THE EVOLUfrCN OF MfCROSTRUCTURE
DURING SINTERING OF C'O AND 'TS EFFECT
UPON MECHANICAL AND TFEH_\MAL PROPERTIES
'ayve Douglas Tuchig
A iOisscrt-,j.on Presented to the Cradiu;t Council
the Uniiver;sity o' Ficrj;
In Partial Fulfillment of rthe Requi;res;.nt fcr the
Degree of IDoctor ;fi Phi o-;op)
U41:VERSITY CF FL'JRID.
Dedicated to my wife, Candy,
and to my parents,
Mr. and Mrs. W. J. Tuohig.
The author wishes to acknowledge the encouragement
and helpful discussions provided during the course of this
research by his chairman, Dr. E. D. Whitney, and Dr. R. T.
DeHoff. Thanks are due also to Drs. L. L. Hench, J. J.
Hren, R. W. Gould and J. W. Flowers for serving on the
The assistance of S. M. Gehl with all aspects of this
work, and contributions by i. H. Halback and R. A. Graham
are sincerely appreciated.
Financial support from the United States Atomic
Energy Commission is gratefully acknowledged.
TABLE OF CONTENTS
ACKNOWLEDGEMENTS . .
LIST OF TABLES . .
LIST OF FIGURES . .
ABSTRACT . . .
S. . . . . . iii
. . . . . . . vi
. . . . . . . vii
. . . . . . xii
S INTRODUCTION . . . . . . .
1.1. The Nature of the Sintering
Process . . . . . . .
1.2. Evolution of Microstructure .
1.3. Effect of Microstructure on
Mechanical and Thermal
Properties . . .
1.4. Objective of the Present Work .
II EXPERIMENTAL PROCEDURE ....
2.1. Material Characterization ..
2.2. Specimen Preparation ..
2.3. Evaluation of Geometric
Properties . . .
2.4. Evaluation of Mechanical
2.5. Measurement of Thermal
III RESULTS AND DISCUSSION ....
3.1. Densification Behavior ...
3.2. The Metric Properties .. ...
3.3. Mechanical Properties .. ...
3.4. Thermal Conductivity ..
TAB I ; i : J'S (continued)
CONCLH SI :' .' s- ::'L\RY . . .
A PRECISE : 1
Bi I NTI RPOVI
OF PY1, 1 '
1 KL\IN ,:
LIST OF REIIPLNCi S
BIOGRAPHICAL SKETCH .
TICE PAAI1E]TI PROGRAM .
Ti "',iL CON )IICTIVTTY
90(. IN INCR E"IFTS CO
1 i ANhl: 300-1200 .
LIST OF TABLES
1 Analytical Impurities in the Arc Fused
UO2 Used in this Investigation . . . 34
2 As-received UO2 Powders were Separated
Into Lots by Sieving . . . . ... 46
3 Surface Areas of the Three Size
Fractions of UO2 S............. 56
4 Metric Properties of UO2 Specimens
Produced by Cold Compaction and
Subsequent Sintering . . . . .. 93
5 Metric Properties of U02 Specimens
Produced by Pressure Sintering at 3,000
psi for 30 minutes at Various Tempera-
tures . . . . . . . ... 115
6 Metric Properties of U02 Specimens
Produced by Pressure Sintering at 3,000
psi at the Indicated Temperature for
Various Times . . . . . ... 117
7 Metric Properties of Specimens Pressure
Sintered at 5,000 psi From Fine Powder
Lot . . . . . . . . ... 134
LIST OF FIGURES
1 Sequence of states through which a
sintering four-particle system passes 11
2 Structural evolution during useful
life of a UO2 fuel pin . . . .. 32
3 SEM photographs of -6 mesh as-received
UO2 powder . . . . . . ... 35
4 SEM photographs of -200 mesh as-received
powder . . . . .. . . . 36
5 Photomicrographs of -6 mesh as-received
powder . . . . . . . . . 38
6 Photomicrographs of -270 +325 as-
received powder . . . . . .. 39
7 Phase diagram of the U-O system for 0/U
ratios between 2.0 and 2.25 . . . . 41
8 Dependence of the lattice constant at
25C upon O/U ratio for cubic UO2 . 42
9 Sinterings prepared from loose stacks
of as-received U02 sintered at 22500C . 48
10 SEM photos of powder from the three size
fractions employed in this investigation 51
11 Schematic of the B.E.T. apparatus used
to determine surface area . ..... 55
12 B.E.T. plot for fine size fraction of
UO2 powder . . . . . . . . 55
13 Punch and die assembly used to cold
compact UO2 . . ... . . ... 59
14 (a) The high temperature Astro sintering
furnace . . . . .. .. . .. 61
(b) Centorr vacuum hot press ...... 61
LIST OF FIGURES (continued)
15 Graphite and boron nitride die assembly
used to pressure sinter UO2 ...... 63
16 Schematic illustration of the counting
measurements on a sinter structure . .. 67
17 Quantimet display of a sintered UO,
microstructure . . . ... ... ... . 70
18 Metallograph-vidicon assembly . . .. 71
19 Distribution of stresses in a diamet-
rally loaded cylinder . . . . .. 77
20 Precision centerless grinder used to
machine UO2 specimens . . . ... 78
21 Comparative cut bar thermal conductivity
apparatus . . . . . . . 80
22 Temperature dependence of the thermal
conductivity of Pyroceram 9606 . . .. 83
23 Densification of three size fractions
of UO2 at constant heating rate followed
by 5 minute arrest at 1800C pressure
sintered at 3,000 psi at 10-4 torr . . 86
24 Variation of volume fraction of porosity
as a function of temperature for three
size fractions of UO2 .......... 88
25 Volume fraction of porosity as a
function of time at temperature ... . 90
26 Dependence of pore volume fraction on
time for isothermal pressure sinterings 91
27 The family of curves which define the
path of change during sintering of the
surface area per unit volume for the
intermediate sized fraction ...... 96
28 The approach to the linear relationship
for a spectrum of initial conditions . 97
LIST OF FIGURES (continued)
29 Surface area per unit mass as a function
of volume fraction of porosity for
specimens prepared by compaction at the
indicated pressure and sintering for
various times and temperatures . . . 99
30 Variation in microstructure for two
different paths of surface change . 101
31 Evolution of microstructure along a
single path of structural evolution . 102
32 The family of curves which define the
dependence of surface area on volume
fraction of porosity for conventionally
sintered coarse UO2 powder . . ... 104
33 Average mean curvature as a function of
volume fraction porosity for UO2 prepared
by conventional sintering from the coarse
size fraction . . . . ... .. . 107
34 Variation of average mean curvature with
volume fraction porosity for conven-
tionally sintered intermediate UO,
powder . . . . . . . . .. 108
35 Comparison of the dependence of curva-
ture on pore volume fraction and particle
size for UO, and dendritic copper . . 109
36 Proposed form of the paths of curvature
change for a spectrum of initial condi-
tions. .... . . . . .... 111
37 Dependence of the shape parameter on
volume fraction porosity for all conven-
tionally sintered UO2 specimens . . 112
38 Dependence of surface area per unit
volume upon the pore volume fraction
for the isochronal pressure sintered
series . . . . . . .. ... 119
LIST OF FIGURES (continued)
39 Variation of surface area with porosity
for specimens pressure sintered at the
indicated temperature at 3,000 psi for
various times . . . . . . . 121
40 Variation of total curvature with volume
fraction porosity for specimens sintered
at 3,000 psi for 30 minutes at various
temperatures . . . . . .. . 123
41 Variation of mean curvature with volume
fraction porosity for isochronal pres-
sure sintered series . . . . .. 124
42 Comparison of mean curvature for iso-
thermal pressure sinterings and that
obtained in the isochronal series . . 126
43 Variation of the mean pore intercept X
with volume fraction porosity for
pressure sintered UO2 ......... 127
44 Photomicrographs of isothermally
pressure sintered UO2 specimens . . 129
45 Dependence of the shape parameter upon
volume fraction of porosity for the
pressure sintered isochronal series . 131
46 Comparison of the dependence of surface
area on volume fraction porosity for
conventional and pressure sinterings . 132
47 Comparison of mean curvature for coarse
UO2 powder prepared by conventional and
pressure sintering techniques . . .. .135
48 Comparison of mean curvature values for
intermediate UO2 powder prepared by
cold pressing and sintering and by
pressure sintering . . . . . . 136
49 Comparison of the geometry of (a) a
copper sinter body, and (b) UO2 sinter-
ing, both approximately 35% theoretical
density. .. . . . . . . .138
LIST OF FIGURES (continued)
50 Failure modes in diametral compression . 142
51 Variation of fracture strength with
pore volume fraction for specimens pre-
pared by conventional sintering of power
from the intermediate size fraction . 144
52 Dependence of fracture strength on
volume fraction of porosity for specimens
conventionally sintered from coarse and
fine UO, powders . . . . ... .... 145
53 Comparison of the strength-pore volume
dependence of three size fractions of
conventionally sintered UO, . . .. 147
54 Fracture strength of specimens from the
pressure sintered isochrenal series as
a function of pore volume fraction . . 148
55 Variation of fracture strength with
vclune fraction corosity fcr snecinens
prepared by isothermal pressure sinter-
ing the intermediate UO, powder at
3, 0OJ psi . . .. . . . . 149
56 SE% fractographs of intermediate iso-
chronal series . . . . . . . 150
57 Path of minimal fracture length for
coarse and intermediate specimens of
comparable density . . . . . . 153
58 Dependence of mean grain intercept on
pore volume fraction for isocbronally
pressure sintered series . . . . 156
59 Dependence of thermal conductivity on
temperature for UDO specimens with
different pore volume fractions ... . 15
60 Thermal conductivity at 500'K as func-
tion of volume fraction of porosity . 159
61 X-ray images of a second phase found
in UO, sinter bodies . ... ..... 162
Abstract of Dissertation Presented to the Graduate Council
of the University of Florida in Partial Fulfillment of the
Requirements for the Degree of Doctor of Philosophy
THE EVOLUTION OF MICROSTRUCTURE
DURING SINTERING OF UO2 AND ITS EFFECT
UPON MECHANICAL AND THER%.AL PROPERTIES
Wayne Douglas Tuohig
Chair-.mn: E. D. Whitney
Major Department: Materials Science and Engineering
A full range of microstructural states, ranging from
30% to near theoretical density, were produced from UO,
powders. Both conventional and pressure sintering (hot
pressing) techniques were employed to fabricate the micro-
stru-tures. Each state was characterized by its associated
metric properties, i.e., volume fraction of joid, area of
void-solid interface, curvature, mean pore and mean grain
iT ercepts, as determined by the procedures of quantitative
metallography. Additionally, tensile strengths at room
temperature and thermal conductivities over the intermediate
temperature range were determined.
The viewpoint was adopted that a sequence of states
defined the path of microstructural change. It was found
that sintering in the presence of an applied load (hot
pressing) proceeds along a different path of microstruc-
tural development than does the same material under conven-
tional sintering conditions.
The evolution of microstructure during conventional
sintering of UO, is shown to be qualitatively similar to
that of metallic systems. The role of precompaction (cold
pressing) upon the subsequent microstructural development
has been elucidated in terms of the area of pore-solid
Tensile strength and thermal conductivity have been
found to be functions of the initial particle size for
densities below about SO of theoretical. Inspection of
fractured surfaces and microstructures indicates that these
properties are sensitive to minimum cross-sectional areas
in the porous solid network. Evidence is presented to show
that this minimum area is in turn related tc initial par-
ticle size. Properties of specimens greater than 80% dense
showed little dependence on initial particle size. Increases
in grain size are thought to be responsible for decreasing
strengths found at very high densities. A marked decrease
in thermal conductivity found for high density specimens is
attributed to the presence of a second phase, believed to be
the result of contaminants in the starting material.
1.1. The N ture of the Sintering Process
Sintering in the presence of a liquid phase is as old
as the nost ancient Clramic artifact. A more modern conno
tatior of the teot ".sintering" implies the coalescence of
particulate matter at temperatures below the melting point
into a solid, coherent body. The driving force for this
Process is the theriodyna iic tendency of a system to lower
its energy by decreasing free surface area (in the absence
of a liquid). The sintering process may be characterized
1) Particle contact -- particles are brought into
contact under the action of gravity, an exter-
nally applied force or vibrating rearrangement.
2) Upon heating to a temperature below the liq-
uidus, points of contact between particles
broaden into areas of contact or necks.
3) The initially continuous network of porosity
becomes less continuous.
4) Both 2 and 3 are accompanied by a macroscopic
contraction or shrinkage. As a result, the
density is observed to increase.
5) The rate of densification decreases rapidly
as theoretical density is approached; average
grain size increases.
of ]I i id
Aus 1 1. '
tiosn; T ]
piC ;9 1
t i oi 1
no: I E; 1 i
Si lh [ 1 :, 1
ensuing ye rs s"
fio icli es t. h 1 o i
fusion and sinic
workers had coi c
under tile actii
that stresses in
and thus plastic
and Wulff  d
produce shrink fif
1 f 't1 Sinterin P'rocess
ii .t w, rk n sintering in the abscice
S1 ly 1', Iaston  in 1725, on plati-
1.:' c i I to hLiich solid species
T ; t ;. i I not ho now until Ro i rts-
Ill 'irfu.i;on of gold in lead. The
siw iri t] t] e ry \. :s contained in the
S] in 10i thnt sinterinp in the
] n-" Iv s brought aboit by surface
I', [-1] obsei nation of spheroidiza-
Sled hii to conclude tliat the phenoni
t surface tension. Ihe wcrk of
p ,i',ied tie conclusion that a liquid
iiitc for sintering to occur. In the
is on single and multicomponcnt systems
. : relationship between solid state dif-
it. By the early 1940's, a number of
1id that material transport occurred
of siurace tension [6-8]. liretblad and
equations of capillarity and concluded
sinteing bodies exceed the elastic limit,
deformation occurs. Pines  and Shaler
stinguished between mechanisms which could
and those which produced only surface
densi fi cat i on,
Kuczynski , in a classic work, utilized a plate-
sphere model to derive sintering rates for different mecha-
nisms of material transport. According to his analysis,
the radius of the neck, x, was related to time as follows:
1) viscous flow -- x c t
2) evaporation-condensation -- x a3 t
3) volume diffusion -- x a t
4) surface diffusion -- x t
From his measurements on copper, Kuczynski concluded
that early stages of sintering may be surface diffusion
controlled but that later stages are volume diffusion con-
trolled. A similar experiment  with glass spheres led
him to conclude that the predominant mechanism was viscous
The calculations of MacKenzie and Shuttleworth 
introduced the concept of vacancy diffusion to external
sites. The results of these calculations, as well as the
observation that shrinkage was not dependent on specimen
size, led them to conclude that material transport during
sintering occurred by plastic flow. Adopting the formalism
of Bingham flow, they derived an expression for shrinkage
which contained several parameters. Suitable choice of
these parameters led to reasonably good agreement with
experimental data. Impetus to this view was added by
Clark and White , who utilized a similar approach and
achieved quite good agreement with experimentally measured
A meciha isr propo y N' rro I 1. j nu 1: t- r h
Ilerring  to explain creep l ow stresses pr vidru a
means to reconcile both the pl stic flow a1nd diffusion:
viewpoints. The NXburro-llrriln ocd 1  sug "
creep deformation can occur by the diffusion of i -terial
from grain boundaries in coiripressicn to grain bou darics
in tension, i.e., a flux of vacancies to rain hoiindaries
experiencing a conpressile stress field. Tu grain
Ibondarics bconc vacancy sinks. Exiseri iintal cvide c- KI
provided by Udin, Shaler and Wulff  an by Gr1cnou [I
Udin et al. attributed the creep of fine copper wires to
the Nabarro-I'Hrring mechanism. Greenolluh repeated th, -
perimnnts using single crystal vires aid observed crece
rates that were two orders of magnitude sr:i]ler than those
measured for polycrystalline materials.
The close relationship between sintering and diffu-
sional creep was pointed out lby Rhines and Cannon ,
who found that sintering in the presence of small comprcs-
sive loads has the same effect on shrinkage rate that addi-
tional stress has on the rate of creep deformation.
The work of Alexander and Baluffi  on twisted wire
compacts, Scigle  on porous brass sheets, and Burke 
on aluminum oxide provided strong evidence for the grain
boundary sink model.
An ingenious experiment by Kuczynski, Matsumura and
Cullity  provided the most direct evidence of diffusion
and the role of the curved surfaces during sintering. A
copper-indium alloy wire compact was sintered at tempera-
tures where the phase diagram predicts the presence of a
single phase solid solution. A subsequent heat treatment
at lower temperatures produced a precipitate rich in indium
at the weld necks. The diffusion coefficient of indium is
greater than that of copper and thus a Kirkendall effect
is observed. The material transported to the weld necks
by diffusion was enriched in indium to the extent that the
two-phase boundary was crossed, allowing precipitation to
On the basis of extensive theoretical and experimental
work on a variety of materials, it is concluded that lat-
tice diffusion is the dominant mode of material transport
during sintering. Exceptions have been noted [NaC1 by
evaporation-condensation, Kingery and Berg (25), glass by
viscous flow, Kuczynski (12)], and it is likely that more
than one mechanism operates at various stages of the pro-
cess. The following factors have been found to influence
sintering behavior : (1) temperature employed,
(2) particle size and size distribution, (3) particle
morphology, (4) occurrence of discontinuous grain growth,
(5) atmosphere, (6) stoichiometry and defect structure,
(7) impurities and additives, and (8) manner and extent
1.1.2. Pressure Sintering
Pressure sintering or hot pressing is defined as the
application of external pressure to a powder compact while
it is at high temperatures. The synergistic effect of
these two variables has led to increased interest in recent
years to production of materials which cannot be fabricated
by any other technique . Hot pressing provides an
additional variable to control microstructure, by virtue
of the fact that it increases the driving force for densi-
fication of a powder compact without significantly increas-
ing the driving force for grain growth . As a result,
densities approaching theoretical have been achieved for a
number of materials.
The mechanism of densification during hot pressing
has been examined by Vasilos and Spriggs , Coble and
illis , Rossi and Fulrath  and Murray et al. .
Although simple sintering models are inadequate to describe
the process, most workers are of the opinion that at tem-
peratures below 20000C and pressures below 7,500 psi as
are normally employed in hot pressing refractory ceramics,
densification takes place by a diffusional mechanism.
Evidence for this comes primarily from agreement between
densification kinetics and lattice diffusion measurements
[28,29]. The plastic flow model proposed by Murray et al.
, and by :McClelland  may, however, he apolirable
to soft materials such as copper, lead, and NiO [2;].
Coble and Ellis  studied neck growth between pairs of
spherical aluminum oxide single crystals under the applica-
tion of load. They concluded that only the initial stage
of neck growth was a result of plastic flow at points of
contact. Deformation occurred until the effective stress
was reduced below the yield stress. Later stages were the
result of a diffusion controlled process.
Murray et al.  have studied the hot pressing
behavior of stoichiometric and hyperstoichiometric U02.
They found that hyperstoichiometric material densified more
rapidly than did the stoichiometric oxide, in agreement with
observations of Williams et al.  on conventionally sin-
tered material. Maximum reported density was 10.55 p/cm3
(97% theoretical density), produced by pressing at 2,000
psi at 1800C for ten minutes.
1.1.3. Sintering of UO2
In the late 1950's, the development of advanced power
reactor designs provided stimulus for extensive study of
the sintering behavior of UO2. Interest continues in both
UOi2 and mixed oxides of uranium and plutonium which fuel
the present generation of breeder reactors.
The effects of powder characteristics and processing
variables on densification -nd microstructure have been
discussed elsewhere  and will net be repeated here.
In general, remarks th: apply to nost sinterable powders
apply to U0, [36,37]. 'orevxer, certain characteristics of
lO2 are not general in nature and deserve further discussion.
Py virtue of the i.ul tiple oxidation states of uranium,
there are at least four thernodynanically stable oxides of
uranium known to exist . Uranium dioxide has the
lowest 0/1) ratio of the stable oxides and is the only oxide
wherein bonding is thought to be predominantly ionic in
character. Another consequence of the multiple valence of
uranium is the hyperstoichiomctry exhibited by U02; i.e.,
its ability to dissolve excess oxygen into the flucritc
lattice without formation of a second phase . Cubic
U02 may in fact have O/U ratios of 2.00 to 2.25. It is
well established that the 0/U ratio of 102 has a very
significant effect on both sintering behavior and physical
The 0/U ratio of U02* may be controlled by controlling
sintering furnace atmosphere and stoichiometry of starting
material. Strongly reducing atmospheres produce O/U ratios
close to 2.00. Sintering in inert gas or vacuum atmospheres
tends to maintain the O/U ratio of the starting material,
although more precise control is obtained by controlling
oxidation potential with CO/CO, mixtures , H2/ N
i' ill be taken to imply stoichiometric i02.00
unless otherwise indicated by context ol the adjective he n
s oi chi on c.
mixtures  or by steam sintering . Williams et al.
 studied the sintering behavior of oxides in the range
O/U = 2.00 to 2.18. They observed that densification in-
creased rapidly between 2.00 and 2.02, but only slightly
above 2.02. The sensitivity of densification to stoichi-
ometry is a manifestation of the influence of defect struc-
ture on cationic lattice mobility.
UO2 is particularly prone to agglomeration, i.e., a
tendency of loose particles to bond together in an assembly.
The bonding forces in agglomerates are generally electro-
static in nature as distinguished from an aggregate wherein
particles are welded together . Insofar as aggregates
and/or agglomerates survive processing, they influence the
microstructure of the sinter body. Steele et al. 
have examined UO2 and BeO powder compacts by the Brunauer-
Emmett-Teller (B.E.T.) technique and by permeability deter-
mination of surface area. They found that aggregates of
UO, survived compaction at 40,000 psi and the result was
a very inhomogeneous distribution of porosity in the sin-
tered microstructure. Although Steele et al., refer to
"strong aggregates," no attempt was made to disperse the
Further, the inference is made that since x-ray crys-
tallite size is much smaller than observed for "particles"
in the microscope, the "particles" are aggregates of crys-
tals. It is well know that x-ray crystallite "size" is
not equivalent to thi traditional concept of particle size
. It seems likely, therefore, that in view of the
definitions given earlier, Steele ct al.  observed
both aggregation and apglo-cration.
1.2. Evolution of Mi crostructure
The path of microstructural evolution may be defined
as the sequence of microstructures which exist in a mate-
rial a, it uidergocs a process which produces changes in
structure [IS]. Examples are, the formation of crystals
and consumption of the matrix during devitrification of a
glass, the formation and growth of equiaxed strain-free
grains during recrystallization, and solid state reactions
involving a phase change. During the sinterini process,
a collection of minute particles are welded together to
form a massive coherent body which ultimately may approach
theoretical density. It is evident that a continuum of
microstructures will exist between these two extremes.
This transformation is illustrated foi a four-particle
systcri in Fig. 1.
The kinetics of sintering mny be viewed as the rate
at which this path is traversed by the system [!5].
Tral i tionally, the linetics of sintering have cbeen s lOiied
hvy measure tcnt cf shrinkage As indicr.ted in the irl\' ( ] i
,cticni, 'srini a 0 n iasure .- .t, on c i c'lrical1y 11 c
c 0 D
Fig. 1. Sequence of states through which a sintering
four-particle system passes. Densification
proceeds as L1>L 2>L>L4'
system, have been used by nany worker. to identify the
rechanisms by which sintering is taking place [11,26,16,47].
These results, however, do not extrapolate well to nany-
particle systems. Dilato irtric measurements of shrinkage
have beei made on three-dimensional systems composed of
many particles. It is usually found that the data can be
fitted to an equation of the form 
=- Kt (1.1)
where 'L = L L(t)
L = initial dimension
L(t) = dimension at time t
t = time
n = the time exponent
and K can be represented as
K = exp (1.2)
where K" = a constant
T = temperature in degrees Kelvin
R = gas constant
Q = activation in energy for the shrinkage
Such measurcrmnts, however, provide no information about
the path of sinterinL
A detailed study of microstructural changes ,l ich
occur during sinilring was first undertaken Ly Rhl is et A!.
. They ob served thatC the total vcli of poru ity
decreased as sintering progressed, but average pore size
increased. Arthur  determined that porosity remained
connected until relatively high densities were attained.
Burke  has observed that exaggerated grain growth
occurs during the latter stages of sintering and can effec-
tively arrest densification. These observations indicate
the complexity of the sintering processes and the defi-
ciencies of simple geometric models.
Techniques for quantitatively characterizing the
nicrostructure of sinter bodies have been available for
some tile. However, only recently has systematic study
been undertaken. An additional parameter of particular
significance to sintered structure characterization was
provided by De!loff  and by Cahn  with the develop-
ment of a technique for measuring quantitatively the curva-
ture exhibited by the interface in a two-phase system (see
Rhincs  has shown that topological concepts may
be used to characterize the sintering process to an extent
not possible with ordinary geometric concepts. Using the
topological approach, Rhines et al.  developed a model
wherein the system of particles, contacts and void channels
is reduced to a node-branch network. It was shown that
the model was applicable to the entire process from loosely
stacked particles to a fully dense body. Aigeltinger 
has experimentally determined the topological properties
of a sinter body using a serial sectioning technique to
synthesize the structure.
Coble  has undertaken to describe the path of
microstructural evolution based on bulk diffusion-controlled
processes. He concluded from examination of micrographs
that the sintering process could be treated in three
1) Initial stage -- growth of interparticle con-
tacts into weld necks. The necks broaden to
the extent that grain growth becomes possible,
thus signaling the end of the first stage.
2) Intermediate stage -- with the onset of grain
growth,intersection of grain boundaries with
void-solid interfaces begin to assume equi-
librium dihedral angles. Porosity is situated
as a continuous network of cylindrical pores
along the lines of intersection of three
grains. During this stage the pores retain
cylindrical configurations and simply shrink.
Two alternate final stages are proposed by
3a) Pores are pinched off and isolated at four
grain corners. If grain growth is inhibited
the pores can continue to shrink until
theoretical density is attained.
3b) If discontinuous grain growth occurs, pores
are isolated from grain boundaries. Most
porosity is closed and spherical. Regions
adjacent to grain boundaries are relatively
free of porosity as a result of boundary
Using a tetrakaidecahedron as a model for grains and
cylindrical or spherical pore shapes, he calculates shrink-
age r:tes for intermediate and final stages of sintering.
Peasonably pood agreement between diffusion coefficients
c lcruatcd from shrinkage rates, based on the model, and
those determined from initial stages of sintering were
The densification and development of microstructure
in UO2 were studied by Francois and Kingery . They
found that rapid heating rates produced a microstructure
that consisted of intergranular porosity as opposed to an
intragranular microstructure observed for conventionally
fired UO2. The "intergranular" microstructure was charac-
terized by measurements of dihedral angle, average number
of sides exhibited by a pore intersection with the plane
of polish, average pore size and grain size. Based on
this data and extraction analysis, they concluded that
carbon in trace quantity in the starting material was
responsible for the unusual microstructures observed after
Rhines et al.  have studied the geometric path of
microstructural change for a number of metallic powders.
Particles of different morphologies, including irregular
dendritic electrolytic copper, spherical copper, nickel
carbonyl and antimony powders, were included in the study.
The effect of particle size, compaction, particle size
distribution and temperature were systematically examined.
The results of these studies are briefly summarized.
1. The sintering process may be divided into three
stages based upon the dominant geometric process which is
occurring: Stage 1 points of contact broaden into weld
Thus t) cr,
n..-n, : f p :-o ity v :,, in to
f pc ty; jd St; *,e 3 -
tic expense of smaller pores
of the sc-ile of porosity.
ip bet.hcn S surface area
ui fraction of poros'ty, has
I r trials d urin, secondi-sta g
ive system ,i there exists a uti
Sare' towards which the system
ccl1train. ts such as precolpact:
thc appro ch to this path in a
3. Tie t t I curiature per unit volume, M\, is ini
tially positive decros o s through zero to a maximum nega-
tive vlue ad ;ror lics zero again as densification
nears coipletio:. (Sce section 2.3.3 for explanation of
Gryc.,  has i ;-silred the sintering force (defined
to he the force neces-,iry to balance axial shrinkage) as
a function of d nsity. Some, iat surprisingly, the sinter-
ing force was found to increase with increasing density,
reaching a maxiri 9 before beginning to decrease. Gregg
found that the variation in the sintering force could be
correlated with the evolution of average mean curvature,
FT, and derived an expression relating capillary forces to
the sitinting forme, based on a spherical pore model.
The evolution of microstructure in a three-dimensional
sinter body can be described by quantitative geometric
properties which uniquely characterize the system. These
properties are experimentally measurable and require no
1.3. Effect of Microstructure on
Mechanical and Thermal Properties
The mechanical and thermal properties of a material
depend primarily upon atomistic considerations such as bond-
ing, band structure, and crystal symmetry. Microstruc-
ture can, however, play an important role in determining
realizable properties for engineering applications. Micro-
structural features which are expected to influence proper-
ties of polycrystals are: (1) grain size, (2) existence of
preferred orientation or anisotropy, and (3) presence, dis-
tribution and morphology of a. second phase. Void phase or
porosity is a special case of feature (3) and has received
a great deal of attention in the ceramic literature.
1.3.1. Mechanical Pronerties
The basis of the mechanical behavior of brittle mate-
rials is the Griffith Theory . Griffith hypothesized
that all materials contained flaws. When a stress is applied
to a body containing the flaw, stresses in the vicinity of
the flaw are very much higher than would be calculated
assuming the body was a homogeneous continuum. As a result,
stresses approaching theoretical strength are achieved at
the tip of the flaw, causing it to propagate and ultimately
produce fracture of the macroscopic body. Inglis ,
utilizing a flat elliptical void as a model, computed
stresses in the vicinity of the flaw. The result of this
and similar calculations based on a variety of geometries
was a relation of the form
S (E)1/2 (1.3)
wheie S = the stress necessary to extend the flaw
o = specific surface energy
I = Young's Modulus
C = characteristic flaw dimension.
Credence was given the flaw theory by observations of
high strengths of pristine glass fibers. Upon prolonged
exposure to the atmosphere, strengths deteriorated by more
than an order of magnitude . The Griffith Theory pre-
dicts that failure by brittle fracture is the result of the
extension of flaws inadvertently introduced prior to,or
nucleated by,the application of a stress.
In light of this hypothesis, the effect of microstruc-
ture on nucleation and propagation of "Griffith cracks"
forms the basis of the present discussion.
It is observed that the fracture strength of "brittle"
material and the yield strength of "ductile" materials
increase as grain size decreases. Several explanations of
this effect have been put forth .
1. Grain boundaries serve to limit the length of
cracks that can subsequently propagate. Since, from equa-
tion (1.3), the fracture stress is directly related to the
flaw dimension, smaller grain size materials have smaller
flaws, and thus exhibit higher strengths.
2. If dislocations are mobile, grain boundaries act
as barriers causing dislocations to pile up and nucleate
a crack according to a mechanism proposed by Zener .
Presumably, larger grains present a more formidable barrier
3. Residual stresses across grain boundaries, due to
thermal expansion anisotropy, can be produced on cooling a
polycrystalline body. Again, the level of stresses in-
creases with grain size.
4. Elastic anisotropy may also produce high local
stress fields across grain boundaries when an external load
is applied. The extent of local stress is expected to be
proportional to grain size.
5. Surface flaws are generally larger in large-grained
In a recent work, Carniglia  has examined 46 sets
of published strength versus grain size data for monophasic
oxide bodies. After "normalizing" for porosity, the data
could be represented by an equation of the form:
o = o + oG-0 (1.4)
where o = the mean strength
G = the grain size
o1, oa and a = constants.
Equation (1.4) is the Petch  equation for oa f 0(6),
the Orowan equation  if oa = 0(7) and the Knudsen equa-
tion if a $ 1/2 . Carniglia concluded that the data
were described by a two-branched curve, one branch described
by the Orowan equation, the other by a Petch relationship.
In all cases, strength was proportional to G-1/2
The effect of porosity on the mechanical properties
of ceramics has received a good deal of attention in recent
years [67-70]. As a result of these studies, several equa-
tions have been proposed which are in reasonably good agree-
ment with published data. Hashin and Shtrikman  de-
rived the expression
E = E P (1.)
where E = Young's modulus for porous bodies
E = Young's modulus for theoretically dense
P = fraction of porosity
A = constant.
Using a dispersed pore model and a Poisson's ratio of 0.2,
Hashin and Shtrikman concluded that A should he equal to 1,
in agreement with the work of Fryxell and Chandler  on
BeO. Values for the constant, A, for Al203 are, however,
in the range 3-5 [73,74].
The most commonly used relationship between strength
and porosity was suggested by Ryshkewitch  and by
a = o e-bP (1.6)
where a = fracture stress, 0o = fracture stress of theo-
retically dense material, b = constant, and P = volume
fraction of porosity.
Carniglia  employed equation (1.6) to normalize
data from strength versus grain size studies. Rudnick et al.
 attribute, in part, the variable dependence of strength
on porosity observed by different workers to differences in
pore size, shape and distribution. Brown et al.  have
derived an expression based on the concept of a projected
area fraction of porosity normal to tensile stress. They
considered pore shape and orientation, summing up the pro-
jected areas in the fracture surface on the normal plane.
DeHoff and Gillard  examined the rupture strength of
porous copper bodies as a function of porosity. They mea-
sured the area fraction of solid supporting the stress
directly on the fractured surface by quantitative micros-
copy, and concluded that the rupture strength was given by
o = o AA min, where o = rupture stress, oo = rupture stress
of solid copper, and AA min = minimal area fraction of solid
(corresponding to projected area of fracture surface).
It is apparent that correlation of properties simply with
volume fraction of porosity is not completely satisfactory.
The morphology, size and distribution of porosity must be
considered if a truly fundamental correlation is to be
1.3.2. Mechanical Properties of UO2
UO2 behaves as a perfectly brittle material at temper-
atures below 10000C. Recent studies by Evans and Davidge
 and by Canon, Roberts and Beals  have shown that
UO2 exhibits a brittle-ductile transition, the precise tem-
perature of which depends upon the deformation rate.
Burdick and Parker  examined the effect of particle
size on the bulk density and strength of UO2 bodies. As
expected, coarser size fractions produced lower densities
and lower strengths. Final grain size was approximately
equivalent as the result of grain growth in finer size frac-
tion material. Knudson, Parker and Burdick  examined
the dependence of flexural strength on porosity and the
effect of Ti02 additions to UO2 bodies prepared from four
different kinds of UO2 powders. They found that their data
(consisting of one microstructural state for each of the
four powders) could be expressed as
S = K G-a e-b (1.7)
where S = flexural strength in four-point loading
G = average grain size (Martin's diameter)
P = volume fraction of porosity
K = 23,700
a =.119 7 constants (room temperature)
b = 3.17 J
The above equation also produced satisfactory agreement
with data taken at 10000C for different values of the con-
stants, K, a and b. At 10000C, Knudsen et al. report a
value for the grain size exponent, a, of .837. As indi-
cated in the previous section, both Orowan  and Petch
 predict a value for a of .5, and values close to this
are observed for a number of ceramic materials . Thus,
the equation of Knudsen et al. must be regarded as empirical.
Forlano, Allen and Beals  studied elastic modulus
and internal friction characteristics of sintered UO2 over
a limited density range (volume fraction porosity .02-.06).
They determined Young's modulus by a sonic technique and
found reasonable agreement with an equation of the form
E = Eo(l-AP) (1.8)
where E = Young's modulus
E = Young's modulus of theoretically dense
A = constant
P = volume fraction of porosity.
Sr d t j.tl e rlier work f r
et [ 1 .' t .n et a [ j.
liv : r 1 lrc t h an f ac I re
charaect i ti l r,,- of te to res.
In the I 1 I. L i thly con iu: c t -It
ci L t
fra ctu( 1 t It e extension of pr-
exi tinp V -. >*;*" tho "Iiht to 1) la e ] r' f "
foui d on I ,' t' 1 i1 spc in .r
fo c It 1 ta a ' n si: a trib-
utCd frbrturi : I ... beli 1(I00C to flaws in tile
forl of0 i cat. 1 a t I o ,,t l no i tsi v teiteria appiroxi-
ratcly 50 to P10 'i ct1cr. These fli;;s are
probably the r it1 a: regacat t ani/or atgloir rates in
the stating mnat i: li .sci ct a 1. , Evans and
Davidge  a l C .t al.  all found that brittle
fracture strength ir -esecd with increasing temperature to
the onset of plnstic.ity.
Roberts and li d:: [87j studied the influence of porosity
on deformation and fr; ctur of UO2. Porosity was produced
by increasing, addit'ons of n:phthalene to the starting
material. Resulling i, icrottructures showed isolated, large,
anisotropic voids si lilar to that seen in irradiated fuel.
Their data could be fitted to the Knudsen expression, equa-
tion (1.4), with ai different choice of constants.
1.3.3. Effect of Microstructure on
Above loom temperature the conduction of heat in oxide
ceramics occurs by coupling of lattice vibrations called
phonons, and the scattering of these waves by anharmonici-
ties limit energy transfer through the lattice. The thermal
conductivity, K, is given by 
K = CvV (1.9)
where K = thermal conductivity
C = heat capacity/unit volume
v = wave velocity
A = mean free path
Above the Debye temperature both C and v change very
little with temperature, and the thermal conductivity is
sensitive only to the mean free path between scattering
events. Theory predicts that the mean free path should be
proportional to 1/T. Experimentally, over intermediate
temperature regimes, many common oxides do in fact show a
1/T dependence . Typically, mean free paths are of the
order of 10-100 A, and thus while microstructural features
have an effect upon thermal conductivity, the influence of
other variables is more pronounced. The presence of varying
impurity levels can completely mask any differences due
to microstructure .
Because of the similarity of the phenomenological
theory, there is a strong analogy between dielectric and
conduction theories of heterogeneous solids. Models con-
sisting of alternate slabs of different materials have been
solved for heat flow parallel and perpendicular to the
slabs . A parallel tube model was employed by Jackson
and Coriell . Analogous to Maxwell's equations for
heterogeneous dielectrics, Euken  has suggested an
equation of the form
2 T- + 1
where Km = material conductivity
K1 = continuous matrix conductivity
K2 = dispersed phase conductivity
V = volume fraction of continuous (matrix) phase.
This equation applied rigorously to systems of phase 1 con-
taining uniform dispersed spheres of phase 2. Such a model
would be a reasonable representation of a high density
sintered material where porosity is isolated and spherical.
If the effective conductivity of the pores is low with
respect to the matrix, the Euken relation reduces to
K = K 1 V(
K K1 1--- (1.11)
Francl and Kingery  have suggested that the relatively
simple Loeb  expression
Km = Ksolid-P) (1.12)
where K soid = conductivity of the solid
P = volume fraction of porosity,
would adequately describe experimental data on a number of
materials. This expression is empirical, however, and
without physical basis.
The effect of grain size on thermal conductivity has
not received a great deal of attention by investigators,
probably again due to the more dominant effect of such vari-
ables as impurity levels, test sensitivity and specimen
reproducibility. It is known that single crystals exhibit
much higher thermal conductivity than polycrystalline speci-
mens of the same composition . Flynn  has pre-
sented a model of a polycrystal comprised of grains sur-
rounded by a boundary region of "width" b. The basis for
such a representation is not clear, but, on the assumption
that the boundary "thickness" and the corresponding conduc-
tivity of the "boundary phase" remain constant, Flynn's
model predicts that conductivity increases with increasing
1.3.4. Thermal Conductivity of UO2
The thermal conductivity of stoichiometric UO2 has
been measured by a number of workers using a variety of
experimental techniques [96- . Ti r. i, c nsid ra;,,l
discrepancy between the values obtained 1 'cn nor; lizs: to
theoretical density by using cqution (1.12). Wor3 by Ross
 and by Deem  suggested, honi, r, tiat (1.121 is
not adequate, particularly at low densities. Ross 
further stated that pore shape and location at grain boun-
daries wcre probably responsible for the loi: values he ob-
tained. He noted that,at higher density, his data are in
agreement with the Loeb expression.
Reiswig  measured the thermal conductivity of UO2
in the range 800 to 21000C. A least squares fit of the
data gave an equation of the form
K = 17.3 + .06T (1.13)
where K = thermal conductivity atitt-
T = temperatures in K for specimen 85%
Bates  reported the findings of the International
Atomic Energy Agency (IAEA) panel that critically evaluated
all reported thermal conductivity for UO2. The panel stated
that the thermal conductivity of UO2 between 20C and
13000C could be best represented by
K = 11 + .0235T (1.14)
where K = thermal conductivity in watts
T = temperature in C for a 95% dense specimen.
The panel further recommended that the correction for
K A KB B (1.15)
be used to normalize all data to 95% theoretical density.
KA = conductivity of specimen of density PA; KB = conduc-
tivity of test specimen of density PB; pB = density of
measured specimen; pA = the desired density; and B = a
parameter that depends upon specimen "characteristics."
B values ranging between 1 and 4 have been reported. The
panel selected 2.5 but recommended a study of the depen-
dence of B on microstructure.
1.4. Objective of the Present Work
The continuing development of nuclear reactors has
resulted in ever more stringent demands on various material
components. In an effort to increase efficiency and opti-
mize performance, higher temperatures, increased fluxes and
higher burnup levels are being specified. The Liquid Metal
Fast Breeder Reactor (LMFBR), now undergoing concentrated
development, will be the primary energy source for the
decades immediately ahead. The breeder reactor has the
capability of converting nonfissionable U238 to fissionable
Pu9 and thus produces more usable fuel than it consumes.
A mixed oxide of uranium and plutonium has been selected
by the AEC as the fuel for the prototype LMFBR. Specifi-
cations call for the LMFBR to produce 1,000 megawatts,
achieve 10% burnup with an output of 100,000 megawatt-days
per ton. The result will be a fission density of 1014 cm3
sec Liquid sodium will leave the core at 5400C. Eighty
thousand fuel pins having a diameter of one-quarter inch
will operate at surface temperatures of 6500C and center-
line temperatures near the melting point of 27600C. At
steady state, gradients up to 9000*C/cm will be sustained
It is estimated that there is a potential production
of one billion pellets of fast breeder fuel over the next
forty years. Shaw  has stated that it is essential
that development "proceed in a disciplined manner so as to
achieve predicted performance based on reproducibility of
materials, properties and behavior from the laboratory
bench through all phases of the program, including the oper-
Reactors for specialized application, such as the
Transient Experimental Test Reactor, may impose very dif-
ferent conditions on the component design than are required
for conventional power reactors. The transient reactor will
utilize U235 dispersed in stabilized ZrO2 to give appro-
priate fission density,resistance to thermal shock and
thermal conductivity .
All reactor fuels undergo changes in microstructure
during operation as the result of exposure to high temper-
atures and large thermal gradients for extended periods
of time, as well as accumulating fission products. Struc-
tural changes which occur during the life of a fuel pin are
illustrated in Figure 2 . It is apparent that these
changes markedly effect performance via changes in both
mechanical and thermal properties.
In summary, fuel technology has as major objectives:
1) microstructural fuel design for optimum
2) attainment of reproducibility and uniformity
for large-scale production of fuel, and
3) prediction of microstructural changes occur-
ring in pile and the effects of these changes
on performance parameters.
The primary objective of the present work is the appli-
cation of the techniques of quantitative metallography to
a wide range of sintered UO2 microstructures, providing a
degree of characterization not previously achieved. The
simultaneous determination of room temperature tensile
strengths and of thermal conductivities which correspond
to these structures provides a sound basis for the identi-
fication of structure-property relationships in a real fuel
material. Such a systematic study is a necessary first
step towards the attainment of the goals previously enum-
10 and 105 MWD/T
Fig. 2. Structural evolution during useful life of a
UO2 fuel pin .
2.1. Material Characterization
2.1.1. Material Specifications
The material employed in this investigation was sup-
plied by the United States Atomic Energy Commission. It
was produced by Mallinkrodt Chemical Company by precipita-
tion from solution as ammonium diurinate (ADU), calcina-
tion to 110UO and reduction to I'02. The resulting product
was then fused in an electric arc furnace by Spencer
Chemical Company. Analytical ipipurities determined by
Battelle Memorial Laboratories are given in Table 1. The
as-received powder was classified into -6 mesh, -20 mesh
and -200 mesh (U.S. Standard Series) lots. Scanning elec-
tron photographs of the as-received materials are shown
in Figs. 3 and 4. The following observations were made:
1) The particles are angular, faceted polyhedra;
i.e., they exhibit very little curvature of
surface and are roughly equiaxed.
2) There are virtually no open pores or voids in
3) There is no size dependence of shape or
topography insofar as can be resolved in the
scanning electron microscope (SEi).
Analytical Impurities in the Arc Fused UO
Used in this Investigation
Carbon 57 ppm
Boron < 0.1
Cadmium < 1.0
Chromium < 5.0
Magnesium < 3.0
Nickel < 3.0
Fig. 3. SEM photographs of -6 mesh as-received UO2
Fig. 4. SEM photographs of -200 mesh as-received powder.
4) There are small particles which appear to be
adhering to surfaces of the larger particles.
These particles are generally smaller than
5 microns and are physically distinct from
the substrate particle.
Similar "surface" particles have been seen by Johari
and Bhattacharyya  on electrolytic iron and by Lifshin
et al.  on SiC. 'ihe latter attribute bonding to elec-
trostatic forces. Effectively, then, each particle is an
agglomerate or assembly of many particles which cannot be
readily separated. It is apparent from the surface topog-
raphy that subsequent to arc fusion the present material
was subjected to a comminution process, wherein large fused
grains were crushed. The small particles observed are
probably the result of this operation.
Figures 5 and 6 are photomicrographs of -6 mesh and
-270 +325 mesh as-received powders. In both cases, nearly
all particles are single crystals, and thus even when
etched are virtually featureless. The -6 mesh particles
(Fig. 5) show residual cracks from the crushing operation,
the presence of aggregates (although their number was
judged to be quite small) and occasional closed porosity.
The -270 +325 specimen of powder shown in Fig. 6 indicates
no aggregates present in this size fraction. It is appar-
ent, however, that particles much smaller than the 44 micron
325 sieve opening have been retained.
Graham  has measured the x-ray domain size of
ball milled powder employed in this investigation. Based
Fig. 5. Photomicrographs of -6 mesh as-received powder;
(a) cracked grain, (hV particle aggregate.
Fig. 6. t ro h of -270 +32 as-received powder.
Fig. 6. Photomicrographs of -270 +325 as-received powder.
on line profile analysis of (200) and (100) reflect ons,
he found an effective domain size of 530 I. This result
is in good agreement with results of other workers 
and indicates a relatively low preparation temperature of
5000 to 6000C .
As a result of the multiple oxidation states of U,
the uranium-oxygen system is among the most complex of
metal-oxide systems. There are at least four thermuodynar
ically stable oxides, and these exhibit polymlorphism and
metastability to varying degrees . Several other
oxides have been reported, but not confirmed. Only the
region between UO2 and U409 (0/U = 2.00 to 2.25), however,
is of primary interest to the nuclear fuel industry.
Although differing in detail, the work of Schaner
, Blackburn , Vaughn et al. , Aronson and
Belle  and Gronvold  established certain general
features of the phase diagram in the region between UO,
and U409. The diagram according to Schaner  is pre-
sented in Fig. 7.
U02 crystallizes in the fluorite structure, i.e., the
cation lattice is FCC and 8 oxygen ions are located in the
tetrahedral interstices. As indicated by the diagram,
Fig. 7, UO2 exhibits considerable solid solubility for
oxygen (hyperstoichiometry). At 900C cubic U02 is stable
Fig. 7. Phase diagram of the U-0 system for O/U ratios
between 2.0 and 2.25,according to Schaner .
E3 S!60 \
" 5.450 \
2.00 2.10 2.20 2.30
UO2 4 09
(/J iO 49
Fig. 8. : of the lattice constant at 2S5C upon
S for cubic UO, .
in the O/U range 2.00 to 2.20, while at room temperature
there is little or no solubility. Virtually all proper-
ties of UO2 are sensitive to some degree to the presence
of excess oxygen in the lattice. Consequently, determina-
tion of O/U ratio is essential to any study of UO2.
Precision lattice parameter measurements and thermo-
gravimetric analysis were employed for this purpose.
Reported values of the room temperature lattice parameter
of stoichiometric DO2 range between 5.473  and 5.469
. Schaner  has determined the lattice parameter
of UO2+x as a function of known O/U ratio. His results,
shown in Fig. 8, are in good agreement with more recent
The lattice parameter of a freshly sintered bulk
specimen from the present study was determined utilizing
a Norelco diffractometer to scan the region 26 = 700 to
1450 at 1/20 26 per minute. Filtered copper radiation
from a fine focus tube operating at 35 KV and 15 ma was
used; 99.99% annealed gold powder served as an internal
standard. Data obtained were fitted by Cohen's Method of
Least Squares . The calculations were performed by
computer, utilizing a program supplied by Mueller (Argonne
National Laboratory) and reproduced in Appendix A. The
choice of correction terms is indicated on the program
description. The value obtained for a specimen sintered
in H2 was a. = 5.4716 .0003 A. From Fig. 8, the O/U
ratio was determined to be 2.0(1 after sint rin in a rce-
nent with the general observation that sintering in 112
produces a stoichiometric material, of the
stoichiometry of the starting oxide.
The measurement was repeated with ball milled powder
dried in air at 900C.
The 0/U ratio of the starting material i:as determined
to be 2.06 based on a lattice parameter of 5.4693 + .0006 ,
A determination of stoichiometry was also made utiliz-
ing a gravimetric technique described by Scott and Harrison
. A precision cloctrobalance* with a reported sensi-
tivity of better than 10 micrograms was used in this experi-
ment. A sample of approximately 100 mg was carefully
weighed on a platinum pan utilizing class S weights. The
specimen and pan were then counter balanced and the micro-
balance recalibrated to yield full scale deflection at 10
mg increase in weight. A null detector** was employed to
indicate balance. The specimen and pan were then trans-
ferred to a platinum boat and oxidized at 450C in still
air for two hours to produce U308 (0/U = 2.667). The speci-
men was returned to the balance and the weight increase was
determined. The procedure was repeated to insure that the
reaction had gone to completion. The weight gain expected
if the starting material had been stoichiometric (O/U = 2.00)
*Cahn Division, Ventron Instrument Company.
**Kiethly Instrument Company, Model No. 155.
was calculated and compared with that observed experimen-
tally. An estimate of stoichiometry could then be made.
This method gave satisfactory results for a bulk sintered
material (O/U < 2.03). Results for ball milled powders
were not satisfactory, probably because of adsorption on
surfaces. It is believed that this situation could be
corrected by in-situ oxidation and/or oxidation-reduction
in a controlled environment. Scott and Harrison  also
reported difficulty with as-received powder, indicating the
problem is not unique to the present investigation.
2.1.3. Size Reduction and Separation
In an effort to evaluate the sinterability and the
effect of particle size on sintering behavior, the as-
received -200 mesh powder was sieved and fractionated
according to Table 2.
Initial attempts to sinter loose stacks uncompactedd)
of -325 powders at 1650C met with limited success. Speci-
mens sintered for two hours and 24 hours showed identical
densities of 5.26 gm/cm3 (48% theoretical density).
Although some sintering occurred (loose stack density
4.43 gm/cm3), specimens were quite fragile.
in order to explore the effect of temperature, arrange-
ments were made to use ultrahigh temperature furnace facil-
ities.* Molybdenum cups were loaded with material from
As-received UO Powders were Separated
Into Lots by Sieving
each powder lot in Table 2 and tapped down manually. The
specimens were sintered in hydrogen at 22500C for one hour.
The results are shown in Fig. 9. Only 4 and 5 could be
considered strong enough to be handled.
It was clear as a result of these studies that par-
ticle size reduction would be necessary in order to extend
the range of initial particle sizes and, hence, the range
of accessible microstructures. As a result of the sieving
operation, it was determined that approximately 80% of the
as-received -200 mesh material was retained on a No. 325
sieve, but would pass a 270 sieve. This material was
selected as a base for all further studies because of the
quantity available, the fairly discrete size distribution,
and evidence of reasonable sinterability in the "as-
Two techniques were employed to produce material of
smaller particle size. A rubber lined ball mill with
Burundum cylinders* was used to wet ball mill the base
material for 16 hours. This was followed by a drying oper-
ation done in air in open Pyrex trays at 900C for 12 hours.
The powder was then granulated and stored in closed con-
tainers until used.
*U.S. Stoneware Company.
- k *
As an alternative to ball milling, an impact pulver-
izer* was employed. Optimum conditions appeared to be
opposing pressures of 80 and 100 psig of argon at the jets.
Although the process produced a powder less than
1 micron in size, it was found to be inefficient. Maximum
production rates were below 10 grams per hour, which was
deemed inadequate for this investigation.
Examination of wet ball milled material indicated
the presence of particles in excess of 10 microns along
with particles of 1 micron or less in considerable quantity.
It was felt that if a separation process could be used to
remove particles >5 microns the remaining powder would be
sufficiently different from the ball milled material to
provide a third point in the scale of starting materials.
Separation was accomplished by a sedimentation tech-
nique, i.e., a dispersion of the particles in a fluid,
preferential settling of the larger particles and recovery
of the remaining particles. In order for such a technique
to be effective, agglomerates had to be dispersed com-
pletely, in such a way that neighboring particles did not
interact. It was found that a commercial pigment stabil-
izer, polyoxyethylene sorbitan monolaurate,** in concen-
trations of about 20 ppm in aqueous solution would
*Gem-T, Trost Equipment Corporation.
**Tween 20, Atlas Chemical Company.
effectively disperse UO,. Experimentally, the suspension
is agitated in a small liquid blender and transferred to a
glass column approximately 90 cm in height, allowed to
stand 80 minutes; the supernatant, containing the fine
particles, is then withdrawn and the particles recovered.
The basis for this technique is given by Stokes Law for a
Sir 3(p p )g = 67rnv (2.1)
where r = particle ratio
p = particle density
(j = liquid density
g = acceleration due to gravity
n = coefficient of viscosity
v = steady state or terminal settling velocity.
For a particle initially at rest a distance h from the
bottom of the vessel, the settling velocity v is
v = h (2.2)
where t is the time required for a particle to settle the
distance h. Substitute (2.2) into (2.1) and rearrange,
t 6 .= n--- (2.3)
73 1T (Pp-P)
Using the viscosity of water at 25C (9 x 10-3 poise),
a particle density of 11 gm/cm3 and the column height of
90 cm, the maximum time required for particles larger than
Fig. 10. SEM photos of powder from the three size
fractions employed in this investigation.
5 i.icrons to settle is 4,800 seconds. Clearly, smaller
particles near the bottom of the column will also settle
out during this tine internal. (Although these are poten-
tially recoverahle by repetitions of the sedimentation
process, no attempt was made to further sep'irate the solid
which settled out of the suspension.) The supernatant wias
drawn off to a clean vessel after the prescribed time
period had clasped. Attempts to deflocculate the suspe
sion using commercial deflocculants of the anionic, cationic
and nonionic types were unsuccessful. Recovery of the
solid: was effected by evaporation of the liquid in shallow
Pyrex trays heated at approximately 900C. The dried cake
was crushed, passed through a 200-mesh sieve, and stored in
Scanning electron micrographs of the powder lots
employed in the present study are shown in Fig. 10. These
lots are referred to respectively as coarse, intermediate
and fine size fractions in the text.
2.1.4. Specific Surface Area
The surface areas of the three powders employed in
this study were measured by a technique devised by Brunauer,
Emmett and Teller . The B.E.T. measurement is based on
a model for adsorption of a gaseous species on the surface
of a solid. The surface area is related directly to
capacity to adsorb atoms by
S = N Am x 10 (2.4)
where S = specific surface m2 /gram
X = monolayer capacity in grams of
m adsorbate/grams of adsorbent
M = molecular weight of adsorbate
N Avogadro's number
A = area occupied by a single adsorbate
molecule in 2.
Based on the B.E.T. model, the monolayer capacity of the
solid can be evaluated from 
S1 C-1 (2.5)
-X(c XmC XiC p
where X = mass of adsorbate in grams per gram
o = saturated vapor pressure
p = system pressure
X = monolayer capacity
C = constant for the system related to
energy of adsorption of the monolayer.
Accordingly, when p/X(po-p) is plotted against p/p the
relative pressures, a straight line is formed having a
S = C- (2.6)
and an intercept
1 = TC (2.7)
Solutions of these two equations simultaneously leads to
X = (2.8)
C = 1 (2.9)
B.E.T. measurements were performed on the three powder
size fractions described previously, using an apparatus
similar to that shown in Fig. 11. Approximately 10 grams
of material were charged into a quartz specimen bulb.
The surface was then activated by heating to temperatures
in excess of 300'C for two hours at 10-5 mm Hg. The bulb
was then cooled to 770K in a liquid nitrogen bath and held
at that temperature until measurements were completed.
Dry nitrogen was introduced into the system with the
specimen stopcock closed and the amount of gas determined.
The specimen stopcock was then opened and the system pres-
sure was allowed to equilibrate before the value was
recorded. Subsequent readings are obtained by decreasing
the volume of the system through a series of mercury cham-
bers and an equilibrium pressure recorded for each incre-
ment. A computer program to solve the P.E.T. equation has
been written by Martin , incorporating the appropriate
parameters for the apparatus employed here. This program
calculates values for p/x(p -p) and P/Po, performs a
least squares fit, calculates the slope and intercept of
the B.E.T. equation, and computes specific surface area.
Man vacuum line,
Fig. 11. Schematic of the B.E.T. apparatus used to
determine surface area .
Surface Areas of the
Three Size Fractions of UO,
As received, -270 +325 (coarse)
Ball milled (intermediate)
0.87 m /gram
1.54 m /gram
*Considerable scatter in the adsorption isotherm
inherent for low values of surface area. All iso-
therms B.E.T. Type II at 77K.
D .05 1 1.5 2
Figure 12. B.L.T. plot for fine size fraction of UO,
The values obtained are given in Table 3. Figure 12
is a plot of the B.E.T. data for the fine size fraction.
The data for the intermediate and coarse materials were less
satisfactory because experimental error increases as the
surface area decreases, as discussed by Crowl . It
should be noted that for all three data sets, the parameter
C, as defined by equation (2.9), is larger than 2. This is
a necessary condition for the isotherm to be Type II, thus
permitting the surface area to be calculated.
2.2. Specimen Preparation
Three techniques were employed to prepare specimens
1) loose stack sintering -- sintering of uncom-
pacted material in a suitable container,
2) cold pressing and sintering -- compaction in
a steel die followed by thermal treatment, and
3) hot pressing or pressure sintering -- sintering
under an applied load in a die.
2.2.1. Loose Stack Sintering
Powder was poured into specially machined molybdenum
cups approximately one inch in height, .625 inch inside
As UO2 powder is not free flowing, it was necessary
to tap down the stack to insure that it filled the cup
uniformly. The conical stack was leveled off even with
the top G th : ,d t cup.; wdre then placed directly
into the furL;..e. The sintering cycle is discussed fully
in the next section.
2.2.2. Cold PrcF sir"
Cold pressed spcci cns were prepared by compacting with
and without the aid of a binder-lubricant. Polyvinyl alco-
hol, stearic acid in petroleum ether and polyethylene
glycol were evaluated for use as binder-lubricants. Poly-
ethylece glycol* was selected for its outstanding green
strength, ease of blending, excellent surface finish and
ease of volatilization prior to sintering. The binder was
added to the powder batch in amounts of 1/2 to 1% by weight
and blended in a polyethylene container. Mixing was
carried out by tumbling the container on a ball mill drive
for one hour.
Specimens were pressed in a specially constructed and
hardened tool steel die. The cylindrical die cavity had
a diameter of .689 inches, incorporated a taper of 8 minutes
per inch, and had an adjustable depth. The die, pressed
into a double acting Ilaller**die table, is shown in Fig. 13.
A 75-ton hydraulic arbor press was used to apply pressures
up to 100,000 psi. In practice, compacting pressures above
75,000 psi frequently produced transverse laminations.
*Mallinkrodt Chemical Works.
callerer Division, Federal-Mogul Corporation.
Fig. 13. Punch and die assembly used to cold compact UO2.
Severe galling, die chatter and specimen cracking were
observed in the absence of a binder-lubricant above 10,000
psi and, as a result, a binder was employed for nearly all
specimens produced by cold pressing.
Pressed compacts were placed on molybdenum trays and
inserted into the hot zone of an Astro high temperature
furnace,* Fig. 14a. The furnace was evacuated and back
filled with commercial grade hydrogen prior to heating.
A flowing hydrogen atmosphere was maintained during all
heating and cooling periods. A one-hour hold at 150-200C
was utilized to volatilize the binder prior to heating to
the desired sintering temperature. Practical sintering
temperatures were limited to about 1800C by the A1203
muffle. Heating and cooling rates of 200-400C per minute
were generally encountered and the sintering "times" that
are presented are the time intervals that specimens are at
the sintering temperature. They do not include the heating
and cooling periods.
Temperatures were measured with a micro-optical pyrom-
eter**sighted directly on the specimens. The temperatures
reported are believed to be accurate to 100C in the range
*Astro Industries, Model 1000B.
**Pyrometer Instrument Company, Model 95.
Fig. 14. (a) The high temperature Astro sintering furnace.
(b) Centorr vacuum hot press.
2.2.3. Hot Pressing
Hot pressed specimens were fabricated in a Centorr
vacuum hot press,* Fig. 14b, using graphite** dies and
punches. Early experimental pressings revealed extensive
reaction between graphite and UO2, particularly at temper-
atures above 17000C. This reaction is undoubtedly respon-
sible for hot pressing behavior reported by Murray .
The situation was corrected by the use of a boron nitride***
die insert and punch faces. The entire die assembly is
shown in Fig. 15. Pressures up to 5,000 psi and temper-
atures to 2000*C in a vacuum of 10- torr were attained.
Temperatures again were measured with an optical pyrometer
sighted on the die body, giving a probable accuracy of z20*C.
A subsequent heat treatment of 90 minutes at 1200C in
hydrogen insured that the specimens were stoichiometric .
2.3. Evaluation of.Geometric Properties
Microstructural examination was carried out on speci-
mens which had been fractured in diametral compression (see
section 2.4). The fracture mode was such that two large
segments of the specimen were recovered. The fracture
*Centorr Associates, Inc.
**Union Carbide Corporation, Grade ATJ.
***Union Carbide Corporation.
A Upper ram
BN punch face
BN die liner
Fig. 15. Graphite and boron nitride die assembly used
to pressure sinter UO2.
surface of one of the segments was then ground and mounted
for metallographic examination. The remaining segments
were held for fractographic study.
Metallographic mounts were prepared using a castable
epoxy compound* and a vacuum impregnation process. Speci-
mens were impregnated by immersing them in a beaker of the
epoxy mounting material and placing the beaker in a vacuum
dessicator connected to a mechanical pump. The dessicator
was gently evacuated until air appeared to be removed from
the specimen; air was then readmitted into the dessicator,
forcing the epoxy into the open porosity in the specimen.
It was found necessary to repeat impregnation through
successive polishing steps for samples of low density and/or
low strength as many as three times in order to obtain satis-
factory results. After impregnation, the specimens were
placed in glass cylinders situated on a glass plate and
additional mounting material was poured into the cylinder
to produce a mount of suitable size. The epoxy was cured
at room temperature for 24 hours, then heated to 50C for
an additional 2-3 hours. It was found that only after the
above curing process could the mount be readily removed
from the glass cylinder.
The metallographic procedure employed to polish the
specimens is as follows :
*AB Buehler, Ltd.
1) Wet grind on a slow wheel with 180-, 320-and
600-grit silicon carbide paper discs.
2) Polish on nylon or silk saturated with 2%
chromic acid and suspension of Linde A alumina
powder in 2% chromic acid using a fast wheel
3) Repeat (2) with Linde B alumina after thor-
oughly cleaning the specimen with distilled
water and alcohol.
4) Wash, dry and examine;the etch used to reveal
grain structure was devised by Cain :
(a) a solution of one part H2S04 to nine
parts 11202 (30%) swabbed on the surface with
cotton for 30 seconds, and (b) the surface
is then immersed for an additional 30-60
seconds, washed, dried and examined. Deter-
ninations of the metric properties of the
pore solid network were made on unetched
specimens, in as much as etching was found
to adversely affect the accuracy of these
measurements. Subsequent to these measure-
ments, the specimens were etched and the
grain boundary intercept count was made.
2.3.2. Quantitative Metallographic Analysis
Three quantitative metallographic parameters were
determined in order to characterize the void-solid network:
(1) Pp, the fraction of points of a test grid imposed on
the microstructure which lies within the feature of inter-
est, e.g., void phase; (2) NL, the number of intersections
per unit length that a test line imposed on the micro-
structure makes with a feature of interest, e.g., void-
solid interface; and (3) TA net, the net number of tangents
that a test line makes with features in the microstructure,
e.g., pores, when swept over a unit area. There are two
kinds of tangents which a test line can make with a bounding
curve, if an interior and an exterior can be distinguished.
Following Rhines et al. , a tangent is considered nega-
tive if the arc at which the tangent is made is convex with
respect to the pore phase and positive when concave with
respect to the pore phase. The number of positive and
negative tangents per unit area traversed are tabulated
separately and the value of TA net is then
TA net = TA TA- (2.10)
TA net may be positive or negative depending on relative
magnitudes of the two tangent counts, and the algebraic
sign of TA net must be included in all calculations involv-
ing the tangent count. The determination of these param-
eters is illustrated schematically on a photomicrograph of
a UO2 specimen in Fig. 16.
The volume fraction of void phase may be determined
from the point count and independently from a determination
of the density of the sinter body. A comparison of these
two values was used as a criterion to ascertain that the
metallographic section was in fact representative of the
three-dimensional sinter body. An agreement between the
point count and bulk density of 3% was used as a criterion
for acceptance or rejection of metallographic sections as
representative of the sinter body.
Bulk densities were determined by the liquid displace-
nint technique described in AST'! Standard 328-60. Open
Fig. 16. Schematic illustration of the counting measure-
ments on a sinter structure.
porosity was filled with paraffin prior to determination
of sample volume. Some sample densities were also deter-
mined by displacement of carbon tetrachloride. No impreg-
nant was used and specimens were allowed to equilibrate
for several hours in the carbon tetrachloride prior to
determining immersed weight, thus excluding "open" porosity
from the sample volume.
The determination of the quantitative metallographic
parameters was made utilizing a Quantimet 720 image analy-
ing computer.* The instrument is capable of performing all
of the counting measurements previously described, by
dividing an image into picture points. Logic circuitry
permits this Quantimet to recognize picture points in which
the image is darker (or lighter) than a preset level. Thus,
if there is a gradation in image intensity, such as there
is between void and solid phase in a sinter body, a point
fraction is obtained by counting the number of picture
points which comprise the void space and dividing by the
total number of picture points utilized to represent the
image. The Quantimet has a capacity of 500,000 picture
points on "Standard Frames," but the size and position of
the computed or "live" frame may be varied. The image is
displayed on a cathode ray tube which also incorporates a
digital display of the counting results. Additionally,
*Image Analysing Computers, Ltd.
the detected image and the computed image may also be dis-
played. Figure 17 shows the displayed image of a sintered
UO2 specimen with the digital display in the upper left of
Intersections and tangents are also based on pre-
programmed logical analysis of the image as represented by
the array of picture points. Intersections are registered
whenever the computer finds that adjacent picture points
differ by an established intensity. As the raster scans
line by line, top to bottom, the structure is sampled by
the equivalent of a test line whose length is the product
of the number of lines in the live frame and the actual
width of the frame. Similarly, the image is scanned line
by line for "end points" or tangents, equivalent to sweep-
ing a test line over the live frame.
A metallograph* is used to provide the image viewed
by the Quantimet vidicon head. A specially designed mount
supports the vidicon and permits it to be moved along the
bellows track of the metallograph. Figure 18 shows the
Grain boundary intercepts were counted manually using
a grid eyepiece. Measurements were performed on specimens
for which void space characterization had been completed,
and which had subsequently been etched to reveal grain
*Bausch and Lomb, Inc., Research I.
Fig. 17. Quantimet display of a sintered U02 micro-
boundaries. Intersections with void-solid boundaries and
grain boundaries between adjacent grains were tabulated
2.3.4. The Metric Properties
The metric properties are determined directly from the
counting measurements described in the preceding section.
1. The volume fraction, Vv, is the total volume of
void space contained in a unit volume of microstructure.
It may be shown that the point fraction P is an unbiased
estimator of volume fraction [126,127]
V = Pp (2.11)
2. S is the surface area of interface per unit
volume of structure. The number of intersections per unit
length made by a test line with the trace of the surfaces
on a representative test plane is directly related to
Sv by [126,128]
S = 2NL (2.12)
3. The means to experimentally determine mean surface
curvature in a three-dimensional volume containing curved
surfaces was devised by DeHoff . The curvature of a
surface at any point is specified by the principal normal
curvatures, K1 and K2, defined as follows: a normal is
constructed at a point on a surface. All possible planes
containing the normal are constructed. The intersection
of the surface with these planes is an arc whose radius is
that of a circle passing through three adjacent points on
the curve. There will exist a plane for which the arc
radius is a maximum and a plane for which the radius is a
minimum. These radii are the principal radii and the
principal normal curvatures are then defined by
K1= 1 K2 (2.13)
1 r1 2 r2
The mean curvature, H, is just the arithmetic average of
the principal normal curvatures or
H (K1 + 2) (2.14)
The mean curvature is defined at every point on the sur-
face. The total curvature M of a surface element dS is
dM = HdS (2.15)
Total curvature can be evaluated for a finite surface by
integrating the mean curvature over the surface,
M = If HdS (2.16)
It is convenient to express the total curvature on a per
unit volume basis, M i.e., perform the above integration
over the surface contained in a unit volume of structure.
Since H has a value at every point on the surface, it will
have an average value defined by
DeHoff  has shown that this quantity is related to the
net tangent parameter by
n TA net
FT = --- (2.18)
where rI has the algebraic sign of TA net (see section
2.3.3). The total curvature per unit volume, M is then
1 TA net
M = Sv -- --- S = i TA net (2.19)
4. A straight line constructed on a plane section
through a sintered structure will form intersections with
traces of the void-solid interface. In structures composed
of a few large pores, the length of line between adjacent
intersections will be greater than for structures composed
of many small pores. Thus, the chord intercept is an
estimator of the scale of the system. The mean pore inter-
cept is given by [45,129]
S= v = P (2.20)
5. Analogous to the mean pore intercept, the mean
grain intercept may be defined as the average chordal dis-
tance between grain perimeters. For systems which contain
porosity, the mean grain intercept is given by
vF v L ---- (L.l
g Sv"aP+Sv a "La "NI,
where NL"P is the surface area of pore-solid interface
and NLa is the surface area of grain boundary between
solid grains. The latter boundaries are shared by two
grains, hence the factor of two. The simultaneous deter-
minations of these properties provide a complete descrip-
tion of the geometric state of the system.
2.4. Evaluation of Mechanical Properties
The diametral compression test was employed in this
investigation to evaluate the tensile strength of UO2
sinter bodies at room temperature. Diametral compression
was developed in the early 1940's simultaneously in Japan
and Brazil . It was originally developed to evaluate
concrete, but has since been used on a variety of materials
[131-134]. Using elasticity theory, Frocht  derived the
stress distribution of a perfectly elastic cylinder loaded
diametrally. His solution was verified photoelastically
by Love . The stress state, shown schematically in
Fig. 19, is biaxial, having large compressive stresses at
both surfaces and a reasonably uniform tensile stress over
the center of the diametral plane.
The present test has several advantages over the more
commonly used bend tests.
1) Specimens are easier to fabricate; in the case
of nuclear fuel, most fuel elements are in the
form of cylindrical pellets. The test may
then be performed on production pellets with-
out resorting to special fabrication tech-
2) Related to (1) is the fact that specimens
tested are representative of those being pro-
duced, whereas specimens made especially for
testing may incorporate differences in micro-
structure due to density gradients, firing
3) Bend tests produce maximum tensile stresses
at outer surfaces and thus are sensitive to
surface preparation. Tensile stresses gener-
ated by diametral compression are distributed
over the entire diametral plane, emerging
only at the ends of the right cylinder.
Testing techniques have been reviewed by Mordfin and
Kerper ,Rudnick, Hunter and Holden , and by
Rudnick et al. . In the present work, specimens were
loaded in an Instron TTD* machine equipped with a CF load
cell in a compression carriage. Hardened steel platens
were constructed to fit the Instron crosshead. Padding to
eliminate concentration of compressive stresses was pro-
vided by two thicknesses of file card stock. Loading rates
of .02 and .002 inches per minute were explored with no
significant effect of loading rate observed. As a result,
a crosshead speed of .02 inch/minute was employed in all
Initially, samples in the as-fired state were tested
directly. However, the presence of surface asperities,
slight taper parallel to the cylindrical axis, subsurface
Fig. 19. Distribution of stresses in a diametrally
loaded cylinder .
Fig. 20. Precision centerless grinder used to machine
defects, etc., indicated a need for precision finishing.
This was accomplished by centerless grinding all specimens
in a specially constructed centerless grinder. The grinder,
shown in Fig. 20, was built from a design developed by
DeMeyer  at Battelle Northwest Laboratories. Toler-
ances of .0002 inch in diameter along the axis were
achieved with a properly dressed wheel. Additionally, the
grinder produced excellent surface finishes and revealed
the presence of subsurface defects not apparent on the as-
fired surface. Cylinder ends were also ground flat and
parallel, utilizing a V-block jig with carbide wear inserts.
The tensile strength may be calculated directly from
the applied load at failure, P, according to
where D is the diameter of the cylinder and t is the
2.5. Measurement of Thermal Conductivity
The thermal conductivity of sintered U02 was measured
using a comparative or cut bar instrument* shown schematic-
ally in Fig. 21. The measurement technique is based on the
establishment of longitudinal heat flow through a composite
consisting of two standard meter bars and the specimen.
Radial heat flow is minimized by the presence of guard
*Thermophysics Corporation, TC-2200.
Fig. 21. Comparative cut bar thermal conductivity
heaters which match the gradient of the stack. Temperatures
along the stack are monitored at the points indicated in
Fig. 21, so that temperature gradients and mean temperature
values can be calculated for each stack component. For
longitudinal heat flow, the integral form of the Fourier
equation can be written as 
Q = kA T (2.23)
where Q heat flux
k = thermal conductivity
A = cross-sectional area
AT = temperature differential through
which Q flows
t = thickness of conductor in the
Since the specimen and the standards are in series,
the heat flux is the sane in each. Then
Q t st tst = xA Tx
where the terms are defined in equation (2.23) and the sub-
scripts "st" and "x" refer to the standard meter bar and
the specimen, respectively. All quantities are known except
kx and, assuming cross-sectional areas are identical,
kx kst T tst (2.24)
Pyroceram 9606 was selected as the standard material
for the meter bars in the present investigation for two
1. The conductivity of 9606 is intermediate between
the reported extremes of conductivity of UO2 over the tem-
perature range of interest. Thus it can be used for all
measurements with reasonable accuracy.
2. There is good agreement between several investi-
gators on absolute conductivity values for 9606 over a wide
range of temperatures [140,141]. Figure 22 presents the
temperature dependence recommended by T.P.R.C. .
Based on tabular data accompanying the T.P.R.C. curve
, a computer program was devised to interpolate between
the published data points. The program generated a table
of conductivity values for 9606 at one degree intervals
between 300 and 1200K. This tabulation is reproduced in
Specimens selected for measurements were centerless
ground to 0.625 inch diameter to conform precisely to the
diameter of the meter bars. The ends were ground flat and
parallel through 600-grit SiC. A precision diamond wafer
saw was used to cut 0.024 inch wide by 0.015 inch deep slots
in the end faces to accommodate platinum/platinum-10%
rhodium thermocouples.* The annular gap between the stack
and the guard was filled with bubbled alumina**. The entire
10-1 ----- l-_T -
102 2 3 4 5 6 7 103
Fig. 22. Temperature dependence of the thermal conductivity
of Pyroceram 9606 .
assembly ;wa: evacu ted to a vacuum of 102 Torr to prevent
oxidation of UO2 and eliminate convective heat transfer.
Flynn  has discussed possible sources of error
associated with cut bar thermal conductivity measurements.
Errors may result front
1) radial heat exchange
2) shunting heat flow through the insulation
surrounding the stack.
3) inaccurate standards.
4) excessive interfacial resistance to heat
flow between stack components.
5) perturbations introduced by thermocouples.
6) uncertainties in the measurement of gage
7) presence of cracks, voids or heterogeneities
not ascribable to microstructure.
8) measurements under nonequilibrium conditions.
RESULTS AND DISCUSSION
The results of this investigation have been separated
according to the manner in which the specimens were pre-
pared: (1) compacted and sintered, including loose stack
sinterings, and (2) pressure sintered. The reason for
such division will become apparent in the course of this
discussion. The data are further subdivided according to
initial particle size. All graphical presentations are
consistent in that a triangular plotting symbol refers to
data obtained from a specimen prepared from the coarse
size fraction (particle size is discussed in Section 2.1.3).
Similarly, round plotting symbols are associated with
intermediate size powder and a square symbol refers to
powder from the fine size lot.
3.1. Densification Behavior
In view of the paucity of information in the litera-
ture on pressure sintering of UO2, the densification
behavior of the powders employed in the present investiga-
tion was systematically characterized in a series of exper-
8 9 10 10.5
Fig. 23. Densification of three size fractions of UO, at
constant heating rate followed by 5-minute arrest
at 1800'C, pressure sintered at 3,000 psi at