the observed strong inhomogeneity in the muon relaxation rate, and the strong and frequency-dependent low-frequency fluctuation. In conclusion, the disorder in the UCus-xPdx system, especially in UCu4Pd, has led

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9 to considerable interest from researchers and a search to look for compounds in the AuBe5 cubic structure that possesses sublattice disorder. When searching for compounds that crystallize in the AuBe5 structure and that display possibly the same behavior as UCus-:i:Pdx, two factors should be taken into consideration. The first factor concerns the substitution of transition metals for Cu using UCu5 as the starting point. For example, the substitution of Au for Cu (i.e., UCus-xAux) leads to an initial increase in TN up to x = 2, but TN decreases above x = 2 (150] while the substitution of Ag for Cu does not show the same rapid suppression of magnetic ordering as UCus -:i:Pdx does [117]. Also, the substitution of Ag or Au for Cu did not result in any NFL behavior. Chau and Maple point out that the Au and Ag atoms have a completely filled d-electron shell and the same valence as Cu [26]. There could be a correlation between substituting atoms with the same valence and lack of NFL behavior since Pd atoms have a partially filled d shell and a different valence Since the complete subshell configuration atoms with d10 show no NFL behavior this might possibly extend to the half filled subshell configuration atoms with d5 due to their stability ( or lower total energy). The second factor concerns how much of a dopant atom may be substituted in the UCu5 cubic cell For example, when x approaches 2.4 for the UCus-:i:Pdx system, a mixture of cubic and hexagonal phases appears and may run until x = 5 [26]. The supposition concerning the secondary hexagonal phase may be related to studies that showed the hexagonal CaCu5 type structure may exist with atomic radii ratios (Ca site/Cu site) ranging from 1.29 to 1.61 and that below this range cubic AuB e5type compounds are formed (42, 19]. A possibility is that the hybridization between the Pd and Cu atoms reduces the apparent radii of those atoms and thus the atomic radii ratio of some U /Cu-Pd atoms (maybe the ratio between n e arest atoms) now lies above 1.29 while other ratios are below 1.29. Thus the mixture of cubic and hexagonal crystal phases.

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It has been known that uranium forms the cubic AuBe5 structure only with Ni, Cu, and Pt atoms [150]. The UCu5 has been well chronicled with its antiferromagnetic ordering around 15 K [101, 104]. In addition, UCu5 undergoes another phase transition around 1 K (in the electrical resistivity and magnetic measurements) and this was the first example of such a distinct enhancement 10 effect that occurs in a magnetically ordered material [117, 115]. Then, Chau and Maple doped UCu5 with Pt and found a region in the phase diagram where the low temperature physical properties exhibit NFL behavior [26]. This then leaves UCu5 to be doped with Ni since Ni has the same valence as Pd and Pt and the d-electron shell is not full or half-full. The main difference between the dopant atoms nickel and palladium is that the replacement Ni atoms are smaller than the Cu atoms as opposed to the larger Pd atoms replacing Cu atoms. Sublattice order for x ,..,, 1 should not occur in UCus-xNix as happened in UCu5_:,;Pdx. Thus, the answer to the question of any NFL behavior in UCus-xNix as TN -+ 0 being due to disorder or quantum critical behavior should be better differentiable. 1.1.2 UCus -xNix The first part of this section will review in chronological order previous works performed on the UCus-xNix system. The surname of the first author and the publication year will serve as the title for each work's review. One will see that the majority of the literature has mainly centered around UCu4Ni, possibly in hopes of searching for interesting behavior as found in UCu4Pd. 1.1.2.1 van Daal 1975 The first work performed on the UCus -xNix system was done by van Daal et al. who measured lattice constants for O x 5 along with the susceptibility, specific heat, electrical resistivity, and absolute Seebeck coefficients as a function of temperature [153]. The susceptibility reveals that UNi5 has a U4+ (tetravalent) state while on the Cu-rich end of the system (especially for O x 1), the

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11 uranium ions are mixed tetravalent and trivalent (U3+). van Daal et al. suggest that this mixed valency is possibly the source of the anomalies observed in the Cu-rich compounds (0 < x < 1): an extra increase of the lattice constants, an extremely high electronic specific heat, a resistivity varying in the paramagnetic range in proportion to log10 T at high temperatures and to 1 -(T /T*)2 at low temperatures and being extremely sensitive to deviations from stoichiometry, and a Seebeck coefficient showing large negative peaks at low temperature [153]. 1.1.2.2 Chakravarthy 1991 Chakravarthy et al. performed neutron diffraction measurements on Cu-rich compounds, in particular, x = 0.0, 0.2, and 0.5 [22]. The conclusions made are that UCu5 is an itinerant magnet involving a strong hybridization of 5f electrons with the conduction electrons. For UCu4.8Ni0 2 the suppression of long-range magnetic order (LRO) by small substitution of Cu by Ni indicates the enhancement of the interaction of 5f electrons with the conduction electrons [22]. However, TN is not significantly affected (12 K for x = 0.2). Thus, the band structure may be responsible for the LRO [159]. The third composition, UCu 4 _5Nio.5 did not show LRO down to 1.5 Kand the authors suggested that the suppression of the ordered magnetic moment of the U ion causes the LRO to disappear in the x = 0.5 system [22]. 1.1.2.3 Lopez de la Torre 1998 Lopez de la Torre et al. made electrical resistivity and magnetic susceptibility measurements down to 0.4 K for UCu4 5Ni0 5 and UCu 4Ni samples [89]. For UCu 4 _5Nio.5 the magnetic susceptibility displays an irreversibility below a broad maximum for a zero-fiel9 cooled (ZFC) and field-cooled (FC) regime and the maximum is the "freezing temperature" for a spin glass at about 6 K. For UCu4Ni, the magnetic susceptibility shows no spin glass or magnetic order feature down to 0.4 K. No saturation in the magnetic susceptibility is apparent at low temperatures

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12 and an asymptotic T112 dependence describes quite accurately the magnetic susceptibility from 0.4 K to 2.5 K [89]. The electrical resistivity measurements for UCu4Ni showed that all samples had linear temperature dependence from 0.4 K to ,....., 30-40 K. Also, annealing did not change the low temperature electrical resistivity properties significantly; however, the electrical resistivity values did show a large sample dependence. The authors raise the question of whether or not this NFL behavior is attributable to a two-channel Kondo effect [136], a quantum phase transition at T = 0 [5, 158], or disorder (specifically Kondo disorder) [39]. 1.1.2.4 Lopez de la Torre 2000 Lopez de la Torre et al. try to address the previous question by applying the Kondo disorder model to the magnetic, electrical, and thermal properties of UCu4 Ni [90]. The claim is that the existence of two nonequivalent copper sites in the AuBe5 cubic structure is the origin of the crystallographic disorder resulting in a distribution of Kondo temperatures [11, 15]. The phenomenological Kondo disorder model given by Bernal et al. [11] was used to describe the magnetic susceptibility data in a 1 T field and the fit described the data over two decades of temperature. Lopez de la Torre et al. and van Daal et al. both agree that UCu4 Ni is in a mixed valence state between U3+ (J = 3/2 where J is the effective angular momentum) and U4+ ( J = 1). The electronic specific heat measurements for the UCu4Ni sample show typical NFL log10 T dependence from 0.9 K to 9 K [90]. A comparison between the experimental specific heat results and a calculation made using a distribution of Kondo temperatures (similar to Graf et al. [55]) and applying the resonant level model for the specific heat of a single Kondo impurity [135] show pretty good agreement from about 1 K to 10 K [90]. Lopez de la Torre et al. observed an upturn in the specific heat around 0.9 Kand they think the origin may be some form of spin-glass-like freezing at temperatures below their experimental limit (0.4 K). The upturn in the specific heat may also be related to

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the inflection in the magnetic susceptibility around 1 K [90). The conclusion by Lopez de la Torre et al. is that the Kondo disorder model could play a significant role in the NFL behavior reported in UCu4Ni. 1.1.2 5 Lopez de la Torre 2003 13 Lopez de la Torre et al. made electrical resistivity measurements of UCu4.75Ni0 _25 and UCtl4Ni over a wide temperature range (0.4 -800 K) [88). In summary, the high-temperature electrical properties of UCu4Ni and UCu4.75Nio.25 were explained in terms of single-impurity Kondo behavior The interesting part of this paper concerns the high values of the electrical resistivities (p(0) "' 440 O cm and pis usually well above 100 O cm over the entire experimental temperature range). The rather poor electrical conductivity would indicate that the electronic mean free path is close to the interatomic distance and kF f is of the order unity where is the mean free path. This class of strongly correlated electron systems that approaches the Ioffe-Regel limit for the metallic state includes high-Tc supercon ductors, fullerenes, and ferromagnetic perovskites (e.g., SrRu03 ) which all have properties suggesting some sort of NFL behavior [154). In the results part of this dissertation these reported high electrical resistivity values will be revisited. 1.1.2 6 Present Work One reason for studying the UCus -xNix system concerns the fact that the Kondo disorder model may not be the best explanation for the NFL behavior present in the experimental data. For example a quantum critical point (QCP) may also be a possibility since the antiferromagnetic temperature ( a second order phas e transition) is suppressed to zero and the QCP has a large influenc e on the measured properties at finite temperatures [143). However some recent research on the isostructural UCus xPd x system has suggested that theories that limit the cause of NFL b e havior to just one phenomena such as disorder or a quantum critical point may not be the best explanation. In fact, theories that

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combine quantum critical points with disorder may explain all the different data of systems such as UCus-:i:Pd:i: and UCus-:i:Ni:i: [16]. One such model in which 14 the magnetic ordering temperature, T order, has been suppres&rl via doping based on the effects of the accompanying disorder is the Griffiths phase disorder model. In the Griffiths phase model, disorder leads to tunneling between closely spaced energy levels in rare strongly coupled magnetic clusters [21]. The Griffiths phase model depends on the strong magnetic fluctuations produced "near" a QCP. The Griffiths phase model predicts that x and C/T follow a power law temperature dependence, T-l+A [20]. One of the unique features of the Griffiths phase model is that once a crossover magnetic field is determined (from magnetization versus field measurements), a magnetic field around the crossover field induces a peak in C /T at low temperatures (C/T:::::: (H2+A/2 /T3-A/2 ) exp(-e/J H/kBT)) and the induced peak broadens and moves to higher temperatures for higher fields. Two systems in which the NFL behavior may be explained by the Griffiths phase model and that demonstrate field induced peaks are Ce1_:i: ThxRhSb [74] and Ce1_:i:La:z:Rhln5 [73]. The field induced peak is unique to the Griffiths phase model. This should not be confused with the peaks in magnetic fields for the multichannel Kondo prob lem [132]. There are distinct differences. First, the Griffiths phase model predicts that for zero magnetic field, the specific heat ( C) follows TA behavior as mentioned earlier. In contrast, the specific heat for a Kondo system like CrCu [149] shows a peak in zero magnetic field. The peak in the specific heat for a Kondo system shifts towards higher temperatures and the height of the peak also grows as the magnetic field is increased The Griffiths phase explanation differs since, although the field induced peak moves up in temperature, it broadens and decreases in size with increasing field.

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15 For the present work, eight different UCus-xNiz compounds were produced with x ranging from 0.6 to 1.2. The reason for such a large variation in the concen trations is to explore whether or not clear distinctions may be made concerning the cause of NFL behavior at different concentrations. In fact, small variant concentra tions (i.e., x = 1.05, 1.1, and 1.2) have been made near UCu4Ni, the concentration where TN is approximately zero. A possible crossover concentration level might be found where one concentration's NFL behavior may be explained by a QCP while increasing the Ni concentration by 5% could cause the NFL behavior to be due to another model, like a disorder model. Also, the Griffiths phase model is predicated upon strong magnetic fluctuations "near" a QCP; it would be interesting to see if "near" could be quantified in terms of the Ni concentrations. The only system investigated by small variations of doping around the QCP was UCus-xPdx, where the quantum critical concentration was x 1 as discussed earlier. The problem with UCu5_xPdx was the preferential sublattice ordering of the larger Pd atoms on the minority 4c site (in the AuBe5 structure) occurring in UCu4Pd as discussed previously [16]. In fact, MacLaughlin et al. concluded that there were still signs of disorder on annealed UCu4Pd [93]. The UCusxNiz system should not have to contend with a preferential sublattice ordering since the Ni atoms are smaller than the Cu atoms. Thus, the smaller Ni atoms will be distributed at slightly less than the 25% level on the majority 16e sites (i.e. the physically smaller Be site in the AuBe5 structure) for UCu4Ni, with some small fraction in the energetically more unfavorable larger 4c sites. This conclusion will be discussed when the lattice parameter values are presented in the "UCus xNiz Results and Discussion chap ter. Thus, all concentrations around UCu4Ni should have a significant amount of disorder present.

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16 In addition to the lattice parameters for all eight concentrations being re ported, direct current (de) resistivity, magnetization as a function of field, al ternating current ( ac) susceptibility down to 2 K direct current (de) magnetic susceptibility down to 2 K, and heat capacity in zero field along with heat ca pacity in magnetic fields for concentrations around the QCP composition will be reported in the "UCus-xNix Results and Discussion" chapter. To date, a complete and thorough characterization of the UCu5_xNix system around the QCP has not been reported in the literature. The measurements reported here will try to answer if clear distinctions can be made about the sources of NFL behavior (i.e., quantum criticality and disorder) at various Ni concentrations around the QCP (i.e., UCu4Ni). Also, the measurements will try to clarify the role of Griffiths phase model for NFL behavior in the UCus-xNix system. An attempt to determine the concentration range for which the Griffiths phase model applies will be made 1.2 Curie Temperature Enhancement in UCu2Si2-xGex A Curie temperature, Tc, enhancement as a function of disorder was pre dicted by Silva Neto and Castro Neto [137]. The fundamental idea behind this enhancement effect concerns electrons scattering from the localized moments and acting as a heat bath for the spin dynamics. Then the dissipation that arises from the electronic diffusion in the case of structurally disordered ferromagnets is what affects the Curie temperature. The study of ferromagnetism in disordered alloys has received renewed interest in recent years due to the development of Ga1xMn x As [114, 110, 112] and ln1x Mn x As [113] as ferromagnetic semi c onductors (with x 1-10%) In fact there are now reports of ferromagnetism ( some at room temperatures and above) in several magnetically doped semiconductors [36], e.g. GaMnP [146], GaMnN [125], GeMn [118], GaMnSb [29]. Howe ver, the observed ferromagnetism in dilute magnetic semiconductor (DMS) systems like GaMnAs is not just associated with

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17 disorder created by the random positions of the magnetic dopants, but also the thermal fluctuations of magnetic moments along with impurity band and discrete lattice effects playing an integral part if the magnetic coupling can be assumed to be a simple local exchange coupling between local impurity moments and carrier spins [36]. Thus, trying to isolate the effects of disorder on the ferromagnetism in a DMS to test the proposed theory by Silva Neto and Castro Neto is impossible due to the aforementioned complexities in a DMS. The choice of a ferromagnetic material to test the theory of Silva Neto and Castro Neto depends upon being able to test the effect of structural disorder on the ferromagnetic properties without introducing sundry complications [138]. De Long et al. investigated over 100 metallic Ce and U compounds to look for trends in the occurrence of ferromagnetism and to consider parameters such as the closest f-atom separation (notated by d) [37]. For example, Hill observed that f-state magnetic order did not occur ford< dH, where dH = 3.4 or 3.5 A, the respective "Hill limits" for f-state localization in Ce-and U-based materials [65]. Thus, when trying to induce structural disorder upon the selected compound it is important not to inadvertently change the f-atom separation because it would be very difficult then to distinguish the change in Tc between structural disorder and f atom separation. De Long et al also mention that hybridization off-levels with non-f conduction states has an effect upon the ferromagnetism (37]. This pretty much rules out any binary ferromagnetic compounds since doping on one of the two atoms not only would create structural disorder, but also the doping would affect the hybridization. The two ferromagnets UCu2Si2 and UCu2Ge2, meet the conditions outlined above. UCu 2 Si 2 is a ferromagnet at 103 K (with an antiferromagnetic transition right above at 107 K) (37] while UCu 2 Ge 2 is a ferromagnet at 107 K (with a controversial antiferromagnetic transition at around 43 K [78, 47]) (37]. UCu 2 Ge 2 and UCu2Si2 are isostructural crystallizing in the ThCr2Si2 structure [28]. The

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18 ThCr2 Sii structure is shown in Fig. 1-2 on page 18. In Fig. 1-2, one can see Figure 1-2: The unit cell for the tetragonal ThCr2 Si 2 crystal structure. The c-axis is up in this diagram, running parallel to the longest dimension of the unit cell. The ThCr2 Si 2 is layered with Th-Si-Cr 2 -Si-Th planes stacked along the c axis. This diagram was taken from the paper by Welter et al. [161]. that for the UCu 2 (Si, Ge)2 compounds, the U atoms replace the Th atoms, the Cu atoms (the transition metal, T) replace the Cr atoms, and the Ge atoms replace the Si atoms for UCu 2 Ge 2 The shading in Fig. 1 2 also highlights the tetraderal coordination of the Si ( or Ge) around the T ion with small T-Si (Ge) distances: 2.40 A for UCu2Si2 and 2.42 A for UCu2Ge2 [28]. The smallest distance between two neighboring U atoms is well above the Hill limit for a U-compound (3.5 A): 3.98 A for UCu 2 Si 2 and 4.05 A for UCu 2 Ge 2 [37]. It was decided that the structural disorder could be intentionally created by doping Ge onto the Si site in UCu2Si 2 and that 9 compounds with differing Ge concentration levels (x = 0, 0.2, 0.4, 0.6, 1, 1.4, 1.6, 1.8, and 2) would be arc-melted to investigate whether or not nonmonotonic behavior exists for Tc as predicted by Silva Neto and Castro Neto.

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19 The replacement of Si atoms with Ge atoms should not affect the magnetic sublattice in the UCu 2 Sh-xGex compounds. The structural disorder Mil occur on the p orbitals deep within the isovalent Si and Ge atoms. The structural disorder will affect the conduction band due to the complex p-d hybridization between the T ion and Si/Ge as seen in Fig. 1-2. Thus, the strong hybridization between the T ions and the U ions should not be directly affected by this intentional structural disorder. This is in agreement with the neutron diffraction and magnetization measurements of Chehnicki et al. that gave no magnetic moment on a copper ion [28]. In fact, the explanation by Chelmicki et al. for why the T ion does not carry a magnetic moment originates from the coordination of a T ion by silicon/ germanium atoms. Four silicon atoms are located at the corners of a flattened tetrahedron around each T ion as shown in the shaded part of Fig. 1-2 on page 18. The short T-Si/Ge distances amount to less than the sum of atomic radii of T and Si/Ge [28]. Thus, the overlap (or hybridization) of electronic shells and electron density transfer from the 3p shell of the silicon/ germanium to the 3d shell of the Cu ion in UCu 2 Si 2 -xGex compounds is what probably vanquishes the magnetic moment on the Cu ion. Mossbauer studies on isostructural NpFe 2 Si 2 [109] and REFe2Si2 (where RE is a rare earth element) intermetallics [51, 108] show that the T ion does not carry a magnetic moment. The information by Chelmicki et al. justifies that the Si/Ge exchange creating sublattice disorder will not affect the long-range magnetic ordering of uranium moments in UCu2Si2-xGex The effective magnetic moments and the isotropic RKKY mechanism de termined by Chelmicki et al. were used by Dr.s Silva Neto and Castro Neto to calculate the nonmonotonic dependence of Tc [137]. The effective magnetic mo ment, elf., for UCu2Si2 was determined to be 3.58 Bohr magnetons (B) from the inverse susceptibility versus temperature curve using the Curie-Weiss law [28]. The

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20 3.58B value is the exact value calculated for a free ion configuration of U4+ as suming 3H4 as a ground state. The elf. value for the U ion in UCu2Ge2 is 2.40B. Possible reasons for why the effective moment is lower in UCu2Ge2 are crystal field effects or magnetic moment compensation [138]. The magnetic interactions of the U ions may be explained by an isotropic RKKY model, in agreement with neutron diffraction and magnetization data [28]. This model was also successful in explaining the magnetic interactions in isostructural UPd2Si2, URh2Sh, and UPd 2 Ge2 [122]. The details of using this isotropic RKKY mechanism will be discussed in the "Theory" chapter of this dissertation. One important point that cannot be emphasized enough concerns the Si/Ge sublattice disorder that is intentionally created and differs from other alloying experiments on the UCu2Si2 and UCu2Ge2 compounds. Since Si and Ge are isovalent, the carrier density is not changed. In contrast, the carrier density changes in the UNi 2 _xCuxGe 2 system along with the magnetic sublattice since the hybridization between the U and Cu ions is altered by the substitution of the Ni atoms. Also studies done on the UNi 2 xCuxGe 2 system [82, 79] show that the ferromagnetic phase only exists for 1.20 :::; x:::; 2 in the UNi 2_xCuxGe2 magnetic phase diagram. In fact, for x 0.75 (i.e., the samples closest to pure UCu 2 Ge2), there is a ferromagnetic-to-commensurate crossover. For example, for x = 0.95, a Tc value of 110 K was observed in ac-susceptibility measurements while at 94 K, the sample underwent another transition to an antiferromagnetic phase [79]. Kuznietz et al. even state that the transition metal sublattices determine the type of ordering on the uranium sublattice in the UM2 X 2 (where M = Co, Ni, Cu and X = Si, Ge) systems [79]. Fo~ the tJCu2Si2 side of the phase diagram, neutron-diffraction results by Kuznietz et al. upon UNi0 30Cu1.10Si2 show that :=:::: 93% of the sample volume orders antiferromagnetically while the other 7% orders ferromagnetically [81]. It should be clear from the examples above that

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21 it would be very difficult to individually distinguish the effects on Tc between the disorder acting on the transition metal's conduction electrons and disorder altering the magnetic sublattice. Thus, familiarity and acknowledgment concerning the tremendous amount of work on the magnetism of UCu 2Si2 [63, 128, 96] and UCu 2 Ge 2 [23, 102, 45, 148] is revealed, e.g., UC02-xCuxGe2 [80, 41] and Ui-x Y xCu 2Sh [64, 62]. However, despite all this research, this UCu2Si2-xGex is unique because it is the first project to try and isolate the effects of disorder upon Tc by creating structural disorder at the Si/Ge site (i.e., the 4e site of the ThCr2 Si 2 crystal structure). A final factor in determining the Tc enhancement for UCu 2 Si 2_xGex con cerns minor changes in the stoichiometry of the UCu 2Si2 -xGex system. Particular attention to the stoichiometry in the UCu 2Si2 -xGex compounds is paid in the "Experimental Techniques" chapter and the "UCu2Si 2 -xGex Results and Discussion" chapter. Kuznietz et al. point out that small deviations from stoichiometry on the copper sublattice alters the number of conduction electrons [79]. The effect of small stoichiometry changes upon the magnetic properties is closely monitored since predictions by Silva Neto and Castro Neto originate from conduction electrons on the Cu sublattice scattering from the localized U spins [137] as discussed earlier. In fact, multiple samples with the same Si/Ge concentration are synthesized in order to compare the stoichiometry differences to the experimentally determined Tc values. The low temperature resistivity on the UCu 2Si2 _xGex compounds is also measured. Low temperature resistivity predictions for the scattering of conduction electrons from localized spin fluctuations have the resistivity varying as T 2 as observed in dilute Pd-Ni alloys [131] and dilute Ir-Fe alloys [70]. This Fermi-liquid like resistivity behavior is expected for the UCu 2Si2-x Ge x compounds. Also the resistivity measurements are expected to provide insight into the type of dissipation

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occurring from the scatter of the conduction electrons. The two main sources of dissipation are Landau damping for clean magnets and electronic diffusion for structurally disordered magnets [137]. The electrons in the Landau damping case have a longer mean free path than the electrons in the diffusive case. Thus, the resistivity for the Landau damping electrons (i.e., the ballistic electrons) is expected to be smaller than the diffusive electrons. 22

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2.1.1 Introduction CHAPTER 2 THEORY 2.1 Non-Fermi-Liquid Theory The discovery of the electron in 1897 by J.J. Thomson has led to many theo ries concerning the behavior of electrons in metals. In 1900, P. Drude formulated his theory of metallic conduction by using a slightly modified method of the kinetic theory of a neutral dilute gas. Unfortunately, the Drude model was not accurate in predicting many physical properties, such as the specific heat of a metal. A quarter of a century passed until Sommerfeld's model solved the problem by using the Pauli exclusion principle's requirement that the electronic velocity distribution is the quantum Fermi-Dirac distribution instead of the classical Maxwell-Boltzmann distribution. After the passing of another quarter century or so, L.D. Landau intrer duced his Fermi-liquid theory that was able to explain many physical properties in metals such as Cu and AL All of the previous models made use of an independent electron approximation or free electron model. As one comes to present day, complex metals have oeen discovered where at low temperatures, the electron-electron interactions cannot be simply ignored or slightly modified with respect to the free electron case. The strong electronic correlations lead to non-Fermi-liquid behavior. In fact, non-Fermi-liquid behavior has been observed in metals with disorder, such as UCus-xPdx [4). The theory will begin with some of Landau's arguments for Fermi-liquid theory and then explore some of the theories characterizing non-Fermi-liquid behavior. 23

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2.1.2 Fermi-Liquids In 1957, L.D. Landau proposed his Fermi-liquid theory. The original intent of the theory was to explain the liquid state of the isotope of helium of mass number 3 [7]. However, Fermi-liquid theory is now being applied to the theory of electron-electron interactions in metals. 24 Landau's Fermi-liquid theory has two main points. First, the electrons that are within kB T of the Fermi energy and that do have interactions with each other do not ruin the success of the independent electron picture in explaining lowenergy metallic properties. Secondly, single electrons are not just being considered anymore, but rather quasiparticles (or quasielectrons). These quasiparticles share many of the properties of non-interacting electrons, but quasiparticles are like electrons that have been perturbed from their non-interacting state by means of interaction [134]. Instead of going through a quantitative analysis as Landau did to obtain respective thermodynamic and transport properties [83, 84, 85] of a Fermi liquid, a qualitative analysis is more appropriate for this dissertation. The quasiparticles that are of most importance are those that are within kBT of the Fermi surface as stated above. Most quasiparticles in metals are so far buried down below the Fermi surface that they are unable to obtain the required energy needed to reach an unoccupied quantum state. Thus, only quasiparticles within kBT of the Fermi surface can contribute kB to the specific heat and the specific heat grows linearly with temperature. Likewise, only quasiparticles within BB (where Bis an external magnetic field) of the Fermi surface can magnetize with a magnetic moment proportional to B leading to a temperature independent magnetic susceptibility [134]. If the temperature is above absolute zero, then some energy levels above the Fermi energy will be occupied within a range of kB T of the Fermi surface. Therefore, the scattering rate for the quasiparticles near the Fermi surface

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25 is proportional to T2 Since the resistivity is proportional to the scattering rate, the low temperature resistivity goes like T2 2.1.3 Non-Fermi-liquids In 1991, Seaman et al. discovered low-temperature measurements of specific heat, magnetic susceptibility, and electrical resistivity on the Y1-xUxPd3 system that were contradictory to Landau's Fermi-liquid theory [136]. Specifically, the compound Y o.s U0 2Pd3 displayed a linear low temperature behavior in its resistivity and a logarithmic relationship in its low temperature heat capacity for over a decade of temperature in both. To date, over fifty systems have been discovered that do not obey Landau's Fermi liquid theory [143]. Since the discovery of Y0 8U0 2Pd3 displaying this non-Fermi-liquid (NFL) behavior, there has been considerable interest in explaining this NFL behavior by condensed matter theoreticians. The various theories are segregated into three general categories: 1) multichannel Kondo models; 2) models where the magnetic phase boundary lies near OK (i.e., the quantum critical point); and 3) models based on disorder. A synopsis of the various theories will be given while particular attention will be paid to models that are applicable to UCus-xNix. 2 1.3 1 Multichannel Kondo Model The multichannel Kondo effect is based upon single-impurity physics. The multichannel Kondo effect is described by a quantum impurity spin S that is coupled antiferromagnetically to n degenerate channels of spinconduction electrons [l]. The so-called Kondo lattice Hamiltonian is derived from the Anderson Hamiltonian to describe the single-impurity multichannel Kondo model [143]: (2.1) k,m,CT k,k1,m,CT,CT1 where k is the conduction -e lectron dispersion relation, aL and akmCT are creation and annihilation operators on electrons with momentum k and spin projection

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m, J is the antiferromagnetic coupling constant between the localized impurity spins and the conduction electrons, Sis the localized spin impurity, and Uuu' are the Pauli spin matrices. Three distinct cases arrive from the above Hamiltonian between the n channels ( or flavors) of the conduction electrons and the impurity spin S [143]: 1. If n = 2S, the conduction-electron channels fully screen the impurity spin channels and a singlet ground state arises. This leads to Fermi-liquid behavior as described above 26 2. If n < 2S, the conduction-electron channels only partially screen the impurity spin channels and no singlet ground state exists. The result is a new effective Kondo effect with a net spin S' = S -n/2 [25]. The ground state is Fermi liquid-like and mirrors the model of Coqblin and Schrieffer [30] (n = 1, S 1/2). 3. If n > 2S, the local spin is "overcompensated" yielding a critical ground state with a non-Fermi-liquid excitation spectrum [75]. The result of this overcompensation is power-law or logarithmic behavior in measured physical quantities like magnetization, resistivity, and specific heat as the temperature and external field approach zero. The third case is particularly interesting since the low temperature dependence of the magnetic susceptibility, specific heat, and resistivity depend upon the number of channels of conduction electrons, n, and the impurity spin S. For example, if n = 2 ("two-channel") and S = 1/2, then the low temperature, zero field magnetic susceptibility and specific heat divided by temperature, C/T, go approximately like log (T /T K) [132]. Such logarithmic temperature dependence has been observed in systems such as Y1-xU:cPd3 [136] and Th1-xUxPd2Ala [34, 38]. Also, the low temperature resistivity at zero-field behaves like p0 A..;T [91]. Unfortunately, this low-temperature resistivity has not been observed in many NFL

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27 systems. The reason may be that the low-temperature resistivity predictions were made in the dilute impurity limit while the NFL behavior in systems crops up more in the concentrated limit. Cox and Zawadowski [32] have addressed this concentrated limit. It is a special case of the multichannel Kondo effect that has a quadrupolar origin. The NFL behavior in this model results from an effective exchange interaction between pseudospins and the electric quadrupole moment of the groundstate [25]. However, no system has met the strict requirements required by this quadrupolar Kondo effect. The multichannel Kondo model portrays NFL behavior as single-ion in nature [21]. This means that each impurity moment is treated independently and concentrated systems might not be of single-ion character since no interaction between the impurities is taken into effect. 2.1.3.2 Quantum Critical Point The second general theoretical category describing non-Fermi-liquid behavior is quantum critical point models. The quantum critical point theories arise from the critical phenomena that occur at or near a zero temperature phase transition. Classically, a phase transition would occur at a nonzero temperature and temper ature would be the control parameter. The temperature parameter would control the thermal fluctuations and if the thermal fluctuations have characteristic energies (hw*, where w* is the frequency associated with the fluctuations) much less than kBTc (where Tc is the critical temperature of a phase transition), then the fluctuations may be described by classical statistics [25]. However, in 1976, Hertz [60] considered the case when the critical temperature is at T = 0. The fluctuations would have zero thermal energies. Thus, quantum mechanical fluctuations would arise that could not be controlled by temperature. These fluctuations may be con trolled by chemical substitution, external pressure, or magnetic field. An example

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28 of pressure control is CePd2Si2 where a pressure of ,.._, 28 kbar suppresses antiferro magnetism, induces superconductivity at 0.43 K, and shows NFL behavior in the electrical resistivity (p(T) oc TL2 ) [58]. The idea is that one of the aforementioned control parameters "tune" a system from an ordered ground state to a non-ordered state crossing a quantum critical point [143]. The assumption is that at low enough temperatures, the system's behavior will be dictated by quantum effects despite not being able to measure thermodynamic properties at T = 0 [139]. At these low temperatures, non-Fermi-liquid behavior appears at or near a quantum critical point since usually a magnetic phase transition is suppressed. The quantum critical point theory is relevant to the UCu5_xNix system because doping UCu5 with Ni suppresses the long range antiferromagnetic order and TN~I approaches zero As mentioned above, measurements at T = 0 cannot be performed. Thus, in order to confirm whether or not the NFL behavior is due to a quantum critical point, one must analyze scaling behavior [152] (either for temperature or frequency) on finite-temperature properties and compare to predictions made by several different models A synopsis of each model with key points is provided below. The first theoretical model was developed by Tsvelik and Reizer [152]. This theory matched the low-temperature thermodynamics measured in Uo.2 Y o.8Pda and UCu3 5Pd1.5 [136, 5, 4]. The theoretical model states that the two previous systems are on the verge of a phase transition that occurs at zero temperature and results in a domination by collective bosonic modes. The model also matched the correct scaling analysis of the low-temperature properties [4]: magnetization : M = :., f ( T:+'Y) specific heat: eu(H, T) eu(O, T) = g (_!!_) T T T/3-+'Y

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29 where,= 0.25 -0.3; f3 + 1 = 1.2 1.3; (the model predicted a scaling dimension of 4/3) and/ and g are nonsingular scaling functions. Along with the above scaling analysis, the specific heat has a logarithmic divergence and the de magnetic susceptibility has a divergent form (T--Y) at low temperatures. A second theoretical model investigating quantum critical phenomena was developed by Hertz [60] and Millis [97]. A major assumption is made to integrate out the fermions (i.e., the conduction electrons) and thus the problem is reduced to the study of an effective bosonic theory describing fluctuations of the ordering field [97]. Results depend crucially upon the value of d + z where d is the spatial dimension and z the dynamic exponent ( z=2 for the antiferromagnet and z=3 for the ferromagnet) of the T = 0 transition [60]. All of the cases considered except for the two-dimensional antiferromagnet have an effective dimension (d+z), greater than their upper critical dimension [60]. Hyperscaling (which is used to derive the scaling analysis mentioned in the previous paragraph) has been shown not to apply to systems above their upper critical dimension [17, 121]. Phase diagrams with crossover temperature relationships between various regions have been obtained for different cases (e.g. two spatial dimensions and dimensions larger than two [97]). None of the derived relationships for measured properties in this model are applicable to the UCus -xNix system A third theoretical model investigating quantum critical phenomena was developed by Moriya and Takimoto [103] and it involves spin fluctuations in heavy electron systems around their antiferromagnetic instability. This idea is particularl y applicabl e to the UCus xNix system since the heavy electron system UCu5 h as its Neel temperature suppressed by Ni doping. This theory is based on exchange enhanced spin fluctuations playing a major role in displaying various anomalous properties around the magnetic phase boundary. Moriya and Takimoto addressed the problem of coupling among the different modes of spin fluctuations in heavy

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30 electron systems [103]. Their answer was to take a phenomenological point of view by using a sum rule for the local spin fluctuations valid in the strong correlation limit: where SLo is the mean square local amplitude of the zero point, SLr is the mean square local amplitude of the thermal spin fluctuations, and SL is the amplitude of the local spin density that takes a constant value. The sum rule is then used to calculate the reduced inverse staggered susceptibility in the low temperature limit, y0 for a nearly antiferromagnetic metal: 1 where TA is a characteristic energy parameter and XQ(O) is the local dynamical susceptibility for the antiferromagnetic wave vector Q. This expression has the same form as in the self-consistent renormalization (SCR) theory for weak itinerant antiferromagnetism [103]. The parameter y O goes to zero as the magnetic instability is approached; in fact, at the critical boundary, y O equals zero [103]. Thus, the value of y0 gives a prediction for the proximity to the magnetic instability [143]. The value of y O is obtained by fitting the specific heat and electrical resistivity data. Moriya and Takimoto made predictions for the specific heat and electrical resistivity due to the spin fluctuations. When y O = 0, the specific heat takes a finite value, 10 and starts to decrease with increasing temperature proportionally to T1l2 Immediately after the square root behavior, the specific heat shows a negative logarithmic behavior in a certain range of temperature ( over about 60% of a decade in temperature above the 'Yo AT0 5 behavior [143]). Interestingly as one gets further from the phase boundary (i.e., y0 =/= 0) F e rmi liquid b e havior ari ses and the range of linear specific heat increases with increasing y 0 The electrical resistivity

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31 at the critical boundary is proportional to T312 at low temperatures and as the temperature increases, there is a certain range where the resistivity is almost linear in T. The electrical resistivity is similar to the specific heat in that as one moves further away from the antiferromagnetic critical boundary, there exists a normal Fermi-liquid behavior at low temperatures. Physically, the interpretation of the departure from the T112 behavior to the logarithmic dependence in the specific heat and crossover from the T312 behavior to the linear dependence in the electrical resistivity is that at the lowest temperatures, the coupling among the different modes of the spin fluctuations is small in magnitude; however, as the temperature increases, the coupling also increases [143]. Application of Moriya and Takimoto's theory will be discussed later on. Several other theoretical models exist describing quantum critical phenomena. However, in the interest of relevance to this dissertation, one should be directed to Dr. Stewart's review article [143] for a complete summary of all theoretical models pertaining to the quanium critical point 2.1.3.3 Disorder The third theoretical category describing non-Fermi-liquid behavior concerns models based on a disorder. These models originate from the multichannel Kondo model. It was previously discussed that when the conduction-electron channels are sufficient to compensate the impurity spin, then Fermi-liquid behavior occurs. T K is the Kondo temperature below which the conduction electrons fully screen the local impurity spin for S = 1/2 and n = 1 (the number of conduction-electron bands). The disorder model has been proposed to reduce TK to lower temperatures for some of the magnetic impurities and thus, some of the long-range magnetic order survives leading to non-Fermi-liquid behavior. The Kondo temperature, TK, is given as follows [76]:

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32 where EF is the Fermi energy, N(O) is the density of states at the Fermi energy, and J is the exchange constant between the local moment and conduction-electron. Mathematically, if disorder could increase N(O), J, or both, then the Kondo temperature could be lowered below the average T K. Thus, if the temperature were at average TK, then not all magnetic impurity spins would be compensated for and the uncompensated spins would lead to NFL behavior. The first disorder driven model was constructed from the work of Dobrosavl jevic et al. [39] and Bhatt and Fisher [12]. Then Bernal et al. [11] used this Kondo disorder" model to explain the large inhomogeneous nuclear magnetic resonance (NMR) linewidths they observed in UCu5_:i:Pd:i:. The large linewidths reflected a broad distribution of local uranium spin static susceptibilities that were considered to be due to a probability distribution, P(TK), of Kondo temperatures. The distribution of Kondo temperatures was assumed to be due to disorder. The uniform magnetic susceptibility, x(H,T) = M(H,T)/H, was thought of as the aver age of x(H T;TK) over P(TK) and fits on x(H,T) were used to obtain parameters characterizing P(TK)The NMR linewidths, which come from the distribution of Knight shifts and measure directly the width of the distribution P(x) of X, were found to agree well with the Kondo disorder model and no further fitting of P(TK) was required. The temperature and field dependence of the specific heat agreed well with the Kondo disorder model. The Kondo disorder model was extended further by Miranda et al. [98, 100, 99], who focused on non-Fermi-liquid behavior due to the interaction between disorder and strong electron-electron correlations. Their theory sums up as a small amount of disorder playing a major role in the low-temperature logarithmic divergence in magnetic susceptibility and specific heat along with the linear behavior in the low temperature resistivity [25].

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Not only was the multichannel Kondo model mixed with disorder, but also spin fluctuations near a quantum critical point were mixed with disorder. Rosch [126] explained that the reason why the resistivity varies as T where a is between 1 and 1.5 for various systems [68, 95, 53] is due to the interplay between quantum-critical antiferromagnetic spin fluctuations and impurity scattering in a conventional Fermi-liquid. In other words, the dependence of the exponent de pended on sample quality. The disorder in a sample was quantified by taking the inverse of the residual resistivity ratio: R(T-+0)/R(T-+300 K). The most relevant disorder model to UCus -xNix involves a model proposed 33 by Castro Neto et al. [21, 20]. The model by Castro Neto et al. takes place in a disordered environment and features the competition between the Kondo effect and Ruderman Kittel-Kasuya-Yosida (RKKY) interaction (i.e. magnetic ordering) as represented by the Hamiltonian in Eq. 2.1. The problem with studying this competition is the fact that both the RKKY interaction and the Kondo effect have origins on the same magnetic coupling between spins and electrons [21]. However perturbation theory may be used to treat the RKKY interaction since the RKKY interaction depends on electronic states on the Fermi-surface and states embedded inside the Fermi-surface while the Kondo effect just affects the Fermi surface. The RKKY interaction leads to an order of the magnetic moments while the Kondo coupling leads to the destruction of long-range order in a magnetically ordered system. In the model by Castro Neto et al., disorder also affects the magnetic order in these systems. For a ligand system (e.g. UCus xNix the metallic Cu atom s are replaced by Ni atoms), if the metallic atoms are replaced with smaller metallic atoms (as is the case for UCus -:i:Nix), then the difference in size between the metal lic atoms leads to a local lattice contraction which modifies the local hybridization matrix elements [21]. Large local effects in the system can occur because the local

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34 hybridization matrix elements are exponentially sensitive to the overlap between different angular momentum orbitals. Also, the local value of the exchange constant between the conduction electrons and the localized moments, Jin Eq. 2.1, changes due to the change in the local hybridization matrix elements. Castro Neto et al. disagree with the interpretations of the Doniach argument [40] which are based on homogeneous changes in the exchange constants between conduction electrons and magnetic moments. It is true that when the local exchange constant, J(i), is below a critical value Jc, the RKKY energy scale is larger than the Kondo temperature as shown in Fig. 2 1 on page 35. However, Castro Neto and Jones argue that since disorder is present in the system, the mer ment can locally order with its environment as the system is cooled down [21]. The Doniach argument differs because it is based on a global change in the exchange constant, J, instead of just a local change. Doniach's picture predicts a change in the exchange constant over the entire lattice and the ordering temperature in Fig. 2 1 vanishes at a quantum critical point where the system goes from ordered state to fully Kondo compensated state [21]. The picture by Castro Neto and Jones represents a quantum percolation problem where moments are compensated due to local effects and that a local change in a coupling constant does not immediately imply a change of the "average coupling" constant. Thus, even if chemical substi tution occurs on a non-magnetic site, individual moments will be compensated for magnetically due to the distribution of exchange constants in the presence of disor der [21]. At some critical doping concentration, long-range magnetic order will be suppressed and the system will enter a paramagnetic phase. However, since Castro Neto and Jones argue that the situation is a percolation problem, the paramagnetic phase can still contain clusters of atoms in a relatively ordered state. The alloying of a metallic atom with a different metallic atom is what leads to this percolation problem. In this percolation problem, the interest lies in the

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35 T T. J + RKKY Figure 2 -1: The Doniach phase diagram taken from Ref. [21]. The thick dashed line is the Kondo temperature, TK EFe -1/N(o)J. The thin dashed line is the RKKY temperature, TRKKY ex: [N(O)J]2. The continuous line that equals zero at Jc is the ordering temperature, TN.

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36 paramagnetic phase or when p > Pc, where pis a percolation parameter (related to the density of quenched moments) and Pc is the percolation threshold of the lattice. When p > Pc, then there are only finite clusters of magnetic moments (i.e., magnetic atoms) which are more coupled than the average [21]. Castro Neto and Jones assumed that these clusters do not have strong interactions amongst themselves and that to a first approximation, they can be thought of as isolated and permeated by a paramagnetic matrix. Castro Neto and Jones termed the behavior of a cluster of N atoms in the presence of a paramagnetic environment as the N-impurity-cluster Kondo effect. The N-impurity-cluster Kondo effect involves a cluster: of N magnetic moments close to a quantum critical point ( due to the presence of disorder). If N is large, then the magnetic cluster may be considered as a large magnetic grain. The ground state is either a full ferromagnet or antiferromagnet. The ground state of the cluster has to be at least doubly degenerate due to time-reversal symmetry and the cluster can fluctuate quantum mechanically (i.e., tunnel) between the two degenerate states in the absence of an applied magnetic field [21]. Since the magnetic clusters can tunnel in the presence of a metallic environment, this produces dissipation (due to particle-hole excitations in the conduction band [21]). Castro Neto and Jones show that the sources for tunneling depend upon the symmetry of the system. To summarize, if the magnetic cluster has XYZ symmetry or very low spin isotropy and N c is the threshold limit of spins in a given cluster above which the Kondo effect ceases to occur, then Ne is the maximum number of magnetic moments that can still tunnel due to the anisotropy in the RKKY interaction. If N > Ne, then there is no Kondo effect and the tunneling ceases along with cluster motion due to freezing. The other case involves XXZ or Heisenberg symmetry For this case, the only source of tunneling is the Kondo effect. This Kondo effect is due to the dissipative dynamics of states [21].

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Di~ipation is vital in this case because it allows tunneling to vanish for a finite number of spins given by Ne 37 As mentioned above, tunneling and dissipation are created when a set of magnetic impurities interacts through a conduction band. Castro Neto and Jones also show that three different energy scales are created in the mean-field-like picture: the ordering temperature, the tunneling energy, and the damping energy [21]. Castro Neto and Jones explored how these different energy scales would affect the Kondo lattice. If the previous example of a ligand system having its metallic atom replaced by a smaller atom is used again, then the lattice locally contracts resulting in local matrix elements that have exponentially large values and the local exchange parameter may be much larger than the average exchange in the lattice [21]. The calculations by Castro Neto and Jones reveal that this problem is equivalent to an anisotropic d+ 1 classical Ising model with long-range interactions in the imaginary-time direction, and short-range interactions in the space direction. The solution to this problem involves extending the quantum droplet model of Thill and Huse [147] in the context of insulating magnets. In the paramagnetic phase, the quantum droplets are the magnetic clusters. A distribution of the energy scales ( or cluster Kondo temperatures) is fixed by the percolation theory mentioned above and this distribution arises from a distribution of cluster sizes. The behavior of this statistical problem reveals that as the critical number of spins, Ne is finite, the distribution for the energy levels diverges logarithmically; however, as Ne ---+ oo, there is a crossover in the problem to a power-law distribution for the energy levels. Now that the distribution of the energy scales has b ee n obtained the actual physical properties of these magnetic clusters were calculated by Castro Neto and Jones Castro Neto and Jones con s idered two distinct domains of t emperature for the physical properties : T < T and T > T* where T* is a cro~over temperature. The

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38 crossover temperature values depend upon the source of tunneling. For example, if the source is RKKY interaction, then the critical number of magnetic clusters for which tunneling ceases is very large and the crossover temperature is effectively zero [21]. For the case where the Kondo effect is the source of tunneling, then the crossover temperature is on the order of magnitude of about 0.5 K for a ligand system [21]. The asymptotic behavior of the magnetic susceptibility and specific heat is considered for temperatures less than the crossover temperature. Interestingly, there are no analytic expressions for the magnetic susceptibility and specific heat of a Kondo system [31]. For T T*, tunneling ceases and the tunnel splitting is zero. The spin cluster motion is frozen and dissipation dominates the spin dynamics. This leads to a divergent behavior in the susceptibility at low temperatures [21]: 1 x(T) ex T ln(W /T) (2.2) where W Ep, the Fermi energy. Similarly, the specific heat diverges for extremely low temperatures [21]: -(T) 1 'Y ex T ln2(W /T) (2.3) Unfortunately, the measurement of temperatures below the crossover temperature is physically impossible except for a few rare earth cases [21]. The temperature range above the crossover temperature and below the average RKKY interaction energy gives rise to physical properties that are indicative of quantum Griffiths-McCoy singularities in a paramagnetic phase [57]. For temperatures above the crossover temperature, a power-law behavior is present for the magnetic susceptibility [21]: x(T) ex T-1+\ where A < 1. In the high temperature limit, the susceptibility goes like normal Curie behavior: x(T) ex 1/T. Likewise, power-law behavior is present in the specific heat: Cv(T) ex T -1+\ with A < 1. The lambda values above do not have to be the same, contrary to an earlier

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39 work [20]. Castro Neto and Jones caution that the temperature above the crossover temperature should not exceed the order of the ordering temperature of the pure system because the magnetic clusters will decompose. Castro Neto and Jones also consider physical quantities with the application of an external magnetic field, H, and in the temperature regime above the crossover temperature. The response functions are calculated by knowledge of the dynamical exponent in the Griffiths-McCoy phase. The first physical quantity to be considered is the magnetization and Castro-Neto and Jones observed that the magnetization has a scaling form H (H T) M(H, T) = Tl-A /A T' Wo (2.4) where /A(x,y) is a simple scaling function and w0 is the attempt frequency of the cluster. The focus will be on the case of w0 T, EH (where EH is the magnetic energy of the cluster that is proportional to H); thus, the scaling function above will just be dependent on H/T. If T EH (i.e., the low-field limit), then Castro Neto and Jones calculated the scaling function to be /A(x,0) 1 when x ---+ 0. The magnetization has a linear dependence with the magnetic field at constant temperature or the magnetization diverges at low temperatures like TAl for ..X < 1 at constant magnetic field. If EH T, then the high-field limit has the magnetization scaling like HA and the susceptibility (x = dM/dH) goes like HA-l [21]. The following conclusion may be drawn about the scaling function: h(x, 0) xA-l asx ---+ oo. One important note that will be further explored in the "UCus -xNix Results and Discussion" chapter is that the lambda in the high-field magnetization should equal the lambda determined from the low-field, low-temperature magnetic susceptibility.

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40 Castro Neto and Jones also calculate low-temperature limits in the context of specific heat. Their calculations yield a scaling form >. (H T) Cv(H, T) = T 9>. T' Wo (2.5) where 9>.(x,y) is a scaling function. Just like the magnetization case, the scaling function will only be dependent upon one variable, 9>. (x, 0), since it is as sumed w0 EH, T. For low fields, the specific-heat coefficient, Cv(H, T)/T, diverges at low temperatures like T>.-i The scaling function behavior is then 9>.(x, 0) --+ 1 for x--+ 0. In the case of high fields, the dominant behavior is a little more complicated: -H2+>./2 {-H} Cv(H, T) oc T2->./2 exp T (2.6) The scaling behavior is 9>.(x, 0) --+ e-x x2+>./2 asx --+ oo. The more complicated scaling behavior is from a Schottky anomaly due to the high magnetic field [21]. The scaling behavior for the magnetization and specific heat is summarized in Fig. 2-2 on page 41 (taken from Ref. [21]). In concluding this theory of Griffiths-McCoy singularities in the paramag netic region close to the quantum critical point for magnetic orders of U and Ce intermetallics, Castro Neto and Jones have made predictions for the behavior of the imaginary part of the average frequency dependent susceptibility, the nonlinear magnetic susceptibility, the Knight shift measurement in NMR, and neutron scattering [21]. All the behaviors at low temperatures are based upon the quantum-mechanical response of magnetic clusters. Experiment has shown that these magnetic clusters may be the source of NFL behavior in Ce1 -:rLB.xRhln5 [73] and Ce1-:r ThxRhSb [74]. 2.2 Curie Temperature Enhancement Theory The enhancement (i.e., the unexpected nonmonotonicity) of the Curie tem perature, Tc, was predicted by Silva Neto and Castro Neto [137]. Silva Neto and

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r --------......... ---...... g).(H/T)-1 f}. (H/T)-1 ---------... __________ ' ' ' ' ' ' ' ' ' ' ' g}. (H/T)-(H/T)2+v2e-Hrr \ ... (Hff )-(Hrrt1 \ I H 41 Figure 2 -2: The Griffiths phase diagram taken from Ref. [21]. T-H phase diagram showing the behavior of the scaling functions for magnetization, b(H/T), and specific heat, g~(H/T). The T"' H line is the crossover behavior between the high and low field limits. r is the average RKKY interaction in the system and above r, the magnetic cluster does not exist.

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Castro Neto believe that their study in the realm of quantum ferromagnets is applicable to a wide class of systems: 42 1. heavy-fermion compounds such as URu2-xRexSi2 [35] and Th1-xUxCu2Si2 [87]; 2. dilute magnetic semiconductors such as Ga1 _xMnxAs [111]; 3 ferromagnetic dichalcogenides such as CeTe 2 [69]; 4. manganites such as La 1 -xSrxMnOa [67]; and 5. two-dimensional electron systems in the quantum Hall regime [10]. The Curie temperature enhancement theory starts from the premise that local moments couple directly to an itinerant electron liquid and this premise can be expressed mathematically by the Hamiltonian [137] H = -JLSi. sj + JK L Si. ct,O' du, u1Ci,u' + He (2.7) (ij) i u ,u' where J is a Heisenberg exchange between localized spins Si (total spin S), JK is an exchange coupling between localized spins and conduction electrons, cl,u ( Ci,u) is the creation (annihilation) electron operator 7t are the Pauli matrices, and He describes the conduction electrons. Silva Neto and Castro Neto find for the case of a metallic system described by the Hamiltonian in Eq. 2. 7 that dissipation ( due to disorder) results from electrons scattering off localized moments and acting as a heat bath for the spin dynamics. The two main sources of dissipation are Landau damping in the case of clean magnets and electronic diffusion in the case of structurally disordered magnets [49, 44]. The effects of dissipation upon Tc will be discussed. To begin their study of the dissipativ e problem Silva N eto and Castro Neto considered an action of the form [124] So(n) = 1/3 dr J ddx { M0A(n) 8rn + 1 (Vn)2 } (2.8)

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43 where f3 = l/T, n is a N-component vector that represents the local magnetization, p~ is the spin-stiffness, and M0 is the magnetization density in the ground state. The reason for showing this action is that the first term of the expansion inside the integral is a topological term (the kinematical Berry phase [123, 59]) described by the vector potential A of a Dirac monopole at the origin of spin space. This term signals the presence of localized moments [137]. This term is the main difference between the action of Silva Neto and Castro Neto and the action used by Hertz in his famous study of itinerant quantum critical phenomena [60]. Hertz did not include such a topological term. The topological term, along with dissipation, plays a vital role in the behavior of the Curie temperature [137]. Silva Neto and Castro Neto determined the effects of dissipation upon the Curie temperature. The phase diagram of the dissipative problem is determined by applying the momentum shell renormalization group and large-N analysis to the partition function of the system [137]. The dissipation depends upon the conduction electron dynamics as mentioned previously: Landau damping for a clean system and electronic diffusion for a dirty system. Silva Neto and Castro Neto show that if the Curie temperature is a function of dissipation, then the Curie temperature decreases faster for Landau damping than for electronic diffusion. The physical interpretation is that the ballistic electrons (from Landau damping) have an infinite mean free path and strongly scatter from the localized magnetic moments in the "cleaner" system. This strong scattering leads to a large amount of thermal and quantum fluctuations in the system. In the other case, the diffusive electrons (from electronic diffusion) have a finite mean free path and do not increase the thermal and quantum fluctuations as much. Interestingly, Silva Neto and Castro Neto predict about a 1 % increase for the Curie temperature of a dirty system with a small amount of dissipation compared to the Curie temperature of a dirty system without dissipation (i.e., no disorder). No increase is expected for the

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44 Curie temperature of a clean system with a small amount of dissipation compared to a clean system without any dissipation. The increase of the magnetism due to diffusion appears to be important in the 2D MOSFET problem also [24]. One final note concerning the Curie temperature enhancement involves the importance of the topological term in the competition between the dissipative and topological terms. If a diffusive system has no topological term, then Tc is rapidly suppressed and a slight increase in Tc is not predicted. To summarize the behavior of the Curie temperature between the ballistic/diffusive electrons and the existent/non-existent topological term, a figure taken from Silva Neto and Castro Neto is provided on page 45 [137]. Resistivity measurements should provide insight into whether or not a system is in the ballistic or diffusive case. Silva Neto and Castro Neto state that ballistic electrons have an infinite mean free path while diffusive electrons have a finite mean free path. Thus, tb > td where t(b,d} represent the (ballistic, diffusive) electrons respectively. Since the resistivity, p, is inversely proportional to the mean free path [7], then one would expect the resistivity for a diffusive system to be larger than the resistivity for a ballistic system. Thus, not only will magnetic susceptibility measurements be performed on UCu 2 Si 2 _xGex compounds, but also resistivity measurements. In summary, disorder along with the competition between the RKKY in teraction and the Kondo effect may lead to NFL behavior in UCus-xNix due to magnetic clusters. On the other hand, disorder may lead to electronic diffusion in ferromagnetic UCu2Si2 -xGex and possible Curie temperature enhancement.

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1.os...--....--.-------------------.--..................... ---.---.---. s 0 95 _, 0 9 ._..., 0 .85 s-S/ 2 -S 3 / 2 ... s-11 2 4 =l toO.l O.SO OJ 0.2 0.3 0.4 O.S 0 6 0 7 0.8 0.9 1 'lo 45 Figure 2 -3: Curie temperature predictions by Silva Neto and Castro Neto. The Curie temperature Tc(11o)/Tc(11o = 0) as a function of dissipation, 77o. Sis the to tal spin. If 6 = 1, then the dissipation is in the ballistic ( clean) regime while 6 = 2 gives the diffusive (dirty) regime. The bare topological constant is represented by c0 and as Co ---.. 0, then the topological term disappears.

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CHAPTER 3 EXPERIMENTAL TECHNIQUES All alloys in this dissertation were created by an arc-melting technique. In or der to accurately categorize a system or compound, several experimental techniques must be employed. The first experimental technique is x-ray diffraction which confirms whether or not the compound formed into the correct crystal structure. The x-ray pattern is also used to determine the lattice parameter values of the fundamental "building block" of the compound, the unit cell. After confirmation of the correct crystal structure, many techniques are used to determine the correct thermodynamic and transport properties of the particular sample. These tech niques (in no particular order) include direct current (de) magnetic susceptibility, alternating current (ac) magnetic susceptibility, de resistivity, and heat capacity measurements. All techniques and measurements previously mentioned will be described in further detail below. 3.1 Arc-Melting The UCus-xNiz and UCu2Si2_xGex systems had their own unique preparation procedures. The general idea behind the arc-melting process will be discussed first, followed by the preparation of the UCus-xNiz system and UCu2Si2-xGez, The arc-melting process is based upon a large amount of current (with low voltage) passing through a tungsten electrode and producing an electric arc in Ar gas that runs from the tungsten tip down to a water cooled copper hearth inside a vacuum-tight chamber. Arc-melting is ideal for melting constituent elements with high melting points together. This de apparatus melts the elements together in a zirconium gettered argon atmosphere. The arc strikes the zirconium first because zirconium has a high absorption rate for certain residual gas components like 46

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47 oxygen. The argon atmosphere is used because argon is an inert gas and the argon helps raise the pressure inside the vacuum chamber so that the electric arc may be struck. Whenever melting elements together with significantly different melting points, the general principle is to melt the element with the lower melting point first and then draw the higher melting point elements into the molten element. In this respect, the mass loss of the lower melting point element is minimized This arc-melting process is very similar to tungsten inert gas (TIG) welding. The arc-melting of the UCus-xNix involves the melting of three constituent elements The uranium and nickel have similar melting points and vapor pressures. The copper has the lowest melting point and the highest vapor pressure. Thus, excess copper("' 0 .5% of the total Cu mass) was added to each UCus-xNix sample to account for the copper loss. Each UCus -xNix sample was arc-melted three to four times. After each melt, the sample bead was flipped over to insure homogeneity. The effort involved in the arc-melting of the UCu 2Si2 xGex compounds was a bit more intensive. The dilemma in arc-melting the UCu 2 Si 2 xGe x compounds came from the explosive nature of melting two semiconductors together, Si and Ge, along with the electric arc thermally shocking the formed UCu2Si2-xGex lattice. Two techniques were employed to solve these problems. First, the U, Si, and Ge constituent elements were melted together first and then subsequently melted together a minimum of at least six times. Second the copper element was then melted into the U, Si, and Ge bead. All elements were melted together a minimum of s ix times to insure homogeneity. The second technique was employed on all arc-melts after the initial one. Instead of moving the electric arc directly from the zirconium bead to the UCu 2Si2 xGe x bead (this tended to blow apart the UCu2Si2-xGe x bead), the electric arc was moved very slowly towards the UCu2Si2xGex bead. Thus, the arc s convection and radiant heat would melt the

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48 UCu 2Si2 _xGex bead and, before the arc was directly over the UCu2Si2-xGex bead, the bead would be molten. These techniques were used in the production of all UCu2Si2-xGex compounds. Excess mass amounts of Cu, Si, and Ge were added before arc-melting. U has a very high melting point and low vapor pressure, so the mass loss of U was assumed to be negligible. Cu and Ge had almost identical melting points and vapor pressures, so the mass loss of Cu and Ge was assumed to be equal. The melting point of Si is about 50% higher than the melting points of Cu and Ge; thus, it was assumed that the mass loss of Si would be about half the mass loss of Cu or Ge. The assumptions above were taken into account so that the appropriate extra masses could be added before arc-melting. Since a minimum of 12 arc-melts (as discussed previously) were performed on each UCu 2Si2 -xGex sample, all melts would "blow away" approximately 1.5% of the total Ge mass present, 0.50% of the total Cu mass, and about 5% of the total Si mass for compounds on the Ge rich side. Arc-melting compounds on the Si rich side would result in a loss of about 2% of the total Si mass, 5% of the total Ge mass, and 1 % of the total Cu mass. Thus, depending on which UCu2Si 2 -xGex compound was being synthesized, excess Cu, Ge, and Si was added according to the above conditions. One final technique that is related to sample preparation and arc-melting is the process of annealing. The purpose of annealing is to eliminate as much disorder as possible. All UCus-xNix and UCu2Si2-xGex compounds were annealed. Annealing involves pieces of sample being wrapped in tantalum foil and the wrapped sample is sealed in a quartz tube under vacuum. The samples are placed in ovens for an experimentally determined time such that the mass loss remains acceptably small ( < 0.5% of the total mass) while the order of the crystal lattice is improved. The order in the lattice may be checked by x-ray diffraction.

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49 3.2 X-Ray Piffraction/Lattice Parameter Determination from X-Ray Diffraction Lattice parameter values can play an important part in determining the site occupation of atoms in a crystal structure along with the lattice values telling the story of whether or not the lattice expands or contracts upon the doping of a certain element. For example, the UCus-xPdx system, which crystallizes in the face-centered cubic (fee) AuBe5 structure, shows that Pd substitution initially goes onto the larger Be I site until about x = 0.8 and for x > 0.8, the Pd atoms also start to occupy the smaller Be II sites also. This was seen not only in muon spin rotation (SR) [92] and extended x-ray-absorption fine-structure (EXAFS) [15] measurements, but also by a change in slope of the lattice parameter values at X 0.8 [77]. The present study is similar to those on the UCus-xPdx system. Instead of doping larger (relative to the Cu atom) Pd atoms on the Cu sites, smaller Ni atoms will be doped on the Cu sites. The knowledge of the lattice parameter values at different Ni concentrations is imperative to gain insight on which copper site the Ni atoms are found (i.e., the Be I or Be II site). Lattice parameters are calculated from x-ray diffraction patterns. X-ray diffraction was run on a Phillips XRD 3720 machine at the Major Analytical In strumentation Center (MAIC) on the University of Florida campus. The complete x-ray diffraction process is described elsewhere [119]. The particular machine on which the x-rays were generated used two different wavelengths of radiation [copper Ka1 = 1.54056 Angstrom (A) and copper Ka2 = 1.54439 Angstrom (A)]. Also, the intensity of the a1 beam was twice as great as the a2 beam. This made resolving two distinct peaks at a particular crystallographic plane sometimes quite difficult since the a1 peak would conceal the a2 peak.

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50 The typical x-ray pattern was generated with a 2(} (degrees) domain from 20 to 120 in 0.02 steps where 2(} is the total angle by which the incident X radiation beam is deflected by a lattice plane. Almost all measurements had a one second step time where the detector on the x-ray machine moved continuously through a 0.02 interval in one second. The reason for such a long total scan time ("' 90 minutes) was to obtain good resolution around the high angle x-ray peaks (> 80). The Phillips XRD 3720 machine operation was controlled with a computer interface. Once the x-ray process was complete, the computer would generate a list of peaks from the x-ray pattern. The computer found the peaks at a respective 2(} value by finding the minimum of the 2nd derivative of the peak (i.e where the change in the slope on the x-ray pattern is least) Once the peaks along with their particular 2(} values are found via the com puter, lattice parameter determination may begin in earnest. The easiest way to explain the lattice parameter calculation [107] is by using an example The UCu5-xNix system will be the example. Since the UCu5-xNix system forms in the cubic AuBe 5 crystal structure, this system has very high symmetry and the perpendicular distance between two parallel lattice planes, d, may be written in terms of the Miller indices (hkl) of the plane [119]: d{hkl) = a Jh2 + k2 + 12 (3.1) where lattice parameter value, a is the side of the cubic crystal one is calculating and the Miller indices are defined as the coordinates of the shortest reciprocal lattice vector normal to a lattice plane, with respect to a specified set of primitive reciprocal lattice vectors (e.g., a plane with Miller indices h,k l is normal to the reciprocal lattice vector hb1 + kb2 + lb3 ) [7].

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The inter-plane distance, d, is related to half the total angle by which the incident X-radiation beam is deflected, 0 by the well known Bragg condition [7]: 51 n.X = 2dsin0 (3.2) where n is a positive integer and .X is the wavelength of the incident radiation beam. If one combines Eq. 3.1 and Eq. 3.2 and assumes that n = 1, then 'a' may be written in terms of .X, 0 and (hkl): .XJh2 + k2 + 12 a=------2sin0 (3.3) The values obtained from Eq. 3.3 will be the ordinate values for the graphical extrapolation method. The reason 'a' cannot be obtained directly from Eq. 3.3 is that Eq. 3.3 would require 0 to equal 90 and 20 would be 180, which is physically impossible for the XRD machine. If 20 were 180, this would mean that the source and detector of the XRD machine were located at the same position. The detector and source at the same position on the XRD machine is not possible. The maximum achievable 20 angle by the XRD machine is 140. This justifies why an extrapolation method is needed to obtain 'a'. The abscissa values used in the graphical extrapolation method take into account some possible sources of error. The function to be used for the x-axis values is advocated by Nelson and Riley [107]: (cos20/0 + cos 20/sin0). This functional form takes into account possible errors caused by absorption and divergence of the x-ray beam. Before the 'a' values can be graphed against the functional x-axis form it has to be determined what (hkl) values correspond with peaks in the x-ray pattern. Thus, a particular 0 value may be linked with a set of (hkl) values. Since it is known that UCu5-xNix crystallizes in the AuBe5 structure [153], a theoretical crystal pattern can be calculated with known information [33, 155] such as a lattice

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52 parameter constant (in this case, used the known UCu5 value: 7.043 A [155]), space group number (216 for UCu5 structure), and atomic positions in the unit cell. This information was used by the PowderCell computer program to provide a theoretical pattern which included peaks with known (hkl) values. A visual inspection between the theoretical patterns and the experimental patterns of the UCus-xNix system could link peaks with particular (hkl) values as shown in Fig. A-1 on page 167 for UCu4Ni annealed 14 days at 750C. A list was generated with (hkl) values and corresponding 20 values. Once the (hkl) values and corresponding 20 values are obtained, the 'a' values and x-axis values may be obtained from Eq. 3.3 and the Nelson-Riley error function respectively. A graph plotting the 'a' values versus the corresponding error function values for annealed UCu4Ni is shown in Fig. A 2 on page 168. The values when plotted should show that the extrapolation line has a negative slope. The reason behind this negative slope is because all the sources of error lead to high values of 0 and so to low values of the lattice parameters [119). It should be stressed here that it is very important to have as many (hkl) values with 20 values greater than 80 as possible. The importance comes from the fact that 0 values close to 90 give Nelson-Riley functional values close to zero, insuring that the extent of extrapolation is not large [119). The graphical extrapo lation method is an excellent technique for determining lattice parameter values on a highly symmetric system such as UCus-xNix. The error in the lattice parameter values as will be seen later for the unannealed and short term annealed UCus -xNix compounds is on the order of 10-3 A. This error may be improved upon by running a cubic Silicon standard along with the respective experimenta l compound or by running the Silicon standard alone to determine the offset in the XRD machine. The latter process was done for this

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dissertation. The determination of lattice parameter values has been facilitated greatly by the advent of computers with software such as Jade. 3.3 Magnetic Susceptibility 53 Magnetic susceptibility measurements were used to measure the low tem perature magnetization of the UCu5_xNix and UCu2Si2_xGe x samples. The susceptibility measurements were taken with two superconducting quantum in terference devices (SQUIDs): an MPMS-5S [can measure with a magnetic field from Oto 5 Tesla(T)] and an MPMS XL (measures up to 7 T) machine both made by Quantum Design. Both machines could take magnetization measurements in the temperature range from 2 K to 300 K. The MPMS XL machine only had the capability to measure de magnetic susceptibility while the MPMS-5S machine could measure both ac and de magnetic susceptibility. Alternating current and de magnetic susceptibility measurements will be discussed below. 3.3.1 DC Magnetic Susceptibility Direct current magnetic susceptibilities are usually made in 1 kiloGauss (kG) magnetic fields. If the signal of the sample is c omparable to the signal of the addenda (i.e. the plastic straw that holds the sample) then a 1 T magnetic field may be used so that the sample s signal is dominant over all other signals. Direct curr ent magnetic susceptibility measurements are based upon the principl es of Lenz s Law. The sample is magnetized by a 1 kG magn etic fie ld and the magnetic moment as a function of temperature of the sample is measured [94]. The magn etic susceptibility is determined by the following ratio: x = M/H. The magn etic mom ent is measur e d by induction t ec hniques. The indu ctive m easure ments are done by moving the sample relative to a set of superconducting pickup coils and the SQUID instruments measure the curr ent induced in superconducting pickup coil s The sampl e is t y pi c ally moved 4 cm through the sup e rconductin g

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54 pickup coils while 48 data points are taken during the sample's movement to pro duce the magnetization curves. The sample is moved through the coils four times and the average of the four measurements is reported for a particular temperature. Not only is the de magnetization measured at various temperatures in a constant magnetic field, but also the de magnetization is measured in different magnetic fields at a constant temperature. The magnetization versus field curves are typically generated at the lowest possible temperature (2 K). The MPMS XL is a particularly good machine for this type of measurement since it has a secondary impedance line that can maintain low temperatures continuously over an extended period of time (on the order of about 12 hours). 3.3.2 AC Magnetic Susceptibility Unlike de magnetic susceptibility measurements where the sample moment is constant during measurement time, ac magnetic susceptibility measurements for the MPMS-5S machine use a small ac drive magnetic field that is superimposed on the de magnetic field, causing a time-dependent moment in the sample. Alter nating current measurements do not require sample motion ( as for the de case) since the field of the time-dependent moment induces a current in the supercon ducting pickup coils. The measurements are usually made in a narrow frequency band, the fundamental frequency of the ac drive magnetic field. The ac suscepti bility measurements in this dissertation were made at three different frequencies: 9.5 Hertz (Hz), 95 Hz, and 950 Hz. These three frequencies stayed within the frequency range of the MPMS-5S machine and avoided any integer multiples of the frequency of a common electrical outlet (60 Hz). Alternating current magnetic susceptibility measurements yield two quantities: the magnitude of the susceptibility, X, and the phase shift (relative to the ac drive magnetic field) This phase shift comes from the fact that the magnetiza tion of the sample may lag behind the ac drive magnetic field [94]. In terms of

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55 complex notation, the ac susceptibility measurements provide an in-phase, or real, component x' and an out-of-phase, or imaginary, component x". The ac magnetic susceptibility measurements on certain UCus-xNix samples were used to determine the antiferromagnetic phase transition temperature, TNeel, for each compound. A peak in the real component of the ac magnetic susceptibility indicated the antiferromagnetic phase transition 3.4 Cryogenics The remaining two experimental techniques de resistivity and heat capacity are primarily measured in a temperature range from 300 milliKelvin (mK) to about 10 K. In order to achieve such low temperatures, one must make use of liquid nitrogen and liquid helium The probe that is used to measure either low temperature resistivity or specific heat is first cooled down to the boiling point of liquid nitrogen("-' 77.4 K [54]). The probe is then quickly lifted out of the liquid nitrogen and placed in a Dewar, a vacuum insulated flask. The Dewar is then filled with liquid helium, which boils at 4 2 K. After a couple of hours, the inside of the probe is cooled down to 4.2 K. Helium 4 can be cooled to below its boiling temperature by reducing the pressure inside the Dewar to below atmospheric pressure. In fact using the combination of a large vacuum pump and blower, a pumped bath of liquid helium 4 can cool a probe down to about 1.1 K. If liquid helium 4 is cooled below its transition temperature or "lambda point" ( "-' 2.17 K [54]), then the helium 4 starts to become a superfluid helium 4 that behaves as if it had no viscosity, i.e. it can flow through tiny holes. Also t~e superfluid helium 4 has no entropy and it flows into a heated area to cool that area and restore the uniform mixture of normal and superfluid helium 4. This last physical property of superfluid helium 4 allows the temperature of the probe to be stable enough such that resistivity or specific heat may be measured. A full dewar of helium 4 in the lab that has a vacuum

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56 pump/blower attached to it can maintain a low temperature of 1.1 K for about 12 to 16 hours In order to achieve a temperature lower than about 1.1 K, helium 3 needs to be used. Helium 3 boils at 3.2 K [at 1 atmospheric pressure (atm)] [54]. Helium 3 is inserted as a gas into the probe and due to its rarity, helium 3 is trapped inside the probe so that it may be reused. Once the probe is cooled down to 1.1 K with the superfluid helium 4, the helium 3 gas is condensed by coming into contact with the 1.1 K probe and the helium 3 collects in the helium 3 pot. The low temperatures down around 300 mK are achieved by reducing the vapor pressure of the collected liquid helium 3 by using the internal sorption pump (i.e. charcoal on the end of a long rod) [66]. The sorption pump is "turned on" by lowering the charcoal into the vicinity of the helium 3 pot. This cools down the "warmed" charcoal to below 20 K since the charcoal was initially at the top of the probe The helium 3 liquid is pumped on by the sorption pump while the sample ( connected to the helium 3 pot via a weak thermal link) is cooled down to around 300 mK. The probe can stay down at such a low temperature for about three to four hours until all the liquid helium 3 evaporates. The sorption pump is then turned off by raising the charcoal in the probe so that it is above 20 K (i. e., above the 4He level in the dewar) which desorbs the helium 3 gas and allows the helium 3 gas condensation cycle to start over again. 3 5 Probes In the above discussion concerning cryogenics the generic term probe has been used. In reality two kinds of probes were used in the lab One probe had a helium 4 pot which did not require the entire Dewar to be vacuum pumped upon. The second type of probe had no helium pot and pumping upon the Dewar was imperative to achieve a temperature around 1.1 K.

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57 A probe with a helium 4 pot has its cross section inside the vacuum can shown in Fig. 3 1 on page 58 [71]. The vacuum can is mounted on the flange's probe with a brass taper joint seal that is lightly coated with silicone high vacuum grease, preventing the superfluid helium 4 to penetrate. The sample platform at the bottom is connected to a copper block and a thermally conducting grease is used so that the temperature gradient between the copper block and sample platform is minimal. The other side of the copper block is connected to a helium 3 pot with a brass thermal link and large diameter Cu wires ( not shown in Fig. 3 -1) run from the copper block to the helium 3 pot for improved thermal conductivity These connections allow the sample platform to reach low temperatures of 300 mK once the sorption pump is turned on by lowering the charcoal inside the pumping line for the helium 3 pot in Fig. 3 -1. Once the helium 3 cryostat in Fig. 3-1 on page 58 is placed in a Dewar and allowed to reach normal liquid helium temperature ( rv 4.2 K), the helium 4 pot may be pumped upon, which allows the helium 3 gas to condense. As the probe is cooling down inside the Dewar, a line connecting the helium 4 pot and the helium 4 bath inside the Dewar is open so that the helium 4 pot may be filled with liquid helium 4. Once the probe cools down to around 4.2 K, the temperature is lowered further by closing the capillary linking the helium 4 pot and the helium 4 bath with a needle valve and then connecting an external vacuum pump to the pumping line connected to the helium 4 pot. Thus, the liquid helium 4 inside the helium 4 pot is just pumped on instead of the entire helium 4 bath inside the Dewar The germanium thermometer close to the sample platform in Fig. 3 1 registers a low temperature of about 1.6 K after the helium 4 pot has been pumped on for rv 20-30 minutes. The other important aspect to the helium 3 probe concerns the wiring for the electronics to measure DC resistivity and specific heat The wires come from the

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58 Pum pin g Lin for 3He Pot Pumping Lin for 4He Pot "' P ing Line for Vacuum Can ump ---e \ -------------I_J Brass Th ermal Link I:: Germanium Thermomete r J Sam ple Platform I r ... ,n I /1 .~, and Tube for Wires Needl e Valve Cop per Heat Sink Capillary Connecting 4 He Pot and 4 He Bath Heat Sinking Pins Copper Block and 4HeP ot 3HePo t Block Heater Heat Sinking Pi ns Heat Sinking Co pper Block Figure 3 -1: Cross-section of a helium 3 probe This simplified cross-section con tains a helium 4 pot. Such a probe is abl e to achieve a low temperature around 300 mK.

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59 top of the probe and run down the pumping line for the vacuum can in Fig 3 -1. The wires from the top of the probe are soldered to the copper block above the helium 4 pot. The copper block is in temperature equilibrium with the Dewar s helium 4 bath by the copper heat sink in Fig. 3 -1. The wires on the top copper block in Fig 3 1 are then usually connected to the copper block right above the sample platform by more wires wrapped around the helium 3 and helium 4 pots and secured to these pots with General Electric (GE) varnish 7031 (a good thermal conductor). The reason for the wires not running from the top of the probe directly to the copper block above the sample platform concerns the amount of heat that would be transferred from the top of the probe which is at room temperature. The intermediate copper block connections allow the heat flow to be minimized The actual wires that are used in the helium 3 probe are either #40 gauge copper or #40 gauge manganin wires. Either type of wire is insulated and requires friction (from sandpaper or an eraser) to remove the insulation. The difference between copper and manganin wires is that manganin wire is about 30 times mor e e lectrically resistive than copper wire [71]. The higher electrical resistivity of the manganin wires is associated with less heat being transferred from the top of the probe Thus manganin wires should be used for low current loads while copp e r wires are used for high current loads The wiring in the probe is compos e d of pairs of the same type of wiring twisted around e ach other so that the e l e ctrical nois e is reduced The probe without the helium 4 pot has the e xact same configuration as in Fig 3 1 except for the h e lium 4 pot and the pumping lin e for the liquid h e lium 4 The Dewar itself may be thought of as the helium 4 pot for the case of the probe without the helium 4 pot.

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60 3.6 DC Resistivity Direct current electrical resistivity is based upon an equation derived from the Drude model for electrical conduction [7]: AR p=-1 (3.4) where pis the electrical resistivity that is being solved for, A is the cross sectional area of the resistivity bar being measured, and Lis the distance between the voltage wires. The electrical resistivity was measured using a standard four wire technique that is discussed below. The first part of the four wire technique involves making resistivity bars. The standard way of making resistivity bars involved cutting the particular sample with a diamond saw. The diamond saw could cut resistivity bars with rectangular cross sectional areas that had dimensions on the order of thirty thousandths of an inch. Another way to produce resistivity bars that avoids possible microcracks in the bars is the "sucker" method. The sucker method is done while arc-melting The idea behind the sucker method is that while the arc has a sample in its molten state, a pressure difference between the arc-melter chamber and an external chamber on the sucker apparatus has enough force to push down the molten sample into a square cross sectional copper area. The copper area is water cooled, so the molten sample should quench as a square resistivity bar ideally. A sucker produced resistivity bar on a UCu4Ni sample will be discussed later on in this dissertation. Once the resistivity bars are made, four platinum wires need to be attached to each bar. The platinum wires have a diameter of 0.002 inches and a purity of 99.95%. There are two methods to attach these platinum wires to a resistivity bar. One method is to use EPO-TEK H31LV silver epoxy to "g lue the platinum wires onto the resistivity bar. The only problem with this method is that extra resistance is added to the measurement with the resistance of the silv e r epoxy

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and possible oxide barriers on the surface of the sample. The second method of attachment was used in this dissertation. It involved spot welding the four wires onto the resistivity bar. Spot welding minimized the contact resistance. The four wires should be spot welded on the same face of the resistivit y bar with two wires on one end of the bar and the other two wires on the opposite end. The two outside platinum wires are the current leads while the two inside platinum wires are the voltage leads. The resistivity bar is then attached to a piece of non e lectrically conducting comp e nsated silicon with GE varnish 7031. The varnish 61 is a good thermal conductor and a poor electrical conductor. The four platinum wires are attached to the silicon base with silver epoxy and there is some slack in the platinum wire between the resistivity bar and silver epoxy to account for the contraction at low temperatures. The silicon base is attached to a low temperature probe with a thermally conducting grease such as Apiezon N grease. The low t empe rature resistivit y measur e ments gather the resistance of the sample at a particular temperature. The resis t anc e in Eq. 3.4 is then used to calculat e the resistivity. One can see from Eq. 3.4 that in order for larg e r resistance measurements (hence larger voltage measurements from Ohm's Law) one should maximize the distance between the voltage leads, L and minimize the cross sectional area of the resistivity bar, A. This helps reduce the scatter in the r e sistan ce m e asur e ments ( another apparatu s that would h e lp r e duc e the s catte r i s an ac resistance bridge) The resistanc e measur e ments are automated. An HP 9000 /300 series comput e r control s the current sour ces and voltmet e r s taking the measur e ments. The scatte r in the resistivity measurements is reduced two ways. One way is to measure the resistivity in one c urrent direction and then reverse the current to measure the res istivit y in the opposit e dir ec tion. The av erage of these two absolut e valu es s hould e limin a t e a ny ( e g the rmo e l e ctri c ) offse t in the voltm e t e r t aki n g m easure m e n ts

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62 A second procedure should eliminate the effect of any drift in the voltmeter. The computer is programmed with an external and internal loop while taking resistance measurements. The internal loop reverses the polarity of the current as described above while the external loop dictates how may times the internal loop should be performed. The external loop averages the measurements taken by the internal loop. Most resistivity measurements in this dissertation had an external loop value of 10 and an internal loop value of 5. 3 7 Specific Heat Specific heat is the quantity of heat needed to raise a unit mass of sample by a unit degree of temperature while keeping the property x (in this dissertation, pressure, p) constant during the rise of temperature: (3.5) Before 1968, the above definition was used in a technique called the adiabatic method [141] to measure specific heat. The adiabatic method added a pulse of power ( dQ) to a sample and the temperature rise ( dT) in the sample was noted. A couple of drawbacks to the adiabatic method are the large sample size needed to minimize the effects of stray heat leaks and the thermal isolation of the sample from its surroundings [71]. In 1968, Sullivan and Seidel published their ac heat capacity technique [144]. The ac method measures small samples that makes use of a commercially available lock-in amplifier. The strength of this technique is its ability to detect very small changes in heat capacity [141]. However, a drawback to this ac temperature calorimetry is in measuring the absolute value of the specific heat of a sample. This ac method usually provides only a relative measurement of the specific heat [71]. The specific heat technique used in this dissertation is the thermal relaxation method [9]. The thermal relaxation method was constructed from the solution of a

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63 one-dimensional heat-flow equation with appropriate boundary conditions [9]: (3.6) where P is the power put into the sample, A is the cross sectional area of the wire linking the sample platform to the copper block K, is the linking wire's thermal conductivity and the heat flows along the z-axis The solution for C in Eq. 3.6 is C = KT1 where r1 is the time constant of T = T0 + ~Te-tin (3.7) with T = T -TO and TO is the copper block temperature. The answer above is interpreted by Fig 3 2 on page 64. In Fig. 3 -2, the sample along with all the addenda on the sapphire (Al203 ) platform is heated a small ~T above the copper block temperature T0 by means of power, P, flowing through the platform heater. Once the power is turned off on the heater, the temperature of the sample and platform decay exponentially as in Eq. 3. 7 with time constant r1 through the linking wires. The time constant, r1 is determined using computer analysis of the temperature decay. By knowing the thermal conductance K of the linking wires one may determine the total heat capacity of the sample and platform. If the addenda are known as in Fig. 3 2 then on e may determine the heat capacity of the sample by subtracting the addenda from the total heat capacity. All components of the addenda will be discussed in detail later on. It should be said that the rise in temperatur e, ~T, should be small enough so that r1 does not change appreciably betw ee n To and T0 + ~T [141]. Whe n performing low temperature specific heat measurements T was usually around 4 %. The absolut e accuracy of the thermal relaxation method to measure specific heat is e stimated to be 5 % [71], which is verified by measuring the known specifi c h eat of a high purity standard e .g., Pt or Au.

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p To+ ~T CTotal = Csample + C Addenda p K, -~T To 64 Sample Sapphire Ge Chip Thermometer Silver Epoxy -1/3 of Au-Cu Wires Thermal Grease Four Au-Cu Wires Copfer Ring Hea Reservoir Figure 3 -2: Schematic diagram outlining the thermal relaxation method. The ther mal relaxation method is used for the specific heat measurements. The addenda is composed of the sapphire, the germanium chip thermometer, EPO-TEK H31LV sil v er epoxy 1/3 of the linking wires, and thermal grease. The linking wires are the four Au-Cu wires connecting the samp l e platform to the copper block.

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(a.) (b.) Au-Cu Wires Copper Ring Evaporated 65 copper block post Solder for Au (solid circle) (44% In, 42% Sn, 14% Cd) 7% i-93% Cr Heater H31LV silver epoxy Ge Chip Thermometer 3/8 in sapphire Figure 3 -3: An overhead and bottom view of the mounted sample platform. (a.) The thermal epoxy used was a two component Stycast 1266 epoxy. The copper block post connects the copper ring to the copper block as shown in Figure 3 -1. The Au-Cu wires connecting the sample platform to the copper ring are Au with 7% Cu to provide the correct magnitude for the thermal link. (b.) The evaporated 7% Ti and 93% Cr heater is a thin continuous film on the bottom of the sapphire disk. The Ge chip thermometer is linked to the silver epoxy with Au-Cu wires.

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In Fig. 3 -3, two views of the sample platform are shown. The Au-Cu wires that were used in this dissertation were Au-7% Cu wires. These wires steady the platform on the sapphire and serve as electrical contacts and thermal links to 66 the copper ring (hence the copper block). The thermal conductance of the wires depends on several factors. The first factor has been mentioned indirectly, the composition of elements making up the wires. For example, Au-1 % Cu wires have a thermal conductance seven times that of Au-7% Cu, while Cu-2% Be has a thermal conductance five times less than Au-7% Cu. The second factor that varies the thermal conductance in the wires is the diameter of the wire. The specific heat measurements in this dissertation used 0.003 inch (in.) diameter Au-7% Cu wires. The thermal conductance of the 0.003 in. diameter wires is nine times that of the 0.001 in. diameter wires [141]. The reasoning behind choosing the 0.003 in. diameter wires is that 0.001 in. diameter wires are a little too fragile while inserting or removing the sample onto or off of the sample platform. The Au-7% Cu wires are attached to the copper ring in part (a.) of Fig. 3 3 with special solder ( 44% In, 42% Sn, 14% Cd) on a silver pad. The silver pad is electrically insulated from the copper ring with a thermal epoxy (in this case, Stycast 1266 epoxy); however, the thermal epoxy is a good thermal conductor. The reason for using the specia l solder is that regular solder (composed of Pb and Sn) will dissolve the Au-Cu wires. The sample itself is mounted on the "rough" side of a smaller sapphire disk. The flat part of a sample (for improved thermal conductivity) is attached to the sapphire disk with GE 7031 varnish. Then, the smooth" side of the sapphire with the sample is mounted on the 3/8 in. sapphire disk in part (a.) of Fig. 3 3 with thermally conductive grease (in this case, Wakefield grease) [9]. Both sapphire disks are pressed firmly together to allow for a continuous and even distribution of thermally conductive grease between the disks. Before each measurement, both

PAGE 79

sapphire disks have to have the grease cleaned off of them with trichloroethane. The mass of all components (sample, GE 7031, sapphire, and grease) has to be known for accurate specific heat values. The platform heater in part (b.) of Fig. 3-3 is composed of a thin film 67 of 7% Ti and 93% Cr on the "roug h side" of the 3/8 in. sapphire disk. This platform heater is created by evaporating a Ti0 07Cr0 .93 sample onto the sapphire disk with evaporator instrumentation. The resistance of this platform heater is around 300 Ohms (fl) [71] and the resistance remains fairly constant with varying temperatures. The doped germanium chip thermometer ( commercially obtained from Cryocal or Lakeshore Cryotronics) in part (b.) of Fig. 3-3 is used for the sample platform thermometer. The reason for using doped germanium was that its resistance is a rapid function of temperature [141]. This sensitivity is vital for the thermal relaxation method since the increase in the platform temperature at each data point is not very large("-' 4%). The calibration of the germanium chip thermometer's resistance versus temperature will be discussed later on. The key to an accurate measurement of a sample's specific heat is the proper subtraction of all components (i.e., the addenda) involved in the thermal re laxation method. As mentioned previously, some of the addenda are listed in Fig. 3 2 on page 64. The sapphire disks that serve as the sample platform have high thermal conductivity (about 1 Watt cm -1 K-1 at T = 4 K) and low spe cific heat (2 J gram-1 K-1 at T = 2 Kand 00 1035 K) [48]. The platform heater in part (b ) of Fig. 3 3 that is composed of Cro.o7Tio.93, which has a mass < 0.01 mg, is assumed to have a negligible contribution to the specific heat of the addenda [71]. The other component on the bottom of the sample platform next to the platform heater is the germanium resistance thermometer that has a specific heat value of 0.018 J/K at 2 K with a mass of 3.8 mg [71]. The leads

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68 attached by the factory to the germanium resistance thermometer are connected to the Au-7% Cu wires by means of H31LV silver epoxy. The silver epoxy is a source of addenda contribution. For example, a mass of 0.63 mg of silver epoxy has a specific heat value of 0.12 J/K at T = 2 K [71). The GE7031 varnish and Wake field grease also add to the addenda. At T = 2 K, the Wakefield grease has a heat capacity of 0.16 J/K for a mass of 0.12 mg [71). The final component of the ad denda concerns the Au-7% Cu wires. The diameter of the Cu wires not only has to be known (0.003 in.), but also the length of the four wires (each wire was 0.25 in. long) as shown in part (a.) of Fig. 3 3 on page 65. Bachmann et al. determined that 1/3 of the Au-7% Cu wire's heat capacity should be included as addendum [9). At T = 2 K, the amount of addenda for 1.5 mg of Au-7% Cu wires is 0.044 J/K. The addenda contribution from the Au-7% Cu wire rises rapidly with temperature due to the low Debye temperature of the wires (00 ,..., 165 K [141)). The tempera ture range (0.3 K to 8 K) at which the specific heat was measured for samples in this dissertation avoided too large an addenda contribution from the Au-7% Cu wires. The computer programming language, HPBASIC, used temperature depen dent and mass dependent polynomial fits for each addenda contribution mentioned above in order to provide a realtime subtraction for the heat capacity measured at a particular temperature. A standard piece of gold was measured using the thermal relaxation method and it was found that if all the aforementioned addenda was not subtracted off, then the specific heat of gold at 2 K would be about 10% too high from its reported standard value (rv 5.001mJmole -1K -1 [13)) [71). Once the cryostat with all of its components is assembled the cryostat parts mentioned above need to be interfaced with instrumentation (i.e., voltmeters and current sources) that is controlled by an HP 9000/300 series computer. The block thermometer (i.e. a resistor) is hooked to a voltmeter and current source so that resistance (i.e., temperature) values may be obtained. The block heater (usually

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made up of a bundle of manganin wire) which controls the temperature of the block thermometer, the copper ring, and the sample platform is connected to a current source so that Joule heating may raise the low temperature of the bottom of the cryostat. The platform heater that provides the small temperature rise to the sample platform is also connected to a current source. The final component concerns the germanium chip platform thermometer whose resistance is very sensitive to small temperature changes. The platform thermometer is half of one arm of an ac Wheatstone bridge. The other half of the arm is connected to a variable resistor (i.e., a resistance box). The other arms of the ac Wheatstone bridge consist of two known resistors ( each resistor is 90 kn). The platform thermometer has a lock-in amplifier connected across it to provide a source of ac excitation current and to serve as a null detector [9]. The ac excitation current 69 is limited by the self heating of the platform thermometer. The other reason for using the lock-in amplifier is to increase the signal-to-noise ratio [141] by filtering out noise at other than the measurement frequency (rv 2700 Hz) [71]. The lock-in amplifier is connected to the HP 9000 /300 series computer through an analog digital converter. The converter digitizes the signal from the ac Wheatstone bridge for the computer during specific heat measurements. Before actual specific heat values are measured, proper calibration of the ger manium chip thermometer has to be performed. The ac Wheatstone bridge is used to measure the platform thermometer resistance at a known block temperature on the bottom of the cryostat [116]. The reciprocal of the platform temperature, T, is then fitted to a polynomial as a function of the natural logarithm of platform thermometer resistance, R: (3.8)

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where n = 4 was used in the calibration. Equation 3.8 is then used (by the HP 9000/300 series computer) to interpolate the platform thermometer temperature value using the resistance value experimentally found. The final calibration concerns measuring the thermal conductivity, K, of the four Au-7% Cu wires in Fig. 3-3 on page 65. The thermal conductivity, "', may be written in terms of the power, P, supplied across the platform heater and the associated temperature rise, 6 T, in the platform thermometer: 70 P = K6T. (3.9) If one starts from a base temperature, T 0 on the copper ring and the sample platform in part (a.) of Fig. 3 3, then a small amount of known current is sup plied through the platform heater and the corresponding voltage drop across the heater is measured in order to determine the power, P. The platform thermometer resistance is determined before and after the power is supplied to the heater so that TO and 6 T are known from the germanium platform thermometer calibration discussed previously. The thermal conductance of the Au Cu wires is then deter mined using Eq. 3.9 at a temperature of To + 6T/2. The thermal conductance of the wires divided by temperature, K/T, may be written as a power series of just temperature or the natural logarithm of temperature (3.10) where n = 4 was usually used by the HP 9000 /300 series computer to find an interpolated conductance value at a particular temperature. The advantage of the second form in Eq. 3.10 is that the same conductance equation may be used over a larger temperature range (30 mK to 10 K) while the first form is usually split into a low temperature equation and a high temperature equation where 1.3 K is the approximate dividing temperature.

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71 The calibrated thermal conductivity equation is then checked by either measuring pure palladium, platinum, gold, or copper and comparing to known standard specific heat values of the aforementioned elements [13]. The standard sample used in this dissertation that was measured to check the conductance values was pure platinum (99.9985% purity). A problem that has to be taken into account when measuring specific heat values by the thermal relaxation method is known as the "T2 effect. The T 2 effect is the thermal lag between the sample and the platform [141]. The T 2 effect comes from large thermal resistance, poor conductivity of the sample, or of the sample-platform contact and throws the temperature decay off from its exponential shape [71]. A couple of procedures exist to account for this T 2 effect. First, the temperature decay curve should be composed of the sum of two exponential curves like T(t) = T0 + Aexp ( ~1t) + Bexp ( ~2t) (3.11) where T is the temperature, TO is the baseline temperature, t is time, T 1 is the time constant of the sample and addenda, T 2 is the second time constant that throws the exponential decay off, and the coefficients A and B are determined by a graphical fit using the HP 9000 /300 series computer. The second procedure for improving the T 2 effect concerns the lock-in amplifier. The signal integration time should be set to less than Ti/40 for a better T 2 correction. Not only is the T 2 effect less smeared, but also a transient which causes rounding of the exponential decay curve near the beginning, is eliminated. When the actual specific heat measur e ments are taken a program developed by Dr. Bohdan Andraka on the HP 9000/300 series computer contro l s the mea surements. Once all known addenda masses are entered into the computer, the computer first prompts the user for the base temperature, T, at which both the

PAGE 84

block thermometer and platform thermometer are stabilized. The base tempera ture, T, is determined by varying the resistance in the ac Wheatstone bridge to match the resistance of the platform thermometer using the lock-in amplifier as the null detector. The experimentally determined resistance is then entered into 72 the computer so that the platform thermometer temperature is interpolated from the calibrated germanium platform thermometer resistance. The computer also "communicates" with the current source and voltmeter to determine the resistance of the block thermometer and hence the temperature of the block thermometer using a calibration curve. The computer then asks for the amount of current to supply to the platform heater such that the temperature rise, ~T, is about 4% higher than T. Since the time constants that were dealt with in this dissertation were usually under ten seconds the new platform temperature usually became stable in under one minute. The variable resistor was then changed to determine the new, higher platform temperature. After the higher platform temperature was determined, the resistance box was manually turned to the average of the two determined resistance values with the current to the platform heater still on. The computer then would perform one sweep to determine the temperature decay curve. This sweep entailed the computer turning off the current to the platform heater and then signal averaging 4000 points from the output of the lock-in amplifier for the platform temperature decay curve. The platform temperature decays down to the base temperature. The 4000 points are plotted on a semilogarithmic graph ( the distance from the decay curve to the base temperature is plotted on the graph) and a least squares fit is used to determine the time constant value Multipl e sweeps may be performed automatically by the computer and signal averaged to improve the signal to-noise ratio. Also, the computer allows the user the option of taking into account the T 2 effect. After the time constant valu e is determined the computer outputs the correct specific heat value of the sample after subtracting

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73 off the addenda contributions. Then, more current is supplied to the block heater such that the next specific heat value may be determined at a higher temperature. A couple of systematic errors one needs to be aware of that might show up as oscillations in the base temperature concerns changes in block heater current ( due to electrical pickup) and fluctuations in the surrounding liquid helium bath [9]. Specific heat measurements were a l so performed in magnetic fields (2 -13 T) for this dissertation. The therma l conductance of the Au-7% Cu wires has to be corrected depending upon the amount of magnetic field used. The thermal conductance of the Au 7 % Cu wires decreases approximately linearly such that at 12 T the thermal conductance of the Au-7% Cu wires is 3% less than the O T thermal conductance values [120]. Also, calibration curves have to be reconfigured for the block thermometer A block thermometer calibration curve has to be constructed for every magnetic field using a field correction according to Naughton et al. [106]. Some drawbacks to measuring in magnetic fields are that the germanium platform thermometer has a large magnetoresistance p(l8 T)/ p(O T) 5.6 at 4.2 K [141] and a noise problem in magnetic fields [71]. The ease of specific heat measurements has been facilitated by advancements in technology. In fact, Quantum Design sells an automated specific heat measure ment system that uses thermal relaxation calorimetry and is named the physical property measurement system (PPMS) [86]. It will be mentioned here that a cou ple of UCu2Si2_xGe x samples in this dissertation had their heat capacity values measured on a PPMS at LANL.

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CHAPTER4 UCus-xNix RESULTS AND DISCUSSION Nine UCu5_xNix compounds were arc-melted and annealed as described in the "Experimental Techniques" chapter. The nine compositions were x = 0.5, 0.6, 0.75, 0.8, 0.9, 1.0, 1.05, 1.1, and 1.2. The "full spectrum" of measurements was performed upon the UCu5_xNix system. The following sections contain lattice parameter measurements, de electrical resistivity measurements, ac and de magnetization measurements and specific heat measurements (in zero magnetic field and various magnetic fields). The development of the NFL behavior in the UCu5_xNix system will be investigated through the perspective of the Griffiths phase disorder model. All tables in this chapter are found at the end of the chapter beginning on page 126. 4.1 Lattice Parameter Values for UCus -xNix The lattice parameter values for the nine cubic UCu5_xNix compounds are found in Table 4 1 on page 126. The unannealed and annealed (for 14 days at 750C) samples that had their lattice parameter values reported came from the same arc-melted bead. The arc-melted bead was cut in half with a diamond wheel saw and half the bead was used as an unannealed sample while the other half was annealed. All lattice parameters were determined using the graphical extrapolation method described in the preceding "Experimental Techniques" chapter. The unannealed and annealed lattice parameter values are shown graphically in Fig.s 4 1 and 4 -2. The unannealed UCu5_xNix compounds show no signs of a change in the slope of the lattice parameter value versus Ni concentration as occurred in UCus xPdx [160]. Annealing the UCu5_ xNix compounds also shows that there is no existence of preferential occupation by Cu or Ni as occurred with 74

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-E 7 05 7 04 7.03 7.02 e 1 .01 U) C> 7. 00 as 6.99 6 98 6 .97 UCu ... Ni ..-X X unannealed 6.96 -----.------,.....-------..----..--------...---0 0 0 2 0.4 0 6 0.8 1 .0 1 2 x -Ni concentration 75 Figure 4-1: Lattice parameter values for unannealed UCus-xNix compounds. The best fit line is for the nine experimentally determined lattice parameters in this dissertation ( represented by hollow squares while the vertical lines are the corre sponding error bars). The equation for the best fit line is as follows: a= 7.04521 0.06233 x. The UCu5 va l ue (represented by a hollow circle) is taken from litera ture [18] and it was an unannealed sample.

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-7.04 7.03 7 02 E 0 7 0 1 .::. en C> 7 .00 cu 6.99 6.98 6 .97 76 0 UCu~.NI. annealed 14 days 750C 0.0 0 2 0.4 0 6 0.8 1.0 1 2 x -Ni concentration Figure 4 -2: Lattice parameter values for annealed UCus-xNix compounds. The best fit line is for the nine experimentally determined lattice parameters in this dissertation (represented by hollow squares while the vertical lines are the corre sponding error bars) The equation for the best fit line is as follows: a= 7.03348 0.05171 x The UCu5 va l ue (represented by a hollow circle) is taken from litera ture [18] and it was an unannealed sample

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Pd in UCu5_xPdx [143]. In fact, the annealing just sharpens the Vegard's law behavior (i.e., the linear behavior of the lattice parameters as a function of Ni doping since all compounds form in the same crystal structure). The difference 77 in the goodness of fits (i.e., the standard deviations) between the best fit lines for unannealed (larger standard deviation) and annealed UCu5_xNix lattice parameters is greater than a factor of two (the best fit lines are seen in Fig.s 4-1 and 4-2). Virtually all nine of the experimentally determined lattice parameters for annealed UCu5_xNix lie along (within their error bars) a straight line in Fig. 4 -2. Not only do the lattice parameters as a function of annealing show no change in the order of the UCu5_xNix samples, but also high angle x-ray diffraction lines provide insight into the order. The (7 3 1) diffraction line occurs at rv 115.9 on an x-ray diffraction scan as seen in Fig. A 1 on page 167. The line width for the (7 3 1) peak is the same for the unannealed UCu5_xNix compounds and the UCu5_xNix compounds annealed at 750C for 14 days. Thus, short term annealing does not increase the order of the UCu5_xNix compounds, contrary to what was observed for UCu5_ xPdx [160]. The lattice parameters' results also allow one to make a few comments regarding the occupation of atomic positions in the cubic unit cell. In order to get a visual representation of the discussion that follows, one may want to refer back to the conventional AuBe5 crystal structure in Fig. 1 1 on page 3 of the "Introduction" chapter. The lattice parameter results show that the 4a sites in Fig. 1 1 are occupied by the U atoms as occurred in UCus x Pdx. The larger minority sites inside the unit cell (i.e., the 4c site) are basi ca lly occupied by the larger Cu atoms (relative to the Ni atoms) while the smaller majority sites (the 16e sites) insid e the unit cell have approximately 25% of the Ni concentration located at one of the four sites in the unit cell. A small percentage of the Ni concentration does occupy the 4c sites even for the annealed cases. The exact amount would

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have to be determined by SR and EXAFS measurements as was done for the UCu5-xPdx system [15, 93]. This is in stark contrast to UCu5_xPdx where the 78 Pd atoms (larger than the Cu atoms) show preferential sublattice ordering as discussed earlier [143]. To summarize, the 4c sites inside the unit cell for annealed UCu4Pd have a > 80% occupation by the Pd atoms while the 16e sites have a less than 5% occupation by Pd [16]. Thus the partial order present (along with disorder) in the UCu5_xPdx system is not a concern in the UCu5_xNix system The lattice parameters in Fig.s 4 1 and 4-2 reveal this. The UCu5_xNix system has a higher degree of disorder than the UCu5_xPdx system with the Ni atoms having a much greater percentage of occupation at the 16e sites as compared to the Pd atoms ("" 25% versus < 5%). The lattice parameter results also show that clear distinctions can be made concerning the roles of quantum criticality and disorder in the NFL behavior of UCu5_xNix without the worry of partial order as occurred in UCus-xPdx. The lattice parameter values are used to determine the smallest U-U separa tion in the lattice. If one goes back to Fig. 1 1 on page 3 in the "Introduction" chapter, one may determine that the smallest U-U distance is ""0.707a (the short est distance is a straight line from a corner 4a site to a nearest face-centered 4a site in Fig. 1 1) where 'a' is the calculated lattice parameter of a particular UCu5_xNix sample The smallest lattice parameter value is for unannealed UCu3 8Ni1.2 where a= 6.97107 A in Table 4 -1. Therefore, the smallest U-U separation is"" 4.93 A. This is not close to the Hill limit of 3.5 A [65] where if the distance of nearest U-U separation, du-u, is l ess than 3.5 A, then the / -e l ectron orbitals of uranium in a lattice will overlap with those of the neighboring U ions and produce itinerant /-electron behavior (i.e., non-magnetic ordering). If du-u > 3.5 A, then uranium f electrons (barring strong hybridization effects) are lo calized and magnetic [143]. As one will see in the specific heat section of this chapter, UCu3 8Ni1.2 does not

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79 display magnetic ordering down to "' 0.3 K. Thus there is significant /-electron hybridization with the d-electron orbitals of Cu and Ni in the UCus -xNix samples since none of the samples in this dissertation have du-u < 3.5 A. This is consistent with the conclusions drawn by Chakravarthy et al. that said hybridization was responsible for the suppression of the long range magnetic order in UCus-xNix [22]. 4.2 DC Electrical Resistivity Results for UCus-xNix The low temperature resistivity results for the select UCusxNix samples that were measured are shown in Tables 4 2 and 4 -3. All but two samples were measured down to "' 0.3 K ( using helium 3 gas as described in the Experim e ntal Techniques chapter). The other two samples (UCu4Ni and UCu3 95Ni1.os, both annealed 14 days at 750C) had their resistivity measured down to 0.060 K using a dilution refrigerator at the NHMFL in Tallahassee, FL. A graph summarizing the resistivity for annealed (14 days 750 C) UCus-xNix samples in the range 0 9 x 1.2 along with unannealed x = 0. 75 is shown in Fig. 4 -3. 4.2.1 DC Electrical Resistivity Discussion for UCus-xNix The UCu s xNix results in Tables 4 2 and 4 3 show large varying residual resistivity, p0 values This was expected since previous literature values for UCu4Ni were sample dependent with p0 ranging from 400 to 800 O. cm [89]. A UCu4Ni r es istivity bar was produced using the sucker method dis c ussed in the Experimental Techniques chapter to investigate whether or not microcracks in the sample were the cause for the large p0 values. An example of microcracks being the cause of larg e p0 values is U2Co2Sn where an arc melted U2Co2Sn resistivity bar gave p0 = 800 O. cm [72] while a "suck e r produced resistivity bar gav e p0 = 60 O. cm [143]. Thus, the sucker method for U2Co2Sn avoided microcracks and the p0 values were reduced by a factor of rv 13. Yet, the quenched UCu4Ni resistivity bar (i.e the s uck e r m e thod) in Tabl e 4 2 (pag e 127) i s only rv 30 % lowe r than the arc m e lted unann e al e d UCu4Ni resistivit y bar. Thu s, microcrack s

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/ 80 UCu .. Ni ..-X X annealed 14 days 750C 1 14 + x = 0.75 (unann. ) 1 V x=0.9 /),. x= 1 0 1.12 0 X = 1.05 X = 1 1 2" x= 1.2 1.10 -:::ii::: N 1.08 T"" a. :::=:.. 1 .06 0 4 o.e 0.1 1 0 12 I-a. 1.04 1.02 1.00 0 2 4 6 8 10 12 T (K) Figure 4 -3: Low temperature normal i zed resistivity for UCus-xNix samples. The UC u s-xN i x samples wer e annealed 1 4 d ays at 750C and have Ni co n centrat i ons be tween 0 9 and 1.2. A l s o t h e resistivity for u nannealed UC u4 .25Ni0 .75 is p l otted. The inset shows the extreme low temperature res i stivity values for annealed UCu4Ni, UCu 3 .95Ni1.os, and UCu 3 9Niu. The graph legend also applies for the inset. The solid lines in the inset are high temperature best fit power law lines ( that yield minimum x2 values) showing that the UCu4Ni p data begin to deviate from the h i gh temperature fit li ne aro un d 0.992 K w hil e the UC u 3 9 5Ni1.os and UCu3 ,9Ni1.1 p data deviate from the lines beginning at 0.834 K and 0 .821 K, respective l y The absolute accuracy of all p data is rv 5%.

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do not appear to be the major cause for the large Po values in the UCus-xNix samples. 81 One column in Tables 4-2 and 4-3 that may provide insight into the cause of the behavior of the resistivity for UCu5_xNix samples is the RRR (i.e., the residual resistivity ratio) column. If one compares the RRR values of the UCu5-xNix samples (annealed 14 days 750C) for 0.9 x 1.2, one sees a monotonic increase in RRR as the Ni concentration increases. This trend may be irrelevant since the RRR values for all short term annealed (i.e., 14 days at 750C) UCu5_xNix samples is below 1.0. In Rosch's theoretical work on the interplay of disorder and spin fluctuations near a QCP [126], he defined a parameter x that was a measure of the impurity scattering. 1/x is equivalent to RRR [143] and this means that all UCu5_xNix samples have an x value greater than 1. Rosch stated that x = 0 is a perfectly ordered sample while x 2:'.: 0.1 is rather disordered [126]. Thus, all UCu5_xNix samples that were annealed for 14 days at 750C are significantly disordered according to their RRR values. An investigation of the data in Tables 4 2 and 4 3 (on pages 127 and 128) and the short term annealed data shown graphically in Fig. 4-3 do not indicate any significant changes brought about by annealing as occurred in UCu4Pd [160]. Annealing UCu4Pd reduced the residual resistivity by a factor of 2.5 [160] and the A value (with appropriate units) in the power law form (p0 + AT) was reduced by a factor of rv 10 (-6.3 to -0.6 [143]). Also, a large change in the qualitative behavior of the resistivity curve was brought about by annealing UCu4Pd. In the temperature region between 2 K and 8 K, the annealed UCu4Pd resistivity data was fit with a Fermi-liquid expansion p -Pr = AT2 + BT4 while the unannealed UCu4Pd resistivity data showed NFL behavior with p -Pr ex: T [160]. The UCus -xNix equivalent to UCu4Pd, UCu4Ni, does not show a significant reduction in its Po value with annealing ( only about a 17% decrease). Also, the A values in

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82 the temperature regions of 2 K and 10 K, and 2 K and 12 K for unannealed and annealed 14 days 750C UCu4Ni do not show a significant difference as occurred in UCu4Pd (-5.52 for unannealed UCu4Ni and -5.03 for annealed UCu4Ni). It is not just the UCu4Ni sample that shows this lack of significant change. A perusal of all UCu5_xNix samples in Tables 4-2 and 4 3 shows that short term annealing causes no significant changes. Despite the extreme sample dependence of the UCu5_xNix system which makes any trends in p0 as a function of Ni concentration enigmatic, a few trends in the short term annealed UCu5_xNix samples may be observed in Tables 4 2 and 4-3. First, the absolute values of A for the low temperature fit regions decrease monotonically as the Ni concentration is increased for the short term annealed UCu5-xNi x samples with A = -93.0 O, cm K-0 224 for x = 0.9 and A= -3 .85 O, cm K-0 743 for x = 1.1. The "high" temperature fit forms show that the resistivity values for 0.9 s x s 1.2 decrease just above a linear rate with UCu3 8Ni1.2 decreasing at a rate almost equal to 1 (0.996). Interestingly, Fig. 4 3 on page 80 shows that unannealed UCu4 25Ni0 75 (unannealed x = 0.75 and x = 0.80 have very similar low temperature curvatures) has upward curvature over its entire measured temperature range Yet, this upward curvature present in unannealed x = 0. 75 is not apparent until below 2 K for short term annealed x = 0.9. This upward curvature is quite apparent for short term annealed x = 1.0 and x = 1.05 at the lowest measurable temperatures. However, the upward curvature gets less steep with increasing Ni concentration and this is seen in the inset in Fig. 4 -3. The "high" temperature fit lines in the inset do not deviate as quickly for x = 1.1 and x = 1.05 as occurred for x = 1.0. In fact, this upward curvature disappears for x = 1.2. The cause of this upward curvature is unknown and remains an open ended question. This upward curvature in the resistivity

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has also been seen in annealed (14 days at 75OC) UCu4Pd below 1 K [160] and annealed (7 days at 9OOC) UCu 4Ni [88]. 83 Figure 4-3, along with Tables 4-2 and 4-3 raise some interesting points concerning the UCu 5_xNix resistivity. First, the resistivity of UCu4_25Nio.15 does not show an antiferromagnetic phase transition at around 1. 9 K as was seen in the specific heat ( and will be discussed in the specific heat section below). The most interesting point concerns a comparison of the resistivity results of two 8 week 85OC annealed UCu 4Ni samples. The first sample is a UCu 4Ni (production date of 2-27-03 in Table 4 -2) resistivity bar that was annealed for 8 weeks at 85OC after the resistivity was measured for the bar when it was unannealed. The p0 value decreases by a factor of,...., 20 and the RRR value is,...., 3.18 (very close to the RRR value of 2.5 for annealed UCu 4Pd [160]). Also a similar result was obtained for a UCu3 _95Ni1.05 (7-14-03) resistivity bar that had its resistivity measured when it was an unannealed bar and then was annealed at 85OC for 8 weeks. The only preparation difference between the UCu 4Ni entries (in Tables 4 2 and 4 3) that were annealed for 8 weeks at 85OC was that the (2-2 7-03) entry (RRR,...., 3.18) had its dimensions sanded really well before annealing so that the spot welded Pt wires were not incorporated into the sample during annealing. The second sample in Table 4 3 is a (10-13-03) entry (RRR,...., 0.313) for UCu 4Ni that had its bar cut from the arc melted bead after the bead had been annealed for 8 weeks at 85OC with no sanding of the resistivity bar dimensions. These minor differences led to significant changes in the resistivity b e havior. The sandi ng of the r es istivity bar was not the cause of the significant chang e in the resistivity behavior because the long term annealed UCu 4Ni sample (prod. date: 4-13-04 in Table 4 -3) was sanded and cleaned right before the Pt wires were attached while the long term annealed UCu3 .95Ni1.05 sample (prod. date: 4-14-04) was not sanded before attaching Pt leads. Both samples s how similar resistivity

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behavior and have almost identical RRR values that are below 1. A couple of possible explanations for the strange resistivity behavior have been formulated. One explanation concerns the possibility of a copper oxide layer forming during the 8 week annealing process and that the resistivity of a copper oxide layer was measured for the resistivity bars that were not sanded. A second possible explanation comes from Dr. Bohdan Andraka pertaining to small Cu "is lands" possibly existing in the UCus-xNix samples and that just pure Cu is present in the grain boundaries. Thus, the Pt wires were possibly attached to pure Cu with some impurities mixed in and the resistivity of a sample similar to the classical examples of a Kondo system (i.e., diluted alloys of Fe and Cr in Cu [162]) were measured. Magnetoresistance measurements need to be performed on the same eight week annealed bars ( that showed such odd resistivity behavior) in order to test the validity of this theory. 84 Magnetoresistance measurements were taken on the short term (14 days at 750C) annealed UCu4Ni (2-27-03) and UCu3 95Niu>.5 (7-14-03) samples. The results are shown in Fig.s B 1 and B 2 of Appendix B. The results in both graphs were taken by Dr. Jungsoo Kim at the NHMFL. The magnetoresistance low temperature results show that for UCu3 95Ni1.05 the approximate Po values in zero field and in a 13 T field only have about a 2.6% difference between them ("' 929 rt. cm in O T and "' 905 O. cm in 13 T). Similarly, the results for UCu4Ni show that when a 13 T field is applied, the p0 value is only reduced by about 2.8% ("' 797 rt. cm in O T and "' 775 O. cm in 13 T). These magnetoresistance measurements suggest that the origin of the large p0 values in the UCus-xNix samples is not of an electronic nature. One last interesting point that is fairly well seen in both figures of Appendix B is that the upward curvature in the temperature dependence of the graphs in zero field flattens out with the application of magnetic field and the temperature d e pendenc e remains fairly constant for fields higher than

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85 4 T. Quantitatively, best fit lines (of the power law form p0 + AT) were fit to each magnetic field data set in Fig.s B-1 and B-2. The o: values obtained for UCu4Ni in 0 T, 4 T, and 13 T fields were 0.432, 0.794, and 0.762 respectively. Theo: values for UCu3 95Ni1.05 in OT, 4 T, and 13 T fields were 0.269, 0.722, and 0.711 respectively. The physical reason for these magnetoresistance results is at present unexplained. A final question that needs to be answered concerning these UCus-xNix resistivity results is whether or not the short term annealed resistivity provides insight into the inherent properties of UCus-xNix, i.e., does quantum criticality or disorder dominate the behavior in the critical concentration of x = 1.0 ( as will also be discussed in the specific heat section)? The answer is no since the short term annealing results for UCu 4 Ni do not vary significantly from the unannealed results for UCu 4 Ni as seen in Table 4 2. The resistivity results for UCu 4 Ni are similar to the resistivity results for unannealed UCu 4Pd [160]. There was a drastic change in the transport properties, e.g., resistivity, of UCu 4Pd after annealing as has been documented earlier Thus, the unannealed UCu 4Pd gave no insight into the intrinsic disordered NFL behavior. Likewise, the resistivity for short term annealed UCu4 Ni (or any short term annealed UCus-xNix sample) may not be connected to its intrinsic NFL behavior. The resistivity results for the short term annealed UCus -xNix samples are most likely stemming from an extrinsic effect that arises from the disorder present in these samples. 4.3 Magnetization Results for UCus-xNix The magnetization results for the short term annealed UCus-xNix samples around the critical concentration, x = 1.0, are shown in Table 4 4 on page 129 and Fig. 4 4 on page 87. The numerical information in Table 4 4 is shown graphically in Fig. 4 -4. Figur e 4 4 shows the e xcellent agreement b e tween the fit lines and the data while the goodness of fits ( the standard deviation and the x2 values) in Ta ble 4 4 confirm the excellent agreement. The reason for the low field magne tization

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86 being fit to a linear form, M ,.,., H, and the high field magnetization being fit to a power law form, M ,.,., H .\, is to investigate whether or not the NFL behavior in the UCu5_xNix system may be fit to the Griffiths phase disorder model [21]. 4.3.1 Magnetization Discussion for UCu5_xNix A couple of trends are readily seen in Fig. 4 4 and Table 4-4. First, the field range over which the linear magnetization form fits is widened as the Ni concentration goes from 0.8 to 1.2. The slope of the linear form fit decreases monotonically with increasing Ni concentration. Likewise, the constant in the front of the field term for the power law fit decreases monotonically with increasing Ni concentration. Also, the exponent value, .X, in the power law form increases monotonically for 0.9 :s; x :s; 1.2. In fact, the high field magnetization power law form (for UCu3 8Ni1.2) is very close to a linear form with .X = 0.953 (for 0.9 T :s; H :s; 7 T). Also, the unphysical constant offsets in the power law form (M = A' + B' H.\) and linear fit form (M =A+ B H) for all Ni concentrations listed in Table 4 4 are recognized. These offsets also show a trend as they get less negative with increasing Ni concentration. The Griffiths phase disorder model of Castro Neto and Jones [21] makes clear predictions concerning such magnetization data shown here. As mentioned earlier, the Griffiths phase disorder model predicts that the magnetization should exhibit low field behavior (M ,.,., H) that crosses over to high field behavior (M ,.,., H .\) at some crossover magnetic field, Hcrossover. In other words, the magnetic spin clusters should show some saturation behavior at higher magnetic fields when the Griffiths phase disappears. This is evident in Table 4 -4, especially around the critical concentration of 1.0. The short term annealed UCu3 95Ni1.05 sample has a little higher .X value (0.860) than the .X values of Ce0 8Th0 2RhSb (0.686 [74]) and Ce0 05Lao.95Rhln5 (0.41 [73]), two known samples that fit predictions made by the Griffiths phase disorder model. Also the magnetization results for samples

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87 UCus. Ni J[ annealed 14 days 750C 650 ---lnNt lnfonnallon : The I.it .... and top .... 600 applylDthexO.landxO.I ...... The right ... and .......... applytD 550 the x 1.0, 1.11, 1 1 and 1.2 ....._ 500 450 400 ,. Q) 15 .. 350 E -300 E Q) 250 -:E 200 + x=0 8 150 l:,. x = 0 9 100 [J x = 1 0 V X = 1 05 50 0 X = 1.1 0 X = 1 2 0 0 10000 20000 30000 40000 50000 60000 70000 H (Gauss) Figure 4-4: Magnet i zation for UCu5 ... xNix samples annealed 14 days at 750C. The magnetization versus fiel d measurements were taken at a constant temperature (2 K) The inset shows where the low fiel d linear form (M ,.,., H) deviates from the data for each samp l e while the primary graph shows the excellent fit of the high fiel d power l aw form (M ,.,., H .x) to the data.

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above the critical concentration (e.g., x = 1.2) do not saturate as quickly as those samples adjacent to x = 1.0 in the phase diagram. This may suggest that the Ni concentration range is limited for which the Griffiths phase model applies. The de magnetic susceptibility results and the specific heat results are intertwined to the magnetization results in the Griffiths phase model since the A value from the magnetization power law form should match the low temperature magnetic susceptibility exponent, x ex T-1+.>., and the exponent in the magnetic field induced peak form in the specific heat C/T,...., (H 2+>-/2 /T3->.f2)e-.e11H/kBT, for H > Hcrossover, where H crossover is determined from the magnetization data. Since saturation is present in the magnetization data, it is recognized that the magnetization and susceptibility of the UCus-xNix samples may be fit with the Kondo disorder model [143). However, as will be discussed below in the specific heat section, it is believed that the Kondo disorder model does not apply to UCu 5_xNix in light of the fact that the Kondo impurity model, with its four fit parameters, was unable to fit the specific heat data in a magnetic field of isostructural UCus xPdx [11] and in fact does not reproduce the peak in C(H) observed for UCus-xNix. Finally, the method (as described in the inset of Fig. 4 -4) of determining Hcrossover from the magnetization data seems rather arbitrary. There was no 88 clear procedure in the lit erat ur e for describing how Hcrossover was determined for Ceo.osL8Q_ 95Rhlns (~ 0.8 T [73]) and Ceo.sTho.2RhSb (~ 1 T [74]). It was attempted in this UCus -xNix study that if the Griffiths phase disorder model applied to UCus -xNix then the rare strongly coupled magnetic clusters (responsible for the NFL behavior) might possibly show hysteresis at each sample's respective Hcrossover Thus, the zero field cooled (ZFC) magnetization at T = 2 K was measured from 0 to 7 T and immediately afterwards, the field cooled (FC) magnetization was measured from 7 to OT. This procedure was performed on three of the short term

PAGE 101

89 annealed samples: x = 0.9, 1.05, and 1.2 The results (not shown graphically here) were that the difference in magnetization values between FC and ZFC for all three samples was almost identical at every magnetic field point. In fact, the magnetization difference, MFc MzFC, for x = 0.9 [with its low Hcrassover (0.3 T)] began to increase at a slightly higher magnetic field than for x = 1.05 and 1.2. Thus, hysteresis measurements provided no additional insight into Hcrossover This topic of Hcrossover will be broached again when de magnetic susceptibility results at high magnetic fields are presented below 4.4 AC Magnetic Susceptibility Results for UCu5_xNix The ac magnetic susceptibility for certain UCu5_xNix samples was measured in a SQUID by Quantum Design using the ac susceptibility option The temper ature range of the results was limited by the temperature range of the machine: 2 K -300 K. Since UCu5-xNix suppresses TN to zero, only UCu5 UCu4.4Nio.6 and UCU4_5Ni0 5 gave TN values in the limited temperature range of the ac sus ceptibility measurements. The results for the unannealed and annealed samples are given in Table 4 -5. The TN values, listed for the three different frequencies (9.5 Hz, 95 Hz, and 950 Hz) at which ac susceptibility measurements were per formed, were determined by the location of a peak in the real component, X~c, of the ac susceptibility data. Such peaks are shown in Fig. 4 5 for UCu 4 .5Ni0 5 (annealed 14 days at 750C). 4.4.1 AC Magnetic Susceptibility Discussion for UCu5_xNix The ac susceptibility results in Fig. 4 5 confirm that the transition below 10 K for annealed UCu 4 .5Ni0 5 is antiferromagnetic and not spin glass in nature If spin glass behavior was apparent, then a temperature shift of the maximum in the ac susceptibility as a function of frequency would occur [77]. A slight temperature shift does occur in Fig. 4 -5; however, the results in Table 4 5 show that the temperature shift is practically within the stated error bars. Another indication

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-3.0 2.9 0 2.8 >< 2.7 C 2.6 2.5 (U -0 2.4 -~ 2.3 -9.5Hz 950 Hz UCuuNl0 5 annealed 14 days 750C 2.2+-....-....----.---.---.---.-........................ __ .............. ___,.___,----,,.......,,...._.--...--.,.....-4 0 2 4 6 8 10 12 14 16 18 20 22 T {K) 90 Figure 4-5: AC susceptibility data for annealed UCu4 5Ni0 5 samples. The real component of the ac susceptibility data is plotted versus temperature. The ac measurements were performed at two different frequencies (9.5 Hz and 950 Hz) as shown. The peak for the 9.5 Hz data is 6.10 Kand the peak for the 950 Hz data is 6.50 K. The shift in the peak between the two different frequencies of measurement is within the error bars in Table 4 -5.

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that is characteristic of spin glasses is a step in the imaginary component of the ac susceptibility data as was seen in UCu2 7Pd2 3 (the data dropped by a factor of rv 4 at the spin glass temperature [77]). The imaginary component of the ac susceptibility data for annealed UCu4.5Ni0 .5 (not shown here) does not show such a step, remaining fairly constant. The data in Table 4 5 also indicate that the transition below 10 K for UCu4.4Ni0 .6 is antiferromagnetic. 91 The ac susceptibility results disagree with the claims made by Lopez de la Torre et al. who claim that the magnetic phase transition for annealed UCu4 5 Ni0 .5 around 6 K is indicative of spin glass or cluster glass behavior [89]. Their claim of this spin glass behavior is based upon the splitting between zero-field cooled (ZFC) and field-cooled (FC) de magnetic susceptibility results below 6 K. However Korner et al. state that the appropriate method for arguing spin glass behavior is to monitor the temperature shift of the maximum in the ac susceptibility as one varies the frequency [77]. The ac susceptibilit y results in this dissertation argue against spin glass behavior for UCu4 5 Ni0 .5 and UCu4 4 Ni0 .6 similar to UCu4 .4Pdo 6 [77]. A phase diagram comparing the UCu5 _xNi x system to the isoelectronic UCu5 xPdx system will be shown later in the chapter; however it is interesting to compar e the TN values of UCu4_5Nio. 5 and UCu4 _4Nio. 6 to UCu4 sPdo.s and UCu4 4 Pdo 6 Chau and Maple r eport that unanneal e d UCu4_sPdo s has a TN 9 .9 K [26] while unannealed UCu4 5Nio. 5 has a TN 7.5 K (from 9.5 Hz ac susc e ptibility m e asurements). Korner et al. state that unannealed UCu4.4Pdo 6 h as a T N 6 3 K (from 95 H z ac susceptibilit y m e asurem ents ) while unanne aled UCu4 4 Ni0 .6 has a TN 4.01 K (from 95 Hz ac susceptibility measurements). This comparison seems to suggest that the dopant Ni atom suppresses the TN value fast e r than the d opant Pd atom. One suppos ition for this f as t e r d ec r ease concerns the pos sibl e s ubl attice orde ring with the Pd atoms whil e s u c h s ubl a t t ice ordering

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92 is not seen with the Ni atoms (from the lattice parameter results); thus, greater hybridization is occurring with the magnetic U atoms for the UCus-xNix case and is causing the faster suppression rate. 4.5 DC Magnetic Susceptibility Results for UCu5_xNix Figure 4--6 on page 93 shows de magnetic susceptibility data for annealed (14 days at 750C) UCu4Ni in different magnetic fields: 1 kiloGauss (kG), 1 Tesla (T) 2 T, 3 T and 4 T. The 1 kG data show a high temperature peak around 130 K and that peak is suppressed by the application of a larger magnetic field At 1 T a slight amount of curvature remains over the temperature range where the peak occurred in 1 kG. At 2 T, the peak appears completely suppressed. Figure 4--6 is representative of all Ni concentrations around the critical concentration of x = 1.0 (i.e., x = 0 9 1.05 1.1, and 1.2) A better perspective of the low temperature susceptibility data for the critical Ni concentration and its adjacent concentrations is shown in Fig. 4 7 on page 94. The reason for the log-log scale and the straight lines will be explained in the discussion section below. Table 4--6 on page 131 follows the progression of the magnetic susceptibility values at T = 2 K and contains other important values that will be used later in the calculation of the Wilson ratio [142]. Except for a couple of concentrations (x = 0.75 and x = 1.1), Table 4 6 shows that the magnetic susceptibility mono tonically decreases with increasing Ni concentration for 0. 75 x 1.2. Also, Table 4--6 provides elf. values [in Bohr magnetons (8)] for each Ni concentra tion. The ef J. values are determined from the inverse magnetic susceptibility values that are in a high temperature range ( up to 300 K) above the high tem perature peak for each respective UCus xNix compound listed in Table 4 -6. The inverse susceptibility may be related to the elf. values by rewriting the Curie Weiss Law [x = N~11_/(3k8(T -8)) where N = 6.022 x 1023 atoms/mole, B = 9.2741 x 10-21 emu G, and k8 = 1.3807 x 10 -16 emu G2 K -1J into the

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0.0095 0.0090 0.0085 0.0080 0.0075 0.0070 -0.0065 CD 0 0.0060 E -0.0055 ::J E 0.0050 CD -0.0045 0.0040 0.0035 0.0030 0.0025 0.0020 UCu4Nl-annealed 14 days 750C 0 50 100 + 0 6 0 [] 150 T (K} H = 4 T (added 0.0035) H = 3 T (added 0.00275) H = 2 T (added 0.002) H = 1 T (added 0.001) H =0.1 T 200 250 93 300 Figure 4-6: DC susceptibility for annealed UCu4Ni in different magnetic fields. The various magnetic fields were 1 kG, 1 T, 2 T, 3 T, and 4 T. The same piece of sam ple was used for all 5 magnetic fields. The shifts in the data sets as indicated allow the distinguishing characteristics of each data set to be seen clearly.

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Q) 0 E :j E Q) UCus-xNix annealed 14 days 750C 0.008 ---------.----------...-------.-------.......... 0.008 HGa ... a x:: 0.9 0 X:: 1 0 6 x:: 1.05 <> x::1.1 V x:: 1.2 The right axis appllN to X 0.9 and X 1.0 data. 0 003 -------....--.-------.---.....-......-...--------.....-----.....0.002 1 10 70 T (K) Figure 4 -7: Low temperature de susceptibility for annealed UCus-xNix samples. 94 All UCus -xNix samples were annealed 14 days at 750C. The abscissa and ordinate are on log10 scales The right ordinate scale applies just to the x = 0.9 and x = 1.0 data. The low temperature fit lines shown are used to determine the.\ values for the Griffiths phase disorder model which predicts that magnetic susceptibility has a power law form x(T) oc T -1+-X. The ,\ values for the lines shown are listed in Table 4-7.

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95 following form [79]: l/x = (7.9972/ ;11.)(T 8) (4.1) where x has the units emu/mole, and Tande, the paramagnetic Curie tempera ture, have the units Kelvin (K). There does not appear to be any trend in eff. or the high temperature peak as a function of x. Finally the x(T = 0 K) values were extrapolated values by fitting the low temperature magnetic susceptibility data (2 K T 10 K) to a fifth order polynomial. 4 .5.1 DC Magnetic Susceptibility Discussion for UCus-xNix The first part of this discussion will pertain to the high temperature peaks observed in the de magnetic susceptibility results of the UCus-xNix samples. Inter estingly, no previous literature has mentioned the observance of a high temperature peak in the de magnetic susceptibility for any UCus xNix sample [89, 90, 153]. The reason why no high temperature peak was observed in two of the articles [89, 90] concerns the field at which the de magnetization was measured H = 1 T while the third article did not show any indications of a high temperature peak in the inverse susceptibility (field unknown) [153]. As has been pointed out previously in Fig. 4 6 1 T almost suppresses the high temperature peak and the slight curvature that remains at 1 T may have been attributed to experimental uncertaint y A possible interpr e tation for the high temperature p e ak may concern spin glass behavior since irreversibility (not shown here) between zero field cooled and field cooled runs at 1 kG begins at the location of the high temperature peak. This possible spin glass behavior will need to be confirmed by ac susceptibility measurements [77] ( technical diffi c ulties hav e n o t allow e d the ac s u sce ptibilit y m easure m e nts to b e performed). Another possibility is that the high temperature peak could be anti ferromagnetic s t e mming from magnetic susceptibilit y measurements of CuO [166]. This is hi g hl y unlik e ly s in ce the majority of the bulk sampl e would hav e to hav e

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oxidized. Also, the high temperature peaks in Table 4-6 are not occurring at the TN value of 230 K for CuO [166]. 96 A comparison of other isostructural compounds may shed light on the high temperature susceptibility peak for UCus-xNix samples. High temperature sus ceptibility measurements for UCus-xP
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97 The final part of the discussion focuses on the de magnetic susceptibility for the critical Ni concentration x = 1.0 and its adjacent concentrations (x = 0 .9, 1.05, 1.1, and 1.2). The low temperature de susceptibility in a 1 kG field is shown in Fig. 4 -7. The equations for the low temperature fit lines in Fig. 4 7 are explicitly stated in Table 4 -7. Both the figure and table show that the low temperature fit lines do not fit the low temperature magnetic susceptibility data very well. The temperature range for the fit lines does not cover a decade of temperature. Also Fig 4 7 shows that the five Ni concentrations have an inflection point occurring around 30 K in their magnetic susceptibility data. The exact source of the inflection point is unknown but a couple of possible explanations exist First the inflection point in the de susceptibility could be due to an extrinsic effect on the UCus xNix samples similar to the supposition made for the resistivity of the short term annealed UCus-xNix samples. Since the Griffiths phase disorder model is being applied to the UCusxNix system, the behavior of strong magnetic clusters (i .e., the Griffiths phase) is what leads to the power law behavior in the magnetic susceptibility: x(T) ex: T -1+>[21]. However the Griffiths phase mod e l predict s that there is a temperature on the order of the average RKKY interaction for a particular system and that above this temperature the magnetic clusters do not exist as well defined objects since temperature fluctuations can ex c ite isolated spin s within the cluster [21]. Thus, the inflection points in Fig. 4 7 could be related to the temperature where the magnetic clusters decompose [20]. Another possible explanation concerning the inflection point is a magnetic origin. If one looks ahead to Fi g.s 4 8 and 4 9 on e sees that the inflection point di s app e ars a t hi g h e r magnetic fields. This inflection point will be left for further studies The Griffiths phase disorder model also states that the expon e n t, \ in the low field magneti c susceptibility power law behavior (x rv T -1+>-) i s equal to the .X in the high fie ld magn e tization b e havior (M rv H.x). If on e compar e s the .X

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98 values for the 1 kG magnetic susceptibility fits in Table 4 7 to the .X values for the magnetization versus field fits in Table 4 4, then one sees that for x = 1.05, the two values are within 2% of each other (0.848 from susceptibility and 0.860 from magnetization) and that the .X values for x = 1.1 and x = 1.2 are almost equal. The susceptibility at 1 kG and the magnetization seem to imply that the antiferromagnetism (i.e., spin fluctuations) suppressed at the quantum critical point concentration of x = 1.0 does not show Griffiths phase behavior with the exponent from the magnetization data (0.841) deviating by more than 2% from the magnetic susceptibility exponent (0. 792). Yet as the Ni concentration is increased slightly (by 5%), the magnetic clusters (and the associated tunneling between energy levels [21]) associated with the Griffiths phase display their behavior in the magnetic susceptibility. The apparent Griffiths phase behavior in the 1 kG magnetic susceptibility continues for x = 1.1 and 1.2 ( the highest Ni concentration synthesized for this dissertation). Since the de magnetic susceptibility was run in five different magnetic fields for the five concentrations around x = 1.0 to suppress the high temperature peak an interesting question concerns to what maximum magnetic field does the Griffiths phase model apply for the de magnetic susceptibility? A semilogarithmic plot and a log log plot are shown in Fig. 4 8 and Fig. 4 9 respectively for UCu4Ni annealed 14 days at 750 C. The fit lines in Fig. 4 8 and Fig. 4 9 along with the other four adjacent Ni concentrations are stated explicitly in Tables 4 7 4 8 and 4 -9. The semilog and log-log plots for the other 4 Ni concentra t ions are shown in App e ndix C The x = 0 9 magnetic su sce ptibility data will b e ignored sin ce there is still an antiferromagnetic transition occurring at rv 0.4 K ( as will be seen in the specific heat data later) despite power law behavior occurring over a large temperatur e rang e at 2 T as s ee n in Tabl e 4 8 The UCu4Ni data i n Tabl e 4 8 s how tha t pow e r law b e havior is pre s e nt ov er an exte nded t empe rature range

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UCu4NI annealed 14 days 750C 0.010 -----..--....... ,._......., _________ ......,..,..... _____ T"""'I Q) 0.009 0.008 0.007 0 E o.006 :; E Q) 0.005 0.004 0.003 0.002 1 + H = 4 T (added 0.0035) <> H = 3 T (added 0.00275) 6 H = 2 T (added 0.002) o H = 1 T (added 0.001) a H=0.1 T 10 100 T (K) on log10 scale 500 99 Figure 4 -8: Semilog plot of de magnetic susceptibility for UCu4Ni. The annealed UCu4Ni was run at various magnetic fields (1 kG, 1 T, 2 T, 3 T, and 4 T). The temperature axis is on a log10 scale. The equations for the best fit lines are stated in Tables 4 -7, 4 -8, and 4 -9. The shifts in the data and lines are for clarity.

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Q) 5 (/) 0 .... g> C: 0 -Cl) 0 E Q) UCu4NI annealed 14 days 750C + H = 4 T {added 0.0035) <> H = 3 T {added 0.00275) t:,. H = 2 T {added 0.002) o H = 1 T {added 0.001) o H =0.1 T 0.002 -+--....... ---,,.......,~ ......... "T"T"S..----....... -......,l""T""l'"l"'T"----,,----..,...... 1 10 100 500 T (K) on log10 scale 100 Figure 4 -9: Log-log plot of de magnetic susceptibility for UCu4Ni. The annealed UCu4Ni was run at various magnetic fields (1 kG, 1 T, 2 T, 3 T, and 4 T). The temperature axis and de susceptibility, X, axis are on a log10 scale. The equations for the best fit lines are stated in Tables 4 -7, 4 8, and 4 9 The shifts in the data and lines are for clarity.

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101 (2-40 K) at 2 T. The A values from the 2 T magnetic susceptibility data and the magnetization data differ by,...., 3%, which is still rather good agreement. However, the magnetization data in Table 4-4 predicts that the Griffiths phase behavior should be suppressed at 2 T with the crossover field being defined as 1.55 T. This crossover field was rather arbitrary in its definition and Ceo.osL8o.9sRhlns had a crossover field of,...., 0.8 T [73] from magnetization data, yet C/T field data did not reveal a peak (predicted to occur when Griffiths phase is suppressed) until 1.5 T. The uncertainty in the crossover field could still allow Griffiths phase behavior to occur at 2 T as is suggested by the magnetic susceptibility of UCu4Ni. The Griffiths phase behavior for UCu 4Ni starts to disappear as the 3 T magnetic susceptibility starts to fall below the power law fit line at 4 K as shown in Fig. 4-9. The 2 T magnetic susceptibility data for UCu 3 .95Ni1.os also implies that Griffiths phase behavior (i.e., tunneling between energy levels) is occurring with a power law fit covering over more than a decade of temperature. The A values from the magnetic susceptibility data and magnetization data are within 5% of each other (0.899 and 0.860 respectively). Interestingly, the 3 T magnetic susceptibility data for UCu3_95Ni1.os shows downward curvature from a power law fit line at lowest measurable temperatures while a semilog line shows excellent behavior (from 2 to 45 K). UCu 3 9Niu and UCu 3 .8Ni1.2 at 2 T cease to show power law behavior over a decade of temperature implying that the Griffiths phase is being suppressed with the magnetic field splitting the energy levels far enough apart such that tunneling between the energy levels does not occur. Like the UCu3_95Nh.os sample UCua 9Niu at 3 T shows semilog behavior over a decade of temperature. The magnetic susceptibility data at various magnetic fields for x = 0.9, 1.0, 1.05, 1.1, and 1.2 seem to suggest that the Griffiths phase disorder model is not sufficient in explaining all the complexities involved in the UCus-xNix system. For example, as mentioned earlier, the magnetic susceptibility for UCu3_95Ni1.os

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displays good power law behavior at 2 T despite magnetization versus field data defining Hcrossover as 1.55 T. An interesting result concerns the semilog behavior 102 at 3 T for the magnetic susceptibility of UCu3 95Ni1.05 which suggests that the "two-channel" Kondo model could be a possibility in describing the NFL behavior of UCu3 95Ni1.05 [143]. This sort of behavior compares to the comments made by Booth et al. [16] who stated that the Kondo disorder model did not match all the experimental data that existed for UCu4Pd and more complex theories such as the Kondo/quantum spin-glass critical point [56] would need to be involved. In order to form as complete a picture as possible for UCus-xNix, the magnetic susceptibility data will be referred to heavily in the upcoming specific heat sections. 4.6 UCus-xNix Specific Heat Results The specific heat was measured for eight of the short term annealed Ni concentrations: x = 0.6, 0.75, 0.8, 0.9, 1.0, 1.05, 1.1, and 1.2. Figure 4-10 on page 103 shows the specific heat for all eight Ni concentrations measured from ,..., 0.3 K to the highest measured temperature (,..., 8 K). The subtraction made in Fig. 4 10 takes away the lattice contribution. The lattice contribution comes from the specific heat of UNi5 which was measured by van Daal et al. [153]. The data from van Daal et al. was replotted by means of a scanner and the low temperature data (0 < T < 15 K) fit the specific heat for a normal metal: C/T = 15.3 + 0.178 T2 + 0.00110 T4 (mJ mole-1 K -2). Thus, the Debye term (i.e., the T2 term in the previous equation) and the next higher lattice term may be subtracted from C/T to isolate just the electronic contribution for the UCus-xNix samples. Unlike magnetic susceptibility data, the specific heat data in Fig. 4 10 were measured down to,..., 0.3 K. The antiferromagnetic transition in UCu5_xNix is present for x = 0 6, 0. 75, and 0.8 as the specific heat has a large upturn with de creasing temperatures and then shows a plateau. The antiferromagnetic transition

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300 280 260 240 ";"Q) 220 o 200 E -, 180 E 160 140 UCu54Nlx annealed 14 days 750C ** X ** * 2 4 T (K) * * ** 6 x= 0.6 X x=0.75 + x= 0.8 a x= 0.9 o x= 1.0 t::. x= 1.05 V x=1.1 <> x= 1.2 ** 8 103 10 Figure 4 -10: Specific heat for eight annealed UCus-xNix samples. The specific heat is plotted from,..., 0.3 K to the highest measured temperature. t::..C/T on the ordinate represents the electronic contribution to the UCus -xNix samples where t::..C/T = C/T (0.178T2 + 0.00111'4) as described in the text.

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104 may be determined from specific heat data. One method of determination is to draw a straight line along the plateau and another straight line along the rapid linear increase of the specific heat data before the data begins to level off to the plateau. The intersection of these two straight lines then gives a TNeel value as shown in Fig. D-1 of Appendix D for annealed UCuuNio .6 The semilogarithmic graph in Fig. D-1 was used to better display the plateau below the TNeel value. This may be questionable, but the semilog plot was used to consistently determine TNeel values (from specific heat data) that are stated in Table 4-10. If one com pares the TNeel values for annealed UCuuNi0 6 in Tables 4 5 and 4-10, then the TNeel values are equal to each other within the temperature uncertainty of each measurement. Figure 4 -11 on page 105 shows the specific heat for five UCus -xNix samples plotted on a semilogarithmic graph: x = 0.8, 0.9, 1.0, 1.05, and 1.1. The fit lines with curvature are Moriya and Takimoto fits that will be explained in the specific heat discussion section. These fit lines along with the y0 values (listed in Fig. 4 -11 and Table 4 10) were determined using a computer program (in Fortran code) developed by Dr.s Toru Moriya and Tetsuya Takimoto at the Science University of Tokyo [103]. Also, Fig. 4-11 shows that the specific heat measurements for x = 0.9, 1.0, and 1.05 were extended further below 0.3 K. These low temperature measurements were performed by Dr. E.-W. Scheidt at the University of Augsburg using a dilution refrigerator. The Ni concentrations around the critical concentration of x = 1.0 are also plotted on a log log plot in Fig. 4 -12 on page 106. Figure 4 -12 helps in distinguish ing whether or not the Griffiths phase (C/T rv T-1+>[21]) applies to a particular Ni concentration. Many more comments concerning Fig. 4 -12 will be made in the specific heat discussion section.

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UCu ... NI. annealed 14 days 750C 450 __ ._..._.,..... __________ ...,...'P"""l""'T"T"'IP""""""---,----,~l"""'T'...,.......,..,.,., -400 350 ~300 ";"Q) o 250 E --, E 200 150 100 o x.l(y1.015) X 0.1 (y1 0.011) CJ X 1.0 (y1 0.-13) 6. x.05 + X 1.1 50 1------------...-.------------.-.................... 0.03 0.1 1 10 T (K) 105 Figure 4-11: UCus-xNix specific heat results on a semilog plot. AC/Ton the semilogarithmic graph is defined as follows: AC/T = C/T (0.178T2 + 0.00111'4). The curved lines ( dashed for x = 0.8, 0.9 and 1.0) are Moriya and Takimoto fits that predict the specific heat to go like C /T = 'Y AT112 at lowest temperatures, followed by C/T"' log Tat higher temperatures (103]. The y0 for x = 0.8, 0.9, and 1.0 is the reduced inverse staggered susceptibility that monitors how close a sample is to the quantum critical point. y0 = 0 marks the quantum critical point. The straight line for x = 1.0 is a semilogarithmic fit for 0.0547 K < T < 1.30 K: AC/T = 150 143 log10 T.

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";"Q) 0 E -, E 5 <] UCu ... Nlx annealed 14 days 750C 400 ________ ___, ______ _... __ ..,...... _______ ....... _..'""'""'aoo 100 o x=0.8 0 x=0.9 a x= 1.0 fl. x= 1.05 V x= 1.1 + x=1.2 100 70 4-_,....... _____ __._, ______ _... __ ..,...... _______ ....... ........ 80 0.03 0.1 1 10 T (K) Figure 4-12: UCus-xNix specific heat results on a log-log plot. The right y-axis applies just to the UCu3 8Ni1.2 data. The straight lines are linear fits that cover the widest possible temperature range: x = 0.9 log10(AC/T) = 2.35 106 0.372log10 T for 0.440 K $ T $ 6.04 K; x = 1.0 log10(AC/T) = 2.17 0.370log10 T for 0.404 $ T $ 2.28 K; x = 1.05 log10(AC/T) = 2.08 0.261log10 T for 0.0547 $ T $ 1.66 K; x = 1.1 log10(AC/T) = 2.02 0.201log10 T for 0.389 $ T $ 2.15 K; and x = 1.2 log10(AC/T) = 2.01 0.0970log10 T for 0.563 $ T $ 1.84 K.

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107 The specific heat for Ni concentrations including and adjacent to the critical concentration of x = 1.0 was measured in select magnetic fields, typically 3, 6, and 13 T. It was noticed that during the collection of data, a Schottky peak (C,...., 1/T2 [73]) was appearing at the lowest measurable temperatures. The appearance of the Schottky peak is exemplified in Fig. D-2 of Appendix Don page 179. These Schottky peaks were similar to the Schottky-like anomalies observed in BaCu02 by Fisher et al. [46]. Thus, the UCus-xNix specific heat measured in a magnetic field needed to account for the nuclear hyperfine specific heat coming from the copper nuclei. Fisher et al. calculated the nuclear hyperfine specific heat from nuclei 63 65Cu and 135 137Ba to be Ch 1(H) = 0.00329 (H/T)2 mJ mole-1 K-1 for Hin Tesla [46]. It was assumed that the primary contributors to the nuclear hyperfine specific heat were the Cu nuclei. This was confirmed by measuring a pure piece of 99.9999% Cu (etched in nitric acid right before measurement) in Dr. Stewart's laboratory at UF in 6 and 13 T. The coefficient in front of the nuclear splitting term (i.e., the Schottky anomaly term C/T,...., 1/T3 ) that was experimentally determined (graph not shown) in the 6 T magnetic field was within 5% of Fisher's value (0.112 versus 0.118 respectively). Similarly, the experimentally determined coefficient in the 13 T magnetic field was within 1 % of Fisher's value (0.560 versus 0.556 respectively). Thus, the t:..C/T values in magnetic fields take into account the nuclear splitting of the Cu: t:..C/T = C/T (5-x) 0.00329 H2 /T3 0.178 T2 0.0011 T4, where H is in Tesla and x is the Ni concentration. The nuclear splitting term needs to be multiplied by the number of moles of Cu since Fisher's term only accounted for 1 mole of Cu with BaCu02 [46]. Figures 4-13, 4-14 and 4-15 show the specific heat of UCu4.1Nio.9 UCu3 9Niu, and UCua.8Ni1.2 in 0, 3, and 6 T respectively while Fig.s 4 16 and 4 17 show the specific heat of UCu4Ni and UCu3 95Nii .05 in 0 2, 3, and 6 T.

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108 300 UCu4.1Niu annealed 14 days 750C -250 a OT 0 3T 6T ... a, 0 200 E -, E -ij 150 100 0 1 2 3 4 5 6 7 8 9 10 T (K) Figure 4 -13: Specific heat of UCu4.1Nio. 9 in 0, 3, and 6 T. UCuuNio 9 was an nealed for 14 days at 750C. The t:..C/T values not only have the lattice contri bution subtracted off, but also the nuclear hyperfine contribution: t:..C/T = C/T 0.0135H2 /T3 -0.178T2 -0.0011 T4 where H is in Tesla The 0 T data are only shown down to "' 0.3 K so as not to conceal the 3 T and 6 T data.

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109 130 D UCu,..Ni1 1 D D annealed 14 days 750C 120 -H=OT Cl 0 H=3 T .... /::,. H = 6 T (I) 110 0 E -, E 100 -ij D 90 80---------------------------0 1 2 3 4 5 6 7 8 9 T (K) Figure 4 -14: Specific heat of UCu 3 9Niu in 0 3, and 6 T. UCu3_9Ni1.1 was annealed for 14 days at 750C. The ~C/T val ues have the lattice and nuclear hyperfine terms subtracted off: ~C/ T = C/T0 0128H2/T3 0.178T2 -0.00111'4. The fits for the 3 T ( do tted line) an d 6 T (solid line ) data are based up o n the Castro Neto Jones model above the crossover magnetic field: ~C/T = A(H2Hx/ 2 /T3')..x/2)e-H/ T + D where A, H, and D are the three v ariab l e parameters in t h e least squares fit while Ax = 0.903 for UCu 3 9Niu (from Tab les 4 4 and 4 -7). The fits for the 3 T and 6 T data are as follows: 3 T -A= 29.6, H = 1.85, and D = 93.1 for 0.381 T 8 .06 K; and 6 T -A= 19.7, H = 2 .74, and D = 91.5 for 0.372 T 8 .22 K. The 3 T data an d the 3 T fit beyond 2 K are truncated for clarity.

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110 118 116 B 114 D 112 D UCus.aNl1.2 110 D annealed 14 days 750C -108 D N D a H=OT 106 \ 0 H=3T ... CD 104 I!.. H=6 T 0 102 E -, 100 E 98 96 D 94 D OD D 92 Doo0~e~~.ti. 90 .ti. .ti. .ti. .ti. 88 .ti. 6. .ti. 86 0 1 2 3 4 5 6 7 8 9 T (K) F i gure 4 -15: Specific heat of UCu3. s Ni1.2 in 0 3, and 6 T UCu3 8Ni1.2 was annealed for 14 days at 750C. The tl.C/T val u es have the lattice and Schottky anomaly terms s u btracted off : tl. O ( T = C/T0.125H2/T3 0.1 78T2 -0 .0011T4. The fit to the 6 T data is based up 0n t h e Castro NetoJon es model above the crossover mag netic field: tl.C/T = A(H2+.x/2 /T3-.\/2 ) e H/T + D where A, H, and Dare the three variable parameters in th~ l east squares fit w h ile A= 0 .95 for UCu3 8Nh.2 {fixed from M vs. Hat T = 2 If and x vs. Tat H = 1 kG). The fit covers the low tem perature range from 0.3si to 3. 77 K with A = 5.87 H = 2.24, and D = 93.2. The 3 T data are truncated at 1.2 K for clar i ty wit h the 3 T data above 1.2 K closely following the 0 T data. I

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D i UCu4NI 200 D D annealed 14 days 750C D D CJ H=OT -D + H=2T 1' D lei 0 H=3T ... !),,. H=6T 'CD 0 150 E -, E -t:: 100 + + + + + + 0 1 2 3 4 5 6 7 8 9 T (K) Figure 4 16: Specific heat of UCu4 Ni in 0, 2, 3, and 6 T. UCu 4 Ni was annealed for 14 days at 750C. The 6.C/T values have the lattice and Schottky anomaly terms subtracted off: 6.C/T = C/T0.0132H2/T3 -0.178T2 0 0011T4. The fit to the 6 T data is from the Castro Neto-Jones model for the specific heat above the crossover magnetic field: 6.C/T = A(H2+A/2 /T3-A/2)e -H/T + D where A, H and D are the three variable parameters in the least squares fit while .X = 0.841 111 for UCu4Ni (fixed from M vs. Hat T = 2 K). The 6 T fit has A= 45.7 H = 1.97 and D = 102 for 0.357 $ T $ 8.15 K. The O T data goes down to rv 0.3 K so that the other field data are not concealed and the 3 T data are truncated at ,...., 2 K for clarity

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112 160 D UCu3 _15Nl1.os ij annealed 14 days 750C H=O T 140 '2i a '2i + H=2T 0 H=3T -% t:. H=6T 'CD 120 t ,.0 0 E -, E 100 ij 80 + + + 4 .6+4.ti,+ 60 0 2 4 6 8 10 T (K) Figure 4 -17: Specific heat of UCu 3 .95Ni1.os in 0, 2, 3, and 6 T. UCu3_95Ni1.os was annealed for 14 days at 750C. The A C / T values have the lattice and nuclear hy perfine terms subtracted off: AC/T = C /T-0 0130H2/T3 0.178T2 -0.0 011T4 The fits to the 3 T and 6 T data are the Castr o Neto-Jones eq u ations for the spe cific heat above the crosso v er magnetic field: AC/T = A( H2H/2 /T3-)t.f2)e-H/T + D where A H, and D are the three variab l e parameters in the least squares fit while .X = 0.86 0 for UCu 3 .95Ni1.os (fixed fro m M vs. Hat T = 2 K). The 3 T fit (dashed line) has A = 45.8 H = 1.90 and D = 84. 2 for 0 .385 T 9 .01 K while the 6 T fit (solid line) has A= 35. 8, H = 2.68, and D = 83. 2 for 0.386 T 9 .09 K. The 0 T data are plotted down to,..., 0.3 Kon this graph for a better view of the field data while the 3 T data and fit are truncate d at 2 K for clarity.

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113 Figures 4-14, 4-15, 4-16, and 4-17 have curves that attempt to fit certain magnetic field data. These are Castro Neto-Jones' fits [C/T "' (H2+>-/2 /T3->./2 )e-l'e11.H/k8T] as was discussed in detail in the "Theory" chapter. These fits are used on the assumption that magnetic spin clusters (disor der induced) are responsible for the NFL behavior in UCu5_xNix. The fit details are listed in the caption of each figure. The 13 T data were not included in any figure for improved clarity. Also, the Castro Neto-Jones' fits to the 13 T data were rather poor for all Ni concentrations that had their specific heat measured in that magnetic field. An example of how poor the Castro Neto-Jones' model fits 13 T data is provided in Fig. D-3 of Appendix D for UCu4Ni 13 T data. Finally, it should be noted that the Wilson ratio, R, was calculated for Ni concentrations where 0.75 x 1.2 in Table 4 -10. The Wilson ratio relates the specific heat and de magnetic susceptibility of a compound [163] and is used in classifying whether or not a heavy-fermion system is magnetic, nonmagnetic, or superconducting [142]. The Wilson ratio is defined as where kB is the Boltzmann constant (1.38 x 10-23 J K-1 ) and g2tJ(J + 1) is equal to ~ff. [where eff. is in terms of the Bohr magneton number, B (9.27 x 10-24 J T -1 )]. Equation 4.2 may be simplified down to terms and units that are listed in this dissertation [142]: R 218. 7x(T = 0) 2 '"'feff. (4.2) (4.3) where x(T = 0) has the units of memu mole-1 c-1 '"Y has the units of mJ mole-1 K-2 and elf. is a dimensionless number of Bohr magnetons. The x(T = 0) and elf. values are listed in Table 4-6 on page 131 as discussed previously. All '"Y values listed in Table 4 -10 were extrapolated using a fifth order polynomial over the

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114 entire temperature range measured. This determination of 'Y may seem arbitrary, but it was consistently done for all Ni concentrations. The extrapolation of x and AC/T as T ._ 0 has been used in Wilson ratio values for samples like CeCu2Si2 [8) and YbRh 2 Si 2 [52). The Wilson ratios in Table 4-10 are by no means definitive, however they will be used for comparisons between samples in the UCus-xNix system. 4.6.1 UCus-xNix Specific Heat Discussion 4.6.1.1 Specific Heat in Zero Magnetic Field Figure 4 -11 on page 105 shows that the antiferromagnetism in the annealed (14 days at 750C) UCu5_xNix samples is not suppressed until x = 1.0 with the plateau at 0.4 K signifying the antiferromagnetic transition temperature (TN) for UCu4.1Nio_9 Thus, UCu4Ni is the critical concentration where TN (or TNl!el) is suppressed to zero. Although the ac susceptibility results above showed the Ni concentrations with x < 0. 75 to have a greater effect upon TN than the Pd concentrations (less than 0.75), x = 1.0 is the same concentration where TN is suppressed to zero for the annealed (14 days at 750C) UCus-xPdx system [160). Yet, as discussed before, the UCu4Ni sample shows no possibility of partial sublattice ordering as seen in UCu4Pd. Figure 4 -18 on page 115 is a phase diagram comparing the TN values for the UCus-xNix and UCus-xPdx system. The TNl!el value being suppressed to zero is also confirmed by the Moriya and Takimoto fits in Fig. 4 -11. As discussed in the "Theory" chapter, Moriya and Takimoto based their theory upon spin fluctuation mode-mode coupling and as T ._ 0, C/T = 'Y AT11 2 The mode-mode coupling increases with increasing temperature and C/T goes like -log T [143). Figure 4-11 shows that x = 0.9 and x = 1.0 increase logarithmically with decreasing temperature and the 'Y AT11 2 curve fits the lowest temperature data (within the experimental uncertainty). An indicator for how close a sample is to a magnetic instability in the Moriya

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1 z .... A UCu ... NI. o UCus-aPd. (taken from Chau, Maple) UCus-aPdx (taken from Koerner) 18-----------.-----------------.--~-.------T"""'I 16 14 12 10 8 6 4 2 0 f __ :f :::j __ -) f :\ :J J !: :::! i : : .. : . :.! ::! J .. ::.::.:. l . I -I I l l----1 1 1 l 11! 1 i I 1 :L:J :-\::::.::.[: TJ1 i T:\:Ll: / :\::l::t 1 1 r 1 1 1 r 1 1 r l 1 1 r 1 .-.::.1.::.::.-.:.-.i:.::.::.:::.1 :.:.-.:.-.::.l.-.:.-.::.::.1:..:.-.:... i::.:: .. t ... ::.::. l .-.::.::.::.1::.:.-.::.: .i:.::.-.:.-.:.l:.::.::.: i.:.::.::..:.1::. :.-.::.:.l:..::.::.:.t:.::.:::.:.I ... l---1--L-l--L .... t.0. ~--l--LJ_J ___ J J t _J . i ::::l t I : l :: L i - 1. & t:. t : :,;.I i . :.l .-i : 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 x (Ni/Pd concentration) 115 Figure 4 -18: Phase diagram for UCus-xNix and UCus-xPdx, The TNeel values for x = 0, 0.5, and 0.6 in the UCus-xNix system {denoted by hollow triangles) are from ac susceptibility measurements in Table 4 5 (the average TNeei value for annealed and unannealed samples measured at 9.5 Hz) while the x = 0.75, 0.8, and 0.9 TNeel values are those listed in Table 4 -10 for annealed {14 days at 750C) UCu5_xNi x samples. The hollow circles are TNeel values taken from de magnetic susceptibility measurements (down to 1.8 K) of Chau and Maple [26] for unannealed UCus-xPdx samples. Similarly, the dark circles are TNeel values for unannealed UCus-xPdx reported by Koerner et al. [77].

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116 and Takimoto fits is y0 the reduced inverse staggered susceptibility (103]. The reduced inverse staggered susceptibility equaling zero signifies a quantum critical point and Fig. 4-11 shows that UCu 4 Ni yields a y0 value almost equal to zero. As one approaches x = 1.0 by increasing the Ni concentration (i.e., coming from the ordered side of the phase diagram), the y0 values get smaller as x approaches 1.0. Thus, UCu 4 Ni is at a quantum critical point. Also, the C/T values for x = 1.05 and x = 1.1 below 1 K rise faster than a log T dependence. The Wilson ratio values in Table 4-10 confirm the conclusions made by the Moriya and Takimoto fits. If one uses the Wilson ratio intervals defined by Stewart (magnetic: R rv 0.8-2.1; nonmagnetic: R rv 0.56-0.75; and superconducting: R < 0.52 (142]), then as Ni is increased from 0.9 to 1.0, the Wilson ratio reveals that UCu4_1Nio. 9 (0.92) is magnetic while UCu4Ni (0.50) is nonmagnetic. The Wilson ratios imply that the antiferromagnetism disappears by UCu 4 Ni. Also, it should be noted that just because the Wilson ratios for x = 1.0 and x = 1.05 are below 0.52, this does not mean that UCu 4 Ni and UCu3_95Ni1.05 are superconducting (similar to a nonsuperconducting CeCu2Si2 crystal that had R = 0.44 as reported by Stewart (142]). The Wilson ratio values should be viewed as consistent with the claim that UCu 4 Ni is at a quantum critical point. Table 4 10 and Fig. 4-10 indicate that once the antiferromagnetic fluctuations are suppressed by increasing the Ni concentration, the C/T values decrease monotonically. This is seen numerically by the decrease in the 'Y values with increasing Ni concentration for x > 0.9 in Table 4-10 and visually in Fig. 4 10. Not only are the magnetic fluctuations depressed, but also the associated degrees of freedom, which contribute to the /-electron part of the entropy, S = J(C/T) dT, at low temperatures. Figure 4 12 plots x = 0.9, 1.0, 1.05, 1.1, and 1.2 on a log-log graph to distinguish which Ni concentrations are consistent with the Griffiths phase disorder

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117 model. The specific heat in the Griffiths phase model has C/T rv T-l+Ac/T (where Ac/T theoretically does not have to equal Ax in x l"V T-1Hx [73]). The power law form fits the x = 0.9 data above the antiferromagnetic transition over more than a decade of temperature (0.440 6.04 K as documented in Fig. 4-12). The power law form fits the x = 1.0 data over a much more limited temperature range (less than a decade of temperature: 0.404 2.28 K) and this behavior will be addressed below. As one increases the Ni concentration by 5%, the power law form fits the x = 1.05 data well over a decade of temperature (0.0547 1.66 K) and down to the lowest measured temperatures. The Griffiths phase power law form fits the x = 1.1 data fairly well down to the lowest measured temperatures but specific heat values at lower temperatures are desired to confirm if the Griffiths phase is applicable to x = 1.1 data. The power law fit for the x = 1.2 data begins to deviate from the data at rv 0.5 K as the upward curvature of the x = 1.2 data increases faster than the power law form. Thus, the disorder induced Griffiths phase is adjacent to the critical Ni concentration of x = 1.0 on both sides of the phase diagram. However, the composition range for which Griffiths phase exists is narrow as the spin fluctuations (required for Griffiths phase) are depressed by x = 1.2 (maybe even for x = 1.1). The quantum critical point spin fluctuations at x = 1.0 are surrounded by Griffiths phase behavior for x = 0.9 (above the antiferromagnetic transition) and X = 1.05. Since UCu 4Ni does not show Griffiths phase behavior in Fig. 4-12, a semilog dependence for UCu4Ni was discovered by a semilog fit (i.e., the solid straight line) in Fig. 4 -11. This C/T rv -log T dependence covers over a decade of temperature (0.0547 to 1.30 K). The semilog dependence does not match the Griffiths phase disorder model [21], but does match predictions by the Kondo disorder model [11] and predictions for a 2-dimensional quantum critical point [143]. The semilog dependence in the specific heat has been measured in 3-dimensional systems

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such as Y1-xUxPd3 [136], U1-xThxPd2Ala [143], and Ce(Ru1-xRhx}2Si2 [143]. Also, Lopez de la Torre et al. found semilog dependence in the specific heat for annealed (7 days at 900C) UCu4Ni over a decade of temperature (0.9 9 K) as has been discussed previously [90]. Lopez de la Torre also mentioned an upturn in the specific heat at ,...., 0.9 K [90] (this upturn causes the specific heat data to increase ,...., 29% above the semilog extrapolation at 0.5 K) that is not seen in Fig. 4-12. This upturn may be some sort of magnetic second phase since the antiferromagnetism for x = 0.8 and x = 0.9 in Fig. 4-12 causes a plateau in the specific heat data. 4.6.1.2 Specific Heat in Applied Magnetic Fields 118 As discussed in the "Theory" chapter, the Griffiths phase disorder model by Castro Neto and Jones makes predictions for the specific heat in applied magnetic fields [21]. A major point in the Griffiths phase model is that above a certain crossover magnetic field ( determined from magnetization versus field data), a field is induced in the specific heat and has the form (H2+~/2 /T3-~l2)e-eJJ.H/ksT (where A is determined from the low temperature magnetic susceptibility and the high field magnetization data). The peak in the specific heat signifies that the tunneling between energy levels (i.e., Griffiths phase) has ceased Another factor in these specific heat discussions will be how well the Griffiths phase is maintained in the magnetic susceptibility at higher magnetic fields ( up to 4 T). Possible correlations in the specific heat and magnetic susceptibility at the same magnetic field will be discussed. The next five paragraphs will discuss the UCus-xNix specific heat in various magnetic fields for x = 0.9 1.0, 1.05 1.1, and 1.2 respectively. The specific heat for annealed (14 days at 750C) UCU4_ 1 Ni0 _9 in 0, 3, and 6 T magnetic fields is shown in Fig. 4-13 on page 108. The crossover magnetic field Hcrossover, for UCu4.1Nio. 9 was determined to be,...., 0.3 T (from Table 4 4), so a field induced peak should be present by 3 T. However, Fig. 4 13 shows no field induced

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119 peak at 3 T and the 6 T data show a very "shallow" peak at lowest temperatures. If one refers back to the de magnetic susceptibility results in Tables 4-8 and 4-9 and Fig. C-1 in Appendix C, then 2 T de magnetic susceptibility data fit the Griffiths phase form (X ,..., T-1+.Xx) very well. As the magnetic field is increased to 3 T and 4 T, the power law form is applicable still over a decade of temperature, but the power law behavior diverges at the lowest temperatures as seen in Fig. Cl. Thus, although the 2, 3, and 4 T de magnetic susceptibility data suggest possible Griffiths phase behavior, the 3 T specific heat data do not agree with predicted Griffiths phase behavior as shown by the lack of a field induced peak (for H > Hcrossover). The Griffiths phase behavior may exist in a magnetic field slightly less than 6 T since a small peak begins to form in the 6 T specific heat data. Yet, if Griffiths phase were the dominant mechanism in UCu4 _1Nio.9, then one would have expected a field induced peak in the 3 T data. Since there is no field induced peak in the 3 T data, possible power law behavior (C/T"' T-1+.Xc ; T) is searched for in the 3 T specific heat data despite the possible inconsistencies with Griffiths phase theory (power law behavior should not exist for H > Hcrossover). Figure D-4 in Appendix D shows the specific heat in 3 T and 6 T fields on a log-log plot. The power law behavior is over a limited temperature range (1.42 4.29 K for H = 3 T and 2.10 7.46 K for H = 6 T). The data plateau below 1 K for the 3 T and 6 T data and this could be attributed to either an imminent field induced peak at lower temperatures or the antiferromagnetic behavior occurring at "' 0.4 K. The specific heat for annealed UCu 4Ni measured in 0, 2, 3, and 6 T magnetic fields is shown in Fig. 4 -16. The 2 T data show no signs of a field induced peak despite being above the determined crossover magnetic field (1.55 T from Table 4 -4) while the 3 T data are very similar in shape to the 3 T data for UCu4.1Nio. 9 Qualitatively, the 6 T data for UCu 4Ni have a "deeper" peak than the 6 T peak for UCu4.1Nio_9. The 2 T data and 3 T data do not suggest possible Griffiths phase

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120 behavior occurring ( no field induced peak or power law behavior as discussed below) despite the de magnetic susceptibility results for 2 T and 3 T indicating power law behavior ( over almost an entire decade of temperature in Table 4-8 and Fig. 4-9). One must remember the zero field specific heat results that proved quantum critical spin fluctuations were the mechanisms for the NFL behavior in UCu4Ni, not the magnetic spin clusters for Griffiths phase behavior. The fit from the Griffiths phase model for magnetic fields above the crossover field to the 6 T data in Fig. 4-16 is very poor and suggests that the Griffiths phase model may not be the accurate description of the NFL behavior. Also, the 2 T and 3 T specific heat data for UCu4Ni are on a log-log graph in Fig. D-5 of Appendix D to investigate possible power law behavior (i.e., Griffiths phase behavior in spite of being above 1.55 T) Figure D-5 shows that the power law behavior is very limited in its temperature range (1.20 4.18 K for H = 2 T and 1.73 4.49 K for H = 3 T). This suggests that Griffiths phase behavior (tunneling between energy levels) is not existent at 2 and 3 T despite the de magnetic susceptibility results. The specific heat of UCu 3 9 5Ni1.os measured in 0, 2, 3, and 6 T magnetic fields is shown in Fig. 4 -17. The 2 T data show no field induced peak and suggest possible Griffiths phase behavior along with the de magnetic susceptibility at 2 T which shows power law behavior (x ,..., T -1+.Xx ) over a decade of temperature (in Table 4-8 and Fig. C-2). Figure D-6 in Appendix D shows that the 2 T specific heat data of UCu3_9sNii.os do not signify Griffiths phase behavior. The power law behavior of the 2 T specific heat data is over a very limited temperature range (,..., 1 3 K). When the magnetic field of UCu 3 _95Nii.os is increased from 2 T to 3 T, the specific heat shows a field induced peak at 3 T. Yet, the peak fit from the Griffiths phase disorder model is very poor as shown in Fig. 4 17. The de magnetic susceptibility at 3 T for UCu 3 _95Ni1.os also indicates that the Griffiths phase is not the correct description for the data since a semilog dependence fits

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121 the UCu 3 _95Ni1.os de magnetic susceptibility at 3 T more accurately (i.e., over a wider temperature range in Table 4-8). The 3 T specific heat and de magnetic susceptibility data for UCu 3 _95Ni1.os are suggestive of a more complex model (than the Griffiths phase disorder model) that might include elements of the Griffiths phase disorder model. The 6 T specific heat data for UCu3_95Ni1.os also display a field induced peak which has greater depth than the 6 T field induced peak for UCu4Ni (12.2 mJ mole1 K-2 for UCu 3 _95Ni1.os versus 5.98 mJ mole-1 K-2 for UCu4Ni where depth is defined as the difference between the maximum l:1C/T value on the peak and the l:1C/T value at the lowest measured temperature). However, Fig. 4-17 shows that the field induced equation from the Griffiths model does not fit the 6 T UCu 3 _95Ni1.os specific data very well. Although the specific heat data of UCu3 _95Ni1.05 in magnetic fields qualitatively match the predictions of the Griffiths model by having the field induced peak move up to higher temperatures and broaden with increasing magnetic field as occurred in Ce1 _xLSxRhln 5 [73] and Ce1-z ThxRhSb [74], the quantitative description of the Griffiths phase model for field induced peaks (C/T rv (H2+.\/2 /T3 .\f2)e-eff .HfksT [21]) does not describe the specific heat data of UCu3_95Ni1.os in magnetic fields well. The specific heat data of UCu 3 9Niu in 0, 3, and 6 T magnetic fields are shown in Fig. 4 14. The 3 T specific heat data of UCu 3 9Ni1.1 show a field induced peak at 3 T (as expected by the determined crossover field of 1.9 Tin Table 4-4). Yet, just as occurred for the 3 T UCu 3 _95Ni1.os heat capacity data, the Griffiths phase model does not match the 3 T specific heat data for UCu 3 9Ni1.1. A possible hint of the Griffiths model not being correct is provided by the de magnetic sus ceptibility results at 3 Tin Table 4-8. A semilog equation fits the UCu 3 9Niu de magnetic susceptibility more accurately than a power law equation. This suggests that tunneling between energy levels in a Griffiths phase is not the accurate de scription at 3 T for UCu3_9Ni1.1. Interestingly, the 6 T data for UCu 3 9Niu are fit

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122 very well by a Griffiths phase field induced peak over almost the entire temperature range (0.372 to 8.22 K) in Fig. 4-14. A possible explanation for the good fit at 6 T may be taken from Fig. 2-2 of the "Theory" chapter where the 3 T data may be too close to the crossover behavior line, T ,.._, H, and the scaling becomes muddled. However, once His increased, the scaling of the specific heat becomes gA(H/T) ,.._, (H/T)2Hl2e-H/T as shown in Fig. 2-2. The final specific heat data measured in magnetic fields concern UCu3_sNi1.2 in Fig. 4-15. Unfortunately, the de magnetic susceptibility for UCu3_sNi1.2 gave no hints about possible Griffiths phase behavior since power law behavior ( or semilog behavior) was not observed over one decade of temperature for any of the magnetic fields. A peak is not seen in the 3 T UCu 3 .8Ni1.2 specific heat data which is consistent with the crossover magnetic field of 3.3 T stated in Table 4-4. The 3 T specific heat data of UCu 3 .8Ni1.2 is explored further in Fig. D-7 of Appendix D. The power law behavior (i.e., Griffiths phase behavior, C/T ,.._, T-1Hc1T) is over a very limited temperature range ( ,.._, 1 3.5 K) and this may be due to the proximity of the crossover field to 3 T and the scaling function in Fig. 2 2 may become "blurred" (a similar argument was suggested for the 3 T specific heat UCu3 .9Niu data). As the magnetic field is increased from 3 T to 6 T, the field induced peak form of the Castro NeterJones model fits the 6 T UCu 3 .8Ni1.2 specific heat data over almost a decade of temperature (0.381 to 3. 77 K) in Fig. 4-15. This is very similar to the UCu 3 .9Niu results except that the Griffiths theory in the high magnetic field limit fits the 6 T UCu 3 .9Niu specific heat data over a little larger temperature range. The smaller temperature range for 6 T UCu 3 .8Ni1.2 data may suggest the start of deviation from Griffiths phase behavior. The discussion of the specific heat data in magnetic fields has raised an interesting point and that concerns the evolution of the 6 T specific heat data for

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123 UCus-xNix samples that are above the critical concentration of x = 1.0. Figure 4-19 shows the 6 T specific heat data for x = 1.0, 1.05, 1.1 and 1.2. The depths of the peaks (as defined earlier) in Fig. 4 19 are 5.98, 12 .2, 12.1, and 3.68 for x = 1.0 1.05, 1.1, and 1.2 respectively. The conclusions drawn from the zero magnetic field specific heat data were that quantum critical fluctuations were the dominant mechanism for x = 1.0 while x = 1.05 (and possibly x = 1.1) had Griffiths phase disorder fluctuations and x = 1.2 did not show Griffiths phase behavior very well. A possible correlation may exist between the depths of these peaks at 6 T and the fluctuations responsible for the NFL behavior with the "deeper" peaks (in x = 1.05 and x = 1.1) corresponding to Griffiths phase fluctuations Also, Fig. 4-19 shows that for temperatures above the field induced peak, the specific heat values for x = 1.0 and x = 1.05 decrease monotonically (almost linearly) while the x = 1.1 and x = 1.2 (better seen in Fig. 4-15) data show curvature above the field induced peaks. The curvature (which helps the Castro NeterJones model fit the data so well) for x = 1.1 continues up to rv 6 K while the curvature for x = 1.2 continues up to rv 4 K. Beyond the two temperatures just mentioned the x = 1. 1 and 1.2 data fall monotonically like the x = 1.0 and x = 1.05 data. The curvature evolving into a monotonic decrease might suggest that UCu 3 .9Ni1.1 and UCu3 _sNi1.2 have a secondary magnetic phase transition. The specific heat data when combined with the de magnetic susceptibility data portray a pretty unclear story concerning the Griffiths phase theory for the UCus xNi x system. UCu4Ni is the concentration on the phase diagram where the quantum critical point occurs and the z ero field UCu4Ni specific heat data suggest quantum critical spin fluctuations to be the primary mechanisms for the NFL behavior. The Griffiths phase theory does not fit the UCu4Ni specific heat data in magnetic fields, but the de magnetic susceptibility data at higher magnetic fields (i.e. above the crossover magnetic field) indicate power law

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130 120 "i(I) 110 0 E -, 100 E 90 80 UCus-xNi. -annealed 14 days 750C 6T 0 1 2 3 4 5 T (K) 6 124 7 8 9 10 Figure 4-19: Specific heat data at 6 T for UCus-xNix samples. Annealed (14 days at 750C) samples are UCu4Ni, UCu 3 .95Nii.05 UCu3 _9Ni1.1, and UCu3_sNi1.2, The specific heat values had their lattice and Schottky anomaly contributions subtracted off: ~C/T = C/T -(O.l 78T 2 + 0.0011T4) (5-x)0.118/T 3 where xis the number of moles of Ni for each sample. The indicated shifts in the data are for improved clarity.

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125 behavior (x rv T-1Hx), predicted by the Griffiths phase theory at fields lower than the crossover magnetic field. If the Ni concentration is increased by 5%, then the zero magnetic field specific heat data indicate Griffiths phase behavior. However, the UCu 3 .95Ni1.os specific heat data in magnetic fields do not match the predictions made by the Griffiths phase theory. The de magnetic susceptibility goes from power law behavior at 2 T to semilog behavior (predicted in a two-channel Kondo model [143]) at 3 T. The Griffiths phase theory matches the UCu3_9Ni1.1 specific heat data at 6 T well while semilog behavior covers a wider temperature range in the 3 T de magnetic susceptibility data than power law behavior. The Castro Neto-Jones model matches the UCu 3 .8Ni1.2 specific heat data at 6 T over a more limited temperature range (compared to UCu 3 9Ni1.1) while the de magnetic susceptibility (between 1 kG and 4 T) gives no hint about a possible theoretical model since semilog and log-log relationships are over limited temperature ranges. Clearly, the data show that no known theoretical model to date can predict all the intricate behaviors presented in the specific heat and de magnetic susceptibility data. Magnetic spin clusters that allow tunneling to occur between energy levels (the premise upon which the Griffiths phase theory is based) may be part of the correct theory since there are elements of the Castro Neto-Jones model that explain some of the data correctly.

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126 Table 4-1: Lattice parameter values for the nine UCus-xNix compounds. a,m and CTa.un represent the lattice parameter values for the unannealed UCus-xNix com pounds and the corresponding errors associated with the unannealed compounds. Likewise, 8.an and CTaon represent the lattice parameter values for UCus-xNix com pounds annealed for 14 days at 750C and their associated error bars. x (Ni cone.): aun (A): aa...n (A): a.an (A): aaon (A): 0.5 7.00891 0.00232 7.01007 0.00432 0.6 7.01762 0.00520 7.00217 0.00277 0.75 6.99817 0.00450 6.99054 0.00260 0.8 6.99353 0.00205 6.99272 0.00211 0.9 6.98361 0.00247 6.98714 0.00223 1.0 6.98279 0.00258 6.98246 0.00194 1.05 6.97971 0.00166 6.97879 0.00226 1.1 6.97907 0.00171 6.97612 0.00165 1.2 6.97107 0.00291 6.97282 0.00123

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Table 4 -2: The low temperature resistivity results for UCus-xNi x samples. The resistivi t y data wer e fit t o a power law form, p0 + AT0 The UCu5_xNix samples with 0.9 x 1.1 had a low temperature power law fit (below 2 K ) and a high temperature power law fit ( above 2 K) and the low temperature fit results are separated from the high tempera t ure fit results by a slash, /. Samples that were annealed with the same production date as t he unannealed samples were cut and annealed from the unannealed samples. RRR is the residual resistivity ratio and x2 is t he measure of t he difference b etw een the pow e r law form and the experimental data. The absolute uncertainty of all resis t ivi t y measurements is 5%. unannealed/ A x2 x-(Ni cone.) annealed/ Po (O cm T depend (goodne ss (prod. date): quenched: (n cm): RRR: K-a): a: range (K): of fit): 0.75 unannealed 781 -56.7 0.285 0.337 10.0 0.459 (4-3-03) 0.80 unannealed 1015 -70.2 0 292 0 344 -10. 0 0.807 (2-27-03) 0.9 unannealed 1150/1030 0 .279 -123/-8.52 0.161/1.03 0.319 2.06 / 0 .0681/ 0.067 8 (4-3-03) 1.91 10.0 0.9 ann. 14 d. 750C 1130/1040 0 297 -93.0/-8 .95 0 224/1.01 0 306 2.06 / 0 .102 / 0.0700 (4-3-03) 1.91 -12. 1 1.0 unannealed 981/944 -41.1 / -5 .52 0.252 / 1 .12 0.435 2.06 / 0.490 / 0 260 (2-27-03) 1.99 10.0 1.0 ann. 14 d 750C 816/778 0.320 -42.5/-5 .03 0 .196/1.09 0 0611 2.04 / 0.0345 / 0.00 48 7 (2-27-03) 1.89 12.1 1.0 ann. 8 wks 850C 48.4/43.8 3.18 -4.76/-0.215 0.0380 /0.468 0.345 -2.41/ 0.00116 / 0.0010 8 (2-27-03) (p measured unann.) 1.63 8.40 1.0 quenched 673/644 0.374 -30.5 / -3.26 0.243 / 1.09 0.383 2 05 / 0.0816 / 0 .0147 (8-15-03) 1.97 12.1 ..... t-,:)

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Table 4 -3: The low temperature resistivity results for UCus-xNix samples. This table is a continuation of Table 4-2. unannealed/ A x2 x-(Ni cone.) annealed/ Po (n cm T depend. (goodness (prod. date): quenched: (n cm): RRR: K-o): a: range (K): of fit): 1.0 ann. 8 wks. 850C 1030/988 0.313 -47.6/-6.96 0.237/1.06 0.339 2.12 / 0.0158/ 0.0191 (10-13-03) 1.93 10.2 1.0 ann. 4 months 850C 650/633 0.370 -19.6/-3.73 0.309/1.05 0.348 2.10/ 0.0111/0.00569 (4-13-04) 1.78 12.1 1.05 unannealed 677/667 0.437 -12.2/-3.10 0.411/1.11 0.297 2.06 / 0.00534/0.00157 (7-14-03) 1.90 12.1 1.05 ann. 14 d. 750C 908/884 0.341 -27.6/-4.25 0.216/1.12 0.0011 2.01 / 0.0339 / 0.00817 (7-14-03) 1.91 12.0 1.05 ann. 8 wks. 850C 64.9/64.0 2.88 -0.908/-0.0689 0.166/0.954 0.349 2.11/ 0 00335 /0.00455 (7-14-03) (p measured unann.) 1.95 8.52 1.05 ann. 8 wks. 850C 1200/1180 0.344 -15.6/-4.46 0.496/1.19 0.339 2.11 / 0.0087 /0.216 (10-13-03) 1.88 12.4 1.05 ann. 4 months 850C 929/919 0.378 -14.5/-4.46 0.443/1.07 0.352 2.12 / 0.0180 / 0.0164 (4-14-04) 1.80 12.2 1.1 unannealed 706/702 0.408 -6.47 /-2.38 0.546/1.15 0.324 2.06/ 0.0278/0.00192 (5-8-03) 1.90 12.1 1.1 ann. 14 d. 750C 782/780 0.527 -3.85/-2.24 0.743/1.14 0.297 2.05 / 0.00293/0 0031 (5-8-03) 1.90 12.1 1.2 ann. 14 d. 750C 453 0.724 -0.703 0.996 0.350 12.2 0.147 (3-26-03) .... tv 00

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Table 4-4: Magnetization data for UCus-xNix annealed 14 days at 750C. The magnetization data was taken at T = 2 K for Ni concentrations around the critical concentration of x = 1.0. The linear fit form was M = A+BH while the power law fit form was M = A'+ B 'HA. The linear fit regions and power law fit regions were selected by finding the minimum standard deviation/x 2 values over the largest possible field range. The linear fit standard deviation and the power law fit x 2 values were calculated using MicroCal Origin 5.0. The crossover field was arbitrarily defined as the point on the standard devia tion versus field range curve where a minimum value was found (for x = 0.9, 1.05, and 1.2) or where an inflection point (the change in the standard deviation slope was a minimum) occurred (for x = 1.0 and 1.1). The H values for the linear fits and the power law fits are in units of Tesla. The linear fits and power law fits are shown graphically in Fig. 4-4 on page 87. Power Law Power Law Power Law Griffiths X Linear Fit Linear Fit Linear Fit Crossover Fit Fit Fit phase ..X Ni cone.: Region(T): (M = ): std. dev.: Field(T): Region(T): (M = ): x2: (M"' HA): 0.8 0 0.125 -l.09+110H 0.00468 1.7 -7 -27.1 + 126H0'1111 0.0126 0.798 0 9 0 0.3 -0.344+81. m 0.0297 0.3 1.9 -7 -27.9+ 103H0 1= 0.00793 0.783 1.0 0 1.55 0.0196+62.3H 0.271 1.55 1.55 -7 -18.1 + 78.8HU.IS4l 0.00137 0.841 1.05 0 1.65 -0.889+56. lH 0.0840 1.65 1.6 -7 -15.9+ 70.0HU.oou 0.00173 0.860 1.1 0 1.9 -0.545+48.0H 0.125 1.9 1.8-7 -10 2+56.5H0 -W-> 0.00332 0.903 1.2 0-3.3 -l.04+35.4H 0.161 3.3 0.9-7 -4.44+38.3H0-ll:>.1 0.253 0.953 ..... tv

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130 Table 4-5: AC susceptibility results for select UCus-xNiz samples. AC susceptibil ity was run for UCu5 (unannealed), UCu4 5Nio.5 (unannealed and annealed), and UCu4.4Nio.6 (unannealed and annealed). The ac susceptibility measurements were performed on a SQUID with a temperature range of 2 K to 300 K. The TN value was determined by finding the temperature value where a peak in the real compo nent x', of the ac susceptibility data was located AC susceptibility measurements were performed at three different frequencies: 9.5 Hz, 95 Hz, and 950 Hz. x-unann./ TN (XAc) [K] TN(XAc)[K] TN (x'Ac) [K] Ni cone.: ann. (14 d. 750C): 9.5 Hz: 95 Hz: 950 Hz: 0 unann. 17 0.25 16.5 0.25 16.75 0.25 0.5 unann 7.50 .25 6 .75 0 .25 8.00.50 0.5 ann. 6.10.10 6.00 0.10 6.50 0.25 0.6 unann. 3.76.25 4.01 0.25 3.76.25 -0.6 ann. 4.01 0.10 4.31 0.10

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Table 4-6: DC magnetic susceptibility results for annealed UCu5_xNi:z:. The UCu5-xNix samples were annealed for 14 days at 750C. The x values at 2 K 131 are reported with their standard deviation value (not the standard deviation of the mean). The UCu4 5Nio.5 and UCu4.4Ni0 6 samples had their low temperature x val ues reported at 6.0 Kand 3.5 K respectively, i.e., the temperature values where the low temperature susceptibility was a maximum. The efl. values were determined with a Curie-Weiss fit for susceptibility values above the reported high temperature peaks. The x(T = 0 K) values were extrapolated from low temperature susceptibil ity data (:$ 10 K) using a fifth order polynomial fit. All x data in this table were measured in a 1000 Gauss field. x-x(T = 2K) ux Hi-T x(T = OK) Ni cone.: (memu mole-1 c-1 ): e!f.(s): peak (K): (memu mole -1 c-1): 0.5 8.7 0.1 3.35 140 K 0.6 8.2 0.4 3.09 115 K 0.75 10.1 0.5 3.23 125 K 16.3 0.8 10.3 0.1 3.34 125 K 16.0 0 9 7.6 0.3 2 .79 130 K 11.8 1.0 5.8 0.2 3.37 130 K 8.2 1.05 4.7 0.2 3.59 155 K 6.2 1.1 5.1 0.5 3.56 135 K 6.1 1.2 3.8 0.4 3 .32 150 K 4.1

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Table 4 -7: Fit results for UCus-xNix de susceptibility data at 1 kG and 1 T. The lines were plotted on semilog graphs and log-log graphs. The temperature ranges were selected such that the maximum temperature range yielded minimum s t andard deviation values. The A values were obtained from the Griffiths phase power law form (x rv T -1+-X) and the respec t i v e magnetic field's log-log behavior. X = 0.9 X= 1.0 X= 1.05 x= 1.1 X = 1.2 1 kG Semilog 0.00903 0.00653 0.00521 0 00545 0.00389 Behavior (x =): 0.00492log10 T 0.00258log10 T 0.00163log10 T 0.00117log10 T 0.000423log10 T 1 kG Semilog T Range (K): 2 4.5 2-4 2 3.75 2 3.76 2 -3 .76 1 kG Log-Log -2.02 -2.18 -2 .28 -2.26 -2.41 Behavior (log10x =): 0.320log10 T 0.208log10 T 0.152log10 T 0.0971log10 T 0.0496log10 T 1 kG Log-Log T Range (K): 2-4.5 2-4 2 -4.26 2 4.75 2 4.01 A1ka: 0 680 0.792 0 848 0.903 0.950 1 T Semilog 0.00887 0.00668 0.00598 0.00521 0.00397 Behavior (x =): 0.00427log10 T 0.00234log10 T 0.00166log10 T 0.00101log10 T -0.0 00314log10 T 1 T Semilog T Range (K): 2 3.50 2 3.05 2 3.05 2 3.20 2 3.50 1 T Log-Log -2.04 -2.17 -2.22 -2.28 -2.40 Behavior (log10x =): 0.263log10 T -0 173log10 T 0.132log10 T 0.0890log10 T -0 0334log10 T 1 T Log-Log T Range (K): 2-4 2-4 2 3.75 2-4 2 5.50 A1T: 0 737 0 827 0.868 0.911 0.967 I-' c.., t--:>

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Table 4 -8: Fit results for UCusxNix de susceptibility data at 2 T and 3 T. The lines wer e plotted on se m ilog graphs and log-log graphs. The temperature ranges were selected such that the maximum temperature range yielded minimum s t andard deviation values. The A values were obtained from the Griffiths phase power law form (x ,.._, T -1+.X) and the r es p ect i ve magnetic field's log-log behavior. X= 0.9 X= 1.0 X= 1.05 x= 1.1 X = 1.2 2 T Semilog 0 00823 0.00644 0.00588 0 00513 0.00400 Behavior (x =): 0.00315log10 T 0.00180log10 T 0.00128log10 T 0.000789log10 T 0.000214log10 T 2 T Semilog T Range (K): 2-6 2-4 2-5 2 3.75 2-8 2 T Log-Log -2.07 -2.19 -2.23 -2.29 -2.40 Behavior (log10x =): 0.215log10 T -0 134log10 T 0.101log10 T 0.0695log10 T 0.0246log1 0 T 2 T Log-Log T Range (K): 2 55 2-40 2-28 2 17 2-9.5 A2r: 0.785 0.866 0.899 0.930 0 975 3 T Semilog 0.00800 0.00655 0 00578 0 00523 0.00408 Behavior (x =): 0.00287log10 T 0.00162log10 T 0.00111log10 T -0 0007 44log1 0 T 0 .000229log10 T 3 T Semilog T Range (K): 2.9 8.5 2 3 8.5 2 45 2 -20 2-5 3 T Log-Log -2.07 -2.17 -2.23 -2 .28 -2.39 Behavior (log10x =): 0.215log10 T 0.131log10 T 0.102log10 T 0.0688log10 T 0 .0261log10 T 3 T Log-Log T Range (K): 4-45 4-38 2.75 30 2 14 2-6 A3r: 0 785 0.869 0.898 0.931 0.97 4 .....

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Table 4 -9: Fit results for UCus-xNix de susceptibility data at 4 T. The lines were plotted on semilog graphs and log-log graphs. The temperature ranges were selected such that the maximum temperature range yielded minimum standard devia tion values. The A values were obtained from the Griffiths phase power law form (x rv T-1+.x) and the 4 T's log-log behavior. X = 0.9 X = 1.0 X = 1.05 X = 1.1 X = 1.2 4 T Semilog 0.00773 0.00639 0.00569 0.00516 0.00406 Behavior (x =): 0.00261log10 T 0.00146log10 T 0.00105log10 T 0.000723log10 T 0.000218log10 T 4 T Semilog T Range (K): 3.75 -10 2.9 20 2 32 3.5 -18 2-4 4 T Log-Log -2.08 -2.18 -2.23 -2.29 -2.39 Behavior (log10x =): 0.210log10 T 0.129log10 T 0.0995log10 T 0.0666log10 T 0.0263log10 T 4 T Log-Log T Range (K): 4-40 4-36 3.2 -28 2 .75 13 2-6 A4T: 0.790 0.871 0.901 0.933 0.974 .... CJ,:>

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135 Table 4-10: Specific heat results for annealed UCus-xNix samples. The UCus-xNix samples were annealed 14 days at 750. The TNeel values were obtained from spe cific heat measurements in H = 0 T as exemplified in Fig. D-1. The y0 values were calculated from Moriya and Takimoto fits shown in Fig. 4-11. The >.c/T values were garnered from the fits displayed in Fig. 4-12. The 'Y values were extrapolated from fifth order polynomial fits of the specific heat over the entire measured temperature range. The Wilson ratios were calculated using 218.7 x(T = 0)/-y~IJ. where x(T = 0) and elf. are listed in Table 4--6. X TNeel .c;T in C/T 'Y (mJ R (Wilson (Ni cone.): (K): Yo: rvT-l+Ac/T: mole-1 K-2): Ratio): 0.6 4.06 0.33 0.75 1.82 0.03 254 1.4 0.8 1.27 0 06 0.065 273 1.2 0.9 0.426 0.035 0.011 0.628 359 0.92 1.0 0.00013 0.630 318 0.50 1.05 0.739 234 0.45 1.1 0.799 148 0.71 1.2 0.903 96.2 0.85

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CHAPTER 5 UCu2Si2-xGex RESULTS AND DISCUSSION The UCu 2 Si 2 -xGex samples (x = 0, 0.2, 0.4, 0.6, 1, 1.4, 1.6, 1.8, and 2) were broken in half after arc-melting. One half had its de magnetic susceptibility mea sured; several unannealed compounds had their de electrical resistivity measured. The other half of each sample was annealed for 14 days at 875C. The length of time and temperature at which annealing occurred gave small mass losses ( < 0.5 % of the total mass of the sample to be annealed) and the sharpest magnetic tran sitions (these transitions are discussed below). The sample of UCu 2 Ge 2 (made in year 2002, listed in Table 5-4) was only annealed for 10 days at 875C due to the larger mass loss (1.21% of the total mass of the sample was lost during annealing) observed in the pure Ge compound. Two other samples of UCu 2 Ge 2 (made in years 2003 and 2004 that are characterized in Table 5-4) were arc-melted with excess Cu and Ge mass ( as discussed in the "Experimental Techniques" chapter) to compensate for the mass loss during annealing and were then annealed for 14 days at 875C. X-ray diffraction peaks of UCu 2 Si 2 and UCu 2 SiGe showed single phase samples in the tetragonal ThCr 2Si2 structure. Lattice parameters were not necessary since the interest is in the magnetic properties of the UCu 2 Si 2_xGex compounds The UCu2Si2-xGex compounds had their de magnetic susceptibility measured in a 1000 Gauss (G) magnetic field. The de magnetic susceptibility was measured in a SQUID from 2 K to 300 K with a particular emphasis (enhanced temperature resolution) from 95 K to 115 K, the range over which Tc occurs in UCu 2 Si 2 -xGex. In order to eliminate as much as possible effects due to preferred crystalline orientation, each sample was aligned such that the bottom of the sample that 136

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137 touched the copper hearth on the arc-melter after the final arc-melt was parallel to the SQUID's magnetic field. The orientation of all samples was consistent. The de magnetic susceptibility versus temperature data were used to deter mine the Tc value for each compound. Tc was taken to be the inflection point on the x(T) curve, i.e., the temperature where d 2x/dT2 = 0. Although this method seems arbitrary, previous works have used the same method to determine Tc for UCu 2Si2 [128, 127]. The computer program MicroCal Origin 5.0 was used to calcu late the numerical derivatives. In order to calculate the first derivative, the average of the slopes of two adjacent points for each data point, (Ti, Xi), is taken using the following generic equation: (5.1) Then, the second derivative is taken by following the same procedure above using first derivative data points. The temperature where d 2x/dT2 = 0 is then the Tc value. A graph demonstrating the Tc determination for annealed UCu2Ge2 is shown on page 138. The uncertainty in the Tc values is then the temperature interval around Tc for which susceptibility values were taken. In most cases the interval was 0.5 K while some measurements were taken in 0.25 K intervals. The de electrical resistivity for each compound was measured for at least one decade of temperature: 1 K T 10 K. The low-temperature resistivity data were then fit to a three variable power law form: p = Po + AT0 The absolute accuracy of the resistivity is ,...., 4% with almost all of the uncertainty stemming from the geometrical factors of the resistivity bars (the uncertainty for the dimensions of the resistivity bar is 0.001 in. while each dimension is on the order of 0.030 in.). However, the temperature precision is good enough (especially for the annealed samples) to determine the resistivity as a function of temperature (i.e., the exponent a mentioned above) quite accurately. An example of the

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4------------------------3 -;-(I) 2 0 E :::::, E .!-1 0 95 100 D 105 T (K) D D DDcJ Dooocooo 110 115 0.20 0 15 0.10 -CD 0.05 3 C: 3 0.00 0 a; ... -0.05.....,, -0.10 Figure 5-1: Tc determination for annealed UCu2Ge2 The hollow squares are 138 the magnetic susceptibility values versus temperature around the ferromagnetic transition of annealed UCu2G~. The solid line is the numerical second derivative showing that Tc occurs at 108.4 K.

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139 precision is shown for the annealed sample of UCu 2 SiGe in Fig. 5-2 on page 140. Finally, resistivity values at room temperature (i.e., rv 300 K) were taken for each sample in order to determine the RRR values, p(300 K)/ p(0). 5.1 UCu2Sh-xGex Results The UCu 2Si2_xGex results are shown extensively in four tables at the end of this chapter. The first two tables on pages 153 and 154 concern data for unan nealed UCu 2Si2_xGex compounds while the last two tables on pages 155 and 156 show data for UCu 2 Sh-xGex compounds annealed 14 days at 875C (except for one UCu2Ge2 sample as indicated). A few general comments may be made concerning the tables of data. First, if one compares the Tc interval ( the temperature range where the numerical second derivative goes from its minimum value to its maximum value as seen in Fig. 5-2) for unannealed samples and then the exact same samples that were annealed for 14 days at 875C, one sees that generally the Tc interval is narrower for the annealed samples. Therefore, these better ordered samples were used to check the theory of Silva Neto and Castro Neto [137]. The narrower Tc interval justifies the previous statement that annealing does "sharpen" the ferromagnetic transition. Also, particular attention was paid to the actual stoichiometry of the UCu2Si2-xGex compounds as seen in the tables (using the assumptions for mass losses mentioned in the "Experimental Techniques" chapter). These actual stoichiometries show that minor changes in the stoichiometry for the annealed UCu2Ge2 samples (in Table 5-4) have a negligible effect upon the Tc values (taking into consideration the error bars for Tc). The original annealed UCu 2 Ge 2 sample (i.e., the one made in year 2002) and the annealed "check" samples (the ones made in years 2003 and 2004) have nearly identical Tc values: 108.4 K (year 2002), 108. 9 K (year 2003), and 108. 7 K (year 2004). The average of these three annealed UCu2Ge2 samples is rv 108.7 K. This average is within the experimental

PAGE 152

5 -f :.:; u, "in Cl. 1345 1340 1335 1330 a x = 1.0, annealed 14 days 875C -p(T,x) = p(O,x) + Ar 1325 ______ ..,....,....... _______ .......,,...... __ ,...... ____ ...,..... 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Temperature (K) Figure 5-2: Resistivity versus temperature for UCu2SiGe. UCu2SiGe was an nealed for 14 days at 875C. The graph shows the good precision at which the resistivity values were obtained. The power law fit in the graph yields 140 p(0, x = 1.0) = 1328 O. cm, A = 0 0426 K -2 33 and a = 2.33. Graph is taken from the work of Silva Neto et al. [138].

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uncertainty of all three annealed UCu 2 Ge 2 Tc values. On the opposite side of the UCu 2 Sh-xGex phase diagram, the annealed UCu2Si2 samples do show some deviations in Tc. The original annealed UCu 2Si2 sample (year 2002) and the annealed check sample (year 2004) deviate by about 2%: 102.9 K (year 2002) 141 versus 100.7 K (year 2004). In addition, the average of these two annealed UCu2Si2 samples (101.8 K) is outside the uncertainty of the two annealed UCu2Si2 Tc values. However, the data show that the nonmonotonic behavior in Tc is on the Ge rich side; thus, effects on Tc caused by deviations in stoichiometry are experimentally shown to be moot for this study. In fact, the nonmonotonic behavior area of the annealed UCu 2Si2_xGex phase diagram was completely redone with annealed UCu2Ge2, UCu2Sio_4Ge1.5, and UCu2Sio.5Ge1.4 samples made again in the year 2004 as shown in Table 5-4 on page 156. The new UCu2Ge 2 UCu2Sio.4Ge1.5, and UCu2Sio.6Ge1.4 samples (made in year 2004) are more accurate in their actual concentrations ( to the nominal stoichiometry) compared to the original UCu2Ge2, UCu2Sio_4Ge1.5, and UCu 2Si0 .6Geu samples (made in year 2002). The nominal concentrations UCu2Ge2, UCu2Sio.4Ge1.5, and UCu 2Sio.6Geu made in the year 2002 had actual concentrations of UCu1.93Ge1.9s, UCu1.91Sio,39Ge1.s9, and UCu1.91Sio.ssGe1.35 (using the mass loss assumptions for Cu, Si, and Ge as discussed in the "Experimental Techniques" chapter) compared to the year 2004 actual concentrations of UCu1.95Ge1.95, UCui.gsSio.41 Ge1.5s, and UCu1.99Sio.s9Ge1.35. The Tc values and their respective error bars in Table 5-4 for the aforementioned year 2002 samples almost exactly match (within their error bars) the Tc values for the more accurate year 2004 samples. Thus, the nonmonotonic behavior in Tc is confirmed. One point that should be noted concerns the effect annealing has upon the UCu2Ge2 samples. The original sample and the check samples undergo almost exactly the same losses of Cu and Ge atoms (based on elemental vapor pressure

PAGE 154

tables) during annealing: about a 2% decrease in the Cu and Ge concentrations. However, the change with annealing in the ferromagnetic transition temperature 142 is consistently the same for all three UCu2Ge2 samples: a 2.5 Krise for the 2002 and 2003 samples (2002 -from 105.9 K for unannealed in Table 5-2 to 108.4 K for annealed in Table 5-4; 2003 -from 106.4 K for unannealed in Table 5-2 to 108.9 K for annealed in Table 5-4) and a 2.6 Krise for the 2004 sample (from 106.1 K for unannealed in Table 5-2 to 108.7 K for annealed in Table 5-4; one sample was made unannealed while the other sample was made for annealing purposes). A brief scan of the resistivity data in both tables shows that all low temper ature resistivity data (except for unannealed UCu2S4uGe1.6 ) fit a power law form very close to p0 + AT2 Thus, the resistivity data fit a Fermi-liquid form and the T2 variation was predicted by Kaiser and Doniach [70) for conduction electrons (in this case, Cu electrons) scattering from localized spin fluctuations (i.e., the localized U spins). Also, large residual resistivity (p0 ) values were obtained for annealed samples where Si/Ge doping was greatest and some of the p0 values are on the order of the Ioffe-Regel values ("' 200-1000 O cm), the theoretical limit for metallic conduction [89). 5.2.1 Tc Enhancement The original annealed UCu2Si2-xGex samples (made in year 2002) show that Tc as a function of Ge doping, x, is not monotonic. In fact, the x = 1.6 sample has a maximum Tc value of 109 8 K, an increase of 1.29% from the Tc value of the annealed UCu2Ge2 sample (108.4 K). This is in agreement with the prediction made by the theory of Silva Neto and Castro Neto that for small enough dissipation, a 1 % increase of Tc with respect to the case of no dissipation would result [137). Now, the phrase "small enough dissipation" may be quantified for the case of UCu2Si2_xGex, a value of x = 1.6 or 20% Si doping on the Ge site.

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143 The phase diagram for the original annealed UCu2Sh-xGe:r samples is shown in Fig. 5-3 on page 144. The theoretical line drawn in Fig. 5-3 is from Silva Neto et al. that takes into account both spin fluctuations and dissipation introduced by the electronic bath [138]. The continuous line is from the following equation [138, 137]: l j d3k 1~ dw kyo(kl)wna(w/Tc) go= (21r)3 -n!> 7r [k(k2 -coW)]2 + ['Yo(kl)w]2' k (5.2) where n8(w/Tc) = (ew/Tc 1)-1 is the Bose-Einstein distribution function, nf = (2kF )2k/-y0(kl) is an energy cutoff, g0 = Na/2..18J2 is the coupling constant, Co= 1/ ..1HJa2 is the topological constant, and ..1H = ..12(kFa)3 /41r2EF[l a3N(O)Uc] ..18 plays the role of the effective exchange between the U / states and conduction electrons. In the calculation (units were used where 1i = ka = 1), further definitions include N(O) = m*kp/1r2 the density of states at the Fermi energy EF = ki/2m; kp = (31r2n)113 the Fermi wave vector; n = Ne/a3 the electronic density per unit cell with lattice spacing a (a= asi(2 -x)/2 + aoex/2 where asi = 5.4 A and 8.Ge = 5.527 A were chosen so that the volume of the tetragonal unit cell was reproduced [138]); l is the electronic mean free path; VF = kp/m, the Fermi velocity; and the dissipation coefficient, 'Yo(kl), is from Fulde and Luther [50]: o(kl = ski arctan(kl) "f, ) vp[l a3N(O)Uc] 1 (kf)-1 arctankl (5.3) The mathematical details of using Eq. 5.2 to create the continuous line in Fig. 5-3 is beyond the scope of this dissertation. However, Fig. 5-3 shows excellent agreement between the theoretical line and the experimental data. 5.2.2 Resistivity displaying electrons in the ballistic or diffusive regime The data in Fig. 5-3 raises an interesting question. A small amount of Si doping on the Ge site induces nonmonotonic behavior in Tc. Thus, one might ask why a small amount of Ge doping on the Si site does not induce a similar

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-110 109 108 ::, 107 G) 106 .! 105 c 104 ICJ 103 CJ annealed for 14 days at 875C theoretical result by Silva Neto et a/. 102 -+----------------------------------------1 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 x (amount of Ge) 144 Figure 5-3: Tc phase diagram for UCu2Si2-xGex. The phase diagram plots Curie temperature values (Tc) as a function of Ge doping. The experimental values are the hollow squares while the solid line is from the theoretical efforts of Silva Neto et al. as described in the text. This figure was taken from the work of Silva Neto et al. [138]. The vertical error bar for each data point is 0 .5 K as described in Ta bles 5 3 and 5-4.

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145 nonmonotonic behavior in Tc? A partial answer is provided with an investigation of the annealed UCu2Sh-xGex resistivity. The annealed UCu2Si2-xGex low temperature resistivity results show a Fermi-liquid form (the temperature dependence for all samples is very close to T 2 ), implying that the Cu conduction electrons are being scattered by magnetic excitations [70]. If the residual resistivity values for the UCu2Si 2 -xGex samples, p(0, x), are assumed to take a functional form of a random binary alloy [138], then p(0, x) = Ps,(2 -x)/2 + Paex/2 + px(2 x) where Ps, is the Po value for annealed UCu2Si2 (8.44 O. cm), Pae is the Po value for annealed UCu2Ge2 (159 O. cm), and pis the contribution from Nordheim's rule [167]. The above functional form for a random binary alloy is expected to be parabolic; however, a brief look at the Po values for annealed UCu2Si2-xGex samples in Tables 5-3 and 5-4 reveals a non-parabolic nature. One would expect the largest p0 value to occur where the most disorder was created, i.e., at UCu 2 SiGe. Yet the data reveals a local maximum Po value occurring for UCu 2Si0 4Ge1.6 the same compound that also has the maximum Tc value in Fig. 5-3. The reason that the UCu 2Si2 -xGex compounds do not obey the random binary alloy form may be attributed to microcracks in the UCu2Si2-xGex samples due to internal stresses arising from doping [138]. The microcrack effects were cancelled out by dividing the residual resistivity of each sample, p(0, x), by the room temperature resistivity of each sample, p(300 K, x). Hence, one obtains the reciprocal of the RRR values listed in Tables 5-3 and 5-4. A plot of RRR-1 for annealed UCu 2Si2 -xGex compounds and the theoretical function for a random binary alloy are shown in Fig. 5-4. The functional form for a random binary alloy, Ps,(2 -x)/2 + Paex/2 + px(2 x), also has to be normalized p(0 K)/ p(300 K) for annealed UCu 2Si2 is"' 0.0159 and replaces Psi in the previous equation. p(0K)/p(300K) for annealed UCu2Ge2 is"' 0.164 and replaces Pae in the above equation. The normalized p from Nordheim's rule (based upon theory

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UCu2S12 .. Gex 0.30 -----------...-----.....--....-----....... -----, ..... 0.25 0.20 >< 0 0.15 o 0.10 0: 0.05 o Experimental data (annealed 14 days 875C) --Random binary alloy 0.00 ----------.-------------------.0.0 0.2 0.4 0.6 0 8 1.0 1.2 1.4 1.6 1.8 2.0 x (amount of Ge) 146 Figure 5-4: The reciprocal RRR values for annealed UCu2Si2-xGex. Hollow squares represent the UCu 2Si2 _xGex compounds (made in year 2002). The solid line is a theoretical function for a random binary alloy by Silva Neto et al. [138] as de scribed in the text. The absolute accuracy of each normalized residual resistivity value is less than 0.5%.

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147 of transport phenomena in solids [138]) that was used in Fig. 5-4 was"' 0.141. Figure 5-4 shows the good agreement between the random alloy expression and the experimental data. Figure 5-4 may also be used to deduce information about the electronic mean free path and the electronic dynamics. The Drude relation is used to relate the resistivity to the mean free path,: p = m*vp/ne2. Qualitatively looking at the normalized p values in Fig. 5-4, one sees that the endpoints of the phase diagram, e.g., UCu 2Si2 have lower resistivity values, implying that the endpoint compounds have larger mean free paths than the compounds with disorder (i.e. those in the middle of the phase diagram). One may calculate the mean free path values for the UCu2Si2-xGex com pounds. First, to match the volume of the tetragonal unit cell and to account for the change in the size of the unit cell with Ge doping in UCu 2Si2 -xGex, one may write a Vegard's law type equation: (5.4) where asi = 5.4A and aae = 5.527 A [138]. The electronic density per unit cell, Ne/a3 may now be calculated with the conduction electrons coming from the Cu atoms and Ne = 8 with each Cu2+ contributing one electron to the conduction band and there are 8 Cu atoms per unit cell as seen in Fig. 1-2 on page 18. The electronic density, n"' 5.08 x 10-2 A-3 is independent of the Si/Ge concentration in the UCu2Si2-xGex compounds. Now, the Fermi wave vector, kp, is"' 1.15 A -1 and it is independent of Si/Ge concentration too. kF is on the same order of magnitude as that for a normal metal. If one takes the residual resistivity value for UCu 2Si2 (8.44 x 10s nm from Table 5 -3) and uses the previous values in the Drude formula relating the resistivity to the mean free path [ = 1ikp / pne 2 (MKS units)], then the mean free path value for annealed UCu 2Si2 is"' 110 A and the

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148 product, kpi, is rv 127. This is an interesting result because the mean free path for annealed UCu2Si2 is on the same order of magnitude as the mean free path of Cu wire at room temperature ( i rv 390 A [2]) despite annealed UCu 2Si2 having a Po rv 1000 times bigger than for normal metals. However, the mean free path should be scaled down by about a factor of 10. The reason concerns a factor of 10 difference between the (smaller) measured values and the (larger) predicted values (from Drude's formula) for the "drift velocity" in a Cu wire at room temperature [138, 2]. Since the drift velocity is directly proportional to the mean free path, the mean free path is divided by 10 so that the correct current density (= -nev where vis the drift velocity) at room temperature is obtained [2]. Since Cu wire and annealed UCu 2 Si 2 have similar transport properties, the mean free path is also scaled down (by a factor of 10) to"' 10 A and the product kpi is rv 10. If one moves across the UCu2Sh-xGex phase diagram to UCu 2Sio,4Ge1.6 then the lattice spacing a expands to rv 5.5016 A using Eq. 5.4. Hence the electronic density and Fermi wave vector become 4 .80 x 10 2 A -a and 1.12 A-1 respectively. The residual resistivity for UCu 2Si0 .4Ge1.6 (6.90 x 105 nm from Table 5-4) is then used in Drude's formula and the calculated mean free path is "" 1.39 A. Instead of scaling down by a factor of 10, UCu 2Sio. 4Ge1.6 is only scaled down by a factor of 2 since the Si concentration has been reduced by a factor of 5. The corrected mean free path is rv 0.70 A and the product, kpi, for annealed UCu2Sio.4Ge1.5 is"' 0.80 [138]. Thus the mean free path for UCu 2Sh is more than an order of magnitude larger than the mean free path for UCu 2Sio_4Ge1.6 Figure 5 4 shows that the smallest mean fr ee path (or the largest resistivity by the Drude relation) theoretically occurs at around x = 1.3, very close to x = 1.6 the compound which has the highest TO value. This implies that the conduction electron dynamics for UCu2Sio_4Ge1.5 are in the diffusiv e regime (also, the product kpi, being of order one for UCu2Sio. 4 Ge1.6 signifies that the electrons are in the diffusive regime)

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149 Referring back to F ig. 2-3 on page 45 in the "Theory" chapter, one may assume that the Ge rich end of the UCu 2Si2 -xGex phase diagram is in the diffusive regime and 6 = 2 ( along with c0 = 1) for Fig. 2-3. Thus, Fig. 2-3 in the "Theory" chapter predicts the nonmonotonic behavior in Tc for the Ge rich end of UCu 2Si2_xGex due to the electron dynamics being in the diffusive regime. The normalized Ge rich end resistivity values in Fig. 5-4 justify the placement of the electrons in the diffusive regime since it is known that electrons in the ballistic regime (i.e., on the Si rich side since kp "' 10 for UCu 2Si2 ) have a mean free path (resistivity) larger (smaller) than electrons in the diffusive regime [137]. Figure 2 3 also sheds light on two other important results from the UCu 2Si2_xGex phase diagram on page 144. A small amount of dissipation, indicated by r,0 in Fig. 2 -3, is predicted to increase Tc by about 1 % [137]. The dissipation is controlled by the disorder (for the Ge rich end of UCu 2 Si 2 -xGex, disorder is introduced by Si doping) Thus 20% Si doping on the Ge site in UCu 2 Ge 2 is a small enough amount of dissipation to induce approximately a 1 % increase in Tc and create nonmonotonic behavior in Tc for UCu 2Si2 -xGex compounds. Also, having taken into consideration Fig. 2 3 from the "Theory" chapter, one may now explain why no nonmonotonic behavior is found on the Si rich side of the UCu2Si2-xGex phase diagram. In the previous paragraph, it was determined that the UCu 2Si2 's electrons were in the ballistic regime. In fact, from Fig 5 4 on page 146, one sees that the mean free paths for Si rich end compounds are much larger than the mean free paths for Ge rich end compounds, implying that the Si rich UCu 2Si2-xGex com pounds have electrons that are in the ballistic regime. Electrons that are in the ballistic regime are notated with 6 = l in Fig. 2 3 of the "Theory" chapter and one sees that the theoretical curve gives monotonic behavior for electrons in the ballistic regime, even when a small amount of disorder (i.e ., dissipation) is introduced. Correspondingly, the Tc values on the Si rich side of Fig 5 3 on page 144 in crease

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150 monotonically as more Ge is doped on the Si sites. This is expected from Fig. 2 3 in the "Theory chapter since the electrons are in the ballistic regime. Thus the nonmonotonicity in Tc as a function of Ge doping for UCu2Si2-xGe x is attributed to the conduction electrons' scattering being modified by disorder. In particular the conduction electron behavior moves from the ballistic regime to the diffusive regime as more Ge replaces Si in UCu2Si2-xGex compounds. Since the UCu2Si2xGex system proves the theory of Silva Neto and Castro Neto concerning the interplay of disorder and spin fluctuations in a ferromagnetic alloy, are there other ferromagnetic alloys that could give credence to this theory or is UCu2Sh-x Ge x just a sport? One work that provides a summary of some ferromagnetic materials is by DeLong et al. [37]. Two ferromagnetic samples from that work UlrAl (Tc ""64 K) and UPtAl (Tc ""52 K) were made as endpoints of a phase diagram and disorder was created on the Ir/Pt sites. Preliminary results show that the T c values are nonmonotonic for unannealed Ulr1_xPtx Al in Fig. 5 5 on page 152. However the Uir1_ x PtxAl system may not be applicable to the theory of Silva Neto and Castro Neto One reason concerns the structure of UPtAl and UlrAl. Both compounds belong to the hexagonal ZrNiAl-type crystal structure [6]. The hexagonal crystal structure is composed of alternating two types of basal-plane atomic layers along the c axis. One plane is composed of all U atoms and 1/3 o f the Pt /Ir atoms while the othe r plane contains the rest of the Pt /Ir atoms with all of the Al atoms [6]. The concern is disorder affecting the magnetic sublattice since there is hybridization of 5f states (from the U atoms) with valence electron states of ligands (from the Pt/Ir atoms). Thus, disorder aff ec tin g t h e conduction electrons may not be the only mechanism having a role upon the magnetism in the Ulr1_xPtx Al s ys tem. Obviously further measur e ments need to b e performed namely low t e mperature resistivit y measur e m e nts to inv es tigat e whe ther or not e lectronic d y namics in the Uir1_ xPtx Al compounds are in the balli s tic or diffu s iv e

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151 regime. Finally, if the dissipation theory of Silva Neto and Castro Neto does not accurately describe the nonmonotonic behavior in the Ulr1_xPtx Al system, then other compounds mentioned by De Long et al. may be good candidates since the magnetic sublattice would not be directly affected as it might be in Ulri-xPtxAL Other possible compounds would include UCoGa 1_xSn x (the endpoints have a T c range from 51 K to 88 K), UPtA1 1 x Gax (52 K -79 K) UPtGa1-xSnx (79 K 30 K) UlrGa1x Sn x (63 K 33 K) and URhAli-x Gax (28 K -44 K) [37]. All of these compounds form in the hexagonal ZrNiAl structure; however the disorder in the aforementioned compounds should occur only on the basal planes without the U magnetic moments [6] just as the disorder did not affect the magnetic sublattice in the UCu2Si2-xGe x compounds

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152 70 D unannealed Ulr1 Pt.AI D D -65 .. 60 D ::::, CD a. 55 D E CD ii 50 u +I "C u 45 -D 1-u D 40 D D D 0.0 0.2 0.4 0. 6 0.8 1 0 x (amount of Pt) Figure 5 -5: Phase diagram for unannea l ed Ulr1_ xPtxA l system The ho llow squares represent the Tc values vers u s Pt doping for unannealed Ulri-xPtxAl compounds The unannealed samp les show nonmonotonic behavior in Tc at the Ir rich end and the Pt rich end of the phase diagram The vertical error bars for each sample are 0.25 K as shown on t h e UlrAl Tc data point

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Table 5 1: Magnetic susceptibility and resistivity results for unannealed UCu2Sh-xGex samples (I). The Tc valu es were obtained from magnetic susceptibility results. The T c interval was arbitrarily defined as the temperature range where the numerical second derivative went from its minimum value to its maximum while passing through zero ( i.e., the T c value) The resistivity data were fit to a power law form, p0 + AT', that minimized chi squared. Nominal Stoichiometry Actual T c Po A T (prod. date): Stoichiometry: Tc(K) arc(K): Interval (K): RRR: ( O.cm ) : (O.cmK-'): a : Range ( K ): UCu2Si2 UCu1.91Sii .99 102.3 0.5 4.00 21 17.4 0.00438 2 .31 1.12-12.1 (10-23-02) UCu2Si2 UCu1.99Si1.98 102.4 0.25 3.49 (10-10-02) UCu2Sh UCu2 .00Sii.99 100.9 0 25 1.99 (10-8-04) UCu2Sii 8Geo.2 U Cu 1.98 Si 1. 76 Geo .11 102.9 0.5 3 .97 (10-17-02) UCu2Si1.6Geo.4 UCu1.98Si1.00Geo.38 103.9 0 5 3.00 4.91 249 0.011 8 2.43 1.0 5 -12.0 (11-18-02) UCu2Si1.4Geo.6 U Cu 1.98 Si 1.31Geo.s8 105.3 0.5 2.50 (11 21-02) UCu2 SiGe UCu1.99Si1.00Ge1.oo 107.9 0.5 2.49 4.54 136 0 021 8 1.76 1.05-13.0 (11-25-02) UCu2Sio .6Ge1.4 U Cu 1.99Sio.s8 Ge1.41 108 .3 0.5 2 01 (12-3-02) C}l (:;j

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Table 5-2: Magnetic susceptibility and resistivity results for unannealed UCu2 Si 2 _xGex samples (II). The T c values were obtained from magnetic. susceptibility results The Tc interval was arbitrarily defined as the temperature range where the numerical second derivative went from its minimum value to its maximum while passing through zero (i.e., the T c value). The resistivity data were fit to a power law form, p0 + AT\ that minimized chi squared. Nominal Stoichiometry Actual T c Po A T (prod. date): Stoichiometry: Tc(K) o-rc(K): Interval (K): RRR: (Ocm): (OcmK-0): a: Range (K): UCu2Sio.6Ge1.4 UCu2.e>oSio.s9Ge1.39 108 1 0 25 1.00 (9-21-04) U Cu2 Sio.4 Ge1.6 UCu1.99Sio_39Ge1.61 107.9 0.5 2.50 3.65 107 0 389 0.835 1.21-10.3 (12-5-02) UCu2Sio_4Ge1.6 UCu2 .00Sio_39Ge1.oo 108.2 0.25 1.74 (9-22-04) UCu2Sio .2Ge1.s UCu1.99Sio.1sGe1.s1 107 .3 0.5 2.50 (11-1-02) UCu2Ge2 UCu1.9sGe1.99 105.9 0.5 4.49 4.13 75.8 0.00861 1.76 1.10-10.0 (11-8-02) UCu2Ge2 UCu1.99Ge2.oo 106.4 0.5 4.01 (1-9-03) UCu2Ge2 UCu1.99Ge2.oo 106.1 0.25 2.24 (9-3-04) -CJl

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Table 5 -3: Magnetic susceptibility and resistivity results for annealed UCu 2 Si 2 -xGex samples ( I) All UCu 2 Si 2 _xGex samples were annealed for 14 days at 875C. The Tc interval was arbitrarily defined as the temperature range where the numerical derivative went from its minimum value to its maximum value while passing through TcThe resistivity data were fit to a form of Po+ ATa. Nominal Stoichiometry Actual T c Po A T (prod. date): Stoichiometry: Tc(K) O"T0(K): Interval (K): RRR: (Ocm): (OcmK-a): a: Range ( K) : UCu2Si2 UCu1.9sSi1.99 102 9 0.5 3.49 63 8.44 0 .00 189 2.57 1.06-12 0 (10-23-02) UCu2Si2 UCu1.99Si1.99 100 7 0.25 1.01 (10-7-04) UCu2Si1.sGeo.2 UCu1.91Si1.16Geo.16 103.1 0.5 3.48 (10-17-02) UCu2Sil.6Geo.4 UCu1.91Sil.60Geo.31 103.8 0.5 3.50 8.47 132 0.00984 2.38 1.09-12.1 (11-18 02) UCu 2Si1.4Geo. 6 UCu1.91Si1.31Geo.s1 105.3 0.5 2.52 (11-21-02) UCu2 SiGe UCu1.9sSi1.00Geo.99 108.3 0.5 2.00 4.21 1330 0.0426 2 33 1.03-14.0 (11-25-02) UCu2Sio.6Ge1.4 UCu1.91Sio. ssGe1.3s 109.3 0.5 2.01 4.37 352 0.0341 2.12 1.04-13.0 (12-3-02) ..... C}l C}l

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Table 5-4: Magnetic susceptibility and resistivity results for annealed UCu2 Si 2 _xGex samples (II). All UCu2 Si 2 _xGex samples were annealed for 14 days at 875C except for one UCu 2Ge2 sample (annealed only for 10 days due to a large mass loss during annealing-1.21% of the total mass) as indicated by a*. The T c interval was arbitrarily defined as the temperature range where the numerical derivative went from its minimum value to its maximum value while passing through TcThe resistivity data were fit to a form of p0 + A~. Nominal Stoichiometry Actual Tc Po A T (prod. date): Stoichiometry: Tc(K) arc(K): Interval (K): RRR: (Ocm): (OcmK-0): a: Range (K): U Cu2 Sio.6 Ge1.4 UCu1.99Sio.s9Ge1.38 109.4 0.25 0.75 (11-9-04) UCu2Sio.4 Ge1.6 UCu1.91Sio.39Ge1.s9 109.8 0 5 2.00 4 10 690 0.0120 2.63 1.26-11.0 (12-5-02) U Cu2 Sio.4 Ge1.6 UCu1.9sSio.41 Ge1.ss 109.7 0.25 0.74 (11-10-04) UCu2Sio.2Ge1.s U Cu 1.9s Sio.1s Ge1.so 109.3 0.5 1.90 4.72 391 0.0125 2.44 1.13-13.0 (11-1-02) *UCu2Ge2 UCu1.93Ge1.9s 108.4 0 .5 2 .01 6.11 159 0.0216 2 16 1.22-10.0 (11-8-02) UCu2Ge2 UCu1.9sGe1.96 108.9 0 25 1.24 (1-9-03) UCu2Ge2 UCu1.96Ge1.96 108.7 0.25 1.00 (10-6-04) ..... CJ1 O'l

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CHAPTER 6 CONCLUSIONS AND FUTURE WORK 6.1 UCu 5_xNix Conclusions The disorder created in the UCu 5_xNix system by the substitution of Ni atoms for ligand Cu atoms suppresses the antiferromagnetism in UCu 5 and creates NFL behavior. The lattice parameters for unannealed and annealed (14 days at 750 C) UCu 5 xNix show no possibility of partial sublattice ordering as has been debated in the UCu 5 _xPdx system. The smaller Ni atoms (compared to the Cu atoms) are distributed equally ( rv 25%) on the 4 smaller Be sites in the AuBe 5 crystal structure as compared to less than 5% of the Pd atoms occupying each smaller Be site in AuBe 5 This lack of sublattice ordering meant that distinctions between quantum criticality and disorder could be made. The specifi c heat for UCu 5_xNix showed that annealed (14 days at 750 C) UCu4Ni exhibited NFL behavior down to the lowest temperature of measurem ent and the NFL behavior was due to quantum critical point spin fluctuations. The quantum critical point TN -----t 0 was demonstrated by the UCu4Ni specific heat data showing no antiferromagnetic transition down to its lowest measur e d temperature (rv 0.060 K) as occurred in annealed UCu4 1Ni0 9 (TN rv 0.4 K) Also fitting of the C/T UCu 5 x Ni x data to the spin fluctuation theory of Moriya and Takimoto predi cts a quantum critical point, y0 -----t 0 in agr ee m ent with the UCu4Ni data. A third jus tifi c ation of quantum criticality occurring at UCu4Ni conc erns the Wilson ratio that was qualitativ e l y c onsistent with UCu4Ni c ro s sin g over from magnetic to nonmagn etic. Small variation s in the Ni con centra tion around UCu4Ni w e r e p e rform e d in order to inv es tigat e the roles of quantum c ri t i c alit y and di s ord e r in UCu 5-xNix. 157

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158 The Griffiths phase disorder model was used to examine the NFL behavior in UCu5-xNix. The Griffiths phase disorder model is a combination of the quantum critical point phenomena with disorder The Griffiths phase is brought about by rare strongly coupled magnetic spin clusters close to a quantum critical point. The closeness for UCu5_xNix is a 5% increase of the Ni concentration from the quantum critical concentration of UCu 4Ni. The Griffiths phase for UCu3 95Ni1.05 was characterized by power law behavior for de magnetic susceptibility and specific heat (i.e., x,...., T-1+..\x ; C/T,...., T-l+..\c;r) According to the specific heat the Griffiths phase existed for UCu3 .95Ni1.05 ( down to ,...., 0.060 K) and UCu3 .9Ni1.1 (down to,...., 0 3 K); UCu3 8Ni1.2 began to deviate from the Griffiths phase behavior at ,...., 0 5 K, signifying that UCu3 8Ni1.2 was too far from the spin fluctuations of the quantum critical point. The specific heat of UCu5_xNix samples around the quantum critical con centration of UCu 4Ni was measured in various magnetic fields. The Griffiths phase disorder model predicts that the Griffiths phase disappears above a certain crossover magneti c field ( det e rmined from magn e tization versus field data wh e r e the magnetization crosses over from linear behavior to power law behavior). The Griffiths phase disorder model predicts a magnetic field induced peak above the crossover field for the specific heat. UCu 4 .1Ni0 9 does not show a fie ld induced peak above its determined crossover field and this lack of a peak ( at 3 T) might have a correlation with the antiferromagnetism still present in UCu4 _1Nio_g. UCu4Ni also does not show a field induced peak abov e its crossover magn etic field and this may b e r e lated to the quantum critical s pin fluctuation s present in UCu 4Ni. UCu3 .95Ni1.05 does show Griffiths phase (in zero field specific heat data) and a field induced peak above its crossover magnetic field at 3 T. However the quantitative fit of the Griffith s phase disorder model does not match the UCu3 9 5Nii .0 5 data at 3 Tor 6 T. U C u3 9Niu i s the only c onc e ntration wh e r e the Griffith s phas e di s ord e r

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159 model matches the specific heat data above the determined crossover magnetic field (i.e., at 6 T) and over the entire measured temperature range. The Griffiths phase disorder model matches the UCu3 8Ni1.2 6 T specific heat data above the determined crossover magnetic field yet the temperature range is limited compared to the UCu3 9Ni1.1 fit. Finally, the de magnetic susceptibility was measured in higher magnetic fields to provide further insight into the behavior of the Griffiths phase. The de magnetic susceptibility at higher magnetic fields for UCu5_xNix just added to the inconsistencie s of the Griffiths phase disorder model especially when compared to specific heat data measured at the same magnetic field. For example the magnetic susceptibility at 2 T for UCu4Ni showed power law behavior over more than a decade of temperature implying possible Griffiths phase behavior. However specific heat data at 2 T do not show power law behavior (predicted by the Griffiths phase disorder model) and it has been already established by the zero field specific heat data that quantum critical fluctuations not magne t ic spin cluster fluctuations were the phenomena occurring in UCu4Ni. This type of inconsisten c y was found at some magnetic field for every Ni concentration around the quantum critical concentration of x = 1.0. Thus, a theoretical model more complex than the Griffiths phase disorder model may be needed to explain all characteristics of the UCus xNix data. 6.2 Future Work Derived from UCu5_ xNix Results The future work on UCu5_ xNix will be divid e d into two parts. The first part involves measurements directly upon the UCu5_ xNix system whil e the second part involves other projects related to the UCu5_xNix system. The most obvious future work on the UCu5_ xNix system would involve measuring the sp ecific heat and magn e tic s u s c e ptibility for the c once ntration s around x = 1.0 down to dilution r e frig erator t emperatures in zero fie ld ( or a l o w

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field for susceptibility) and 0.5 T field intervals up to ,..._, 6 T. One might be able to say then where the NFL behavior in UCu3 9Niu is attributable to Griffiths phase and where the theory explaining the NFL behavior in UCu3 9Niu should 160 be developed more by possibly combining different components of the Kondo disorder model, self-consistent renormalization model, and quantum Griffiths phase together. Also, one could determine a little more accurately which Ni concentrations had their NFL behavior described sufficiently by Griffiths phase behavior. Those Ni concentrations described by Griffiths phase would have a little smaller range for where the crossover magnetic field occurs due to the onset of a field induced peak, signifying that the splitting between energy levels is too large such that tunneling ceases. Additional insight could be gained about Griffiths phase behavior ending with UCu3 8Ni1.2 being too far from the quantum critical point and its spin fluctuations. Further measurements upon the UCus-xNix samples would be performed to investigate the amount of disorder in the UCus-xNix system. For example EXAFS measurements should be carried out on UCu4Ni to determine how much Ni is on the larger Be site and the smaller Be sites in the AuBe5 structure just as was done on unannealed and annealed UCu4Pd [15, 16]. It would also be interesting to perform SR and NMR studies upon UCu4Ni so that further insight might be gained into the disorder in the UCus-xNix system. A further extension of this dissertation would concern more doping of the ligand Cu atoms with Ni to search for the onset of spin-glass behavior. Work by Chau and Maple along with work by Koerner et al. determined that spin glass behavior began above UCu3 5Pd1.s [26, 77]. One might expect spin glass behavior to begin above UCu3 5Ni1.5 in light of the fact that antiferromagnetism is suppressed for annealed UCu4Pd [160] and annealed UCu4Ni.

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161 The second part of this future work's section concerns new projects that are offshoots of the UCus -xNix system just as UCus-xNix was an offshoot of UCus-xPdx. Other transition meta l s have been tried as dopants for UCu5 Chau an,d Maple suppressed antiferromagnetism in UCus-xPtx and found NFL behavior while the doping of Cu using Ag or Au did not result in the suppression of magnetic ordering or NFL behavior [26]. For this dissertation, two other elements on the same row of the periodic table as Ni were attempted: Fe and Co UCu4Fe had its magnetic susceptibility measured and the susceptibility values were on the order of hundreds of memu/mole (as compared to UCus -xNix being on the order of just memu/mole) and did not show NFL behavior The UCus-xCox system had magnetic susceptibility values that were on the order of memu/mole as shown in Fig. 6--1 on page 162. Figure 6 1 also shows that the variation in Co concentrations (0. 75 x 1.5) does not suppress the antiferromagnetic transition temperature, TN, or show NFL behavior at low temperatures. A couple of explanations may exist for the lack of suppression in UCus -xCox. First, when the Cu is doped with Co, the hybridization may move the 4s1 valence electron from the Cu atom [7] and combine it with the 3d7 4s2 valence electrons from the Co atom [7] and create a filled 3d10 valence shell. Chau and Maple have suggested that a completely filled d-electron shell may be the reason why UCus -xAgx or UCus -xAux does not show NFL behavior. Second, the ligand atoms used in UCus-xNix, UCus-xPdx, and UCus xPtx are involved in hybridization effects with the U 5/ electrons [117] that lead to the good possibility of an intermediate electronic configuration of the uranium ions (U3+ and U4+ as discussed previously). Schneider et al. have done photoemission work and concluded that there was no evidence for two different final-state 5/ multiplets in the valence-band spectrum of UCu5 [133]. Thus, hy bridization between the U, Cu and Co/Fe atoms could result in an integral valency

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162 UCusCo 0 0050 ~ + + X = 0.75 0 0045 ++ I::),. x= 1.0 ++ + 0 X = 1.25 +++ + + D x= 1.5 0.0040 ++ ++ Q) ++ 0 0.0035 t::. t::. ++ + E t::. t::. + t::. + ::, t::. t::. t::. E 0.0030 oooo t::. t::. t::. Q) ooo t::. 000 0 0 0025 0 ~Do0 0.0020 Do Doooo D D 0.0015 0 10 20 30 40 50 T (K) Figure 6 -1: DC magnetic susceptibility res ults for UCus-xCox. The low temperature de magnetic susceptibility for UC u s-xCox samples was measured in a 1 kG magnetic field. The anti ferromagnetic transition temperature, TN, is not sup pressed with the change in Co concentration. The TN values are the maximum x values in the graph: TN = 5 50 K for UCu4 .2 5 Coo.75; TN = 5 00 K for UCu4Co; TN= 4.75 K for UCu 3 ,15Co1.2s; and T N = 4 .7 5 K for UCu3_5Co1.5.

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of the uranium ions. This integral valency could be the reason for the persistent ordering temperature in samples like UCus-xCox and UCu4Fe. A couple of systems involving exploratory synthesis to investigate possible 163 NFL behavior are UCus-xRhx, UCus-xMnx and UCus-xCrx. One possible negative to UCus-xRhx and UCus-xlrx is that hybridization could create a completely filled d shell using the 4s1 valence electron of Cu and the valence electrons of Rh and Ir. The possible full d-electron shell could hinder NFL behavior according to Chau and Maple [26). A similar type of argument might be made for UCus-xCrx since the 4s1 valence electrons of Cr and Cu could combine to create a stable configuration with the 3d5 and 3d10 valence electrons of Cr and Cu respectively. If the Cu in UCu5 were doped with Mn, a partially filled d shell would probably occur as happened in UCus-xNix, UCus-xPdx, and UCus-xPtx. The only concern (although this should not inhibit one from synthesizing a few samples) about doping Cu with Mn is that hybridization between the U, Cu, and Mn atoms could lead to an integral valency in uranium as was discussed at the end of the previous paragraph. Thus, the possibility of UCus-xMnx not showing NFL behavior could occur as happened with UCus-xCox and UCu4Fe. 6.3 UCu2Si2-xGex Conclusions The disorder created in the UCu 2 Sh-xGex system by doping the Si atoms with Ge atoms does create nonmonotonic behavior in Tc on the Ge rich side of the phase diagram with a maximum Tc value occurring for UCu 2Si0 _4Ge1.6 as seen in Fig. 5 -3. The Tc behavior of the UCu 2Si2 -xGex system is directly attributable to the Si/Ge disorder since the magnetic sublattice of the UCu 2Si2 -xGex system is not affected by the Si/Ge substitution and minor stoichiometric differences in the Cu, Si, and Ge do not vary the Tc values. The Si/Ge disorder brings about dissipation as electrons scatter from localized moments. The dissipation combined with the

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164 thermal and quantum fluctuations is responsible for the nonmonotonic behavior in T c The reason for nonmonotonic behavior occurring on the Ge rich side of UCu 2Si2 _xGe x and not the Si rich side is due to the source of dissipation. The dissipation on the Ge rich side is due to diffusive electrons which are predicted by Silva Neto and Castro Neto [137] to increase Tc by rv 1 % compared to the ferro magnetic case without dissipation (i. e ., UCu 2 Ge 2). The dissipation on the Si rich side is brought about by ballistic electrons. The dissipation by ballistic electrons when combined with quantum and thermal fluctuations is not predicted to enact nonmonotonic behavior on Tc as confirmed by the Si rich side of UCu 2Si2 -xGe x The distinction between diffusive and ballistic electrons is made by the normalized residual resistivity values. The ballistic electrons have a much larg e r mean free path than the diffusive electrons which experimentally means that the resistivity values in the ballistic regime should be much smaller than the resistivit y values in the diffusive regime. The normalized residual resistivity values are about a factor of 10 larger for UCu 2Si0 .6 G e1.4 and UCu 2Si0 .4Ge1.6 (i.e the diffusive regime) compared to UCu 2Si2 (i.e. the ballistic regime) The occurrence of the diffusive regime in UCu2Sio.6Ge1.4 and UCu2Sio.4Ge1.6 is also the plac e in the UCu 2Si2-xGex phase diagram where nonmonotoni c behavior in T c occurs (i.e. ,...., 1% increase in the T c value of UCu 2Si0 .4Ge1.6 as compared to the T c valu e of UCu2Ge2). 6.4 UCu2Si2-xGe x Futur e Work Som e of the fut ur e w o rk p e rtainin g to UCu 2Si2 x Gex h as al ready b ee n addressed in the UCu 2SbxGe x Results and Dis c ussion chapter. The primary focus of any futur e work would be to try and find po s sible t e rnary ( and mayb e binary) syst e ms that di s play nonmonotonic b e havior with T c in c r e asing compared to a non di s ord e red ferromagn e t Cre ating disord e r in a ferromagn etic s y s t e m i s

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165 not difficult to achieve; however, creating structural disorder so that it is the only different physical mechanism is difficult since structural disorder usually affects the magnetic sublattice in a system such as U(Nii-xCux)2Si2 [81]. The Ulri xPtxAl system in Fig. 5 5 of the "UCu 2Si2 _xGex Results and Discussion" chapter shows nonmonotonic behavior in Tc as a function of Pt concentration The future work for Ulr1 -xPtxAl concerns measuring the resistivity to see if the electronic behavior may be separated into a diffusive and ballistic regime as occurred for UCu2Si2-xGe x Other ferromagnetic systems that could be candidates for nonrnonotonic behavior in Tc are listed in the work of De Long et al. [37]. Possible systems that could be synthesized to measure their Tc values for nonmonotonic behavior are URhGa1 x Snx, URhGa1 x Al x UlrAli x Snx, UlrGa1-xSnx, UC0Ga1 x Snx, and UPtGa1 -xSn x The endpoint compounds for all the systems listed previously crystallize in the hexagonal ZrNiAl structure The structural disorder would be created on the basal plane (of the ZrNiAl structure) not containing t he U atoms ; thus the structural disorder should not affect the magnetic sublattice.

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APPENDIX A LATTICE PARAMETER GRAPHS

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2 0 1 8 UCu4Ni annealed 14 days 750C -1. 6 u, 1 4 C: ::::> 1 2 1 0 c 1l l l fk l fl ~l l t f ... 0 8 s ... ....... N a. N' N 0 -~ .-. .-..-. '!!.0 N 0.6 T N .-.Q N ....-.0 M N u, .-N ..M N MN 1 -if iii .-co co C: l M l ~T 1 CD 0.4 if -C 0 2 0.0 20 40 60 80 100 120 Angle [28] Figure A -1: Theoretical and experimental x ray diffraction patterns for annealed UCu4N i T h e top x ray diffractio n pattern is the theoretical pattern for UCu5 that was generated from literature values [33, 155]. The bottom x-ray diffraction pattern is the experimental diffraction pattern for UCu4Ni that was annealed 14 days at 750C The (hkl) values are pointed out for the theoretical and experimental x-ray diffraction patterns. 167

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7.00 -----------------------------------E C> 6.98 C :.=,. cu .!. i E 6.96 cu a. E cu ..J D UCu4NI 8 annealed 14 days 750C D 6.94 -+-----r---..----r-----------...--........ _,.---,--...--........ _,.---,----4 0 0 0 6 1.2 1.8 2.4 3.0 3.6 4.2 4.8 5.4 Error Function (1/2)[(cos2(0)/sin(0))+(cos2(0)/0)) 168 Figure A -2: Lattice parameter values versus corresponding error function values for annealed UCu4Ni. The latti ce parameter values are represented by the hollow squares. The best fit line equation for the lattice parameter values (a) versus the error function values (f) is a= 6.98616 0.00649 f. Thus, the intercept provides the lattice parameter value for annealed UCu4Ni. The intercept has 0.00370 A sub tracted from it due to the x-ray machine's offset determined by running a standard piece of Si as discussed in the dissertation. After the subtraction, the 6.98246 A value matches the value reported in Table 4 1 for annealed UCu4Ni.

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APPENDIX B MAGNETORESISTANCE GRAPHS

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795 UCu4NI annealed 14 days 750C 790 OT 0 t::,. 1T a 4T 785 V 10T + 13T -E 780 (.) g_ -77 5 a. 770 765 0 0 0 2 0 4 0.6 0 8 1 0 T (K) Figure B -1: Low temperature magnetoresistance measurements of annealed UCu4Ni. The resistivity measurements were taken in fields of 0 1 4 10 and 13 T. Best fit lines (not shown in the graph) were determined for each set of data: p = 797 24.8 T0 432 for H = 0 T, p = 792 18.9 '1'721 for H = 1 T p = 793 17.0 T0 794 for H = 4 T p = 783 14.3 T0 780 for H = 10 T and p = 775 13. 0 T0 762 for H = 13 T. 170

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171 UCu3 15Ni1 05 annealed 14 days 750C 920 OT 1T 4T 915 10T 13T 910 18T -905 E (.) Cg_ 900 a. 895 1111() 890 880 ; 870 880 885 850 -840 880 0 2 4 8 8 10 0 0 0.2 0.4 0.6 0 8 1 0 T (K) Figure B -2: Low temperature magnetoresistance measurements of annealed UCu 3 _9sNii.05 The resistivity measureme nts were taken in fiel ds of 0, 1 4, 10, 13, and 18 T. The inset shows a l arger temperature range for 13 T. The 13 T data in the inset and the primary graph are within 0. 7% of each other at rv 0 .38 K despite having their resistivity taken with differe n t probes Best fit lines (not shown in the graph) were determined for each set of data: p = 929 23.8 T0 269 for H = 0 T p = 921 15.7 T593 for H = 1 T, p = 922 14.7 T722 for H = 4 T, p = 913 12.7 T745 for H = 10 T, p = 905 -11.6 T0 711 for H = 13 T, and p = 890 10.4 T750 for H = 18 T. p = 900 11.7 T0 662 is the best fit line for the 13 T data in the inset.

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APPENDIX C UCus -xNix MAGNETIC SUSCEPTIBILITY GRAPHS

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G) 0 010 0.009 0.008 0 007 15 0.006 -E 0.005 ,!. 0.004 0 1 C: 0 0.003 0 002 0.001 0.01 UCu.._1NI._. annealed 14 days 750C 10 + H 4 T (added 0.003) 0 H "'3 T (added 0.00175) L> H 2 T (added 0.00075) o H 1 T (IUbnclld 0.00020) o H 0.1 T (IUblnlc:l8cl 0 00080) 100 T (K) on log10 scale UCu.._1NI._. annealed 14 days 750C + H 4T (added 0 003) 0 H 3 T (added 0 00175) L> H 2 T (added 0.00075) o H 1 T (IUbnclld 0.00020) o H 0.1 T (aublracllld 0.00080) 500 1E-3 -+---.---r--.-........ .......-.---..--......--....................... ---,.-..-.-1 10 100 500 T (K) on log10 scale Figure C -1: Semilog and log-log plots of UCu4 1Ni0 9 de susceptibility. The top graph is a semilog plot of annealed (14 days at 750C) UCu4 1Ni0 9 de magnetic susceptibility at various magnetic fields. The bottom graph is a log-log plot of the same de magnetic susceptibility data. All best fit lines are stated explicitly in Tables 4 -7, 4 8 and 4 -9. 173

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-0.0095 0.0090 0 .0085 0 0080 0.0075 0 0070 ..!!! 0.0065 0 E o.ooeo ] 0 0055 .!, 0 .0060 0.0045 0 0040 0 0035 0 0030 0 0025 UCu1.11Nl1_. annealed 14 days 750C + H = 4 T (added 0 004) <> H 3 T (added 0.003) ti. H = 2 T (added 0.002) o H 1T (added 0 .001) a H.1T 0.0020 -+--"T"""""T""""T"""l ........ "TT"l-----r-........ --r......... -rr----r-........-"""T""i 1 10 T (K) on log10 scale UCu1.11Nl1_. annealed 14 days 750C + H 4 T (added 0 .004) <> H 3 T (added 0 003) ti. H 2 T (added 0 002) o H = 1 T (added 0.001) a H 0.1 T 10 T (K) on log10 scale 100 500 100 500 174 Figure 0-2: Semilog and log-log plots of UCu3 95Ni1.05 de susceptibility. The top graph is a semilog plot of annealed (14 days at 750C) UCu3 95Nii.05 de magnetic susceptibility at various magnetic fields. The bottom graph is a log-log plot of the same d e magnetic s usce ptibility data. All b est fit lines are stated explicitly in Tables 4 7 4 8 and 4 -9.

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0.0090 0.0085 0.0080 0.0075 0.0070 0 0065 CD 0 0.0060 0.0055 E o.0050 CD 0.0045 >,( 0 0040 0 .0035 0.0030 0.0025 UCuuNl1 1 annealed 14 days 750C + H 4 T (added 0.004) <> H 3 T (added 0.003) 6 H 2 T (added 0 002) o H 1 T (added 0.001) D H.1T o.0020------.--.............. ...--....... --.--..................... r---..--....-......-4 1 10 100 500 T (K) on log10 scale UCu,_.Nl1 1 annealed 14 days 750C 0.01 ------.--.....-...... ...---............... ............. ...--....... ""T"" ........ ~~+t-+:":11_ 1 :11,..1 : 1~~s~l*-eel~ll86I-Hl.l-t+l.llf+l,I-IIH-l:l l-li,++l;;;;::.~s:r,-,.. . .._ s;ss ::Nte: ......... os::., ~.,--,.~ -:.:~~~ + H 4 T (added 0 .004) <> H 3 T (added 0 .003) 6 H 2 T (added 0 002) o H 1 T (added 0.001) D H.1T 0 .002----.--"""'T" ............... ......, ....... ---""T""T"T" ...... ..,....-...-........ ......-1 1 10 100 500 T (K) on log10 scale 175 Figure C -3: Semilog and log-log plots of UCu3 9Niu de susceptibility. The top graph is a semilog plot of annealed (14 days at 750C) UCu3 9Niu de magnetic s usc eptib ility at various magnetic fields. The bottom graph i s a log-log plot of the same de magnetic susceptibility data. All best fit lines are stated explicitly in Tables 4 -7, 4 8, and 4 -9.

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-0 0080 0 0075 0 0070 0 0085 0 0080 G) 0 0 0055 E 0 .0050 ,! 0 0045 x 0 .0040 0.0035 0.0030 0 0025 UCuuNlu annealed 14 days 750C !O eecn:: mu:: 0 .0020--...... --...,....,-~------~--___.......,_ CD 0 i C 0 I E X 10 100 500 T (K) on log10 scale UCuuNlu annealed 14 days 750C 0 009 --.................. ...,...., ................ ....... -...................... T'TT----,,--"T"'""T"""> 11111111111111111111111111111111111:::::;;;;;: 3 iJ8Eji Jl. a one::: meow + HT~CLIIIM) 0 HT(-IUIID) 6 HT~O.GOZ) o HT~O.II01) a HIIO o .002----...... ...,....,.....-. ........ ---........ ....,......,..TTT----,,--"T"""....-i 1 10 100 500 T (K) on log10 scale 176 Figure C-4: Semilog an d log -log plot s of UCu3 8Ni1.2 de susceptibility. The top graph is a semilog plot of annealed (14 days at 750C ) UCu3 8Ni1.2 de magnetic susceptib ility at various magnetic fields. The bottom graph is a l ogl og plot of the same de magnetic s u scept ibility data. All best fit lines are stated exp licitl y in Tables 4 7 4 -8, and 4 -9.

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APPENDIX D UCusxNix SPECIFIC HEAT GRAPHS

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300 280 260 N 240 ... UCu.uNi0 1 Cl) 0 annealed 14 days 750C E 220 -, AC/T = C/T-(0.178 T2 + 0.0011 T') E -200 t:: u
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179 UCu4Ni annealed 14 days 750C 150-,----.------.------.---.----,,---.-----, I I I I I I I I 6. D H=6T 6 H = 13T 140-N t ..' Q) 0 130-E --, E t:: 120-. 110---,---,---,---,---,--.... ,-.... ,-.... ,.---o.2 o.4 o.6 o.8 1.0 1.2 1.4 1.6 1 8 2.0 T (K) Figure D-2: Specific heat of annealed UCu4Ni in 6 and 13 T. The specific heat data below 2 K is shown The specific heat for both sets of data had the lattic e contribution subtracted off: ~C/T = C/T-0.178T2 0.00111'4. The upturn s at the lowest measured temperatures are believed to be Schottky like anomalies due to the Cu atoms.

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180 UCu4Ni annealed 14 days 750C 120 115 ~<>oo <>o 110 <><> <>o <>o N 105 <>o ";'"CD 100 0 E 95 <> -, <> E <> -90 t:: <> 85 <> 80 <> 75 <> 0 1 2 3 4 5 6 7 8 9 10 T (K) Figure D -3: Specific heat of UCu4Ni in 13 T with Castro Neto-Jones fit. UCu4Ni was annealed for 14 days at 750C The specific heat had its lattice and Schot-tky anomaly contributions subtracted off: ~C/T = C/T 0.178T2 -0.0011T4 -2.22/T3 The solid line is a Castro Neto-Jones fit to the 13 T data from 0 357 K to 8 98 K: ~C/T = AH2Hl2 e H/T /T3->./2 + D where A = 32.7 H = 3 35, A = 0.841 (fixed from magnetization versus field data in Table 4 4) and D = 96.3.

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UCu ... 1Nlu annealed 14 days 750C 400 300 ~66666 CD 300 00000 0000 en g> C: 0 1' .... CD 0 0 H=3T E -, l:l. H=6T E t: (.)
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182 ucu,NI annealed 14 days 750C 200 0 H=3T + U) H =2T 0 ... O> 0 *+~++ C +++++ + 0 ++++ N -;-Q) 0 E 100 -, E I:: (.)
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183 UCu3 15Ni1 05 annealed 14 days 750C 200--------------------------,..-------__, G) + H=2T u, 0 .... C) 0 C 0 N + ++ +++++ ++ + ";100 G) 0 E -, E t:: u
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184 UCu3 1Nl1.2 annealed 14 days 750C Q) 0 H=3T "' 0 ... C> 0 C 0 100 N ... Q) 0 E -, E 0 R:PcP c9 t: 0 8 90 0 .3 1 1 0 T (K) on 10910 scale Figure D 7 : UCu3 8Nii.2 specific heat data in 3 Ton a log-log plot. UCu3 8Ni1.2 was annealed for 14 days at 750C. The linear fit was determined with the maximum temperature range yielding the minimum standard deviation: log10(~C/T) = 2 .00 0.0587 log10 T for 0.902 S T S 3.46 K. The specific heat data have the lattice contribution and Schottky anomaly contribution subtracted off: ~C/T = C/T (0. l 78T2 + 0.0011 T4) 0.0125H2 /T3

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BIOGRAPHICAL SKETCH Daniel Mixson was born in Orlando, FL, on May 17, 1977. Daniel lived in Gainesville, FL, from 1978 to 1990. Daniel moved with his family to Melbourne FL, and lived there from 1990 to 1995. During the Summer of 1994 he participated in the Summer Science Training Program (SSTP) at the University of Florida (UF) In 1995 Daniel graduated from Eau Gallie High School. Daniel lived in Starkville, MS, from 1995 to 1999 where he attended Missis sippi State University (MSU). Daniel graduated from MSU in 1999 with a Bachelor of Science in physics Dani e l lived in Gainesville, FL, from 1999 to 2005 to attend UF for gradu a t e studies One of the highlights of his graduate career was being able to work at Los Alamos National Laboratory (LANL) in New Mexi c o for the Summ e r of 2004. 195

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I certify that I have read this study and that in my opinion it conforms to acceptable standards of scholarly presentation and is fully adequate, in scope and quality, as a dissertation for the degree of D]f Philosop3/. . Gregory R. Stewart, Chair Professor of Physics I certify that I have read this study and that in my opinion it conforms to acceptable standards of scholarly presentation and is fully adequate, in scope and quality, as a dissertation for the degree of Doctor of Philosophy. ~L ~~PVL~ ........ ~-Bohdan Andraka Associate Scientist of Physics I certify that I have read this study and that in my opinion it conforms to acceptable standards of scholarly presentation and is fully adequate, in scope and quality, as a dissertation for the degree of Doctor of Philosophy. ? '\?tJ ku 1./Aa/ Pradeep Kumar Professor of Physics I certify that I have read this study and that in my opinion it conforms to acceptable standards of scholarly presentation and is fully adequate, in scope and quality, as a dissertation for the degree of Doctor of Philosophy. J i ~ C-0 ~Cr-@-t-Dinesh Shah Professor of Chemical Engineering I certify that I have read this study and that in my opinion it conforms to acceptable standards of scholarly presentation and is fully adequate in scope and quality, as a dissertation for the degree of Doctor of Philosophy. David Tanner Distinguished Professor of Physics

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This dissertation was submitted to the Graduate Faculty of the Department of Physics in the College of Liberal Arts and Sciences and to the Graduate School and was accepted as partial fulfillment of the requirements for the degree of Doctor of Philosophy. May 2005 Dean, Graduate School

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DIFFERING ROLES OF DISORDER: NON-FERMI-LIQUI D BEHAVIOR IN UCu5_xNix AND CURIE TEMPERATURE ENHANCEMENT IN UCu2Si2-xGex Daniel J. Mixson II (352) 392-0477 Department of Physics Chair: Gregory R. Stewart Degree: Doctor of Philosophy Graduation Date: May 2005 Disorder is created when an element on the periodic chart of elements replaces atoms of another element in a metallic compound. Cu atoms in UCu 5 are replaced by Ni atoms while Si atoms are replaced by Ge atoms in UCu 2Si2 The low temperature ( < 20 K) magnetic behavior of UCu 5 is suppressed towards zero as the Ni atoms replace the Cu atoms. The magnetism is suppressed to zero for UCu4Ni and the low temperature physical properties for UCu4Ni ( and adjacent Ni concentrations) display atypical metallic properties. The UCu 5_xNix results test theorists predictions that try to describe such abnormal low tempera ture properties. The replacement of semiconducting Si atoms by semiconducting Ge atoms enhances the magnetic transition temperature nonlinearly in UCu 2Si2 Measure ments upon UCu 2Si2_xGex reveal information about the interactions occurring on the microscopic level. These interactions that lead to transition temperature enhancement could have important implications for semiconductor technology

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