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An electron microscope and field ion microscope study of defects in quenched platinum

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An electron microscope and field ion microscope study of defects in quenched platinum
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Newman, Robert William, 1939-
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1967
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English
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xi, 169 leaves : ill. ; 28 cm.

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Subjects / Keywords:
Crystals ( jstor )
Electric fields ( jstor )
Electrons ( jstor )
Geometric planes ( jstor )
Ions ( jstor )
Magnetic fields ( jstor )
Metal foils ( jstor )
Microscopes ( jstor )
Platinum ( jstor )
Stacking faults ( jstor )
Dissertations, Academic -- Metallurgical and Materials Engineering -- UF
Electron microscopes ( lcsh )
Metallurgical and Materials Engineering thesis Ph. D
Microscope and microscopy ( lcsh )
Platinum -- Metallography ( lcsh )
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bibliography ( marcgt )
non-fiction ( marcgt )

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Thesis:
Thesis - University of Florida.
Bibliography:
Bibliography: leaves 163-168.
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Manuscript copy.
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Vita.

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AN ELECTRON MICROSCOPE AND FIELD

ION MICROSCOPE STUDY OF DEFECTS

IN QUENCHED PLATINUM










By
ROBERT WILLIAM NEWMAN













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










UNIVERSITY OF FLORIDA
December, 1967




































UNIVERSITY OF FLORIDA
1 11111111111111111111262 08552 33111111111111111111
3 1262 08552 3313
































Dedicated to My Wife,

Mary Katherine












ACKNOWLEDGMENTS


The author would like to acknowledge the assistance

of his advisory committee. He is especially indebted to

his chairman, Dr. J. J. Hren, who contributed unselfishly

of his time in the form of stimulating discussions, advice,

and encouragement throughout the course of this investi-

gation.

Thanks are also due Drs. E. D. Adams and T. A. Scott

of the Physics Department for their suggestions concerning

cryostat design, the late Mr. R. J. Harter, chief metal-

lurgist of the Sperry Rand Vacuum Tube Division, who aided

in the microscope design, Mr. E. J. Jenkins for his as-

sistance in the laboratory and Dr. R. C. Sanwald for the

use of his computer program.

The author would like to acknowledge the members

of his family, too numerous to mention, whose encouragement

and support has been invaluable.

The writer is also grateful to the National

Aeronautics and Space Administration, without whose

support this research would not have been possible.


iii














TABLE OF CONTENTS


ACKNOWLEDGMENTS . . .

LIST OF TABLES . . .

LIST OF FIGURES . . .

ABSTRACT . . . .

INTRODUCTION . . .


Page

. . iii

. . V

. . vi

. . xi

. . 1


Chapter

I. DEFECTS IN QUENCHED PLATINUM . .

II. ELECTRON MICROSCOPY . . . .

III. FIELD ION MICROSCOPY . . . .

IV. EXPERIMENTAL EQUIPMENT AND PROCEDURE

V. RESULTS AND DISCUSSION . . . .

VI. CONCLUSIONS AND SUGGESTIONS FOR
FURTHER STUDY . . . . . .


Appendices

I. INDEXING FIELD ION MICROGRAPHS . .

II. DESIGN CONSIDERATIONS IN CONSTRUCTING
THE FIELD ION MICROSCOPE . . .

III. CALIBRATION OF THE ELECTRON MICROSCOPE


BIBLIOGRAPHY . . . . . . . . .

BIOGRAPHICAL SKETCH . . . . . . .


. . ,24

. . 49

. . 69

. . 81



. . 137


. . 144



. . 150

. . 157


* . 163

. . 169













LIST OF TABLES


Table

1. Best Values of the Thermodynamic
Properties of Point Defects in
Some Common Metals . . . .

2. Collected Values for the Energies of
Formation and Motion of Vacancies
in Platinum . . . . . .

3. Expected Contrast from Voids as a
Function of Diffraction Conditions

4. Expected Contrast from Voids as a
Function of Void Size . . .

5. Magnification Calibration of Philips
EM 200 with the Goniometer Stage .


Page


10


. . . 19


. . . 47


. . . 48


. . 158











LIST OF FIGURES


Figure Page

1. Transformation of a Frank loop to a perfect
prismatic loop .. . . . . . . 13

2. The stacking fault tetrahedron . . . .. 15

3. Reflecting sphere construction for
electron diffraction . . . . ... .28

4. Diffracted intensity versus the inter-
ference error, s, according to the
kinematical approximation . . . . 29

5. Schematic illustration of the origin
of fringe contrast . . . . . . 30

6. Diffraction of electrons by a foil con-
taining an edge dislocation at E . . .. .34

7. Burgers vector convention for dislo-
cation loops . . . . . . ... 37

8. Relative position of the dislocation
loop as the set of planes, g, is
rotated through the Bragg orientation . 39

9. Relative positions of the diffraction
spot and Kikuchi line due to the
same reflection . . . . . . .. 41

10. Diagram showing the displacement of
reflecting planes by a stacking
fault to give contrast in (b) but
not in (c) or (d) . . . . . . 44

11. Schematic drawing of a field ion
microscope . . . . . . . .. 50

12.' Potential diagrams for an electron
in field ionization . . . . ... 52









LIST OF FIGURES--Continued


Figure Page

13. Detailed schematic of the ionization
process illustrating the relation-
ship between the atom positions
and the cones of emitted ions . . .. 54

14. Current-voltage characteristic of
the helium field ion microscope . . .. 55

15. Diagram of (111) plane showing how
single and double spirals can be
produced on (220) plane with Burgers
vectors of a/2 [101] and a/2 [110],
respectively . .. . . . . . 58

16. Pure edge dislocation causing a single
spiral on (204) plane edges . . ... 60

17. Three possible spiral configurations
resulting from the emergence of a
dislocation loop . . . . . ... 62

18. Two sets of plane edges visible in
the region of the defect . . .. .... 63

19. Possible stable configuration for a
dislocation in a field ion specimen . . 67

20. Schematic drawing of the field ion
microscope body . . . . . ... 70

21. Schematic drawing of the vacuum system
for the field ion microscope . . . 72

22. Schematic illustration of the principle
of operation of the magnetic beam
tilt device . . . . .... .... ... 74

23. Schematic drawing illustrating the
principle of operation of the
transmission electron microscope . .. 75

24. Schematic drawing of apparatus employed
for preparing electron transparent
foils of platinum . . . . . . 80


vii









LIST OF FIGURES--Continued


Figure Page

25. Polyhedral voids in pulse quenched
platinum foil after partial melting
in the electron microscope . . . ... .83

26. Schematic drawing illustrating various
void shapes . . ... . . 85

27. Schematic drawing illustrating various
void shapes . . . . . . . 86

28. Voids in platinum foil exhibiting
fringe contrast . . . . . ... . 88

29. Voids in the same platinum foil
imaging by strain contrast . . .. . 89

30. Electron micrograph of a dislocation
pinned at a void . . . .... . . 90

31. Bright field electron micrograph of
polyhedral voids in a [110]
oriented foil . . . . . ... 92

32. Bright field micrograph of the same
region after 350 tilt . . . . . 93

33. Bright field micrograph of the same
region after tilting to [331] . . .. 94

34. Dark field micrograph of the same area
illustrating the contrast behavior of
the voids along the low angle boundary . 95

35. Isolated colony of voids in a foil that
was annealed for 100 hours at 5000C . . 97

36. An octahedral void viewed along two
crystallographic directions . . ... .98

37. Field ion micrographs of vacancy clusters
in platinum . . . . . . . . 105

38. A field evaporation sequence through a
25 A diameter tetrahedral void near
the (224) pole . . .. . . . . 106


viii









LIST OF FIGURES--Continued


Figure

39. Schematic drawing illustrating the
relationship between the surfaces
of a tetrahedron and an octahedron .

40. A sequence of three electron micrographs
showing a prismatic loop moving on its
glide cylinder . . . . . .


Page


. . Ill


114


41. Schematic drawing combining the infor-
mation from the three electron
micrographs of Figure 40 . . . ... 117

42. Stereogram used for the analysis of
the oscillating defect . . . . ... 118

43. Electron micrograph of a large
prismatic loop . . . . . . ... .120

44. Field ion micrograph of a prismatic
loop intersecting the (313) plane
edges . . . . . . . . ... 121

45. Field ion micrograph of a prismatic
loop intersecting the (111) plane
edges . . . . . . . . ... 122

46. Field ion micrograph of a Frank sessile
dislocation loop . . . . . ... .125

47. An enlargement of the (002) region in
the previous micrograph . . . ... 126

48. Computer simulation of the region con-
taining the defect in the previous
micrograph . . . . . . . .. 127


49. Electron micrograph of a foil con-
taining large prismatic loops and
heavily jogged dislocation lines . .

50. Dark field electron micrograph of the
same region with g = (002) . . .


130


132









LIST OF FIGURES--Continued


Figure

51. Dark field electron micrograph of the
same region with g = (002) . .


52. Electron micrograph of dislocation
intersections resulting in the
formation of Lomer-Cottrell
barriers . . . . . . .

53. Qualitative plot of the observed
defect density versus annealing
temperature . . . . . .

54. Projection of a random direction onto
a planar surface with the projection
point chosen so that X = S . .
p s
55. Photograph of the field ion microscope

56. Schematic drawing of the liquid
hydrogen cryostat . . . . .

57. Plot of intermediate lens current
versus magnification for the Philips
EM 200 fitted with the Goniometer
Stage . . . . . . . .


Page


. . . 133


* . 136



* . 140



S. 145

* . 151


S. 153




. .. 160


58. Plot of intermediate lens current
versus image rotation for the
Philips EM 200 fitted with the
Goniometer Stage . . . . . ... .162









Abstract of Dissertation Presented to the Graduate
Council in Partial Fulfillment of the
Requirements for the Degree of
Doctor of Philosophy


AN ELECTRON MICROSCOPE AND FIELD ION MICROSCOPE
STUDY OF DEFECTS IN QUENCHED PLATINUM


By

Robert William Newman

December 19, 1967


Chairman: Dr. John J. Hren
Major Department: Metallurgical and Materials Engineering


Results of a survey study of the secondary defects

existing in quenched platinum are presented. Transmission

electron microscopy used in conjunction with field ion

microscopy has yielded direct experimental evidence for

the existence of prismatic dislocation loops (both glissile

and sessile) as well as polyhedral voids.

For the most part, the dislocation loops were

observed as black spot defects in the electron microscope

and were resolvable only via field ion microscopy. The

loop density was estimated to be 1013/cm3 with an average

size of approximately 50 A. In one instance a defect

interpreted as a Frank loop with Burgers vector a/3 [111]

was observed in the field ion microscope. Resolvable








0
loops (i.e., > 100 A) were found among networks of heavily

jogged dislocation lines.

The void concentration reached a maximum of

7 x 1014/cm3 after annealing at 4000C for 24 hours and

fell sharply on either side of this temperature. The

shape of the voids was found to be a function of the

concentration. At low density the voids can be described

as regular octahedra, some of which are truncated by {100}

and occasionally by {111} planes. Small voids appear

spherical but careful tilting experiments reveal hex-

agonal cross sections implying that the shapes are {100}

truncated octahedra. It is shown that the apparent

sphericity can be attributed to strain contrast arising

from the matrix immediately surrounding the void.

Small tetrahedral voids have been discovered in

field ion specimens, and it is postulated that these

clusters are the nuclei for both voids and dislocation

loops, depending upon the number and efficiency of the

vacancy sinks in the local environment. The voids are

shown to be extremely stable almost to the melting point.












INTRODUCTION


The development of the field ion microscope by

E. W. Muller (1951) opened the way for the study of the

defect structure of materials on the atomic scale. Rela-

tively little progress has been made in this direction,

however, since defect analysis on the atomic level is far

from routine. Advances are being made in image interpre-

tation but at the present time it is imperative that

experimental results be correlated with evidence obtained

by other means. For some reason this has not been done.

In the present investigation extensive use has been made

of both field ion microscopy and transmission electron

microscopy to determine the nature of the defect structure

of quenched and annealed platinum.

The type of defects to be considered in the body

of this manuscript are usually referred to as secondary

defects. Although grouped under a common label,

secondary defects may be any one of a number of known

crystallographic imperfections. These defects are all

related in that they all have their origin in a super-

saturation of vacant lattice sites (vacancies). Point

defects are commonly produced by one of three methods:


- 1 -




- 2 -


(1) deformation, (2) radiation, (3) quenching. The

latter has been chosen for this study'because it does

not introduce additional defects such as interstitials,

dislocation tangles, and displacement spikes which

would only complicate the analysis of this first study.

Vacancies are equilibrium defects and it is

well known that the number of these point defects in

thermodynamic equilibrium with the system increases with

temperature. Therefore, a piece of metal equilibrated

at some elevated temperature will contain a larger

number of vacancies than would be in equilibrium at a

lower temperature. Rapid quenching from near the

melting point results in the retention of most of the

high temperature vacancy concentration at some lower

temperature, say room temperature. Since this is a non-

equilibrium situation, the system lowers its free energy

by allowing isolated vacancies to cluster into ener-

getically more favorable configurations if it is permitted

to recover with time. These cluster configurations are

referred to as secondary defects.

The importance of secondary defects lies in

their effect on the mechanical properties of crystals

and crystalline materials. It is now accepted that the

mechanical behavior of a crystal is governed by the

motion of the line defects or dislocations through the




- 3 -


crystalline lattice (Read 1953, Cottrell 1953). It

follows that any obstacle interfering with this motion

will have some effect on the mechanical properties of the

crystal. Secondary defects are such obstacles. While it

is the ultimate aim to understand the effect of secondary

defects on the deformation behavior of a metal in terms

of their interaction with dislocations, it is first neces-

sary to understand the atomic geometry of the cluster

configurations and their density distribution. Conse-

quently, a large portion of the literature in the field

concerns itself with the geometry of these two and three-

dimensional defects.

The idea that excess vacancies could condense

into secondary defects was suggested by Frank (1949) and

Seitz (1950) in their discussions of the origin of dislo-

cations in crystals. The growing amount of data on the

unusual behavior of quenched materials, much of which is

reviewed by Cottrell (1958), led a number of workers to

expect evidence of vacancy clustering from transmission

electron microscopy. This expectation was fulfilled in

a paper published by Hirsch et al. (1958) which pre-

sented direct experimental evidence for the clustering

of vacancies in quenched aluminum. Frank (1949) pro-

posed that vacancies in FCC material would agglomerate

on a single {111} plane to form an area of stacking fault




- 4 -


surrounded by a dislocation with Burgers vector a/3 <111>.

This defect was appropriately called a Frank loop. Hirsch

et at. (1958), however, found the loops in quenched alumi-

num to be prismatic with a Burgers vector a/2 <110>.

They suggested that the Frank loops would be energetically

unstable because of the high stacking fault energy of

aluminum, and would, therefore, transform to a perfect

prismatic loop by a reaction:


a/3 <111> + a/6 <112> a/2 <110>


as suggested by Kuhlmann-Wilsdorf (1958). In other

words, the stacking fault could be eliminated by the

nucleation of a Shockley partial dislocation.

The success of the electron microscope work on

aluminum prompted Silcox and Hirsch (1959) to examine a

lower stacking fault energy metal in the quenched state,

namely gold. As a result of this investigation a totally

new defect, the tetrahedron, was discovered. The de-

scription of the stacking fault tetrahedron in terms

of its component stair-rod dislocations and fault planes

is not now disputed but the scientific community has yet

to agree on the mechanism of its formation. See, for

example, de Jong and Koehler (1963), Kuhlmann-Wilsdorf

(1965), and Chik (1965).





- 5 -


Further studies on quenched metals and alloys

employing transmission electron microscopy have re-

vealed the existence of polyhedral voids and an unknown

defect sometimes referred to as "black death." The

latter appear as small, unresolvable black spots on an

electron micrograph and their character or configuration

is not yet certain.

In addition to transmission microscopy, several

indirect methods, notably resistivity, have been em-

ployed to study materials in the quenched state. For

the most part, these methods are capable only of studying

the kinetics of the clustering process. Very little

information can be obtained as to the precise geometry

of the secondary defects, but the kinetics of resistivity

change do give an indication as to the type of defect

formed. It is at this point that direct observation

with the electron microscope becomes necessary. Un-

fortunately, some materials are not amenable to thin

film microscopy for one reason or another. Platinum,

until recently, was such a metal. Specifically it was

not possible to electropolish a platinum foil-thin

enough to be transparent to an electron beam without

altering the structure, although Ruedl et at. (1962)

and Ruedl and Amelinckx (1963) observed platinum in

transmission after beating the foil to less than 1000




- 6 -


0
A thick. This is not suitable for quenching studies

though, since the defects would most likely be affected

by the large stresses introduced by quenching such a

thin specimen (Jackson 1965a).

Studies of quenched platinum have been limited

to electrical resistivity, except for that of Piercy

(1960) who correlated this data with other physical and

mechanical property measurements. From these data and

his own studies Jackson concludes that the annealing

behavior of platinum is much different from that of

other quenched metals. In fact, he went so far as to

say that neither loops nor tetrahedra would exist in

quenched and annealed platinum. Ahlers and Balluffi

(1967) have published information on an electrolytic

solution with which one can prepare thin foils of

quenched platinum while maintaining sub-zero temperatures.

Thus, for the first time, it became possible to see if

secondary defects exist in platinum following various

annealing treatments of the quenched material.

The work of Ruedl and Amelinckx (1963) indicated

that the defect clusters in platinum would be much smaller

(possibly by an order of magnitude) than those in alumi-

num and gold. This suggests that it would be informa-

tive to use the field ion microscope in conjunction with

the electron microscope. Field ion microscopy has already





- 7 -


proven its value for studying small defect clusters

induced by a-particle bombardment (Millcr 1960) and

neutron radiation (Uowkett et al. 1964). Employing a

technique known as field evaporation, layers of atoms

can be stripped from the surface of the specimen enabling

the investigator to cause the visible surface to pass

through the bulk of the specimen. Hence, one has a tool

with which he can determine, in three dimensions, the

atomic configuration of defects within the metal tip.

This, then, was the aim of this research; to use

both field ion microscopy and transmission electron

microscopy in a survey study of the defect structure

of quenched and annealed platinum. It is doubtful that

all stable configurations have been discovered for the

work on aluminum is still underway. Almost ten years

after the initial studies, multilayer defects are only

now being discovered (Edingdon and West 1966). It is

felt that complementing the electron microscope studies

with field ion microscopy not only reduces the chance of

misinterpretation, as happened in the case of aluminum

(Loretto et al. 1966), but is in fact a unique way to

study the defect structure of quenched and annealed metals.












CHAPTER I

DEFECTS IN QUENCHED PLATINUM


Defect Formation


Vacancies


thermal

tration

(1926).

defects

(1963).


The first author who realized that crystals in

equilibrium should contain a well-defined concen-

of point defects appears to have been Frenkel

The thermodynamics and kinetics of these point

is discussed extensively by Damask and Dienes


The concentration of vacant lattice sites in a

crystal increases with increasing temperature according

to the familiar Arrhenius relation


C = A exp(-Ef/kT)


where A is an entropy factor (~1), Ef the energy of

formation for a vacancy (~1 eV), and k is the Boltzmann

constant. Very large supersaturations of vacancies can
4 -1
be produced by rapidly quenching (>10 deg sec-) a piece

of metal from temperatures near the melting point. The

excess vacancies retained in the crystal can be eliminated

by annealing at some intermediate temperature (-1/2 Tmp)


- 8 -





- 9 -


thereby causing them to diffuse to some form of sink. In

addition to the pre-existing or fixed sinks such as dislo-

cations and surfaces (internal as well as external), there

is evidence for the existence of variable sinks. These are

variable in that their size and/or shape changes as more

vacancies are annihilated, resulting in a change in the

annealing kinetics. These variable sinks take on several

forms: (1) voids, (2) dislocation loops, (3) stacking

fault tetrahedra; but they are identical in that they all

originate from the very defects which they are helping to

eliminate. The geometry of these sinks will be discussed

in the next section.

Equation (1) gives information as to the total

number of vacancies at equilibrium but says nothing

about where they are. However, reasonable assumptions

suggest that 90% are isolated single vacancies with the

remainder in clusters of up to about six vacancies. The

relative numbers of each of these configurations is

dependent upon the respective binding energies. From the

data in Table 1 it is evident that the divacancy is the

most mobile of these defects since higher order complexes

are immobile as such.

During an annealing treatment, single vacancies

and divacancies migrating through the crystal will inter-

act to form trivacancies, tetravacancies, etc. with a corre-

sponding reduction in the internal energy of the crystal





- 10 -


TABLE 1

BEST VALUES OF THE THERMODYNAMIC' PROPERTIES OF
POINT DEFECTS IN SOME COMMON METALS


Property Cu Ag Au Al Ni Pt

Iv
E (eV) 1.17 1.09 0.94 0.75 1.4 1.5

Iv
E (eV) 1.0 0.85 0.85 0.65 1.5 1.4
m


E (eV) 0.65 0.58 0.65 0.3 0.72 1.1
m

2v
Eb (eV) 0.15 0.2- 0.1- 0.17 0.23 0.37
0.4 0.3


Cxl04 2.0 1.7 7.2 9.0 0.05 6.0-
10.0

Q (eV) 2.1 1.91 1.81 1.35 2.9 2.9


y(erg/cm2) 85 20 50 280 150- 95
450


- energy


- energy


- energy


of formation


of motion of


of motion of


Sa vacancy


vacancy


divacancy


- binding energy between two vacancies


- concentration of vacancies at T
mp


Iv
Ef


m

E2v
m

2v
Eb


C





- 11 -


Q activation energy for self diffusion

y stacking fault energy


as a whole. As these clusters increase in size they

tend to: (1) form into spherical cavities, (2) become

polyhedral-shaped cavities, (3) collapse to form Frank

loops, (4) collapse to form perfect prismatic loops, or

(5) form stacking fault tetrahedra. There are, as yet,

no hard and fast rules as to what kind of defect will

form in a particular material after a given heat treatment

but all of the parameters listed in Table 1 will have a

definite effect. The stacking fault energy is perhaps

mentioned most often in the literature, but the problem of

using it as a criterion is that there is so much controversy

over its magnitude.


Secondary Defects

Cavities of various sizes and shapes have been

observed in metals and alloys, and they can usually be

classified as either spherical or polyhedral. It is

not at all understood precisely what determines the

final shape, but it is probably a combination of defect

size and the surface energy of the material. The

polyhedral surfaces are generally made up of low index

planes and the voids are therefore quite symmetric.




- 12 -


Frank dislocation loops can be envisioned as the

removal of part of the <111> plane from the lattice. The

result is a fault in the stacking sequence, as the planes

above and below the missing plane will collapse to fill

the gap. The region of stacking fault is surrounded by

a partial dislocation with a Burgers vector a/3 <111> and

has the appearance of a pure edge dislocation (Figure la).

The dislocation is sessile and the loop is usually hex-

agonal in shape with the sides parallel to <110> directions.

A second type of loop commonly found is the per-

fect prismatic loop. It can be obtained from the Frank

loop by the nucleation of a Shockley partial, according

to the reaction


a/3 <111> + a/6 <211> a/2 <110>


The resulting configuration is shown in Figure lb. It is

entirely possible that the prismatic loop forms directly

from the collapsed cluster, but the question is academic.

It is generally felt that the prismatic loop will be

favored in materials with a high stacking fault energy,

but recent papers by Loretto et al. (1966) and Humble

et al. (1967) place this conclusion in some doubt.

The prismatic loop can sometimes lower its

energy by becoming rhomboidal in shape (it is usually

elliptical) and rotating toward a (110} plane, thereby




- 13 -


%o &c^?o^ou? C 0lane
oo ooO oO 0 faui plane
00 00 O00?0000
o 0oO o0 o 000
00 000 000
000o o00000 [ plan

o o0(E) foo %o
Cj ? 0~, 0 0 (D 000o


extra
plane
loop


half ooo oo
above o o00' 0- -o
o o00o00oOoo000o
0 S 00oo-00 loop p lo-
-- oo 0 0oo0 P-loop plane

0 00 ooO 00 oooooo 00 '\ extra half plane
00000 00 below loop


Figure l.--Transformation of a Frank Loop to a
perfect prismatic loop. (a) Side view of a Frank
loop showing HCP stacking sequence across the
loop plane. Viewing direction is [110]; (b) the
same loop after being converted to a perfect
prismatic loop. The FCC stacking sequence has
been restored, but there are two extra half
planes, one above and one below, at the ends
of the loop. (After Bell and Thomas 1966.)




- 14 -


becoming nearly pure edge in character. That is, the habit

plane is not quite {110}. Both the prismatic and rhomboidal

(often referred to as rhombus) loops are glissile and can

move by conservative glide in the <110> direction.

The stacking fault tetrahedron, as its name

implies, is a four-sided defect. Each of the faces is a

{111} plane containing a stacking fault and the six lines

of intersection of the faces is a stair-rod dislocation

of Burgers vector a/6 <110> (Figure 2). Several mecha-

nisms of formation of tetrahedra have been proposed

(Silcox and Hirsch 1959, de Jong and Koehler 1963, and

Kuhlmann-Wilsdorf 1965) but these are as yet unproven.


Review of the Work on Platinum


In view of the fact that platinum is a relatively

easy metal to work with in quenching studies (Doyama 1965),

it is rather surprising that so little information has

been published on it. Perhaps the answer can be found

in the difficulty of employing direct observation

techniques with platinum. Whereas both aluminum and

gold are amenable to thin film microscopy, platinum,

until recently, was not. Therefore, quenching and

annealing studies could not be extended beyond the

somewhat limited resistivity investigations.




- 15 -


C / Y_-Tl----- ^ B




Figure 2.--The stacking fault tetrahedron. The faces
are {lll} containing a stacking fault. The inter-
secting faults give rise to stair-rod dislocations
at the edges.




- 16 -


The first published work on quenched platinum was

an electrical resistivity study by Lazarev and Ovcharenko

(1955). They reported values of 1.18 eV and 1.08 eV for

the energies of formation and migration of vacancies

respectively. Soon after, Bradshaw and Pearson (1956)

found the energy of formation to be 1.4 eV and attributed

the discrepancy to an insufficient rate of quenching in

the previous work. It was also concluded that there was

only one recovery stage (non-exponential) and that there

was no evidence for vacancy agglomeration. In a .later

paper (Pearson and Bradshaw 1957) no significant effect

was found with the addition of rhodium and gold as

impurities. Successful experiments with gold prompted

Ascoli et at. (1958) to make new measurements on platinum.

The energy of.formation was determined to be 1.23 eV.

The annealing curves exhibited exponential behavior

(unlike Bradshaw and Pearson's data) from which the

migration energy was a surprisingly large 1.42 eV. Of

equal significance was the calculation of the number of

jumps made by a typical vacancy during anneal, before

annihilation. Whereas Bradshaw and Pearson (1956) had

calculated 10 jumps, Ascoli et al. (1958) arrived at a
7 8
value.of 10 to 10 However, they also found no evidence

for defect clusters.




- 17 -


Bacchella et at. (1959) were the first authors to

suggest that the complex kinetics observed after high

temperature quenches might be due to some clustering of

vacancies. Measured values of the activation energies

were not significantly different from those of Ascoli

et at. (1958), i.e.,


Ef = 1.20 eV and E =1.48 eV
f m

Muller (1960) made a vacancy count on quenched

platinum using the field ion microscope and calculated a

value of 1.15 eV for Ef. However, Pimbley et al. (1966)

found the number of vacancies to be anomalously high and

attributed this to a stress effect inherent in field ion

microscopy.

Piercy (1960) made a rather thorough investigation

of point defects in platinum, using deformation and neutron

radiation as well as quenching to introduce an initial

excess of point defects. He also complemented electrical

resistivity measurements with x-ray line broadening,

hardness, and density measurements. Quenching from above

16000C, Piercy found E = 1.13 eV in good agreement with

the work of Bradshaw and Pearson (1956). Values of E

for the irradiated specimens compare well with those of

Ascoli et at. (1958) and Bacchella et at. (1959). Piercy




- 18 -


attributes the lower value to the motion of divacancies

and the higher to single vacancies.

The order of reaction is a measure of the rate of

change of a number of jumps required by a defect to reach

a sink during the recovery process. Therefore, it should

be possible to determine the type of sink from measurements

of the relaxation time and the jump frequency. Piercy
8 9
argues that 10 to 10 jumps (his calculation) is much too

high for the recombination of defects but, if the defects

are being annihilated at dislocations, the order of reaction

might be expected to be unity. He reasons that the ob-

served value of 1.46 may be caused by a change in the

dislocation network due to extensive climb. Thus the

last defects will migrate to a much different dislocation

network than was initially present.

Jackson (1965a) quenched platinum wires from

various temperatures in the range from 7000C to 17500C

in an attempt to resolve the discrepancy between the

reported activation energies. His findings are listed

in Table 2, along with previously obtained values. The

evidence is quite convincing for assigning the lower

value, 1.1 eV, to the motion of divacancies and the high

value, 1.4 eV, to single vacancies. His data also verify

that there is only one clearly resolved annealing state,





- 19 -


LO
Ln




Lfl

O" 0 o
I n -

S 0 m l o
H C 7 m m
0 0 o 1-1
O U C) H 5 Q0


0 ) 0 un ~1r o- ci
z cc o- (0 c H
E4d C o o -o -. O ,--





O l o :0 4 >Y > 0









14 1 o o o o O o o o r -
cn o :H o o o C d o 4Cd











0 a) O O O O O.0 O >i O O t, l
SH

4f0 J OU U U U 0 U U U








< 0 0 O O Oa "0 (u O u -
c O O o o o o o o o o
O (0 0 0 0 :C ) 00 0 0 4
H r C) C) C) C) -g C) (4- C) C) Cd


P WH U) r id
u H 0 o o0 0 0 o C 0 0 4~
4 Mo U o U o o rd 0 U o 4-i "




0 r "1 0 4 0-l
m O O O O Cf O ; O O W


h u H U
< 1- a ^ a a ^ ^ ^ o c a i












W ) 0 U U U 0 U U U U 0
$0 C q r-i (1 ( )




0 H H * H 4 -

0 -) 0 0- (- -) .

MT CN C4' LO LO
3 Q O '0 O'O 'O 1
i-


















M




- 20 -


regardless of initial concentration. Jackson also states

that the shape of the isothermal annealing curves corre-

spond to diffusion of point defects to sinks that become

less efficient with time. He concludes that the very low

resistivity increment remaining after anneals below

1/4 Tmp and the large number of jumps (two orders of

magnitude greater than in gold) for vacancy annihilation

argue that the sinks for vacancies in platinum are much

different from those in other metals.

Amelinckx's group in Belgium has been alone in

the use of TEM (transmission electron microscopy) to study

quenched platinum foils. Ruedl et al. (1962) and Ruedl

and Amelinckx (1963) were principally interested in

radiation damage, but many of their findings are quite

applicable to the present work. This is particularly

true in the case of foils quenched prior to irradiation.

However, one must be aware that quenching strains in the
0
extremely thin (1000 A) foils could have a significant

effect on these results. This problem has been investi-

gated by Jackson (1965b), and the principal effect seems

to be a change in the vacancy structures produced by

subsequent aging.

Ruedl et aZ. (1962) reported finding defects which

were interpreted as spherical voids and some instances of
polygonal features in the neighborhood of 00 A diameter,
polygonal features in the neighborhood of 100 A diameter,




- 21 -


the contrast of both being quite different from that of

dislocation loops. The presence of these cavities rather

than loops is attributed to the high surface energy of

platinum. It is felt that the energy barrier in trans-

forming from a spherical to a penny-shaped cavity would be

rather large, and would therefore inhibit the collapse of

clusters into loops. It should be pointed out, however,

that the concept of surface energy become ambiguous when

dealing with very small surfaces. In fact, it has been

suggested by Jackson (1962) that the energy of a cluster

might better be calculated as the energy of formation of

a vacancy divided by its surface area. If this be the

case, the energy of a void will always be less than that

of a Frank loop, whereas the reverse is true if the bulk

surface energy is used (Friedel 1964). Thus, as Clarebrough

(1966) points out, it is impossible to decide which type of

defect is more stable at small sizes, without detailed

knowledge of surface energies for very small voids.

Bauer and Sosin (1966) found stage IV recovery of

electron irradiated platinum to be a diffusion-controlled

process up to approximately 50% recovery. The rest of the

recovery is considerably slower than predicted by theory.

According to them, the possible mechanisms which may

account for this delay include: (1) clustering of the

vacancies, (2) exhaustible sinks, (3) concurrent trapping





- 22 -


of vacancies during the diffusion process. The authors

choose to explain their results by the third mechanism.

Their reason for ruling out the second are understandable,

but their basis for ruling out the first is open to

question (Chik 1965) It is worth noting that they

measured the activation energy of stage IV recovery to

be 1.36 eV; i.e., approximately equal to the energy of

motion of single vacancies.

Cizek (1967) investigated the irreversible

component of resistivity remaining after repeated

quenching of platinum wires. After subtracting out the

non-recoverable resistivity increment attributable to

dimensional changes in the specimen, some 20% of the

irreversible change was unaccounted for. The author

suggests that while vacancy clusters and/or voids may

contribute, it is more reasonable to investigate the

possibility of more stable defect configurations such

as the oxygen stabilized stacking fault tetrahedra

present in silver up to 930C (Clarebrough 1964).

It should be mentioned at this point that Ruedl

et al. (1962) observed dislocation configurations

indicating the possibility of dissociation into partial

(i.e., Lomer-Cottrell barriers). This was complemented

by a common occurrence of annealing twins and only rare




- 23 -


observations of cross slip which, when it did occur, was

rather complicated. The authors are cognizant of the

fact that the stacking fault energy of platinum is

reportedly high (75-95 erg/cm2).

While a discussion of irradiation experiments is

perhaps not appropriate here, the defects observed by

Ruedl et al. in foils bombarded by neutrons, fission

fragments, or a particles are of interest. Both black

spot defects ("black death") and resolvable loops were

present. The prismatic nature of the loops was inferred

from motion in <110> directions during observation. This

is consistent with the concept of conservative glide on

a prismatic cylinder. Evidence was also found for

interaction between these defects and dislocation lines.

The resulting ragged appearance could be due to climb or

stress field interactions. Large polyhedral voids and

prismatic loops were found to occur in foils exposed to

a-particles and subsequently annealed at temperatures up

to 5000C. The voids were presumed to be filled with

helium gas, the presence of which may stabilize the

cavities. This may be substantiated by the fact that

the voids remained after anneals in excess of 7000C.











CHAPTER II

ELECTRON MICROSCOPY


Contrast Theory


When the electron microscope is used with thin

metal foils, extensive use is made of the phenomena of

diffraction of electrons by a crystal lattice. The

radius of the Ewald sphere is extremely large for electron

diffraction; so large, in fact, that it is almost planar

over the solid angle subtended in the electron microscope.

The small curvature that does exist is compensated for by

the rod-like nature of the reciprocal lattice points.

The physical reason for the existence of these "relrods"

is the relatively small number of reflecting planes in

the thickness direction. There simply are not enough

scattering centers to attain complete destructive inter-

ference for non-Bragg conditions. Therefore, the dif-

fraction peak (i.e., reciprocal lattice point) is broadened

in the direction of the small dimension and the extent of

the streaking varies inversely as the foil thickness.

(This phenomenon is analogous to particle size broadening

encoUntered in x-ray diffraction.) As a result, the

diffraction pattern that is projected on the microscope


- 24 -




- 25 -


screen is actually a plane section through the reciprocal

lattice of the crystal. Most of the commonly observed

patterns display a high degree of symmetry and are rela-

tively easy to identify.

The normal procedure is to intercept all diffracted

beams with an aperture allowing only the transmitted beam

to pass through the lens system to be magnified and pro-

jected onto the fluorescent screen. Thus, any regions of

the crystal which are diffracting strongly will appear

dark on the screen.

When studying defects it is often desirable to

view what is called the "dark field" image. This is a

procedure whereby the above mentioned objective aperture

is moved so that only one of the diffracted beams passes

through the lens system. According to the Kinematical

Theory developed by Hirsch et al. (1960), the dark field

and bright field images should be complementary because

of the two beam assumption. In practice this is not

always found to be the case, but the discrepancies can

usually be explained with the more complex Dynamical

Theory (Howie and.Whelan 1961).


Diffraction by a Perfect Crystal

Representing an electron wave at the position r

by the function exp (2i r) and the scattered wave by
0




- 26 -


exp (2ri k'r), the total amplitude of electron waves

scattered from an assembly of unit cells is:


A = EF exp (2ri Krn ) (2)
n

where F is the electron scattering factor, K = k

rn = nla + n2b + n38, and the summation extends over all

atom positions in the crystal. The total scattered ampli-

tude is a maximum (i.e., the .exponential is unity) when K

is a reciprocal lattice vector.


K = ha* + kb* + Z* g (3)


which simply says that the Bragg law is satisfied. By

definition, the magnitude of a reciprocal lattice vector

is equal to the reciprocal of the spacing between the

planes described by that vector (see Figure 3a). Hence


Igl = i/d = 2 sin


which is the Bragg equation.

In general there is a distribution of scattered

radiation such that the crystal need not be in the exact

Bragg position to result in some diffracted intensity.

If the deviation is described by the vector s we have


A = Fn exp [2Ti(g + s) n] (5)
n




- 27 -


where K = g + s as in Figure 3b. Recognizing that g-r is
n
an integer and approximating the summation by an integral,

we have, for a given s


A(s) = f/ exp(27Ti srn )dT (6)


For a crystal of infinite dimension in the x and y di-

rection and thickness t


A(s) = F/t/2exp(2Tisz)dz = sin7ts (7)
-t/2 rs

From which

.2
I() c sin rts (8)
Its) = 2 (8)
(7rs)

This intensity distribution is plotted in Figure 4. In

other words this says that the thinness of the crystal

causes sufficient relaxation of the Bragg condition which

in turn allows a considerable amount of diffraction to

occur even though the crystal is not quite in the proper

orientation; the misorientation being described by the

vector s.

The above equation also indicates that the intensity

of the transmitted and diffracted beams oscillates with

depth as illustrated in Figure 5. At successive depths

to, the diffracted intensity is zero and the transmitted









































k ko

Ikol=



S

(hK
s







Figure 3.--Reflecting sphere construction for electron
diffraction. (a) When the reciprocal lattice point is
on the Ewald sphere, (b) displaced from the Ewald sphere
by the vector i.




- 29 -


Intensity












2/t








Figure 4.--Diffracted intensity versus the inter-
ference error, 9, according to the kinematical
approximation.




- 30 -


Direct


Figure 5.--Schematic illustration of the origin of
fringe contrast. (a) Section through the crystal
showing kinematical intensity oscillations of
direct and diffracted waves. AB represents a
grain boundary or stacking fault, CD a wedge,
and E a hole. (b) Section normal to beam
showing dark fringes f (extinction contours)
as they would appear in a bright field image.
(After Thomas 1962.)




- 31 -


intensity reaches a maximum. The depth periodicity of

this intensity oscillation is 1/Is" and reaches a maximum

at IsI = 0. That is


lim t =
as
|sj + 0 (9)


where 1 is defined as the extinction distance. Note that

this is not quite rigorous since r is a function of both

the operating reflection and the material under observation.

With this information we can explain two contrast

effects commonly observed in the electron microscope:

extinction contours and bend contours. Practically all

specimens used in transmission microscopy are slightly

bentand non-uniform in thickness. Extinction contours

will occur in wedge-shaped regions of the specimen as a

result of the sinisoidal variation of the transmitted and

diffracted beams discussed above. The contours will

appear as continuous alternating bands following equi-

thickness paths, as schematically illustrated in Figure 5.

Local curvature of the foil will cause some regions (con-

tinuous surfaces) to be rotated into diffracting orien-

tation giving rise to continuous dark bands called bend

contours. The two can easily be distinguished since the

latter is very sensitive to the angle between the incident




- 32 -


beam and the foil normal while the former is dependent

principally on the thickness of the crystal. Hence, a

small amount of specimen tilt will cause a bend contour

to move much more rapidly across the field of view.


Diffraction by an Imperfect Crystal

Any defect within a crystal which produces a

distortion of some set of lattice planes {hkl} will alter

the diffraction conditions of that set of planes in the

vicinity of the defect. If the atom at rn is displaced

by the vector R, equation 6 becomes


A(s) = If exp(27Ti K(r R) ] d (10)
+
Neglecting the term s-R and again assuming the crystal to

be finite only in the z-direction, we have


F t/2 -g d
A(s) / exp[2Trisz] exp[2Ti g.R]dz (11)
-t/2

where a = 2ig'R is an additional phase factor due to the

presence of the defect. The contrast at a defect is then

determined by computing the difference between the in-

tensity diffracted by the perfect and imperfect crystal,

all other parameters being equal.




- 33 -


Defect Interpretation


Dislocations

It is sufficient for the present purpose to consider

the intuitive explanation for contrast at dislocations as

originally presented by Amelinckx (1964). Let us assume

that we have an edge dislocation in a crystal. This

could be depicted schematically as in Figure 6. Suppose

that the set of planes outside the region E1 E2 would

satisfy the Bragg condition for diffraction if the foil

were rotated slightly counterclockwise about the-normal

to the paper. Note that the planes in the region E1 E

have undergone such a rotation due to the presence of the

dislocation, while the same set of planes in E E2 have

rotated in the opposite sense. As mentioned previously,

the fact that the foil is much thinner in one dimension

makes it possible to have some diffraction even though

the crystal is not precisely oriented. Under these

conditions (thin foil) a considerable intensity is

diffracted away in the perfect part of the foil outside

E1 E2; the remaining part is transmitted. The figure

reveals that the Bragg condition is better satisfied on

the left than on the right of the dislocation. Conse-

quently, more intensity will be diffracted away from E1

(to be intercepted by the above mentioned aperture) and




- 34 -


F 11 F












Figure 6.--Diffraction of electrons by a foil
containing an edge dislocation at E. In E2,
less intensity is diffracted away than in
the perfect part while more is diffracted
away in E1. (After Amelinckx 1964.)




- 35 -


less away from E2. Therefore, when the transmitted beam

strikes the fluorescent screen, the intensity at E1 will

be lower than background and greater than background at E2.

That is, a black line will be observed slightly to the EI

side of the actual dislocation. It can be shown that this

analysis holds equally well for any arbitrary dislocation

and Burgers vector.


Determination of the Burgers Vector

It follows from the intuitive picture presented

above that contrast effects are to be expected only from

those lattice planes which are deformed by the presence

of the dislocation. To a first approximation it can be

assumed that the planes parallel to the Burgers vector

will not be affected and, therefore, diffraction from

these planes will not exhibit contrast effects. In other

words, if the foil is oriented so that this particular set

of planes is in the reflecting condition, the dislocation

will be invisible.

Since the diffraction vector g is normal to the

set of diffracting planes, we can state that the dislo-

cation will be invisible if the relation gb = 0 is

satisfied. Knowing two vectors g for which this equation

holds'with respect to a single dislocation, it is possible

to determine b for that dislocation. To avoid ambiguity




- 36 -


in the analysis, it is necessary to employ the dark field

technique. The procedure is to tilt the specimen until a

particular defect disappears. Assuming the brightest spot

on the diffraction pattern to be the cause of the observed

contrast, it follows that the displacement vector R (in

this case R = b) is parallel to the set of planes g. If

the correct reflection has been chosen, the defect will

also be invisible in the dark field image of this spot.


Dislocation Loops

Although a dislocation cannot terminate within a

crystal (Frank 1951), it may close on itself to form the

so-called dislocation loop. The nature of the dislo-

cation requires that a sign convention be set up to avoid

confusion in analysis. The actual convention is a matter

of personal preference, but must be consistent.

Define the Burgers vector as the closure failure

FS after traversing the circuit in a clockwise direction

while looking in the positive direction of the dislo-

cation line (Bilby et al. 1955). This circuit is also

defined as a right hand screw. Using this FS/RH con-

vention, a 900 counterclockwise rotation of the Burgers

vector points in the direction of the extra half plane

for the case of a pure edge dislocation. See Figure 7a.

It follows that the Burgers vector of a right hand screw





- 37 -


ELECTRON BEAM



F S



Wb




o b c







Figure 7.--Burgers vector convention for dislocation
loops. (a) FS/RH convention for defining the Burgers
vector; (b) applied to a vacancy loop; (c) applied to
an interstitial loop.




- 38 -


dislocation will point along the negative direction of the

dislocation line while a left hand screw will have a

Burgers vector in the positive sense of the line.

Now define the positive sense of going around the

dislocation loop as clockwise when viewed from above; i.e.,

in the direction of the electron beam. Thus, a vacancy

loop will have a component making an acute angle with the

upward drawn normal to the plane containing the loop.

That is, if we use a "left hand rule" to describe a

vacancy loop and a "right hand rule" for the interstitial

loop, the fingers of the hand point in the positive

direction round the loop and the thumb defines the sense

of the Burgers vector. This is schematically illustrated

in Figure 7b and c.

In the light of our knowledge concerning the po-

sition of the dislocation line relative to its image,

consider three intermediate positions of a vacancy loop

as it is rotated counterclockwise through the Bragg

condition about an axis normal to gand b. In Figure 8,

the dotted line is the actual position of the loop while

the solid line represents the image of the loop. Choosing

s as positive when the reciprocal lattice point associated

with g lies inside the Ewald sphere (angle of incidence

on the reflecting planes is greater than the Bragg angle),




- 39 -


ELECTRON BEAM


S

Figure 8.--Relative position of the dislocation
loop as the set of planes, 4, is rotated through
the Bragg orientation.




- 40 -


the image of the loop will lie inside or outside the

actual position of the loop depending on whether the

sign of (g*b)s is positive or negative respectively.


Kikuchi Lines

The above discussion leads to the question of how

to determine the sign of s. All of the previous develop-

ment assumes the electrons to be elastically scattered by

the atoms, but it is known that there will be some ine-

lastic scattering resulting in an incoherent beam of

electrons. Their origin is not completely understood but

it is postulated that the divergent beam can undergo

Bragg diffraction and produce a pair of nearly straight

lines on the diffraction pattern, one dark and one light.

The two will be separated by a distance commensurate with

the magnitude of the associated vector g. Figure 9 is a

diagram showing the relation between the sign of s and

the positions of the dark and light Kikuchi lines. Note

that the light line is always furthest from the main beam.


Stacking Faults

The discussion of loops also leads us to consider

the contrast arising from the presence of stacking faults.

The formation of the stacking fault on the interior of a

Frank dislocation loop of Burgers vector a/3 was




- 41 -


S>O

0I *I
D L


S=O


D L


S
o *
D L


Figure 9.--Relative positions of the diffraction
spot and the Kikuchi line due to the same re-
flection. The open circle represents the main
beam and the solid circle is a particular dif-
fracted beam.





- 42 -


discussed in Chapter I. We are concerned here with the

interpretation of such a defect with transmission electron

microscopy.

Contrast arises at a stacking fault because such

a defect displaces the reflecting planes with respect to

each other across the plane of the fault. Using the

appropriate value of R in equation 11, we find that the

observed contrast is a function of the position of the

plane in the foil. In fact, the observed intensity is a

periodic function since the diffracted intensity oscillates

with depth into the crystal. For the general case of a

fault inclined to the electron beam, the depth periodicity

will become visible as alternating contrast fringes

parallel to the line of intersection (or projected line

of intersection) of the fault plane and the surface of the

foil. This fringe contrast is illustrated in Figure 5.

Clearly, if the extinction distance t is known, the

dimension of the fault can be obtained (to within the

error between to and ) from the product nto, where n

is the number of fringes. The fringe contrast also

provides valuable information for determining the plane

of the fault.

This information is usually sufficient to specify

the nature of the fault but a cross check is possible

with a g-b criterion. The stacking fault displacement





- 43 -


vector R is defined by the shear at the fault, or the

Burgers vector in the case of the Frank loop. Referring

again to equation 11 we find that there is no contribution

to the intensity for the case of a = 2rn, i.e., when g-R = n.

In words this means that the fault will be invisible when

the vector R moves the reflecting planes normal to them-

selves by an integral number of spacings between the

planes or when the displacement is parallel to the re-

flecting planes as in Figure 10. One other criterion for

the invisibility of stacking fault fringes involves the

dimensions of the fault plane. If the fault does not

extend over a depth in the crystal of more than an

extinction distance for the operating reflection, no

fringe contrast will be observed. The fault will, however,

appear either dark or light depending on its position in

the foil.

The dislocation line bounding a faulted loop

presents a problem quite different than that encountered

in the unfaulted or prismatic loop mentioned above, as

it is a partial dislocation. Under these circumstances,

the g-b criterion no longer applies since b is not a

lattice vector. Therefore, the scalar is not necessarily

an integer but, rather, it is usually found to be a

multiple of 1/3. Gevers (1963) has shown that the

variation in contrast will not be significant unless






- 44 -


4-4
tQ)










Q -P
041







0
CL
(tP























o A


. .
-z




O
O

C




-- 0

0













r >. r--

O --Q

0 0Q
*d
-4-





























t -
r-
5o .0


4J m


Q) QP
I 00



(I M





**-1 F


C

o L
0
U, 0-


E
0
o

------ .




- 45 -


Ig'bl > 2/3. However, for s > 0 and g-b < 0 the image of

the dislocation line will be superimposed on the fault

contrast and probably not be visible. Silcock and Tunstall

(1964) showed that the dislocation would be in good con-

trast for gb = + 2/3 but would be in poor contrast for

g.b = 2/3, provided the deviation from the Bragg

orientation is rather large, i.e., t s > 0.6. Loretto

et al. (1966) used this criterion to show that, contrary

to common belief, 95% of the loops in quenched aluminum

are faulted. This is significant in that the loops were

too small to exhibit stacking fault contrast.


Voids

Another defect commonly observed in quenched

materials is the void or large vacancy cluster, van

Landuyt et. al. (1965) have shown that the contrast at

a void is adequately represented by a phase angle

a = 27sf, where f is the thickness of the void. Further,

their theory predicts odd contrast behavior such as:

(1) contrast variation as a function of depth, void

size, the parameter s, total foil thickness, and (2) a

possible lack of contrast reversal from bright field to

dark field. The interpretation is relatively simple

for the case of a thick foil (> 5 t ) with s = 0, since

the contrast will be mainly due to normal absorption.




- 46 -


However, the voids will have to be larger than 1/2 t before

they produce a clear positive contrast (i.e., lighter than

background). Unfortunately, it is not always possible to

see defects in the region of s = 0 and one must usually

work in regions of s > 0 (anomalous transmission region).

An attempt has been made to generalize the results

of van Landuyt as they apply to the case of secondary

defects in platinum foils: (1) the foils are considered

as being thick, (2) 1/4 to < f < t (3) the absorption p

is relatively high, (4) the defects will be confined to

the center of the foil. As can be seen from Tables 3

and 4, the contrast in both bright and dark fields is

quite unpredictable. Therefore, some knowledge of defect

size and the diffraction conditions is required in order

to determine whether contrast should be positive or

negative. Using both bright and dark field images, the

above mentioned table's, and large tilt angles, one should

be able to distinguish voids from loops. In fact it is

possible to specify the geometry of the defect as shown

in Chapter V.





- 47 -


TABLE 3

EXPECTED CONTRAST FROM VOIDS AS A FUNCTION
OF DIFFRACTION CONDITIONS


Void
Dimension Bragg Error Bright Field Dark Field
(f) ( = to) ( I 1 ( I -


1.8 t 0.2 N > P P
o
0.5 P > N N>P

1.0 N > P P=N


1.0 t 0.2 P = N P = N

0.5 N N>P

1.0 P P




Assume the absorption coefficient, p, to be 3r/T,
where To is the absorption length and is usually taken
as 10 t.

The parameter x is a measure of the misorientation
from the Bragg angle.

N indicates that the void will appear darker than
background and P indicates that the void will appear
lighter than background.




- 48 -


TABLE 4

EXPECTED CONTRAST FROM VOIDS AS A FUNCTION
OF VOID SIZE


Void Dimension Bright Field Dark Field
(f) (I I,) (I I )


1/8 t P > N N>P


1/4 t P > N N>P


1/2 t N > P N > P


1 t N N > P
o


Assume x = st = 0.5.
o












CHAPTER III

FIELD ION MICROSCOPY


Basic Theory


As discussed in the Introduction, the field ion

microscope has resolving power and magnification capa-

bilities enabling the direct observation of the atomic

lattice. Since the concept of the field ion microscope

is relatively new (Muller 1951), there are almost as many

designs as there are microscopes. However, they all have

the same basic components (Figure 11). The specimen is a

short fine wire polished to produce a sharp hemispherical
0
tip of 100 to 1000 A radius which is connected to metal

electrodes immersed in a cryogenic fluid such as liquid

N2, Ne, H2 or He. Facing the tip, a few centimeters

away, is a phosphor screen which emits photons when

bombarded by ionized atoms and is an integral part of

the vacuum chamber enclosing the specimen. The system

is evacuated to 10- to 10 Torr, backfilled with high

purity (99.9995%) helium gas to a pressure of 1 to 10p,

and a positive potential of up to 30 kV is impressed on

the tip relative to the screen. The strength of the

resulting field at the surface depends on both the


- 49 -




- 50 -


1I.T. loads


vacuum n K image gas
pump


specimen


fluorescent/
screen





Figure l1.--Schematic drawing of a field ion
microscope.


coolant


r




- 51 -


applied voltage and the radius of the specimen (Muller

8
1960, Gomer 1961), but is in the neighborhood of 10 to
9 o
10 volts/cm or about 5 volts/A near the tip. This is

equivalent to the removal of about one-third of an

electron from each atom, and means that the "free

electron cloud" is drawn back into the metal, exposing

the positive ion cores on the surface.

A neutral atom of the imaging gas coming under

the influence of the field around the tip becomes slightly

polarized and acts as an oriented dipole. That is, the

more weakly bound electrons are pulled toward one side

of the atom causing it to act like a small magnet which

then accelerates toward the specimen. When the polarized

gas atom is a few tens of Angstroms away from the tip,

the potential well of the atom is distorted by the

presence at the potential field at the tip. Therefore,

an electron in the atom no longer sees the symmetric

potential well of the nucleus as in free space but, rather,

as an asymmetric barrier that reaches a maximum and has a

finite width on the side nearest the specimen.

According to wave mechanics, ionization is possible

by tunneling of the electron through the potential barrier

into the metal tip, provided there is an available energy

level. This process is schematically illustrated in

Figure 12. The resulting ion is then repelled by the





- 52 -


O r


N C
-H-H Cd

0 -4
S'-H .Q 0
xu






0 Q)
-H H




-H
OW

0 W4-






4 -H .
-H H






s3 Er


4 ) -H
r-l C
*H 0 Z




cO
WA- C)-1








0 H




Id Q)

1 4J O


0 A:
C41-1 0 4




-o- (0 0
S'-I ( O-




3S rHl
-H Cd QiW
-r d 0t ^ -




- 53 -


positive tip and travels along a trajectory (approximately

elliptical) defined by the electrostatic lines of force to

the screen. The field ion image is, therefore, a sensitive

contour plot of the surface field distribution. Bright

spots, corresponding to regions of high electric field

(i.e., surface atom positions), give rise to a very regu-

lar spot pattern which can be interpreted directly in

terms of the atomic lattice (Figure 13).

The current-voltage characteristic of the helium

field ion microscope has the form shown in Figure 14

(Southon and Brandon 1963). A stable field ion image is

formed in the region BC and the terminus of the curve at

C corresponds to field evaporation of the specimen. At

this point, the field at the surface of the specimen is

sufficiently large to ionize and remove the loosely bound

metal atoms on the surface. All too frequently, field

evaporation occurs at' a field lower than that required

to obtain stable images. Thus, while field evaporation

limits the materials capable of being studied in the

field ion microscope, it is also the very process which

makes the instrument unique by permitting three di-

mensional micro-dissection of the specimen. By controlled

field evaporation of individual atoms from the surface of

the specimen, the structure of the bulk can be deduced

in atomic detail.




- 54 -


Figure 13.--Detailed schematic of the ionization
process illustrating the relationship between the
atom positions and the cones of emitted ions.




- 55 -


Ion
Cur
Arr


*rent
ps C




B ,

Tip Radius =570 A
He Gas p= 6.103 T
/ Tip Temperature=7

10-11

/ O
-0

A
-Field
10
-3 4 -5 6 V/A
I 9 1, 1 12 132 14 15 16 kV
Voltage


orr
8*K


Figure 14.--Current-voltage characteristic
of the helium field ion microscope. (After
Southon and Brandon 1963.)





- 56 -


Image Interpretation


Indexing

Normally, the first step to be taken when attempting

to interpret a field ion image is to properly index the

planes (or poles) on the micrograph. Although Muller

(1960) has used an orthographic projection to index a

micrograph, Brenner (1962) considers the stereographic

projection to be a better approximation. More recently

Brandon (1964) has shown experimentally that the true

projection is somewhere between these two. It is possible

to obtain a simple equation for accurately calculating

the angles between poles on a field ion image (Newman et

al. 1967) with the result that:


d = MR8 (12)


where d is a linear distance measured on the micrograph,

M is the combined magnification of the optics, R is the

radius of the projection sphere, and 8 is the inter-

planar angle. This equation is derived and discussed in

detail in Appendix I.


Computer Model

The computer model originally developed by Moore

(1962) has been extended by Sanwald et al. (1966) to

enable the interpretation of defects in the field ion image.




- 57 -


The image is simulated by plotting the positions of those

atoms whose centers lie inside a thin spherical shell

passing through a point lattice. The resulting array

looks very similar in appearance to an actual field ion

image. It is then a simple matter to introduce the strain

field of a defect into the point lattice to determine its

effect on the image. By adjusting the radius and thickness

of the shell, and by varying the parameters associated

with a particular defect (e.g., Burgers vector and habit

plane for a loop), it is possible to obtain quite good

agreement with experimental micrographs.


Defect Analysis

It has been proposed (Pashley 1965, Ranganathan

1966a) that a dislocation will appear as a spiral con-

figuration in a field ion image. Furthermore, the exact

nature of this configuration will be'given by the scalar

product g-b where g is a vector normal to the set of

planes being disturbed by the emergence of the dislo-

cation and b is the Burgers vector of that dislocation.

It is worthwhile pointing out that g and b are geometrical

in nature so the scalar product is simply a measure of

the displacement component in the direction normal to the

set of planes g, (Figure 15). If one is consistent in

using the correct plane notation (i.e., {hkl} unmixed




- 58 -


a. A[iol= b
\\ A


d220 -I


[lJo]


--- [112]


b=- [Rio]


PLANE OF CUT (ii)
PERPENDICULAR TO (223)


Figure 15.--Diagram of (111) plane showing how single
and double spirals can be produced on (220) plane
with Burgers vectors of a/2 [101] and a/2 [110],
respectively.


fl220 1





- 59 -


for FCC, etc.), the dot product is an integer which

determines the number of "leaves" in the spiral con-

figuration, regardless of the dislocation character

(i.e., edge or screw). Any dislocation, for example,

with t = 1/2 [110) intersecting the surface in the

vicinity of a (204) pole will produce a single spiral as

illustrated in Figure 16. The sense of the Burgers vector

will determine the direction of rotation of the spiral

for a given pole.

It is well known that one of the principle

secondary defects formed after annealing a quenched

specimen is the dislocation loop. It was mentioned in

the section on electron microscopy that the dislocation

loop is described by a single Burgers vector. It is

implicit in this definition that the reference coordinate

system move around the perimeter of the closed dislo-

cation line to maintain consistency. However, it is

impossible to distinguish it from a dislocation dipole

(i.e., two individual dislocations with opposite Burgers

vector) in an FIM image without a controlled field

evaporation sequence. Provided there is no appreciable

interaction between the strain fields, the two points of

*
Defining both vectors in terms of lattice unit
vectors i, j, k, the a-factor or lattice parameter term
is not included in the Burgers vector notation.




- 60 -


(i0) PROJECTION
EDGE DISLOCATION


.. P


Figure 16.--Pure edge dislocation causing a single
spiral on (204) plane edges.





- 61 -


emergence of the dislocations may be considered separately,

with the result that the theory predicts spirals in oppo-

site directions. Figure 17 illustrates possible configu-

rations.

Single dislocations, dipoles, or total dislocation

loops can be analyzed by inspection using the g-b criterion;

at least the number possibilities can be reduced to a point

where it is only necessary to determine the plane on which

the dislocation lies in order to specify the Burgers

vector. If the dislocation emerges at a point where two

different sets of rings are disturbed (Figure 18), the

spiral count will usually give a unique Burgers vector.

Loops bounded by partial dislocations present a

different problem since g.b is not necessarily an integer.

Partials have been found by computer analysis to cause

various types of disturbances depending upon the location

of the defect. For instance, high index planes appear to

be split or sheared by the presence of a Frank loop,

while a pinching type distortion occurs in low index

regions of the field ion image. Thus, the g.b criterion

does not seem to yield as much information for the case

of partial. Hopefully, any obvious defect which cannot

be interpreted in terms of total dislocations can be

analyzed in terms of partial dislocations. For the case

of a Frank loop, the bounding dislocation is a partial






- 62 -


OHr
Qc I
S-l 00


: ro o -A
n *--O 0


SO -O


Q -) o ,I
O-1 O 0 -H


m- ( 4
p o 0
-A 40
0 d O -





H -H O a-

S 0Q) 0
HO-





S-: 0 0 0 m
o 0 to ao-iQ
*H C-IJ m




d *o 0 0) 0
OH 0 r4



*H W cd
,--I r-
a Q a (

En H *LH ( P




O4 H
0 r-U ) -l r (l-
0 0 0 0-1




0 -I 0 04



0r~ o 0
*O *O W C
0 ) 0 44





-HrtO -HOX
0 w z 0
S0 4J O 4

r-A -4l (1 4 -P
H En rl En U
*H 0 & H U

504 04 00
s Cd 0 "1 "H -A
r- I 4-4 '4-4 1 V Cd




- 63 -


Dislocation Visible on Two Sets
of Plane Edges


m33l) Rings

x-Dislocation:
b= a. lio]
da 20


-(220) Rings







Figure 18.--Two sets of plane edges visible in the
region of the defect. Note that g-b criterion is
satisfied for each set of planes.




- 64 -


and g.b will normally predict a fraction of a spiral. Not

only is this difficult to detect but it is also difficult

to understand geometrically. Random choices of Frank

loops which have been plotted by computer seem to indicate

that streaks (Ranga.nathan et al. 1965) may form parallel

to the fault plane. There is also evidence of ring

distortion which is consistent with the concept of adding

or removing a lattice plane to produce the fault.

Analysis of voids or large vacancy clusters is

straightforward in that one must only determine size and

shape. Polyhedral voids should be recognizable as such

and should be amenable to geometric analysis employing

the pseudo-stereographic projection mentioned above.

More complex defects, such as stacking fault

tetrahedra and multilayer defects (Edington and West

1966), have not been considered to date, but should not

present any particular difficulties since they are only

dislocation arrays. It will probably be necessary to

use computer analysis to determine their nature in the

field ion image.


Effect of Stress

The applied electric field generates a hydrostatic

tension, oN, normal to the surface of the specimen, given

by Muller (1958a) as





- 65 -


oN = F2/87 = 44.3 F2 (13)

0
where F is in volts/A and aN is in kg/mm 2 A spherical

specimen of an isotropic metal will experience a uniform

dilitation and the shear stresses are therefore zero. For

a hemispherical cap attached to a cylindrical shank, the

tensile stress in the shank will be approximately aN, so

that the maximum shear stress, T, is given by:


T O N/2 (14)


These shear stresses are large enough to cause

plastic deformation and may well be expected to have an

effect on glissile dislocation configurations in the

specimen. Unfortunately, it is not yet known whether

there will be an increase or decrease in the probability

of observing such a defect. The effect on sessile dislo-

cations is equally uncertain but one would expect the

hydrostatic component to aid motion by climb.

A cause for dislocation motion in the absence of

a field is the force arising from the mirror dislocation

outside the crystal (Cottrell 1953); an effect that can

be quite important because of the small size of the

crystal tip. Using equations developed by Bullough (1967),

Hren (1967) has calculated this stress by treating the

specimen as a stack of cylinders of decreasing radius.




- 66 -


The results indicate the equilibrium position for a screw

dislocation to be along the specimen axis. The image

forces will increase as the dislocation approaches the

surface of the cylinder, but the increasing size of the

successive cylinders makes it difficult to determine

whether the entire dislocation will slip out of the crystal

or whether it will reach a stable curved configuration,

being "effectively pinned" at the wire axis somewhere up

the shank (Figure 19). The superposition of the field

stress can only confuse the issue further. In short, it

is not known whether or not the sampling probability will

be improved by the stresses on the tip.

Pimbley et at. (1966) have reported that the vacancy

concentration in the {012} region of annealed platinum tips

to be of the order of 10-2, well above the 6 x 10-4 value

Miller (1959) found in quenched platinum. The present

author has observed d large number of single vacancies in

platinum wire quenched from near the melting point and

annealed at 5000C for 24 hours. Previous studies (Jackson

1965a) indicate that there should not be any appreciable

quantity of isolated point defects after this treatment.

It seems clear that these vacancies are stress induced

artifacts as suggested by Pimbley et at.




- 67 -


Figure 19.--Possible stable configuration
for a dislocation in a field ion specimen.


--Irb ;




68 -




Thus, there is little doubt that stress effects

can be important in field ion microscopy, and even though

the stress distribution is not known, the possible results

of such stresses must not be overlooked.












CHAPTER IV

EXPERIMENTAL EQUIPMENT AND PROCEDURE


The Field Ion Microscope

The basic design and operational characteristics

of the field ion microscope were discussed in Chapter III,

In this section further discussion will be limited to the

instrument used in this investigation; a stainless steel,

liquid hydrogen cooled microscope designed to operate in

conjunction with an Air Products and Chemicals Inc. Cryo-

Tip refrigerator. Design considerations for the construction

of the microscope are discussed in Appendix II. A schematic

drawing of the microscope is presented in Figure 20. As

illustrated, the FIM body consists of an outer shell

flanged at the bottom to mate with a 4" diameter viewing

port and at the top tb receive the flanged cryostat tube.

The cryostat itself, is a Pyrex tube with two pairs of

0.050" tungsten wire leads at the bottom, and is graded to

Kovar only 1-1/2" from the top flange to avoid any diffi-

culty from low temperature phase transformations in the

Kovar. Although the cryostat tubulation is designed for

use with the Cryo-Tip, it may also be used by filling it

with a cryogenic fluid. Suspended between the outer

jacket and the glass cryostat is a stainless steel liquid


- 69 -




- 70 -


Cryotip--r
(Liquid H2 Generalc


Imaging Gas


To ---' _i
Pump "
Radiation Shield High Voltage
hd Leadthrouqh
S1 Specimen Lt1



Fiber Optic Window







Figure 20.--Schematic drawing of the field ion
microscope body. The microscope is constructed
almost entirely of stainless steel, is designed
for use at liquid hydrogen temperature, and
incorporates a fiber optic viewing port.






- 71 -


nitrogen dewar which performs the dual role of radiation

shield and cryopumping surface. To improve the shielding

characteristics, the bottom of the dewar is made of

copper, and an aluminum cylinder in thermal contact with

the copper almost completely surrounds the specimen.

Three 1-1/2" diameter ports extend radially from the

specimen chamber (at specimen level) and are flanged to

accept an ion gauge, a high voltage lead through, and a

flexible bellows for making a connection to the vacuum

system.

Normal photographic technique involves the use of

high speed 35 mm film in specially fabricated camera

bodies fitted with f/l (or faster) lenses. However, this

microscope has been fitted with-a 4" diameter fiber optic

faceplate permitting the use of direct contact photography,

thereby eliminating the need for intermediate optics.

This technique, its advantages and disadvantages are

discussed extensively in the literature (Hren and Newman

1967).

The heart of the vacuum system (Figure 21) is a

liquid nitrogen baffled 2" oil diffusion pump, backed by
-8
a 2 cfm fore pump. The system is capable of 108 mm Hg

(without bakeout) within 1-1/2 hours of specimen change.

Mild bakeout (300-4000C) results in pressures on the low
-9
end of the 10 scale of the ion gauge.
















U)



O


(e3
23 a
LL
/


V)

C\
s-k


0


0
-,4


't
r-4






44


-P






0
U







0




-t--



0 4-P
fa
S0
no
















0n
u




























H 0
^c


s CL .g


- 72 -


I-
3- 0


X z




- 73 -


The imaging gas system is presently set up to

supply helium, neon, or a preset mixture of the two. The

gas is bled in with the variable leak valve number 1 and

then passes through the liquid nitrogen dewar into the

specimen chamber. However, additional gases can be

readily admitted to the system by means of the variable

leak valve number 2. This is sometimes desirable for

improving image quality in nonrefractory metals (MUller

et at. 1965) or if one desires to study the effect of

adsorbed gaseous impurities (Fortes and Ralph 1966).


The Electron Microscope

The electron microscope employed was a Philips

EM 200 fitted with the new Goniometer Stage which permits

full 3600 rotation and 450 tilt of the specimen. In

addition, a magnetic beam tilt device enables the

operator to obtain high resolution dark field micrographs.

The operating principle of the device is schematically

illustrated in Figure 22 and the overall picture of the

technique is illustrated in Figure 23. The normal

operation of the microscope is as shown in (a); the

incident beam makes an angle 8, the Bragg angle, with a

set of diffracting planes in the crystal. The transmitted

and diffracted beams intersect the Ewald sphere at

reciprocal lattice points separated by the familiar




- 74 -


Figure 22.--Schematic illustration of the principle
of operation of the magnetic beam tilt device.




- 75 -


Beam Tilt Device


Diffracting
Planes in Crystal


---Aperture---
Axis of Microscope
Column


Bright Field
(a )


Dark Field
(b)


Figure 23.--Schematic drawing illustrating the
principle of operation of the transmission electron
microscope. (a) Operating under bright field
conditions. (b) Operating under dark field con-
ditions. (After Bell et aZ. 1965.)




- 76 -


vector g. As mentioned earlier, the reflecting sphere

(Ewald sphere) is almost planar for electron waves and

coincides with the back focal plane of the objective lens

of the microscope. Bright field images are obtained by

inserting an aperture to eliminate all but the transmitted

beam. Dark field images can be obtained by moving the

aperture to allow passage of a selected diffracted beam

but the spherical aberration of the magnetic lenses for

any noncentral beam causes a great deal of astigmatism.

As pointed out by Bell et aZ. (1965), to obtain a high

quality dark field image from a strongly diffracting beam,

the incident beam is tilted in the direction away from

the operating reflection through an angle twice that of

the Bragg angle. (For electrons, this is of the order of

a few degrees.) Thus, the operating reflection in dark

field is -g. That is, the dark field image is actually

due to reflection off the negative side of the planes

which were favorably oriented for Bragg diffraction in

bright field (Figure 23b). Without the magnetic beam

tilt facility one must accomplish this tilt by reorienting

the electron gun, an inconvenient operation at best, or

be satisfied with an astigmatic image. A further advantage

of the Philips device is that one can go from bright field

to dark field with the flick of a switch. Because of the

symmetry commonly found in electron diffraction patterns,




- 77 -


it is often possible to adjust the unit to permit a simple

switching between bright field and ei-ther two or four

consecutive dark field images.

The magnification and image rotation calibration

data is presented in Appendix III.


Specimen Preparation

The platinum purchased from Englehard Industries

was of 99.9% purity. Lengths of wire (6" x 0.005") and

foil (6" x 1/4" x 0.0015") were heated electrically in

air and quenched into brine at 0C. The quenching

temperature was estimated from two independent methods

to be within 1000C of the melting point: Cl) the voltage

was increased until melting occurred in a dummy specimen

and the remaining specimens were heated at approximately

one volt less potential. (2) An optical pyrometer reading

of 16800C 500C was obtained after correcting for emis-

sivity and non-blackbody conditions. Short lengths were

then cut from the original 6" length to be annealed for

various times between 2500C and 6000C. No extensive

table will be presented describing individual heat

treatments, but instead, specimen history will be stated

in the text as it applies to the overall discussion. The

author feels that this is desirable in that the results

are presented as general trends rather than as being due




- 78 -


to specific and/or involved quenching and annealing

treatments.

Early in the investigation, field ion specimens

were prepared from the wire by electropolishing in an

aqueous potassium cyanide solution (Muller 1960).

Sometime later, Dr. R. W. Balluffi informed us that his

laboratory at Cornell had been successful in polishing

platinum foils with an aqueous solution of calcium

chloride maintained at -300C (Ahlers and Balluffi 1967).

This electrolyte was also found to work extremely well

for preparing field ion specimens employing a platinum

counter-electrode and a variable 0-15 volt A.C. power

supply (Newman et aZ. 1967).

Electron transparent foils were initially prepared

using the well-known window method, along with the above

mentioned solution. Although satisfactory, an improved

technique resulted from the persistence of Mr. E. J.

Jenkins, the electron microscope technician. The method

involves jet polishing a platinum disc that has been precut

to fit the microscope specimen holder. The disc is placed

on a platinum mesh screen and the cold CaCl2 solution is

allowed to flow in a small stream over the foil. A

potential of 80-100 volts A.C. is impressed between the

mesh and a platinum electrode immersed in the electrolyte





- 79 -


bath above the specimen. The apparatus is illustrated in

Figure 24. This stage of the polishing procedure is

continued until the center of the disc is noticeably

thinner (i.e., "dimpled"). The final stage is carried

out at 8-10 volts A.C. with the specimen immersed in the

electrolyte bath until a hole appears. Large areas

suitable for transmission microscopy are obtained in this

manner. A final cleaning is accomplished by applying 20

volts D.C. for 30 seconds followed by a rinse in distilled

water and then ethyl alcohol. The low temperature of the

polishing solution insures that no annealing takes place

during the preparation of the foil and the elimination of

the need for stop-off lacquer reduces the occurrence of

dirty foils.




- 80 -


:lectrdyte


Stopcock


>ecimen


.Receiving
Beaker


Figure 24.--Schematic drawing of apparatus employed
for preparing electron transparent foils of plati-
num.


AC
Supply


1--f' ''' ~-,r._;i
---
_:::
-:_:'._ --I


.....












CHAPTER V

RESULTS AND DISCUSSION


Ruedl et at. (1962) found voids in heavily irradi-

ated platinum foils upon pulse heating in the electron

microscope, whereas irradiation followed by a mild anneal

resulted in the formation of vacancy loops. Therefore,

one might expect to find loops or voids depending upon

the vacancy supersaturation. That is, it can be con-

vincingly argued that an instantaneously high concen-

tration of mobile vacancies would favor the formation of

voids, while a lower vacancy concentration would favor

prismatic loops. This is consistent with the present

experimental observations in that either voids or loops

are formed, but the two rarely occur in the same region.

Furthermore, dislocations are almost nonexistent in areas

of high void concentrations while large prismatic loops

are generally found in the midst of heavily jogged

dislocations. This is quite reasonable in light of the

evidence for dislocations being efficient vacancy sinks.

Thus, in some regions, small clusters and dislocations are

competing for vacancies while in others, the clusters

accumulate essentially all of the migrating point defects.


- 81 -





- 82 -


Void Analysis

A high concentration of large voids (cavities) was

obtained by repeated pulse quenching in air followed by a

one hour anneal at 5000C. Some of the cavities were more
0
than 1000 A in diameter, large enough to break through one

or both surfaces of the foil, while the majority were of
0
the order of 300 A. This is in contrast to foils subjected

to a single quench followed by a 24-hour anneal at 4000C.

Under these circumstances the size distribution is more
0
uniform and centered about a smaller diameter (i.e., 150 A).

Figure 25 is an electron micrograph of the pulse quenched

and annealed foil after partial melting in the microscope.

(This was accomplished by removing both condenser apertures

while the specimen was under observation.) It is apparent

that some voids are still present in areas within a micron

of the melted edges, and it is thus reasonable to state

that the void, once formed, is an extremely stable defect.

This stability could well explain the presence of the

large cavities in the pulse quenched specimen if one argues

that the nuclei are formed during the first quench (a

reasonable assumption since the air quench is relatively

slow) and grow by vacancy absorption during each successive

quench. This defect configuration is most likely the one

contributing to the irreversible resistivity increment

measured by Cizek (1967).




- 83 -


Figure 25.--Polyhedral voids in pulse quenched
platinum foil after partial melting in the electron
microscope. The average void size is approximately
0
300 A.




- 84 -


Kiritani et al. (1964) have suggested that the

voids in aluminum are regular octahedra with {111} faces,

and a similar conclusion was drawn for the voids in gold

(Yoshida et al. 1965). Clarebrough et al. (1967) have

just published a rather complete study of voids in quenched

copper, silver, and gold. (The author would like to

acknowledge receipt of their manuscript prior to publication.)

Although Clarebrough et al. found a few voids that closely

approximated regular octahedra, the majority are better

described as octahedra truncated by (111} and/or {100} and

an occasional {110}. However, these voids were much

larger and the authors concede that they may have been

regular at smaller sizes. To remain as such after growth,

the vacancy flux would have to be uniformly distributed

over the surface of the defect.

The voids in platinum are definitely polyhedral in

shape, but the facet configuration seems to be somewhat

variable. By and large the resolvable voids can be

described as {100} truncated octahedra (Figure 26) which,

because of the associated strain fields, may appear

spherical. On the other hand, there are instances where

it is necessary to use more complex truncations involving

only single sets of {100} as in (b) or {111} planes as in

(d). Clarebrough et al. have suggested the truncations

pictured in Figure 27.






- 85 -


0
C d

c0
0 *0





00-J
) f



>o 4P
(ad
-A0
c


(a 0


S ) (
Vi rm o










o r-










> 0 C0
04









$4 rj OH

4C4
4r U (1
cOl


44> C C
Hr-i 4r








01 04-) C
S4 C 0
C 'l r-)-



4 Cn)








CO 4 4H
* CU C a-





1 C->
I -r1 i7
I O1
* C!r-1-r-
br 0, 3 4-
CM e





- 86 -


0 q




O




0


c, 1
,0-
En 0 3








H -C N
k





0 0











rr
*H aC) H





4O0,


0~ 4




ato
do

*H z)


Q) ruf








rOO
* 0- H



N OH

*HEC) ru




- 87 -


Unfortunately, the analysis is not so straightforward

for platinum since the voids are as much as an order of

magnitude smaller than those observed in copper and

aluminum, and the strain fields, although small, generally

tend to obscure the boundaries of the defect. Figure 28

is a singular case where a clear fringe pattern was ob-

served. It is postulated that the fringes (arrowed) occur

as a consequence of the wedge-shaped nature of the defect.

Only with low order reflections would the extinction

distance be short enough to give rise to contours.

Figure 29 is the same area with the defects exhibiting

strain contrast. In agreement with the Ashby and Brown

theory (1963a), the line of no contrast is normal to the

operating g-vector. Strain must also be responsible for

the black patch contrast sometimes observed at various

points within the confines of the void. Additional experi-

mental evidence for the existence of a strain field around

a void in platinum is presented in Figure 30. The dislo-

cation line is apparently pinned at the void, and where

the strain fields overlap, the perimeter of the void is

invisible. Note that this void can also be seen in

Figure 28 at the point X. Under these diffraction con-

ditions the entire void is visible.

It can also be seen that the edges of the voids in

these micrographs are parallel to projected <110> directions.




Full Text

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AN ELECTRON MICROSCOPE AND FIELD ION MICROSCOPE STUDY OF DEFECTS IN QUENCHED PLATINUM By ROBERT WILLIAM NEWMAN A DISSERTATION PRESENTED TO THE GRADUATE COUNCIL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY UNIVERSITY OF FLORIDA December, 1967

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?IDA liiiiiii

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Dedicated to My Wife, Mary Katherine

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ACKNOVJLEDGMENTS The author would like to acknov;lcdge the assistance of his advisory conimittee. He is especially indebted to his chairraan. Dr. J. J. Hren, wlio contributed unselfishly of his time in the form of stimulating discussions, advice, and encouragement throughout the course of this investigation. Thanks are also due Drs. E. D. Adams and T. A. Scott of the Physics Department for their suggestions concerning cryostat design, the late Mr. R. J. Harter, chief metallurgist of the Sperry Rand Vacuum Tube Division, who aided in the microscope design, Mr. E. J. Jenkins for his assistance in the laboratory and Dr. R. C. Sanwald for the use of his computer program. The author would like to acknowledge the members of his family, too numerous to mention, whose encouragement and support has been invaluable. The writer is also grateful to the National Aeronautics and Space Administration, without whose support this research would not have been possible. Ill

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TABLE OF CONTENTS Page ACKNOWLEDGMENTS iii LIST OF TABLES V LIST OF FIGURES vi ABSTRACT xi INTRODUCTION 1 Chapter I. DEFECTS IN QUENCHED PLATINUM 8 II. ELECTRON MICROSCOPY 24 III. FIELD ION MICROSCOPY 4 9 IV. EXPERIMENTAL EQUIPMENT AND PROCEDURE .... 69 V. RESULTS AND DISCUSSION 81 VI. CONCLUSIONS AND SUGGESTIONS FOR FURTHER STUDY 137 Appendices I. INDEXING FIELD ION MICROGPAPHS 14 4 II. DESIGN CONSIDERATIONS IN CONSTRUCTING THE FIELD ION MICROSCOPE 150 III. CALIBRATION OF THE ELECTRON MICROSCOPE . . . 157 BIBLIOGRAPHY 163 BIOGRAPHICAL SKETCH ' 169 IV

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LIST OF TABLES Table Page 1. Best Values of the Thermodynamic Properties of Point Defects in Some Com:Tion Metals 10 2. Collected Values for the Energies of Formation and Motion of Vacancies in Platinum 19 3. Expected Contrast from Voids as a Function of Diffraction Conditions 47 4. Expected Contrast from Voids as a Function of Void Size 48 5. Magnification Calibration of Philips EM 200 with the Goniometer Stage 158

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LIST OF FIGURES Figure Page 1. Transformation of a Frank loop to a perfect prismatic loop 13 2. The stacking fault tetrahedron 15 3. Reflecting sphere construction for electron diffraction 28 4. Diffracted intensity versus the interference error, s, according to the kinematical approximation 29 5. Schematic illustration of the origin of fringe contrast 30 6. Diffraction of electrons by a foil containing an edge dislocation at E 34 7. Burgers vector convention for dislocation loops 37 8. Relative position of the dislocation loop as the set of planes, g, is rotated through the Bragg orientation ... 39 9. Relative positions of the diffraction spot and Kikuchi line due to the same reflection 41 10. Diagram showing the displacement of reflecting planes by a stacking fault to give contrast in (b) but not in (c) or (d) 44 11. Schematic drawing of a field ion microscope 50 12." Potential diagrams for an electron in field ionization 52 VI

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LIST OF FIGURES — Continued Figure Page 13. Detailed schematic of the ionization process illustrating the relationship between the atom positions and the cones of emitted ions 54 14. Current-voltage characteristic of the helium field ion microscope 55 15. Diagram of (111) plane shov/ing how single and double spirals can be produced on (220) plane with Burgers vectors of a/2 [lol] and a/2 [110] , respectively 58 16. Pure edge dis].ocation causing a single spiral on (204) plane edges 60 17. Three possible spiral configurations resulting from the emergence of a dislocation loop 62 18. Two sets of plane edges visible in the region of the defect 63 19. Possible stable configuration for a dislocation in a field ion specimen .... 67 20. Schematic drawing of the field ion microscope body 70 21. Schematic drawing of the vacuum system for the field ion microscope 72 22. Schematic illustration of the principle of operation of the magnetic beam tilt device . . . . 74 23. Schematic drawing illustrating the principle of operation of the transmission electron microscope 75 24. Schematic drawing of apparatus employed for preparing electron transparent foils of platinum 80 Vll

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LIST OF FIGURES — Continued Figure Page 25. Polyhedral voids in pulse quenched platinum foil after partial melting in the electron microscope 83 26. Schematic drawing illustrating various void shapes 85 27. Schematic drawing illustrating various void shapes 85 28. Voids in platinum foil exhibiting fringe contrast 88 29. Voids in the same platinum foil imaging by strain contrast *. . . 89 30. Electron micrograph of a dislocation pinned at a void 90 31. Bright field electron micrograph of polyhedral voids in a [110] oriented foil 92 32. Bright field micrograph of the same region after 35° tilt 93 33. Bright field micrograph of the same region after tilting to [331] 94 34. Dark field micrograph of the same area illustrating the contrast behavior of the voids along the low angle boundary ... 95 35. Isolated colony of voids in a foil that was annealed for 100 hours at 500°C .... 97 36. An octahedral void viewed along two crystallographic directions ........ 98 37. _ Field ion micrographs of vacancy clusters in platinum • 105 38. A field evaporation sequence through a 25 A diameter tetrahedral void near the (224) pole 106 Vlll

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LIST OF FlGURES--Continued Figure Page 39. Schematic dravving illustrating the relationship between the surfaces of a tetrahedron and an octahedron Ill 40. A sequence of three electron micrographs showing a prismatic loop moving on its glide cylinder 114 41. Schematic drawing combining the information from the three electron micrographs of Figure 40 117 42. Stereogram used for the analysis of the oscillating defect 118 43. Electron micrograph of a large prismatic loop 120 44. Field ion micrograph of a prismatic loop intersecting the (313) plane edges 121 45. Field ion micrograph of a prismatic loop intersecting the (111) plane edges 122 46. Field ion micrograph of a Frank sessile dislocation loop 125 47. An enlargement of the (002) region in the previous micrograph 126 48. Computer simulation of the region containing the defect in the previous micrograph 127 49. Electron micrograph of a foil containing large prismatic loops and heavily jogged dislocation lines 130 50. Dark field electron micrograph of the same region with g = (002) 132 IX

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LIST OF FIGURES — Continued Figure Page 51. Dark field electron micrograph of the same region with § = (002) 133 52. Electron micrograph of dislocation intersections resulting in the formation of Lomer-Cottrell barriers 136 53. Qualitative plot of the observed defect density versus annealing temperature 14 54. Projection of a random direction onto a planar surface with the projection point chosen so that ^^ ^ 145 55. Photograph of the field ion microscope .... 151 56. Schematic drawing of the liquid hydrogen cryostat 153 57. Plot of intermediate lens current versus magnification for the Philips EM 200 fitted with the Goniometer Stage 160 58. Plot of intermediate lens current versus image rotation for the Philips EM 200 fitted with the Goniometer Stage 162

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Abstract of Dissertation Presented to the Graduate Council in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy AN ELECTRON MICROSCOPE AND FIELD ION MICROSCOPE STUDY OF DEFECTS IN QUENCHED PLATINUM By Robert V7illiam Newman December 19, 1967 Chairman: Dr. John J. Hren Major Department: Metallurgical and Materials Engineering Results of a survey study of the secondary defects existing in quenched platinum are presented. Transmission electron microscopy used in conjunction with field ion microscopy has yielded direct experimental evidence for the existence of prismatic dislocation loops (both glissile and sessile) as wel] as polyhedral voids. For the most part, the dislocation loops were observed as black spot defects in the electron microscope and were resolvable only via field ion microscopy. The 13 3 loop density was estimated to be 10 /cm with an average o size of approximately 50 A, In one instance a defect interpreted as a Frank loop with Burgers vector a/3 [111] was observed in the field ion microscope. Resolvable XI

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loops (i.e., > 100 A) were found among networks of heavily jogged dislocation lines. The void concentration reached a maximum of 3 4 3 7 X IQ-/cm after annealing at 400°C for 24 hours and fell sharply on either side of this temperature. The shape of the voids was found to be a function of the concentration. At low density the voids can be described as regular octahedra, some of which are truncated by {100} and occasionally by {111} planes. Smal]. voids appear spherical but careful tilting experiments reveal hexagonal cross sections implying that the shapes are {100} truncated octahedra. It is shov.m that the apparent sphericity can be attributed to strain contrast arising from the m.atrix iramediately surrounding the void. Small tetrahedral voids have been discovered in field ion specimens, and it is postulated that these clusters are the nuclei for both voids and dislocation loops, depending upon the number and efficiency of the vacancy sinks in the local environment. The voids are shown to be extremely stable almost to the melting point.

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INTRODUCTION The development of the field ion microscope by E. W. Miiller (1951) opened the way for the study of the defect structure of materials on the atomic scale. Relatively little progress has been made in this direction, however, since defect analysis on the atomic le?vel is far from routine. Advances are being made in image interpretation but at the present time it is imperative that experimental results be correlated with evidence obtained by other means. For some reason this has not been done. In the present investigation extensive use has been made of both field ion microscopy and transmission electron microscopy to determine the nature of the defect structure of quenched and annealed platinum. The type of defects to be considered in the body of this manuscript are usually referred to as secondary defects. Although grouped under a common label, secondary defects may be any one of a number of known crystallographic imperfections. These defects are all related in that they all have their origin in a supersaturation of vacant lattice sites (vacancies) . Point defects are commonly produced by one of three methods: 1 -

PAGE 15

2 (1) deformation, (2) radiation, (3) quenching. The latter has been chosen for this study because it does not introduce additional defects such as interstitials , dislocation tangles, and displacement spikes which would only complicate the analysis of this first study. Vacancies are equilibrium defects and it is well known that the number of these point defects in thermodynamic equilibrium with the system increases with temperature. Therefore, a piece of metal equilibrated at some elevated temperature v^ill contain a larger number of vacancies than would be in equilibrium at a lower temperature. Rapid quenching from near the melting point results in the retention of most of the high temperature vacancy concentration at some lower temperature, say room temperature. Since this is a nonequilibrium situation, the system lowers its free energy by allowing isolated vacancies to cluster into energetically more favorable configurations if it is permitted to recover with time. These cluster configurations are referred to as secondary defects. The importance of secondary defects lies in their effect on the mechanical properties of crystals and crystalline materials. It is now accepted that the mechanical behavior of a crystal is governed by the motion of the line defects or dislocations through the

PAGE 16

3 crystalline lattice (Read 1953, Cottrell 1953). It follows that any obstacle interfering with this motion will have some effect on the mechanical properties of the crystal. Secondary defects are such obstacles. While it is the ultimate aim to understand the effect of secondary defects on the deformation behavior of a metal in terms of their interaction with dislocations, it is first necessary to understand the atomic geometry of the cluster configurations and their density distribution. Consequently, a large portion of the literature in the field concerns itself with the geometry of these tv/o and threedimensional defects. The idea that excess vacancies could condense into secondary defects was suggested by Frank (1949) and Seitz (1950) in their discussions of the origin of dislocations in crystals. The growing amount of data on the unusual behavior of quenched materials, much of which is reviewed by Cottrell (1958) , led a number of workers to expect evidence of vacancy clustering from transmission electron microscopy. This expectation was fulfilled in a paper published by Hirsch et at. (1958) which presented direct experimental evidence for the clustering of vacancies in quenched aluminum. Frank (1949) proposed that vacancies in FCC material would agglomerate on a single {111} plane to form an area of stacking fault

PAGE 17

4 surrounded by a dislocation with Burgers vector a/3 <111>. This defect was appropriately called a Frank loop. Hirsch et at. (1958), however, found the loops in quenched aluminum to be prismatic with a Burgers vector a/2 <110>. They suggested that the Frank loops would be energetically unstable because of the high stacking fault energy of aluminum, and would, therefore, transform to a perfect prismatic loop by a reaction: a/3 <111> + a/6 <112> -^ a/2 <110> as suggested by Kuhlmann-Wilsdorf (1958) . In other words, the stacking fault could be eliminated by the nucleation of a Shockley partial dislocation. The success of the electron microscope work on aluminum prompted Silcox and Hirsch (1959) to examine a lower stacking fault energy metal in the quenched state, namely gold. As a result of this investigation a totally new defect, the tetrahedron, was discovered. The description of the stacking fault tetrahedron in terms of its component stair-rod dislocations and fault planes is not now disputed but the scientific community has yet to agree on the mechanism of its formation. See, for examp-le, de Jong and Koehler (1963) , Kuhlmann-Wilsdorf (1965) , and Chik (1965) .

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5 Further studies on quenched metals and alloys employing transmission electron microscopy have revealed the existence of polyhedral voids and an unknov/n defect sometimes referred to as "black death." The latter appear as small, unresolvable black spots on an electron micrograph and their character or configuration is not yet certain. In addition to transmission microscopy, several indirect methods, notably resistivity, have been employed to study materials in the quenched state. For the most part, these methods are capable only of studying the kinetics of the clustering process. Very little information can be obtained as to the precise geometry of the secondary defects, but the kinetics of resistivity change do give an indication as to the type of defect formed. It is at this point that direct observation with the electron microscope becomes necessary. Unfortunately, some materials are not amenable to thin film microscopy for one reason or another. Platinum, until recently, was such a metal. Specifically it was not possible to electropolish a platinum foil thin enough to be transparent to an electron beam without altering the structure, although Ruedl et at. (1962) and Ruedl and Amelinckx (1963) observed platinum in transmission after beating the foil to less than 1000

PAGE 19

6 V A thick. This is not suitable for quenching studies though, since the defects would most likely be affected by the large stresses introduced by quenching such a thin specimen (Jackson 1965a) . Studies of quenched platinum have been limited to electrical resistivity, except for that of Piercy (1960) who correlated this data with other physical and mechanical property measurements. From these data and his own studies Jackson concludes that the annealing behavior of platinum is much different from that of other quenched metals. In fact, he went so far as to say that neither loops nor tetrahedra would exist in quenched and annealed platinum. Ahlers and Balluffi (1967) have published information on an electrolytic solution with which one can prepare thin foils of quenched platinum while maintaining sub-zero temperatures. Thus, for the first time, it became possible to see if secondary defects exist in platinum following various annealing treatments of the quenched material. The work of Ruedl and Amelinckx (1963) indicated that the defect clusters in platinum would be much smaller (possibly by an order of magnitude) than those in aluminum and gold. This suggests that it would be informative to use the field ion microscope in conjunction with the electron microscope. Field ion microscopy has already

PAGE 20

7 proven its value for studying small defect clusters induced by a-particle bombardment (Miiller 1960) and neutron radiation (Bowkett et at. 1964). Employing a technique known as field evaporation, layers of atoms can be stripped from the surface of the specimen enabling the investigator to cause the visible surface to pass through the bulk of the specimen. Hence, one has a tool v/ith v;hich he can determine, in three dimensions, the atomic configuration of defects within the metal tip. This, then, was the aim of this research; to use both field ion microscopy and transmission electron microscopy in a survey study of the defect structure of quenched and annealed platinum. It is doubtful that all stable configurations have been discovered for the work on aluminum is still underway. Almost ten years after the initial studies, multilayer defects are only now being discovered (Edingdon and West 1966). It is felt that complementing the electron microscope studies with field ion microscopy not only reduces the chance of misinterpretation, as happened in the case of aluminum (Loretto et at. 1966) , but is in fact a unique way to study the defect structure of quenched and annealed m^etals

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CHAPTER I DEFECTS IN QUENCHED PLATINUM Defect Formation Vacancies The first author who realized that crystals in thermal equilibrium should contain a well-defined concentration of point defects appears to have been Frenkel (1926). The thermodynamics and kinetics of these poj.nt defects is discussed extensively by Damask and Dienes (1963) . The concentration of vacant lattice sites in a crystal increases with increasing temperature according to the familiar Arrhenius relation C = A exp(-E^/kT) (1) where A is an entropy factor (~1) , E the energy of formation for a vacancy (-1 eV) , and k is the Boltzmann constant. Very large supersaturations of vacancies can 4 -1 be produced by rapidly quenching (>10 deg sec ) a piece of metal from temperatures near the melting point. The excess vacancies retained in the crystal can be eliminated by annealing at some intermediate temperature (-1/2 T ) 8 -

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9 thereby causing them to diffuse to some form of sink. In addition to the pre-existing or fixed sinks such as dislocations and surfaces (internal as well as external) , there is evidence for the existence of variable sinks. These are variable in that their size and/or shape changes as more vacancies are annihilated, resulting in a change in the annealing kinetics. These variable sinks take on several forms: (1) voids, (2) dislocation loops, (3) stacking fault tetrahedra; but they are identical in that they all originate from the very defects which they are helping to eliminate. The geometry of these sinks will be discussed in the next section. Equation (1) gives information as to the total number of vacancies at equilibrium but says nothing about where they are. However, reasonable assumptions suggest that 90% are isolated single vacancies with the remainder in clusters of up to about six vacancies. The relative numbers of each of these configurations is dependent upon the respective binding energies. From the data in Table 1 it is evident that the divacancy is the most mobile of these defects since higher order complexes are immobile as such. During an annealing treatment, single vacancies and divacancies migrating through the crystal will interact to form trivacancies, tetravacancies , etc. with a corresponding reduction in the internal energy of the crystal

PAGE 23

10 TABLE 1 BEST VALUES OF THE THERMODYNAMIC PROPERTIES OF POINT DEFECTS IN SOME COMMON METALS Property

PAGE 24

11 Q activation energy foj: self diffusion Y stacking fault energy as a v/hole. As these clusters increase in size they tend to: (1) form into spherical cavities, (2) become polyhedral-shaped cavities, (3) collapse to form Frank loops, (4) collapse to form perfect prismatic loops, or (5) form stacking fault tetrahedra. There are, as yet, no hard and fast rules as to what kind of defect will form in a particular material after a given heat treatment but all of the parameters listed in Table 1 will have a definite effect. The stacking fault energy is perhaps mentioned most often in the literature, but the problem of using it as a criterion is that there is so much controversy over its magnitude. Secondary Defeats Cavities of various sizes and shapes have been observed in metals and alloys, and they can usually be classified as either spherical or polyhedral. It is not at all understood precisely what determines the final shape, but it is probably a combination of defect size and the surface energy of the material. The polyhedral surfaces are generally made up of low index planes and the voids are therefore quite symmetric.

PAGE 25

12 Frank dislocation loops can be envisioned as the removal of part of the <111> plane from the lattice. The result is a fault in the stacking sequence, as the planes above and below the missing plane will collapse to fill the gap. The region of stacking fault is surrounded by a partial dislocation with a Burgers vector a/3 <111> and has the appearance of a pure edge dislocation (Figure la) . The dislocation is sessile and the loop is usually hexagonal in shape with the sides parallel to <110> directions A second type of loop commonly found is the perfect prismatic loop. It can be obtained from the Frank loop by the nucleation of a Shockley partial, according to the reaction a/3 <111> + a/6 <211> ->' a/2 <110> The resulting configuration is shov'/n in Figure lb. It is entirely possible that the prismatic loop forms directly from the collapsed cluster, but the question is academic. It is generally felt that the prismatic loop will be favored in materials with a high stacking fault energy, but recent papers by Loretto et al . (1966) and Humble et al . (1967) place this conclusion in some doubt. The prismatic loop can sometimes lower its energy by becoming rhomboidal in shape (it is usually elliptical) and rotating toward a {110} plane, thereby

PAGE 26

13 o°o°o°>««o°o°/c?°o° ^1 plane (a oooooooooo tool] (ml CMO] extra half ^oooooo^ooo^'^ plane above ^®°o°o^o°o^cPo°c°o°o° -en., ® O O (D O CJ ® O O O loop o°/»°o"o°o°/o°o°o° --<5'o°cfo°o°>o°oV°o°--"oop plane ^o o^'o o ® o o o <^^o ,„ Wo°°o
PAGE 27

14 becoming nearly pure edge in character. That is, the habit plane is not quite {110}. Both the prismatic and rhomboidal (often referred to as rhombus) loops are glissile and can move by conservative glide in the <110> direction. The stacking fault tetrahedron, as its name implies, is a four-sided defect. Each of the faces is a {111} plane containing a stacking fault and the six lines of intersection of the faces is a stair-rod dislocation of Burgers vector a/6 <110> (Figure 2) . Several mechanisms of formation of tetrahedra have been proposed (Silcox and Hirsch 1959, de Jong and Koehler 1963, and Kuhlmann-Wilsdorf 19 65) but these are as yet unproven. Review of the Work on Platinum In view of the fact that platinum is a relatively easy metal to work with in quenching studies (Doyama 1965) , it is rather surprising that so little information has been published on it. Perhaps the answer can be found in the difficulty of employing direct observation techniques with platinum. Whereas both aluminum and gold are amenable to thin film microscopy, platinum, until recently, was not. Therefore, quenching and annealing studies could not be extended beyond the somewhat limited resistivity investigations.

PAGE 28

15 Figure 2. — The stacking fault tetrahedron. The faces are {111} containing a stacking fault. The intersecting faults give rise to stair-rod dislocations at the edges.

PAGE 29

16 The first published work on quenched platinum was an electrical resistivity study by Lazarev and Ovcharenko (1955). They reported values of 1.18 eV and 1.08 eV for the energies of formation and migration of vacancies respectively. Soon after, Bradshaw and Pearson (1956) found the energy of formation to be 1.4 eV and attributed the discrepancy to an insufficient rate of quenching in the previous work. It was also concluded that there was only one recovery stage (non-exponential) and that there was no evidence for vacancy agglomeration. In a later paper (Pearson and Bradshav/ 1957) no significant effect was found with the addition of rhodium and gold as impurities. Successful experiments with gold prompted Ascoli et at. (1958) to make new measurements on platiniom. The energy of formation was determined to be 1.23 eV. The annealing curves exhibited exponential behavior (unlike Bradshaw and Pearson's data) from which the migration energy was a surprisingly large 1.4 2 eV. Of equal significance was the calculation of the number of jvimps made by a typical vacancy during anneal, before annihilation. Whereas Bradshaw and Pearson (1956) had calculated 10 jumps, Ascoli et at. (1958) arrived at a 7 8 value. of 10 to 10 . However, they also found no evidence for defect clusters.

PAGE 30

17 Bacchella et at. (1959) were the first authors to suggest that the complex kinetics observed after high temperature quenches might be due to some clustering of vacancies. Measured values of the activation energies were not significantly different from those of Ascoli et at. (1958) , i.e. , E. = 1.20 eV and E = 1.48 eV f m Miiller (1960) made a vacancy count on quenched platinum using the field ion microscope and calculated a value of 1.15 eV for E^ . However, Pimbley et at. (1966) found the number of vacancies to be anomalously high and attributed this to a stress effect inherent in field ion microscopy. Pierc_y (1960) made a rather thorough investigation of point defects in platinum, using deformation and neutron radiation as well as quenching to introduce an initial excess of point defects. He also complemented electrical resistivity measurements with x-ray line broadening, hardness, and density measurements. Quenching from above 1600°C, Piercy found E = 1.13 eV in good agreement with the work of Bradshaw and Pearson (1956) . Values of E m for the irradiated specimens compare well with those of Ascoli et al. (1958) and Bacchella et at. (1959). Piercy

PAGE 31

18 attributes the lov/er value to the motion of diyacancies and the higher to single vacancies. The order of reaction is a measure of the rate of change of a number of jumps required by a defect to reach a sink during the recovery process. Therefore, it should be possible to determine the type of sink from measurements of the relaxation time and the jump frequency. Piercy Q Q argues that 10 to 10 jumps (his calculation) is much too high for the recombination of defects but, if the defects are being annihilated at dislocations, the order of reaction might be expected to be unity. He reasons that the observed value of 1.4 6 may be caused by a change in the dislocation network due to extensive climb. Thus the last defects will migrate to a much different dislocation network than was initially present. Jackson (1965a) quenched platinum wires from various temperatures in the range from 700°C to 1750°C in an attempt to resolve the discrepancy between the reported activation energies. His findings are listed in Table 2, along with previously obtained values. The evidence is quite convincing for assigning the lower value, 1.1 eV, to the motion of divacancies and the high value, 1.4 eV, to single vacancies. His data also verify that there is only one clearly resolved annealing state.

PAGE 32

19 w < O D Cm s?; H Cn ^ o < en CM H H 2 O H « W H W S K < Eh U < o Cm Cm O Ciq D <-^ < > Q tq Eh O O 0) u (1) 0) Q) 0^ -P tl > (U 4-1 » LA

PAGE 33

20 regardless of initial concentration. Jackson also states that the shape of the isothermal annealing curves correspond to diffusion of point defects to sinks that become less efficient with time. He concludes that the very low resistivity increment remaining after anneals below 1/4 T and the large number of jumps (two orders of magnitude greater than in gold) for vacancy annihilation argue that the sinks for vacancies in platinum are much different from those in other metals. Amelinckx's group in Belgium has been alone in the use of TEM (transmission electron microscopy) to study quenched platinum foils. Ruedl et at. (1962) and Ruedl and Amelinckx (1963) were principally interested in radiation damage, but many of their findings are quite applicable to the present work. This is particularly true in the case of foils quenched prior to irradiation. However, one must be aware that quenching strains in the o extremely thin (1000 A) foils could have a significant effect on these results. This problem has been investigated by Jackson (1965b) , and the principal effect seems to be a change in the vacancy structures produced by subsequent aging. Ruedl et at. (1962) reported finding defects which were interpreted as spherical voids and some instances of o polygonal features in the neighborhood of 100 A diameter,

PAGE 34

21 the contrast of both being quite different from that of dislocation loops. The presence of these cavities rather than loops is attributed to the high surface energy of platinum. It is felt that the energy barrier in transforming from a spherical to a penny-shaped cavity would be rather large, and would therefore inhibit the collapse of clusters into loops. It should be pointed out, however, that the concept of surface energy become ambiguous when dealing with very small surfaces. In fact, it has been suggested by Jackson (1962) that the energy of a cluster might better be calculated as the energy of formation of a vacancy divided by its surface area. If this be the case, the energy of a void will always be less than that of a Frank loop, whereas the reverse is true if the bulk surface energy is used (Friedel 1964). Thus, as Clarebrough (1966) points out, it is impossible to decide which type of defect is more stable at small sizes, without detailed knowledge of surface energies for very small voids. Bauer and Sosin (1966) found stage IV recovery of electron irradiated platinum to be a diffusion-controlled process up to approximately 50% recovery. The rest of the recovery is considerably slower than predicted by theory. Accor(;aing to them, the possible mechanisms which may account for this delay include: (1) clustering of the vacancies, (2) exhaustible sinks, (3) concurrent trapping

PAGE 35

22 of vacancies during the diffusion process. The authors choose to explain their results by the third mechanism. Their reason for ruling out the second are understandable, but their basis for ruling out the first is open to question (Chik 1965) . It is worth noting that they measured the activation energy of stage IV recovery to be 1.36 eV; i.e., approximately equal to the energy of motion of single vacancies. Cizek (1967) investigated the irreversible component of resistivity remaining after repeated quenching of platinum wires. After subtracting out the non-recoverable resistivity increment attributable to dimensional changes in the specimen, some 20% of the irreversible change was unaccounted for. The author suggests that while vacancy clusters and/or voids may contribute, it is more reasonable to investigate the possibility of more stable defect configurations such as the oxygen stabilized stacking fault tetrahedra present in silver up to 930°C (Clarebrough 1964) . It should be mentioned at this point that Ruedl et at. (1962) observed dislocation configurations indicating the possibility of dissociation into partials (i.e., Lomer-Cottrell barriers). This was complemented by a common occurrence of annealing twins and only rare

PAGE 36

23 observations of cross slip v;hich, when it did occur, was rather complicated. The authors are cognizant of the fact that the stacking fault energy of platinum is 2 reportedly high (75-95 erg/cm ) . While a discussion of irradiation experiments is perhaps not appropriate here, the defects observed by Ruedl et at. in foils bombarded by neutrons, fission fragments, or a particles are of interest. Both black spot defects ("black death") and resolvable loops were present. The prismatic nature of the loops was inferred from motion in <110> directions during observation. This is consistent with the concept of conservative glide on a prismatic cylinder. Evidence was also found for interaction betvv'eeii these defects and dislocation lines. The resulting ragged appearance could be due to climb or stress field interactions. Large polyhedral voids and prismatic loops were found to occur in foils exposed to a-particles and subsequently annealed at temperatures up to 500°C. The voids were presumed to be filled with helium gas, the presence of which may stabilize the cavities. This may be substantiated by the fact that the voids remained after anneals in excess of 700°C.

PAGE 37

CHAPTER II ELECTRON MICROSCOPY Contrast Theory When the electron microscope is used with thin metal foils, extensive use is made of the phenomena of diffraction of electrons by acrystal lattice. The radius of the Ewald sphere is extremely large for electron diffraction; so large, in fact, that it is almost planar over the solid angle subtended in the electron microscope. The small curvature that does exist is compensated for by the rod-like nature of the reciprocal lattice points. The physical reason for the existence of these "relrods" is the relatively small number of reflecting planes in the thickness direction. There simply are not enough scattering centers to attain complete destructive interference for non-Bragg conditions. Therefore, the diffraction peak (i.e., reciprocal lattice point) is broadened in the direction of the small dimension and the extent of the streaking varies inversely as the foil thickness. (This phenomenon is analogous to particle size broadening encountered in x-ray diffraction.) As a result, the diffraction pattern that is projected on the microscope 24 -

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25 screen is actually a plane section through the reciprocal lattice of the crystal. Most of the commonly observed patterns display a high degree of syimnetry and are relatively easy to identify. The normal procedure is to intercept all diffracted beams with an aperture allowing only the transmitted beam to pass through the lens system to be magnified and projected onto the fluorescent screen. Thus, any regions of the crystal which are diffracting strongly will appear dark on the screen. When studying defects it is often desirable to view what is called the "dark field" image. This is a procedure whereby the above mentioned objective aperture is moved so that only one of the diffracted beams passes through the lens system. According to the Kinematical Theory developed by Hirsch et al . (1960), the dark field and bright field images should be complementary because of the two beam assumption. In practice this is not always found to be the case, but the discrepancies can usually be explained with the more complex Dynamical Theory (Howie and Whelan 1961). Diffraction by a Perfect Crystal Representing an electron wave at the position r by the function exp (2TTi k -r) and the scattered wave by

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26 -> -> exp (2iTi k'r) , the total amplitude of electron waves scattered from an assembly of unit cells is: A = ZF exp {2TTi K-r ) (2) n where F is the electron scattering factor, K = k k , n ^ ' o r = n,S + n„b + n^6, and the summation extends over all n 1 2 3 ' atom positions in the crystal. The total scattered amplitude is a maximum (i.e., the .exponential is unity) when K is a reciprocal lattice vector. K = ;2a* + kh* + Ic* = g ' (3) which simply says that the Bragg law is satisfied. By definition, the magnitude of a reciprocal lattice vector is equal to the reciprocal of the spacing between the planes described by that vector (see Figure 3a) . Hence I"*"! 1 /J 2 sin9 |gl = i/d = — X — (4) which is the Bragg equation. In general there is a distribution of scattered radiation such that the crystal need not be in the exact Bragg position to result in some diffracted intensity. If the deviation is described by the vector s we have A = IF exp [27ri(g + s) -r ] (5) n ^ ^ n n

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27 Where K = g + s as m Figure 3b. Recognizing that g-r is an integer and approximating the siojnmation by an integral, we have, for a given s A(s) = ^/^exp(2Tri S'r^)dT (6) For a crystal of infinite dimension in the x and y direction and thickness t A(s) = F/^/^exp(2Trisz)dz = £HlIlts ^^^ -t/2 "^^ From which l(s) cc £i^|£ (8) (lis) This intensity distribution is plotted in Figure 4. In other words this says that the thinness of the crystal causes sufficient relaxation of the Bragg condition which in turn allows a considerable amount of diffraction to occur even though the crystal is not quite in the proper orientation; the misorientation being described by the vector s. The above equation also indicates that the intensity of the transmitted and diffracted beams oscillates with depth as illustrated in Figure 5. At successive depths t , the diffracted intensity is zero and the transmitted

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Zb (a) lkol=^;. ib) Figure 3 . --Reflecting sphere construction for electron diffraction. (a) When the reciprocal lattice point is on the Ewald sphere, (b) displaced from the Ewald sphere by the vector ^.

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29 Intensity Figure 4 . --Diffracted intensity versus the interference error, t, according to the kinematical approximation .

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30 p<'-a'i', B Direct wave (i-l) Diffracted wave( Irxadsnt electron beam (intensity= i ) Figure 5 . --Schematic illustration of the origin of fringe contrast. (a) Section through the crystal showing kinematical intensity oscillations of direct and diffracted waves. AB represents a grain boundary or stacking fault, CD a wedge, and E a hole. (b) Section normal to beam showing dark fringes f (extinction contours) as they would appear in a bright field image. (After Thomas 1962. )

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31 intensity reaches a maximum. The depth periodicity of this intensity oscillation is l/|s| and reaches a maximum at |s| = 0. That is lim t = c o as Isl -> (9) where C is defined as the extinction distance. Note that this is not quite rigorous since c is a function of both the operating reflection and the material under observation, With this information we can explain tv/o contrast effects commonly observed in the electron microscope: extinction contours and bend contours. Practically all specimens used in transmission microscopy are slightly bent and non-uniform in thickness. Extinction contours will occur in wedge-shaped regions of the specimen as a result of the sinisoidal variation of the transmitted and diffracted beams discussed above. The contours will appear as continuous alternating bands following equithickness paths, as schematically illustrated in Figure 5. Local curvature of the foil will cause some regions (continuous surfaces) to be rotated into diffracting orientation giving rise to continuous dark bands called bend contours. The two can easily be distinguished since the latter is very sensitive to the angle between the incident

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32 beam and the foil normal while the former is dependent principally on the thickness of the crystal. Hence, a small amount of specimen tilt will cause a bend contour to move much more rapidly across the field of view. Diffraction by an Imperfect Crystal Any defect within a crystal which produces a distortioii of some set of lattice planes {Jikl] v/ill alter the diffraction conditions of that set of planes in the -> vicinity of the defect. If the atom at r is displaced ' n by the vector R, equation 6 becomes A(s) = |/^exp[27Ti K.(?^ + R)]dT (10) -> -> Neglecting the term s-R and again assuming the crystal to be finite only in the z-direction, we have F t /2 ->-> A(s) = irzS ' exp[2TTisz] exp[27Ti g-Rjdz (11) ^-t/2 where a = 2TTg*R is an additional phase factor due to the presence of the defect. The contrast at a defect is then determined by computing the difference between the intensity diffracted by the perfect and imperfect crystal, all other parameters being equal.

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33 Defect Interpretation Dis locations It is sufficient for the present purpose to consider the intuitive explanation for contrast at dislocations as originally presented by Amelinckx (1964) . Let us assume that we have an edge dislocation in a crystal. This could be depicted schematically as in Figure 6. Suppose that the set of planes outside the region E, E„ would satisfy the Bragg condition for diffraction if the foil were rotated slightly counterclockwise about the -normal to the paper. Note that the planes in the region E, E have undergone such a rotation due to the presence of the dislocation, while the same set of planes in E E„ have rotated in the opposite sense. As mentioned previously, the fact that the foil is much thinner in one dimension makes it possible to have some diffraction even though the crystal is not precisely oriented. Under these conditions (thin foil) a considerable intensity is diffracted away in the perfect part of the foil outside E, E„; the remaining part is transmitted. The figure reveals that the Bragg condition is better satisfied on the left than on the right of the dislocation. Consequently, more intensity will be diffracted av/ay from E, (to be intercepted by the above mentioned aperture) and

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34 F Figure 6 . --Diffraction of electrons by a foil containing an edge dislocation at E. In E2^ less intensity is diffracted away than in the perfect part while more is diffracted away in E]_. (After Amelinckx 1964.)

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35 less away from E^. Therefore, when the transmitted beam strikes the fluorescent screen, the intensity at E will be lower than background and greater than background at EThat is, a black line will be observed slightly to the E. side of the actual dislocation. It can be shown that this analysis holds equally v;ell for any arbitrary dislocation and Burgers vector. Determination of the Burgers Vector It follows from the intuitive picture presented above that contrast effects are to be expected only from those lattice planes which are deformed by the presence of the dislocation. To a first approximation it can be assumed that the planes parallel to the Burgers vector will not be affected and, therefore, diffraction from these planes will not exhibit contrast effects. In other words, if the foil is oriented so that this particular set of planes is in the reflecting condition, the dislocation will be invisible. Since the diffraction vector g is normal to the set of diffracting planes, we can state that the dislocation will be invisible if the relation g«S = is satisfied. Knowing two vectors g for which this equation holds "with respect to a single dislocation, it is possible to determine b for that dislocation. To avoid ambiguity

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36 in the analysis, it is necessary to employ the dark field technique. The procedure is to tilt the specimen until a particular defect disappears. Assuming the brightest spot on the diffraction pattern to be the cause of the observed -> contrast, it follows that the displacement vector R (in -> -> -> this case R = b) is parallel to the set of planes g. If the correct reflection has been chosen, the defect will also be invisible in the dark field image of this spot. Dislocation Loops Although a dislocation cannot terminate within a crystal (Frank 1951) , it may close on itself to form the so-called dislocation loop. The nature of the dislocation requires that a sign convention be set up to avoid confusion in analysis. The actual convention is a matter of personal preference, but must be consistent. Define the Burgers vector as the closure failure FS after traversing the circuit in a clockwise direction while looking in the positive direction of the dislocation line (Bilby et al . 1955). This circuit is also defined as a right hand screw. Using this FS/RH convention, a 90° counterclockwise rotation of the Burgers vector points in the direction of the extra half plane for the case of a pure edge dislocation. See Figure 7a. It follows that the Burgers vector of a right hand screw

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37 EUECTROM BEAM i M F S Figure 7. --Burgers vector convention foj: dislocation loops. (a) FS/RH convention for defining the Burgers vector; (b) applied to a vacancy loop; (c) applied to an interstitial loop.

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38 dislocation will point along the negative direction of the dislocation line while a left hand screw will have a Burgers vector in the positive sense of the line. Now define the positive sense of going around the dislocation loop as clockwise when viewed from above; i.e., in the direction of the electron beam. Thus, a vacancy loop v/ill have a component making an acute angle with the upward drawn normal to the plane containing the loop. That is, if we use a "left hand rule" to describe a vacancy loop and a "right hand rule" for the interstitial loop, the fingers of the hand point in the positive direction round the loop and the thumb defines the sense of the Burgers vector. This is schematically illustrated in Figure 7b and c. In the light of our knowledge concerning the position of the dislocation line relative to its image, consider three intermediate positions of a vacancy loop as it is rotated counterclockwise through the Bragg condition about an axis normal to g and b. In Figure 8, the dotted line is the actual position of the loop while the solid line represents the image of the loop. Choosing s as positive when the reciprocal lattice point associated with g lies inside the Ewald sphere (angle of incidence on the reflecting planes is greater than the Bragg angle) ,

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39 ELECTRON BEAM mil <:0 Figure 8. — Relative position of the dislocation loop as the set of planes, §, is rotated through the Bragg orientation.

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40 the image of the loop will lie inside or outside the actual position of the loop depending on whether the sign of (g*b)s is positive or negative respectively. Kikuchi Lines The above discussion leads to the question of how to determine the sign of s. All of the previous development assumes the electrons to be elastically scattered by the atoms, but it is known that there will be some inelastic scattering resulting in an incoherent beam of electrons. Their origin is not completely understood but it is postulated that the divergent beam can undergo Bragg diffraction and produce a pair of nearly straight lines on the diffraction pattern, one dark and one light. The two will be separated by a distance commensurate with the magnitude of the associated vector g. Figure 9 is a diagram showing the relation between the sign of s and the positions of the dark and light Kikuchi lines. Note that the light line is always furthest from the main beam, Staoking Faults The discussion of loops also leads us to consider the contrast arising from the presence of stacking faults. The formation of the stacking fault on the interior of a Frank dislocation loop of Burgers vector a/3 was

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41 Lit S>0 s=o S<0 o D } t D L Figure 9. — Relative positions of the diffraction spot and the Kikuchi line due to the same reflection. The open circle represents the main beam and the solid circle is a particular diffracted beam.

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42 discussed in Chapter I. We are concerned here with the interpretation of such a defect with transmission electron microscopy. Contrast arises at a stacking fault because such a defect displaces the reflecting planes with respect to each other across the plane of the fault. Using the appropriate value of R in equation 11, we find that the observed contrast is a function of the position of the plane in the foil. In fact, the observed intensity is a periodic function since the diffracted intensity oscillates with depth into the crystal. For the general case of a fault inclined to the electron beam, the depth periodicity will become visible as alternating contrast fringes parallel to the line of intersection (or projected line of intersection) of the fault plane and the surface of the foil. This fringe contrast is illustrated in Figure 5. Clearly, if the extir^ction distance t is known, the dimension of the fault can be obtained (to within the error between t and r) from the product nt , where n o ^ o' is the number of fringes. The fringe contrast also provides valuable information for determining the plane of the fault. This information is usually sufficient to specify the nature of the fault but a cross check is possible with a g'b criterion. The stacking fault displacement

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43 vector R is defined by the shear at the fault, or the Burgers vector in the case of the Frank loop. Referring again to equation 11 we find that there is no contribution to the intensity for the case of ot = 2r,n, i.e., when g'R = n, In words this means that the fault will be invisible when the vector R moves the reflecting planes normal to themselves by an integral number of spacings betv;een the planes or when the displacement is parallel to the reflecting planes as in Figure 10. One other criterion for the invisibility of stacking fault fringes involves the dimensions of the fault plane. If the fault does not extend over a depth in the crystal of more than an extinction distance for the operating reflection, no fringe contrast will be observed. The fault will, however, appear either dark or light depending on its position in the foil. The dislocation line bounding a faulted loop presents a problem quite different than that encountered in the unfaulted or prismatic loop mentioned above, as it is a partial dislocation. Under these circumstances, the g*b criterion no longer applies since b is not a lattice vector. Therefore, the scalar is not necessarily an integer but, rather, it is usually found to be a multiple of 1/3. Gevers (1963) has shown that the variation in contrast will not be significant unless

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44 E o CD (tf

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45 |g«b| > 2/3. However, for s > and g-S < the image of the dislocation line will be superimposed on the fault contrast and proably not be visible. Silcock and Tunstall (1964) showed that the dislocation would be in good con-> -> trast for g*b = + 2/3 but would be in poor contrast for -*• -> g-b = 2/3, provided the deviation from the Bragg orientation is rather large, i.e., t s > 0.6. Loretto et at. (1966) used this criterion to show that, contrary to common belief, 95% of the loops in quenched aluminum are faulted. This is significant in that the loops were too small to exhibit stacking fault contrast. Voids Another defect commonly observed in quenched materials is the void or large vacancy cluster. van Landuyt et. at. (1965) have shown that the contrast at a void is adequately represented by a phase angle I a = 27TSf, where f is the thickness of the void. Further, their theory predicts odd contrast behavior such as: (1) contrast variation as a function of depth, void size, the parameter s, total foil thickness, and (2) a possible lack of contrast reversal from bright field to dark field. The interpretation is relatively simple for the case of a thick foil (> 5 t ) with s = 0, since o the contrast will be mainly due to normal absorption.

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46 However, the voids will have to be larger than 1/2 t before they produce a clear positive contrast (i.e., lighter than background) . Unfortunately, it is not always possible to see defects m the region of s = and one must usually work in regions of s > (anomalous transmission region) . An attempt has been made to generalize the results of van Landuyt as they apply to the case of secondary defects in platinum foils: (1) the foils are. considered as being thick, (2) 1/4 t < f < t , (3) the absorption y is relatively high, (4) the defects will be confined to the center of the foil. As can be seen from Tables 3 and 4 , the contrast in both bright and dark fields is quite unpredictable. Therefore, some knowledge of defect size and the diffraction conditions is required in order to determine whether contrast should be positive or negative. Using both bright and dark field images, the above mentioned tables, and large tilt angles, one should be able to distinguish voids from loops. In fact it is possible to specify the geometry of the defect as shown in Chapter V.

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47 TABLE 3 EXPECTED CONTRAST FROM VOIDS AS A FUNCTION OF DIFFRACTION CONDITIONS Void Dimension (f) Bragg Error Bright Field (I i^) Dark Field (I i„) 1.8 t 1.0 t 0.2 0.5 1.0 0.2 0.5 1.0 N > P P > N N > P P = N N P P N > P P = N P = N N > P P Assume the absorption coefficient, y, to be Stt/t , where Tq is the absorption length and is usually taken as 10 t^. ' o The parameter x is a measure of the misorientation from the Bragg angle. N indicates that the void will appear darker than background and P indicates that the void will appear lighter than background.

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48 TABLE 4 EXPECTED CONTRAST FROM VOIDS AS A FUNCTION OF VOID SIZE Void Dimension (f)

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CHAPTER III FIELD ION MICROSCOPY Basic Theory As discussed in the Introduction, the field ion microscope has resolving power and magnification capabilities enabling the direct observation of the atomic lattice. Since the concept of the field ion microscope is relatively new (Miiller 1951) , there are almost as many designs as there are microscopes. However, they all have the same basic components (Figure 11) . The specimen is a short fine wire polished to produce a sharp hemispherical o tip of 100 to 1000 A radius which is connected to metal electrodes immersed in a cryogenic fluid such as liquid N2 , Ne, H^ or He. Facing the tip, a few centimeters away, is a phosphor screen which emits photons when bombarded by ionized atoms and is an integral part of the vacuum chamber enclosing the specimen. The system -7 -9 is evacuated to 10 to 10 Torr, backfilled with high purity (99.9995%) helium gas to a pressure of 1 to lOy , and a positive potential of up to 30 kV is impressed on the tip relative to the screen. The strength of the resulting field at the surface depends on both the 49 -

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50 H.T. loads fluorescent screen image gas iff spectmen Figure 11 . --Schematic drawing of a field ion microscope .

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51 applied voltage and the radius of the specimen (Miiller 1960, Gomer 1961), but is in the neighborhood of 10^ to 10 volts/cm or about 5 volts/A near the tip. This is equivalent to the removal of about one-third of an electron from each atom, and means that the "free electron cloud" is drawn back into the metal, exposing the positive ion cores on the surface. A neutral atom of the imaging gas coming under the influence of the field around the tip becomes slightly polarized and acts as an oriented dipole. That is, the more weakly bound electrons are pulled toward one side of the atom causing it to act like a small magnet which then accelerates toward the specimen. When the polarized gas atom is a few tens of Angstroms away from the tip, the potential well of the atom is distorted by the presence at the potential field at the tip. Therefore, an electron in the atpm no longer sees the symmetric potential well of the nucleus as in free space but, rather, as an asymmetric barrier that reaches a maximum and has a finite width on the side nearest the specimen. According to wave mechanics, ionization is possible by tunneling of the electron through the potential barrier into the metal tip, provided there is an available energy level. This process is schematically illustrated in Figure 12. The resulting ion is then repelled by the

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52 Qa c

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53 positive tip and travels along a trajectory (approximately elliptical) defined by the electrostatic lines of force to the screen. The field ion image is, therefore, a sensitive contour plot of the surface field distribution. Bright spots, corresponding to regions of high electric field (i.e., surface atom positions), give rise to a very regular spot pattern which can be interpreted directly in terms of the atomic lattice (Figure 13) . The current-voltage characteristic of the helium field ion microscope has the form shov/n in Figure 14 (Southon and Brandon 1963) . A stable field ion image is formed in the region BC and the terminus of the curve at C corresponds to field evaporation of the specimen. At this point, the field at the surface of the specimen is sufficiently large to ionize and remove the loosely bound metal atoms on the surface. All too frequently, field evaporation occurs at' a field lower than that required to obtain stable images. Thus, while field evaporation limits the materials capable of being studied in the field ion microscope, it is also the very process which makes the instrument unique by permitting three dimensional micro-dissection of the specimen. By controlled field evaporation of individual atoms from the surface of the specimen, the structure of the bulk can be deduced in atomic detail.

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54 Polarized gas atOj«i Cones of scl ions \ Figure 13 . --Detailed schematic of the ionization process illustrating the relationship between the atom positions and the cones of emitted ions.

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55 Tip Radius = 570 A He Gas p = 6.10'^Torr Tip Temperature = 78*K 10 n 12 13 1< 15 16 kV Voltage Figure 14. — Current-voltage characteristic of the helium field ion microscope. (After Southon and Brandon 1963.)

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56 Image Interpretation Indexing Normally, the first step to be taken when attempting to interpret a field ion image is to properly index the planes (or poles) on the micrograph. Although Miiller (1960) has used an orthographic projection to index a micrograph, Brenner (1962) considers the stereographic projection to be a better approximation. More recently Brandon (1964) has shown experimentally that the true projection is somewhere between these two. It is possible to obtain a simple equation for accurately calculating the angles between poles on a field ion image (Newman et al. 1967) with the result that: d = MRG (12) where d is a linear distance measured on the micrograph, M is the combined magnification of the optics, R is the radius of the projection sphere, and 6 is the interplanar angle. This equation is derived and discussed in detail in Appendix I. Computer Model The computer model originally developed by Moore (1962) has been extended by Sanwald et al . (1966) to enable the interpretation of defects in the field ion image

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57 The image is simulated by plotting the positions of those atoms whose centers lie inside a thin spherical shell passing through a point lattice. The resulting array looks very similar in appearance to an actual field ion image. It is then a simple matter to introduce the strain field of a defect into the point lattice to determine its effect on the image. By adjusting the radius and thickness of the shell, and by varying the parameters associated with a particular defect (e.g., Burgers vector and habit plane for a loop) , it is possible to obtain quite good agreement with experimental micrographs. Defect Analysis It has been proposed (Pashley 1965, Ranganathan 1966a) that a dislocation will appear as a spiral configuration in a field ion image. Furthermore, the exact nature of this configuration will be given by the scalar -> -> -* product g«b where g is a vector normal to the set of planes being disturbed by the emergence of the dislocation and b is the Burgers vector of that dislocation. It IS worthwhile pointing out that g and b are geometrical in nature so the scalar product is simply a measure of the displacement component in the direction normal to the set of planes g, (Figure 15). If one is consistent in using the correct plane notation (i.e., {hkl) unmixed

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58 n220 5^[ioi]= b '220 f [110] b = a^ [liJJ PLANE OF CUT Cn) PERPENDICULAR TO (223) Figure 15. — Diagram of (111) plane showing how single and double spirals can be produced on (220) plane with Burgers vectors of a/2 [101] and a/2 [110] , respectively .

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59 for FCC, etc.)/ the dot product is an integer which determines the number of "leaves" in the spiral configuration, regardless of the dislocation character (i.e., edge or screv/) . Any dislocation, for example, -> * with D = 1/2 [110] intersecting the surface in the vicinity of a (204) pole will produce a single spiral as illustrated in Figure 16. The sense of the Burgers vector will determine the direction of rotation of the spiral for a given pole. It is well known that one of the principle secondary defects formed after annealing a quenched specim.en is the dislocation loop. It was mentioned in the section on electron microscopy that the dislocation loop is described by a single Burgers vector. It is implicit in this definition that the reference coordinate system move around the perimeter of the closed dislocation line to maintain consistency. However, it is impossible to distinguish it from a dislocation dipole (i.e., two individual dislocations with opposite Burgers vector) in an FIM image without a controlled field evaporation sequence. Provided there is no appreciable interaction between the strain fields, the two points of * Defining both vectors in terms of lattice unit vectors i, j, k , the a-f actor or lattice parameter term is not included in the Burgers vector notation.

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60 (111) PROJECTiON IE D^SLOCATIOr^ .V--....•'•••^ • •-.s"* ^ ->^ • •...•..• ' '^ Figure 16. — Pure edge dislocation causing a single spiral on (204) plane edges.

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61 emergence of the dislocations may be considered separately, with the result that the theory predicts spirals in opposite directions. Figure 17 illustrates possible configurations . Single dislocations, dipoles, or total dislocation loops can be analyzed by inspection using the g-b criterion; at least the number possibilities can be reduced to a point where it is only necessary to determine the plane on which the dislocation lies in order to specify the Burgers vector. If the dislocation emerges at a point where two different sets of rings are disturbed (Figure 18), the spiral count will usually give a unique Burgers vector. Loops bounded by partial dislocations present a different problem since g-b is not necessarily an integer. Partials have been found by computer analysis to cause various types of disturbances depending upon the location of the defect. For instance, high index planes appear to be split or sheared by the presence of a Frank loop, while a pinching type distortion occurs in low index regions of the field ion image. Thus, the g'b criterion does not seem to yield as much information for the case of partials. Hopefully, any obvious defect which cannot be interpreted in terms of total dislocations can be analyzed in terms of partial dislocations. For the case of a Frank loop, the bounding dislocation is a partial

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62 CD

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63 Dislocation Visible on Two Sets of plane Edges ^331) Rings .-Dislocation: a, 2 b=4^ [no] <"0) Rings Figure 18. --Two sets of plane edges visible in the region of the defect. Note that g-b criterion is satisfied for each set of planes.

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64 " and q'h will normally predict a fraction of a spiral. Not only is this difficult to detect but it is also difficult to understand geometrically. Random choices of Frank loops v;hich have been plotted by computer seem to indicate that streaks (Ranganathan 2t at. 1965) may form parallel to the fault plane. There is also evidence of ring distortion v/hich is consistent with the concept of adding or removing a lattice plane to produce the fault. Analysis of voids or large vacancy clusters is straightforward in that one must only determine size and shape. Polyhedral voids should be recognizable as such and should be amenable to geometric anaZysis employing the pseudo-stereographic projection mentioned above. More complex defects, such as stacking fault tetrahedra and multilayer defects CEdington and West 1966), have not been considered to date, but should not present any particular difficulties since they are only dislocation arrays. It will probably be necessary to use computer analysis to determine their nature in the field ion image. Effect of Stress The applied electric field generates a hydrostatic tension, a^, normal to the surface of the specimen, given by Muller (1958a) as

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65 °H = fVstt = 44.3 F^ (13) where F is in volts/A and o^ is in kg/mm . A spherical specimen of an isotropic metal will experience a uniform dilitation and the shear stresses are therefore zero. For a hemispherical cap attached to a cylindrical shank, the tensile stress in the shank will be approximately a , so that the maximum shear stress, x, is given by: f "" Ojj/2 C14) These shear stresses are large enough to cause plastic deformation and may well be expected to have an effect on glissile dislocation configurations in the specimen. Unfortunately, it is not yet known whether there will be an increase or decrease in the probability of observing such a defect. The effect on sessile dislocations is equally uncertain but one would expect the hydrostatic component to aid motion by climb. A cause for dislocation motion in the absence of a field is the force arising from the mirror dislocation outside the crystal (Cottrell 1953); an effect that can be quite important because of the small size of the crystal tip. Using equations developed by Bullough (1967) , Hren (1967) has calculated this stress by treating the specimen as a stack of cylinders of decreasing radius.

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66 The results indicate the equilibrium position for a screw dislocation to be along the specimen axis. The image forces will increase as the dislocation approaches the surface of the cylinder, but the increasing size of the successive cylinders makes it difficult to determine whether the entire dislocation will slip out of the crystal or whether it will reach a stable curved configuration, being "effectively pinned" at the wire axis somewhere up the shank (Figure 19) . The superposition of the field stress can only confuse the issue further. In short, it is not known whether or not the sampling probability will be improved by the stresses on the tip. Pimbley et al . (1966) have reported that the vacancy concentration in the {012} region of annealed platinum tips -2 -4 to be of the order of 10 , well above the 6 x 10 value Miiller (1959) found in quenched platinum. The present author has observed d large number of single vacancies in platinum wire quenched from near the melting point and annealed at 500°C for 24 hours. Previous studies (Jackson 1965a) indicate that there should not be any appreciable quantity of isolated point defects after this treatment. It seems clear that these vacancies are stress induced artifacts as suggested by Pimbley et al .

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67 Figure 19. — Possible stable configuration for a dislocation in a field ion specimen.

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68 Thus, there is little doubt that stress effects can be important in field ion microscopy, and even though the stress distribution is not known, the possible results of such stresses must not be overlooked.

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CHAPTER IV EXPERII4ENTAL EQUIPMENT AND PROCEDURE The Field Ion Microscope The basic design and operational characteristics of the field ion microscope v;ere discussed in Chapter III, In this section further discussion will be limited to the instrument used in this investigation; a stainless steel, liquid hydrogen cooled microscope designed to operate in conjunction with an Air Products and Chemicals Inc. CryoTip refrigerator. Design considerations for the construction of the microscope are discussed in Appendix II. A schematic drawing of the microscope is presented in Figure 20. As illustrated, the FIM body consists of an outer shell flanged at the bottom to mate with a 4" diameter viewing port and at the top tb receive the flanged cryostat tube. The cryostat itself, is a Pyrex tube with two pairs of 0.050" tungsten wire leads at the bottom, and is graded to Kovar only 1-1/2" from the top flange to avoid any difficulty from low temperature phase transformations in the Kovar. Although the cryostat tubulation is designed for use with the Cryo-Tip, it may also be used by filling it with a cryogenic fluid. Suspended between the outer jacket and the glass cryostat is a stainless steel liquid 69 -

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70 Cryotip _ ( Liquid H2 Generator) To Pump ( p=— Im oging Gas > K Radiation Shield Spednnen t=^=z=z inzE Fiber Optic Window Liquid N2 Cryost-at -Liquid H2 vVvVsl 'f',';'i'v' • ' • -AVvVsl High Voltage Leadthrouqh ^v-, Figure 20. — Schematic drawing of the field ion microscope body. The microscope is constructed almost entirely of stainless steel, is designed for use at liquid hydrogen temperature, and incorporates a fiber optic viewing port.

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71 nitrogen dewar which performs the dual role of radiation shield and cryopumping surface. To improve the shielding characteristics, the bottom of the dewar is made of copper, and an aluminum cylinder in thermal contact with the copper almost completely surrounds the specimen. Three 1-1/2" diameter ports extend radially from the specimen chamber (at specimen level) and are flanged to accept an ion gauge, a high voltage lead through, and a flexible bellows for making a connection to the vacuum system. Normal photographic technique involves the use of high speed 35 nm. film in specially fabricated camera bodies fitted with f/1 (or faster) lenses. However, this microscope has been fitted with a 4" diameter fiber optic faceplate permitting the use of direct contact photography,thereby eliminating the need for intermediate optics. This technique, its advantages and disadvantages are discussed extensively in the literature (Hren and Newman 1967) . The heart of the vacuum system (Figure 21) is a liquid nitrogen baffled 2" oil diffusion pump,backed by — 8 a 2 cfm fore pump. The system is capable of 10 mm Hg (without bakeout) within 1-1/2 hours of specimen change. Mild bakeout (300-400°C) results in pressures on the low -9 end of the 10 scale of the ion gauge.

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72 o •O r-l 0) 'K «»-t o 0) -p ca >t CO e O as > 0) o C-H (« M -O O rf +J e (U si o CO I CD . 0) CN O o M O Di O

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73 The imaging gas system is presently set up to supply helium, neon, or a preset mixture of the two. The gas is bled in with the variable leak valve number 1 and then passes through the liquid nitrogen dewar into the specimen chamber. However, additional gases can be readily admitted to the system by means of the variable leak valve number 2 . This is sometimes desirable for improving image quality in nonrefractory metals CMiiller et al . 1965) or if one desires to study the effect of adsorbed gaseous impurities (Fortes and Ralph 1966) . The Electron Microscope The electron microscope employed was a Philips EM 200 fitted with the new Goniometer Stage which permits full 360° rotation and ± 45° tilt of the specimen. In addition, a magnetic beam tilt device enables the operator to obtain high resolution dark field micrographs. The operating principle of the device is schematically illustrated in Figure 22 and the overall picture of the technique is illustrated in Figure 23. The normal operation of the microscope is as shown in (a) ; the incident beam makes an angle 9, the Bragg angle, with a set of diffracting planes in the crystal. The transmitted and diffracted beams intersect the Ewald sphere at reciprocal lattice points separated by the familiar

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74 Figure 22 .--Schematic illustration of the principle of operation of the magnetic beam tilt device.

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75 '^ lo Beam Tilt Device / \ EI EI Diffracfing Ranes in Crystal Ewald Sphere Aperture Axis of Microscope Column ~ Bright Field (a) Dark Field (b) Figure 23. — Schematic drawing illustrating the principle of operation of the transmission electron microscope. (a) Operating under bright field conditions. (b) Operating under dark field conditions. (After Bell ei at. 1965.)

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76 vector g. As mentioned earlier, the reflecting sphere (Ewald sphere) is almost planar for electron waves and coincides with the back focal plane of the objective lens of the microscope. Bright field images are obtained byinserting an aperture to eliminate all but the transmitted beam. Dark field images can be obtained by moving the aperture to allow passage of a selected diffracted beam but the spherical aberration of the magnetic lenses for any noncentral beam causes a great deal of astigmatism. As pointed out by Bell et at. (1965), to obtain a high quality dark field image from a strongly diffracting beam, the incident beam is tilted in the direction away from the operating reflection through an angle twice that of the Bragg angle. (For electrons, this is of the order of a few degrees.) Thus, the operating reflection in dark field is -g. That is, the dark field image is actually due to reflection off the negative side of the planes which were favorably oriented for Bragg diffraction in bright field (Figure 23b). Without the magnetic beam tilt facility one must accomplish this tilt by reorienting the electron gun, an inconvenient operation at best, or be satisfied with an astigmatic image. A further advantage of the Philips device is that one can go from bright field to dark field with the flick of a switch. Because of the symmetry commonly found in electron diffraction patterns.

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77 it is often possible to adjust the unit to permit a simple switching between bright field and either two or four consecutive dark field images. The magnification and image rotation calibration data is presented in Appendix III. Specimen Preparation The platinum purchased from Englehard Industries was of 99.9% purity. Lengths of wire (6" x 0,005") and foil (6" X 1/4" X 0.0015") were heated electrically in air and quenched into brine at 0°C. The quenching temperature was estimated from two independent methods to be within 100°C of the melting point: CD the voltage was increased until melting occurred in a dummy specimen and the remaining specimens were heated at approximately one volt less potential. (2) An optical pyrometer reading of 1680°C ± 50°C was obtained after correcting for emissivity and non-blackbody conditions. Short lengths were then cut from the original 6" length to be annealed for various times between 250°C and 600°C. No extensive table will be presented describing individual heat treatments, but instead, specimen history will be stated in the text as it applies to the overall discussion. The author feels that this is desirable in that the results are presented as general trends rather than as being due

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78 to specific and/or involved quenching and annealing treatments . Early in the investigation, field ion specimens were prepared from the wire by electropolishing in an aqueous potassium cyanide solution (Mviller 1960) . Sometime later, Dr. R. W. Balluffi informed us that his laboratory at Cornell had been successful in polishing platinum foils with an aqueous solution of calcium chloride maintained at -30°C (Ahlers and Balluffi 1967). This electrolyte was also found to work extremely well for preparing field ion specimens employing a platinum counter-electrode and a variable 0-15 volt A.C. power supply (Newman et al . 1967). Electron transparent foils were initially prepared using the well-known window method, along with the above mentioned solution. Although satisfactory, an improved technique resulted ffom the persistence of Mr. E. J. Jenkins, the electron microscope technician. The method involves jet polishing a platinum disc that has been precut to fit the microscope specimen holder. The disc is placed on a platinum mesh screen and the cold CaCl~ solution is allowed to flow in a small stream over the foil. A potential of 80-100 volts A.C. is impressed between the mesh and a platinum electrode immersed in the electrolyte

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79 bath above the specimen. The apparatus is illustrated in Figure 24. This stage of the polishing procedure is continued until the center of the disc is noticeably thinner (i.e., "dimpled"). The final stage is carried out at 8-10 volts A.C. with the specimen immersed in the electrolyte bath until a hole appears. Large areas suitable for transmission microscopy are obtained in this manner. A final cleaning is accomplished by applying 20 volts D.C. for 30 seconds followed by a rinse in distilled water and then ethyl alcohol. The low temperature of the polishing solution insures that no annealing takes place during the preparation of the foil and the elimination of the need for stop-off lacquer reduces the occurrence of dirty foils.

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80 Pt Wire AC Supply Electrolyte Stopcock pecimen O^Pt Gauze ^Receiving Beaker Figure 24 . --Schematic drawing of apparatus employed for preparing electron transparent foils of platinum.

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CHAPTER V RESULTS AND DISCUSSION Ruedl et al . (1962) found voids in heavily irradiated platinum foils upon pulse heating in the electron microscope, v/hereas irradiation followed by a mild anneal resulted in the formation of vacancy loops. Therefore, one might expect to find loops or voids depending upon the vacancy supersaturation. That is, it can be convincingly argued that an instantaneously high concentration of mobile vacancies would favor the formation of voids, while a lower vacancy concentration would favor prismatic loops. This is consistent with the present experimental observations in that either voids or loops are formed, but the two rarely occur in the same region. Furthermore, dislocations are almost nonexistent in areas of high void concentrations while large prismatic loops are generally found in the midst of heavily jogged dislocations. This is quite reasonable in light of the evidence for dislocations being efficient vacancy sinks. Thus, in some regions, small clusters and dislocations are competing for vacancies while in others, the clusters accumulate essentially all of the migrating point defects. 81

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82 Void Analysis A high concentration of large voids Ccavities) was obtained by repeated pulse quenching in air followed by a one hour anneal at 500°C. Some of the cavities were more o than 1000 A in diameter, large enough to break through one or both surfaces of the foil, v/hile the majority were of o the order of 300 A. This is in contrast to foils subjected to a single quench followed by a 24-hour anneal at 400°C. Under these circumstances the size distribution is more o uniform and centered about a smaller diameter Ci.e., 150 A). Figure 25 is an electron micrograph of the pulse quenched and annealed foil after partial melting in the microscope. (This was accomplished by removing both condenser apertures while the specimen was under observation.) It is apparent that some voids are still present in areas within a micron of the melted edges, and it is thus reasonable to state that the void, once formed, is an extremely stable defect. This stability could well explain the presence of the large cavities in the pulse quenched specimen if one argues that the nuclei are formed during the first quench (a reasonable assumption since the air quench is relatively slow) and grow by vacancy absorption during each successive quencJi. This defect configuration is most likely the one contributing to the irreversible resistivity increment measured by Cizek (1967) .

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83 Figure 25 . --Polyhedral voids in pulse quenched platinum foil after partial melting in the electron microscope. The average void size is approximately 300 A.

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84 Kiritani et al . (1964) have suggested that the voids in aluminum are regular octahedra with {111} faces, and a similar conclusion was drawn for the voids in gold (Yoshida et al . 1965). Clarebrough et al . (1967) have just published a rather complete study of voids in quenched copper, silver, and gold. (The author would like to acknowledge receipt of their manuscript prior to publication.) Although Clarebrough et al . found a few voids that closely approximated regular octahedra, the majority are better described as octahedra truncated by {111} and/or {100} and an occasional {110}. However, these voids were much larger and the authors concede that they may have been regular at smaller sizes. To remain as such after growth, the vacancy flux would have to be uniformly distributed over the surface of the defect. The voids in platinum are definitely polyhedral in shape, but the facet configuration seems to be somewhat variable. By and large the resolvable voids can be described as {100} truncated octahedra (Figure 26) which, because of the associated strain fields, may appear spherical. On the other hand, there are instances where it is necessary to use more complex truncations involving only single sets of {100} as in (b) or {111} planes as in (d) . Clarebrough et al. have suggested the truncations pictured in Figure 27.

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85 h

PAGE 99

86 1

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87 Unfortunately, the analysis is not so straightforward for platinum since the voids are as much as an order of magnitude smaller than those observed in copper and aluminum, and the strain fields, although small, generally tend to obscure the boundaries of the defect. Figure 28 is a singular case where a clear fringe pattern was observed. It is postulated that the fringes (arrowed) occur as a consequence of the wedge-shaped nature of the defect. Only with low order reflections would the extinction distance be short enough to give rise to contours. Figure 29 is the same area with the defects exhibiting strain contrast. In agreement with the Ashby and Brown theory (1963a) , the line of no contrast is normal to the operating g-vector. Strain must also be responsible for the black patch contrast sometimes observed at various points within the confines of the void. Additional experimental evidence for the existence of a strain field around a void in platinum is presented in Figure 30. The dislocation line is apparently pinned at the void, and where the strain fields overlap, the perimeter of the void is invisible. Note that this void can also be seen in Figure 28 at the point X. Under these diffraction conditions the entire void is visible. It can also be seen that the edges of the voids in these micrographs are parallel to projected <110> directions.

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88 '2 It I 8=002 > Figure 28. --Voids in platinum foil exhibiting fringe contrast. The specimen was quenched from near the melting point and annealed at 400°C for 24 hrs.

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89 r \ 9 -in t N = [110] Figure 29. --Voids in the same platinum foil imaging by strain contrast. Note that the small voids which appeared as black spots in the previous figure can be recognized as hexagonal in cross section.

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90 9 = 001 Figure 30 . --Electron micrograph of a dislocation pinned at a void. The overlapping strain fields apparently cancel one another.

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91 Initially this was misleading, for it was presumed that the rhomboidal defects were prismatic loops and that the hexagonal ones were Frank loops. However, they do not exhibit the behavior expected of dislocation loops. Making full use of the new Goniometer Stage obtained during the latter part of this investigation, tilting of the specimen through large angles revealed the three dimensional nature of the defects. Figures 31 and 32 illustrate quite well the negligible change in shape of the voids after 35° of tilt. Note, however, the marked difference in contrast between the two photographs. This is the type of behavior van Landuyt et at. predict for void contrast. The variables here for any one void are foil thickness, extinction distance, operating reflection, and excitation error s. Although direct experimental evidence is lacking, one might speculate as to the reason for the string of voids at the top of the micrograph. The only logical explanation that comes to mind is that these particular cavities lie along a low angle boundary. Since the boundary would be a preferential sink for vacancies, this model would explain the relatively large size of these voids. The contrast behavior in bright and dark fields (Figures 33 and 3.4) indicates that these voids lie on the surface rather than on a line. That is, contrast reversal of some

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92 Figure 31. --Bright field electron micrograph of polyhedral voids in a [110] oriented foil. The specimen was annealed for 24 hours at 400°C. Void density is 7 x IQ^^/cm^ , with an average diameter of 150 A.

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93 ri fp.' % \ g=220 Sfi N=[111] Figure 32. — Bright field micrograph of the same region after 35° tilt. New orientation is [111] Although there is some change in contrast, the voids have not changed significantly in shape.

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94 Figure 33. --Bright field micrograph of the same region after tilting to [331] . Many of the voids are seen only in residual contrast.

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95 Figure 34. --Dark field micrograph of the same area illustrating the contrast behavior of the voids along the low angle boundary.

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96 but not all of the defects means that they lie at different levels in the foil. Note also the increased contrast in the dark field image. Other features of interest in these four micrographs are worth pointing out. Many of the voids, particularly in Figure 31, exhibit dark patches within the confines of the void. There are several instances of interaction between voids and dislocations, and there appears to be enhanced contrast at the point of contact. An extremely interesting feature which is quite difficult to explain is the contrast arising from the dislocationvoid complexes along the low angle boundary. Observations to date indicate that voids occur in all quenched specimens annealed between 250° and 600°C, with the highest density at 400°C after 24 hours. However, annealing at 500°C for 70-100 hours produces isolated colonies (one or two per specimen) containing a high density of large spherical voids (^ 300 A) as shown in Figure 35. Almost without exception, the lower the concentration of voids, the more regular they appear (i.e., tending toward a simple octahedron). Figure 36 is such a void viewed along two crystallographic directions, [100] .and [112] , The appearance of the void is in quite good agreement with what Kiritani et al . (1964) predict for an octahedral void in this orientation. Although not

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97 >!^ 2^ Figure 35 . --Isolated colony of voids in a foil that was annealed for 100 hours at 500°C. Average void diameter is 300 A.

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98 m o -P O Q) S-C Tl O Du, (0 trv • O r-l .-I CN r-{ iH (U rH -P -cn >< w o o o 4J -P o ci k O-rH g 0) 0) :s M •rH o • >^ o r-\ O (C .H M" -a 0) W (0 -P o o c < I o •H +J o Q) U •H 0) 0) 3 •H CO

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99 apparent in the micrograph, a small square was visible, under direct observation, at the "bottom" of the void in (a). This can be attributed to a {100} truncation of a regular octahedron as illustrated schematically in Figure 26. In general, the isolated, regular shaped voids are of the order of 300 A, While on the subject of void size, it would be appropriate to discuss the density of defects and the concentration of vacancies required to obtain this density. Estimating the foil thickness to be 1000 A from the projected length of dislocation line, the void density is calculated as 7 x lO"*"^ voids/cm^. This figure does not take into account either the large cavities which extend through the foil or the ones that have formed along the low angle boundary. Taking an average void radius to be o 80 A, the volume fraction of void in Figure 31 is found to be 1.5 X 10 . Assuming the volume occupied by a vacancy cluster to be equal to the volume occupied by an atom cluster, we can estimate the retained (quenched-in) vacancy concentration at 1.5 x lo""^ which is in good agreement with the value given in Table 1. If the vacancy volume is assumed to be 0.25 of the atomic volume (Mukherjee 1966) , the initial vacancy concentration would be 6 X 10 . Since there will be some relaxation, but not as much as at a single vacancy, a realistic value

PAGE 113

100 is probably somewhere between these two. A value of 2.5 X 10 will be assumed. Each void requires approxi5 mately 2 x lo vacancies and therefore drains the matrix of all vacancies within a 500 A radius. This calculation assumes that all voids are visible which, according to theory, is not necessarily true, nor does it include the very large voids. However, the number which are completely invisible will be quite small, not more than a few percent. Studies involving various quenching atmospheres reveal a strong influence on void size and density (Clarebrough et al . 1967, Siedman 1967). No attempt was made to study the effect of quenching atmosphere in the present work, but it is entirely feasible that oxygen content could be a factor since the wires were heated in air. It is doubtful, however, that there would be enough gas present to account for the void concentration in Figure 31. Ruedl et al . (1962) explained the presence of voids in a-irradiated platinum as being due to accumulated helium gas which was certainly not present in this investigation. Furthermore, the void density in this specimen has been calculated at lO"*""^ to 10''"^/cm"^, several orders of magnitude higher than that observed by Clarebrough et al . There is a possible explanation for the rather high calculated vacancy concentration, which again brings

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101 us to the problem of strain contrast. If the void strains the surrounding lattice and if the void images by some form of strain contrast, the siiie of the defect will be overestimated, since the strain must occur outside the actual cavity. If instead, the cavity is defined by the inner radius of the black circles, the vacancy concentration could be lower by as much as a factor of four. This estimate is in much better agreement v/ith that in Table 1, but still does not account for the vacancies that are tied up in the larger voids. The strain images of voids in platinum are strikingly similar to micrographs of internally oxidized Cu-£i slowly cooled to room temperature (Ashby and Brown 19 63b) ; from this the authors calculate the strain to be approximately 10 . If it is then assumed that the strain in the platinum matrix due to the presence of the void is the same order of magnitude, an equation can be developed to approximate the surface energy of platinum. Bullough (1967) has suggested that y should be estimated from the equation for the internal energy of a void inclusion. If a sphere of radius r is removed from the matrix and the hole is allowed to shrink to a radius r', then the state of the strain is given by

PAGE 115

102 u = r

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103 Taking into account the surface energy of the void E^ = 4Trr'^Y=^^i^ ^(1 + e)^Y E^ = 4iTr^ (1 + 2£)y (20) Thus, the total energy of the void inclusion is the sum of these two parts: E = STiyr^ e + Aur ^(1 + 2e)y (21) Now since the energy is constant, dE/de = 0, and we find Y = 2yr^e = ^^^ (22) Substituting Darling's values for the elastic constants of platinum, recognizing that e is negative because the _3 matrix collapses, and assuming that e = 10 , Y = 6.25 X 10^ ergs/cm^ Thus, we find the value of the surface energy to agree with that of Blakely and Mykura (1962) to within a factor 3 2 of two (i.e., Y = 3 x 10 ergs/cm ). It has been suggested (Jackson 1962) that the surface energy of a small void should be evaluated in terms of the formation energy of the vacancies contained

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104 in a defect and its surface area. It is interesting to note that a calculation of this type, assuming spherical voids, gives a value of the surface energy in good agreement with that obtained above for voids up to o approximately 20 A in diameter (i.e., of the order of 4 2 • 10 ergs/cm ) . For much larger voids, the value of o becomes unreasonably high, and we must assume that the approximation is no longer valid. Field ion microscope investigations may shed some light on this problem. Large polyhedral voids have not been found in field ion specimens, but small vacancy clusters have been observed with some frequency. Figure 37 illustrates two kinds of cluster configuration that have been encountered. The first is a rather disorganized cluster, whereas the second has a definite geometric shape. The straight edges can be indexed consistently with {111} planes, in which case the cluster can be interpreted as tetrahedral in nature. A field evaporation sequence through another void of this type (Figure 38) o places its size in the neighborhood of 25 A. Note that this defect would more than likely have appeared as a o black spot in TEM. A larger void (~ 100 A) appears in the last two photographs in this sequence. It has evidently reached a size level where it is no longer possible to retain the equilibrium configuration. In other

PAGE 118

105 Figure 37. --Field ion micrographs of vacancy clusters in platinum. (a) An irregular cluster on a {420} plane. (b) A tetrahedral cluster near {220} plane. Both defects are about 25 A in diameter.

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106 Figure 38. --A field evaporation sequence through a O — 25 A diameter tetrahedral void near the C224) pole, (a) 240 layers into the specimen.

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107 Figure 38. — (b) Same single (002) plane, somewhat larger. specimen after removing a Note that the void is

PAGE 121

108 Figure 38.-(c) Same specimen after evaporating a second (002) plane. A large void has appeared near the [111] pole.

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109 Figure 38.-(d) Same specimen after evaporating a third (002) plane. The void has decreased in size, The large void has become quite irregular.

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110 words, the stresses have become so large that the matrix collapses when the void is intersected by the surface, and preferential field evaporation occurs. It may be that the imaging stresses inherent in the field ion microscope will prove a disadvantage when one is studying large cavities. Images of irradiated tungsten and iridium always display irregular cavities and one wonders if the irregularity is real. . There is a region of uncertainty but it seems clear that the nuclei for the polyhedral voids otjserved with TEM are tetrahedral, and remain so shaped up to at o o least 25 A diameter. In the vicinity of 100 A diameter, the defects become polyhedral, i.e., truncated octahedra. This transformation requires that the void increase, by a factor of two, its {111} type surfaces by a mechanism which cannot be easily explained. However, Figure 39 is a sketch of the relation between a tetrahedron and an octahedron. Suitable {111} truncation of the tetrahedron at the four apices will transform the shape into an octahedron, a process which can occur either by atomic migration over the inner surface of the void or a change in the growth pattern as vacancies are absorbed. If it is assumed that the surface energy plays a major role, then the size at which the transition occurs may well

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Ill Figure 39. — Schematic drawing illustrating the relationship between the surfaces of a tetrahedron and an octahedron. The latter can be obtained by truncating the apices of the former.

PAGE 125

112 define the point where the concept of surface energy becomes meaningful. Thus, at smaller than this critical size, some means other than the classical surface energy must be used to determine stability of the defect configuration. It is quite possible that the use of vacancy formation energy is appropriate in this region. These small tetrahedral clusters are undoubtedly the nuclei for the larger voids, and it is relatively safe to say that these clusters will co-exist with both voids and dislocation loops, as there will naturally be a size distribution regardless of the vacancy concentration. It is postulated that the small clusters (tetrahedral) are the nuclei for loops as well as voids; the factors determining the final defect configuration are the number of vacancies available for growth and the rate at which these vacancies can be supplied to the growing defects. Dislocation Loops Large resolvable dislocation loops have occasionally been observed in quenched and annealed platinum, but the majority appear in the form of black spot defects. The maximum concentration of the latter is at the limit 13 3 of making a reasonable estimate, ~ 10 /cm , and occurs after 2 hours at 500°C. Even this figure may be somewhat uncertain, because the very nature of the black spot

PAGE 126

113 defects makes identification somewhat ambiguous. Clearly, as seen in the last section, some small voids appear as such, while others may be Frank loops, tetrahedra, or both, The most convincing TEM evidence that at least some of these defects are prismatic loops is the fact that they have been observed to oscillate while under observation, probably due to local electron beam heating. Figure 40 is a sequence of micrographs showing a particular black spot defect in three different positions. This loop was observed to oscillate and then occassionally moved several hundred Angstroms along its glide cylinder. Determining the foil normal to be [112] , the slip trace at B (Figure 41) is (111) . The possible Burgers vectors for this system are ± a/2 [110] , ± a/2 [Oll] , or ± a/2 [101] . The dislocations at C must lie on (111) , since the imaginary trace made by these dislocation would be approximately [l32] . (See Figure 42.) Thus the possible Burgers vectors are ± a/2 [110] , ± a/2 [101] , and ± a/2 [Oil] . The projected direction of oscillation, X, of the defect at A in Figure 41 is contained in the zone given by the solid line in Figure 42. Now, since only dislocations lying in (111) or (111) could have this Burgers vector, it follows that the defect must be a small prismatic loop moving on its glide cylinder. That is,

PAGE 127

114 t o •r+ 0) J4^ c to Q) o en (ti O m CU-P cs o M 0) O t O O 0) -O 0) •r4 O .H C Cr> o H +J

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115 0) e o CO 0) > o e CO +J o V o 0) 4J O •H O O

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116 O 4J > o e 01 CO CU o o 0) p CO o o V 10 (I) e o CO u. -p < (0 • u (0 O o 0) CN e o o -p 0) o E -P 0) 0) Em P

PAGE 130

117 -

PAGE 131

118 II I Figure 42 . --Stereogram used for the analysis of the oscillating defect.

PAGE 132

119 it has clearly been shown that dislocations lying in either of these two planes have length, thereby eliminating the possibility of the defect being an "end-on" dislocation. Figure 43 is a micrograph of a resolvable prismatic loop which oscillated in a direction normal to the line of no contrast. This is in agreement with theoretical predictions for the line of no contrast being normal to the operating reflection, g = [022] in this case, and for the loop to move in its glide cylinder which must be ± [Oil] . The only pictorial evidence for oscillation is the fuzziness of the loop contrast. The loop was out of contrast for g = [111] , which is also consistent with a Burgers vector of ± a/2 [Oil] . The FIM evidence is perhaps even more convincing in that the loops can be atomically resolved. Employing the g*b criterion described earlier, the two defects in Figures 44 and 45 can be identified as prismatic dislocation loops. Indexing the disturbed pole in Figure 44 as (313) , the only Burgers vectors which will produce a single spiral are a/2 [llo] and a/2 [Oil] . The local radius of the specimen in the (202) region is approxio mately 800 A. Using the equation d = MR9 , we find the o loop diameter to be 40 A. Field evaporation through the defect sets an upper limit of about 50 A for the dimension

PAGE 133

120 Figure 43. — Electron micrograph of a large prismatic loop. The defect was observed to oscillate normal to the line of no contrast.

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121 Figure 44. --Field ion micrograph of a prismatic loop intersecting the (313) plane edges.

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122 Figure 45. — Field ion micrograph of a prismatic loop intersecting the (111) plane edges.

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123 normal to the tip surface. Because of its small size and the limited field evaporation data, it is not possible to determine the habit plane of the loop. Figure 45 is another loop in the same tip, but o some 50 to 100 A deeper into the specimen. This loop intersects the surface in the vicinity of the (111) pole and is about 75 A in diameter. In this case a/2 [110] , a/2 [101] , and a/2 [Oil] are all acceptable Burgers vectors for the defect. If we further assume that the loop originally formed on the (111) plane, a reasonable assumption considering the orientation of the defect, the a/2 [101] type defect can be eliminated since it does not lie in (111) . It is not necessary to require that the loop remain in its habit plane and, in fact, it may well have rotated as far as the (202) plane. The original habit plane could not have been (111) , since there are no a/2 <110> type displacements in that plane that can give rise to a single spiral on the (111) plane. This, of course, is a consequence of the geometry of the g-b criterion. Other instances of prismatic loops have been observed in the FIM, but none quite so clear and unambiguous as those just described. Unfortunately, as evidenced by TEM, the defect density is extremely low and the stress fields on the FIM tip probably cause many

PAGE 137

124 of these highly mobile defects to slip out of the surface. At any rate, they will most likely migrate to the edge of the image where the stresses are considerably lower. In Figure 46 a streak is circled that has been attributed to the presence of a Frank dislocation loop. If it is assumed that the streak connects the two intersections with the surface of the bounding partial dislocation (i.e., coincides with the stacking fault), then the loop must lie on the (111) plane and have a Burgers vector a/3 [111] . Figure 47 is an enlargement of this same region, with lines defining the plane edges to aid interpretation. Calculating the average radius in the o region of the (3113^) plane to be 1050 A and employing the usual d = MR9 relation, the length of the streak is 50 to 60 A. The computer was employed to simulate this region of the specimen, and two defects were introduced into the model (Figure 48) . The defect in (a) is the Frank loop discussed above. There is good agreement with experiment here, particularly as regards the collapsing of the (002) plane edges aroundthe defect. Also important is the way the spiral configuration merges into the streak, rather than showing a clear beginning and end as did the prismatic loops pictured previously. To remove any ambiguity, a prismatic dislocation loop with Burgers vector a/2 [oll]

PAGE 138

125 Figure 46. — Field ion micrograph of a Frank sessile dislocation loop. The plane of the fault is (111) and it intersects the surface in the (002) region.

PAGE 139

126 Figure 47. — An enlargement of the C0Q2) region in the previous micrograph. The plane edges have been emphasized to aid interpretation.

PAGE 140

127 Frank loop plane V 002 115 ; I t ^ ^ ' h I I s « . . « M I Mill t t ! J ,1 rv,v\ .*.' Figure 48 .--Computer simulation of the region containing the defect in the previous micrograph. (a) The presence of a Frank loop has been simulated,

PAGE 141

128 Prismatic loop plane 002 I Figure 48. — (b) Same region, only the presence of a prismatic loop has been simulated.

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129 was introduced into the same region. The dislocation a/2 [loi] also lies in (111) and would give the same result, whereas a/2 [110] is in the (002) plane and would therefore be invisible. Figure 48b is the result. The important difference between the two simulated images is the absence of any collapse of the (002) rings near the a/2 [Oll] defect. The evidence is much in favor of interpreting the loop as being sessile in nature. That is, the defect is in a high-stress region of the tip, and if it were glissile it would not be stable there. Furthermore, all previous work both experimental and computer, indicates that streaks are associated with stacking faults, Stacking faults will be discussed later in this chapter. Figure 49 illustrates the behavior that one would expect if all quenched-in vacancies were annihilated at dislocations, as has been suggested by Jackson (1965a). However, this type of structure has been noted in only two regions in two different foils, both of which were annealed for 24 hours at 500°C. The efficiency of dislocations as vacancy sinks is treated extensively by Kuhlmann-Wilsdorf et at. (1960). Briefly, the authors assume dislocations to be classified into two groups, old and new. New dislocations are those which formed or moved at fairly low temperatures and not subjected to any elevated temperature treatment. Conversely, old

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130 i^^^ 1 Figure 49 . --Electron micrograph of a foil containing large prismatic loops and heavily jogged dislocation lines. Note the preponderance of line segments lying along projected <110> and <112> directions.

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131 dislocations are described as those which have undergone annealing while stationary. Experimental evidence indicates that new dislocations climb by the Bardeen-Herring mechanism/ i.e., simply absorbing point defects, whereas old dislocations absorb vacancies by nucleating super jogs. The electron micrograph shown here is a classical example of super jogs. Note that there is a preponderance of dislocation segments along projected <110> and <112> directions, indicating that a large number of the jogs and pinched-off dislocation loops lie on {111} and {110} type planes. Figures 50 and 51 are dark field micrographs of the same area with the operating reflection reversed while s is held constant. In other words, the foil is tilted approximately 1° to bring the same region into good contrast with the new operating reflection. The procedure is carried out entirely under dark field conditions. The micrographs illustrate two important points. First, the small spot defects exhibit a clear black-white contrast which is characteristic of the strain fields around small vacancy or interstitial defects such as dislocation loops. The direction of the white end of the contrast is known to be. a function of the depth into the foil as well as the character of the defect. From the history of these foils one would hardly expect to find interstitial defects,

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132 Figure 50. — Dark field electron micrograph of the same region with g = (002) . Defects exhibiting black-white contrast are arrowed.

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133 Figure 51. — Dark field electron micrograph of the same region with g = (002). Loops exhibiting a size change are arrowed.

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134 so the black spots are undoubtedly vacancy loops. This can be verified experimentally but requires precise depth measurements using a stereo technique. Also of significance is the fact that there are numerous examples of loops changing size upon reversing g. As mentioned in the chapter on electron microscopy, this is positive evidence for a/2 <110> prismatic loops. Stacking Faults At present there is no definite TEM evidence for the existence of Frank loops (i.e., imperfect prismatic loops) . Hov/ever, FIM work indicates that these faulted defects do exist. Computer simulation studies (Sanwald 1967) reveal that stacking faults with their associated partial dislocations are the only planar defect capable of producing a streak in a field ion image. Referring again to Figure 46, it can be seen that there are several instances of streaking. In at least one of these cases the streaks can be deduced as lying on a {111} plane. Many such cases have been observed in images of quenched and annealed platinum, and these streaks always occur at the edges of the specimen. It is possible that the stresses set up in the field ion microscope are sufficient to cause dislocations to split into partials. As pointed out by Ruedl et at. (1962) the occurrence of Lomer-Cottrell

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135 barriers (Figure 52) implies a dissociation into partial dislocations . The point of this discussion is the following: The generally accepted value of the stacking fault energy for 2 platinum is 95 ergs/cm . The value for aluminum is approxi2 mately 200 ergs/cm and that for nickel has been reported 2 to be anywhere from 150 to 450 ergs/cm . Loretto et at. (1966) have shown that faulted loops occur in quenched aluminum, and more recently Humble et at. (1967) have observed faulted dislocation loops and stacking fault tetrahedra in zone refined nickel. It would therefore seem quite reasonable that, under the proper conditions, these more complex defects involving stacking faults should be present in quenched platinum. While transmission microscopy has not produced any such evidence, this author maintains that faulted defects have been observed in quenched platinum by means of field ion microscopy. It is only a matter of time before the conditions will be met to make them visible in the electron microscope. Suggestions will be presented in the following chapter.

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136 Figure 52. — Electron micrograph of dislocation intersections resulting in the formation of LomerCottrell barriers.

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CHAPTER VI CONCLUSIONS AND SUGGESTIONS FOR FURTHER STUDY The picture is by no means complete, but several points have been clarified. Direct evidence has been presented for the clustering of vacancies in quenched and annealed platinum. It has been shown via TEM and FIM that at least some of these clusters collapse to form prismatic dislocation loops, v/hile others grow into polyhedral voids. The latter defect is felt to be the cause of the irreversible change in resistivity measured by Cizek (1967) . It is entirely possible that many of the black spot defects are Frank sessile dislocation loops and there may even be some stacking fault tetrahedra, although no evidence for the latter has been found. The author does feel, however, that the field ion micrograph in Figure 46 along with additional features observed in both TEM and FIM is convincing evidence for the presence of faulted loops and Shockley partial dislocations. The field ion microscope could well be a useful tool for determining stacking fault energies for materials having a relatively high value of this parameter. Of course this will require that more be understood about the imaging stresses than is presently known. Perhaps the 137 -

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138 experiment could be performed in reverse to study the field stresses in the specimen. The maximum size of a particular defect is felt to have a fundamental meaning in terms of the energy of the matrix material and the component dislocations or surfaces comprising the defect. Certainly the shape change between o o 25 A voids and 150 A voids is significant. As mentioned in the text, one would like to obtain accurate values of the surface energy from these types of data. It is suggested that a strain analysis (Ashby and Brown 1963a, b) be carried out to obtain an accurate measure of the lattice strain around the void. The sequence in which the void surfaces facet has been found to be consistent with the values of McLean and Mykura (1966) for the surface energy anistropy of platinum. That is, the {111} plane is the most stable, with {100} and {110} following in that order. Although the "spherical" voids in platinum have been interpreted by this author to be truncated only by {100} planes, the analysis is not unambiguous. In other words, {110} facets may also be present, but the strain in the lattice and the small defect size does not permit identification. . One method to further investigate this question is to employ field ion microscopy on large voids. A study of this type is now in its early stages but has yet to provide

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139 any useful results. The difficulty at present is that the larger voids appear as a depression in the surface, with a considerable amount of lattice collapse and/or distortion of the image (Figure 38) . This behavior is more than likely due to preferential field evaporation of the atoms around the perimeter of the intersection of the void with the surface, rather than being due to local lattice strain. If this is the case, then techniques such as hydrogen promotion (Miiller et at. 1965) may be useful. Recent developments in the theory (Miiller 1967) of hydrogen promotion and the findings of Swanson et at. (1967) that xenon in the imaging gas also reduces the field necessary for imaging are encouraging. Techniques such as this may be the key to determining the precise atomic geometry of the polyhedral void in quenched platinum. Figure 53 is a qualitative plot of the densities of the two types of defects observed in this investigation. Sampling can be a problem in field ion microscopy, since — 10 2 the surface area viewed is on the order of 10 cm . If o one field evaporates through 1000 A, the total volume sampled is only 10 cm . It is therefore obvious that the defect density should be at least 10 /cm . A program is now being set up whereby the defects will be introduced via electron, proton, and/or a-particle irradiation. It is felt that this treatment will increase

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140 10* 8 low E 10 '3 P 10 12 LOOPS VOIDS 200 300 400 600 600 TEMPEFlfl.TURE "C Figure 53 .--Qualitative plot of the observed defect density versus annealing temperature. The maximum concentration of voids occurs at 400°C while the maximum density of black spot defects occurs at a slightly higher temperature.

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141 the defect density and, according to Ruedl and Amelinckx (1963) , both intrinsic and extrinsic dislocation loops are formed after quenching, irradiating with a-particles, and annealing platinum foils. A study is being proposed which would combine transmission electron microscopy, field ion microscopy and computer simulation in order to test this thesis. There is little doubt that intrinsic defects can easily be differentiated from extrinsic defects in simulated images, but it remains to be seen if the differences can be detected experimentally. If it is possible, FIM will certainly be a useful tool to this end, particularly since TEM requires exacting conditions to distinguish between the two. Indeed, there is still a great deal of controversy as to the nature of these defects in neutron irradiated copper. See, for example, Mclntyre (1967) and Riihle and Wilkens (1967). It is further suggested that any studies involving a correlation between field ion microscopy and electron microscopy be carried out on the same starting material. Although wire may be rolled to obtain foil specimens, it is perhaps wiser to prepare field ion tips from the foil. Rao and Thomas (1967) have only recently reported a successful technique for preparing specimens from molybdenum foil.

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142 In sununary, the author feels that this preliminary study of quenched and annealed platinum clearly demonstrates that FIM in conjunction with TEM can provide the researcher with a powerful tool for studying the defect structure of metals. This is particularly true for imperfections which are at or beyond the resolution capabilities of the electron microscope; but the technique is not necessarily limited to these. Furthermore, it appears that the field ion microscope can provide independent measurements of such parameters as stacking fault energy and surface free energy, if one is imaginative in the design of the experiment. The possibilities are many.

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APPENDICES

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APPENDIX I INDEXING FIELD ION MICROGRAPHS Derivation Assuming a constant local radius, r, between any two poles separated by a curvilinear distance, S. , along the surface of a tip: S^ = re (I-l) and the corresponding length along the surface of a projection sphere of radius R is (Figure 54): S = Re (1-2) s If a projection point is now chosen such that the projected length X is equal to the arc length, S , we have for any zone line passing through the center of the image : X = Re (1-3) P This is not any standard type of projection since the projection point must vary with the angle 6 in order to satisfy equation 1-3. In general, the length R is not equal to the specimen-screen distance, but the relationship of equation 1-3 can be maintained by orthographically projecting the information on the projection plane to the screen. Thus, 144 -

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145 Screen Image Point Projection Plane Projection Point Figure 54 . --Pro jection of a random direction onto a planar surface with the projection point chosen so that X = S . P s

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146 the linear distance d on the micrograph is related to the length X on the projection plane Cor the screen) by the ir expression: d = M^M X = MX (1-4) L p p p ^ ' where M^ is the magnification of the camera optics and M is the magnification introduced during the printing of the photographs. Therefore, equation 1-3 becomes simply: d = MR0 (1-5) While the choice of these three projections (gnomonic, pseudo-stereographic , and orthographic) appears arbitrary, it is not invalid to assume that the three straight line segments approximate the actual ion trajectories proposed by Drechsler and Miiller (1952) . The justification for the nature of the intermediate projection is that it has the desirable property of maintaining a one to one correspondence between radial distances before and after projection. Discussion It is interesting to calculate precisely what type of projection is required to satisfy equation 1-3. Knowing the points (x^^, y^) and (x , y ) in Figure 54, it is a simple matter to determine the coordinates of the projection point. Thus:

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147 Y_ 9 cos 6 sin 9 (1-6) R " 9 sin e In the limit as 9 -* 0, y ^-2R. Choosing 6 = 60° as an upper limit, we find y = -1.890R. Thus the projection point is approximately two radii behind the tip — the same as that proposed by Brandon. This result suggests that it may be meaningful to compare equation 1-5 with Brandon's (1964) equation for a projection from the center of the second sphere: , -.3 sin 9 ' ,^ ^, " = Rt"-; K (1-7) 2 + cos 9 v-L '; where R = MR of equation 1-5 and 9 has the same meaning as in equation 1-5. Taking the first two terms of the series expansion of sin 9 and cos 9, equation 1-7 reduces to equation 1-5 exactly. In fact, the difference between the calculated d-values is less than 1% over the angular range of a field ion image. Brandon has already shown that the pseudo-stereographic projection is inherently more accurate than either the orthographic or stereographic projections. He also mentions that for any given projection, local variations in tip radius (Miiller 1958b) will result in a variation of the radius of the projection sphere. This is probably the major source of error in determining the angle to any one

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148 pole but appears to be minimal when averaged over the entire micrograph. It can also be shown using spherical trigonometry and projective geometry that the present method may be employed to compute angles between poles, both of which are considerably displaced from the image center. In fact, the linear distance (e.g., measured on a micrograph) between two points both of which are 45° from the center is only 10% larger than the actual curvilinear distance on the projection sphere for small angular separations. This error drops to zero at 90° separation. Therefore, it can be confidently stated that cross checks on pole indexing can be made from any place on the image within 45° of the center. Experimental Procedure Since the projection sphere is not tangent to the microscope screen due to the focusing of the ion beam (Drechsler and Miiller 1952; Miiller 1960), R must be chosen by a trial and error method analogous to that used for indexing an x-ray Laue pattern. That is, one must make use of symmetry and knowledge of specimen history to make an assumption as to the indices of the central pole, to be used as a reference, and at least one other pole. Strictly speaking, the reference pole should be located

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149 at the geometric center of the image where, for a symmetrical tip, the projection sphere is tangent to the projection plane. However, it is sufficient to use the pole nearest the center of the photograph. Using the appropriate value of e in equation 1-5, a corresponding value of the product MR is obtained. (It is usually unnecessary to separate these two parameters.) Then using this MR, equation 1-5 is solved for using a d-value for a third unknown pole. This 6 is then compared with tabular values of angles between various planes and the reference pole. It may be necessary to make several choices for the second pole in order to obtain a value of MR that will give self-consistent values of for the third, fourth, etc., poles. Once an appropriate value of MR is obtained, equation 1-5 is solved repeatedly until the entire micrograph is indexed. When indexing any micrograph using this method, one must keep in mind that, due to the geometry of the surface, only those planes which satisfy the conditions analogous to Bragg diffraction will appear (Drechsler and Wolf 1958, Ranganathan 1966b). For example, in an FCC crystal, it is the {002} planes {h, k, I, unmixed) which are visible as concentric rings--not the {001} planes as is sometimes stated.

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APPENDIX II DESIGN CONSIDERATIONS IN CONSTRUCTING THE FIELD ION MICROSCOPE There are essentially five subsystems in the field ion microscope discussed here: (1) a cryostat, C2) an ultra-high vacuum system, (3) a controlled source of pure imaging gas, (4) an adjustable high voltage source, and (5) a phosphor screen for viewing and recording the image. Figure 55 is a photograph of the entire system. Cryostat In cryostat design, one must be aware of the low heat capacity of cryogenic fluids that necessitates extreme care be taken to avoid any large heat leaks to the cryostat. Since radiation becomes a significant means of heat transfer at these temperatures, it is desirable to shield the liquid hydrogen cryostat from the room temperature surroundings. This has been accomplished by means of a liquid nitrogen dewar which almost completely surrounds the cryostat and specimen. Convection is a small, but real problem since the microscope body must be back-filled with an imaging gas. In order to minimize heat transfer by this mechanism, the 150 -

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151 0} e w a. m > tP (1) -H E • (L) a • O ro O m — O g . M 0) -P O -P M -H W O m C •H -d U 0) 0) > > •H 4-1 P u m (C o O 4-> +J x: o s-( (CMC !-< O 0) o -P • 0) -H Cn ji: oj p^ -p 1 • H I -o o • 0) > in 5 in O x; 0) M -H M (T3 ^ Cr> 0) •H M • Cm (d •^ O •H

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152 gas is precooled in the liquid nitrogen dewar before it passes into the specimen chamber. Conduction is perhaps the most difficult mechanism to deal with. This is particularly true when dealing with a metal FIM body where a high voltage connection must be made to the specimen, must be electrically insulated from the body, and must not be too large a heat leak. This has been accomplished using 0.015" diameter Nichrome wire for making the electrical contact between the high voltage feedthrough and the specimen. This wire is sheathed in a Pyrex capillary, over most of its length, to prevent discharges between it and the FIM body. A major problem is encountered in making the connection to the specimen itself. It is absolutely imperative that the specimen assembly not be thermally shorted to room temperature, so one must be clever in making this connection. Figure 56 illustrates how this was done. By having the tungsten leads re-entrant through the liquid hydrogen bath, the cryostat is admittedly shorted to room temperature. More important, however, is the fact that the specimen is still thermally connected only to the liquid hydrogen.

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153 Pyrex tube Liquid H2 -Tungsten leads to H.T Specimen Figure 56 . --Schematic drawing of the liquid hydrogen cryostat. The 0.050" thick tungsten leads are glass coated inside the cryostat. The high voltage connection is 0.015" thick Nichrome wire. The liquid hydrogen bath is maintained between 16 and 21°K.

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154 Vaouum System The most important consideration in designing the — 8 —9 vacuum system is that it be capable of 10 to 10 Torr and that this pressure be attained in a reasonable length of time. This system employs a liquid nitrogen-trapped, 100 liter/sec, 2" oil diffusion pump which is capable of — 8 10 Torr within two hours of specimen change. With mild -9 bake-out, 10 Torr is attainable. The small diffusion pump can be quenched and exposed to air some ten minutes after shut-down, which eliminates the need for a roughing line. Imaging Gas The imaging gas supply has only one unique feature other than the mixing capability mentioned in Chapter IV. That is, the gas line passes through the liquid nitrogen shroud and is therefore precooled before entering the specimen chamber. It is believed that this increases thermal accommodation between the gas and the specimen. High Voltage Generator The high voltage power supply has continuously variable voltage control and provides up to ± 30 kV. The supply is extremely stable (0.01% ripple) and can compensate for up to 10% change in line voltage with only 0.005%

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155 change in output voltage. This is an absolute necessity since slight variations in applied potential can easily cause a tip to flash. In order to eliminate the danger g from high voltage discharges, a 5 x lo ohm resistor is placed in series with the generator and specimen assembly. With a maximum current output of 1 ma, the maximum supply -4 m the vicinity of the operator is 10 amp or 3 watts. Viewing Port Normally, a Pyrex or 7052 glass viewing port is used in field ion microscopes. The glass window is made electrically conducting by evaporating stannous oxide on the surface. A layer of Willeraite is then deposited on the glass to provide a fluorescent screen. While this is quite suitable for viewing the image, it is not very efficient for photographically recording the image, without the use of image intensif iers . However, a fiber optic faceplate has been incorporated into this microscope which enables the operator to record the image by placing a photographic emulsion in intimate contact with the outer surface of the window. In other words, it is not necessary to focus a lens system onto the phosphor which is on the vacuum side of the window, as is the case with a Pyrex viewing port. Rather, with the fiber optics, the image is transmitted through the glass fibers (15 microns in diameter)

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156 to the outer surface of the plate. Since the image is in focus to within the resolution of the individual fibers, it can be recorded directly. It has been observed experimentally that the exposure times are reduced by an order of magnitude over 35 mm techniques, and the quality of the final micrograph is much improved because the 4x5 negative need not be enlarged as much as the 35 mm film.

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APPENDIX III CALIBRATION OF THE ELECTRON MICROSCOPE As the current in the intermediate lens of an electron microscope is increased, not only is the magnification increased, but the image also undergoes a rotation about the column axis. Before any quantitative work can be accomplished on defects in metals, the variation of these two parameters with lens current must be measured. This information is presently available for the Philips EM 200 fitted with a Rotating Tilting Specimen Stage (Feltner and Sefton 1964) ; however, the data is not valid for the newly acquired Goniometer Stage. All calibrations have been carried out with the intermediate, objective, and condenser I and II lenses set at negative (-) polarity and the magnification selector switch (MSS) set at position (2) . The fine adjust knob of the intermediate lens control was set at full clockwise. Magnification Calibration The magnification at 100 kV, as given in Table 5, was determined at each position of the intermediate lens control by photographing a replica of a ruled grating 4 (5.48 X 10 lines/inch) and measuring the line spacings 157 -

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158 TABLE 5 MAGNIFICATION CALIBRATION OF PHILIPS EM 200 WITH THE GONIOMETER STAGE intermediate Lens

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159 from the 35 mm film and the glass plates. For completeness, the magnification after printing full-frame is also given. Since the lens current may vary slightly with specimen position, lens current has been plotted versus plate magnification in Figure 57. Rotation Calibration When going from a diffraction pattern to a bright field image, the intermediate lens current is changed giving rise to a relative rotation between the diffraction pattern and the image. Before crystallographic directions from the diffraction pattern can be transferred to the image, this rotation must be accounted for. Groves and Whelan (1962) pointed out that there is an additional 180° rotation between the diffraction pattern and the image because the intermediate lens is not energized when viewing the diffraction pattern. However, with the Goniometer Stage, the MSS set at position (2), the intermediate lens at (1) , and the fine adjust turned full clockwise, the intermediate lens is on. Therefore, there is no additional 180° rotation for this set-up. The rotation measurements were made by photographing the intersection of two slip traces in a platinum foil oriented so that the beam direction was [110] . Knowing this, and the width of the two slip traces, indices could

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160 01 ^ UOipO!^!u6D/\| 8iD|cJ ^ —

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161 be assigned to the slip planes. As the magnification is increased, the image rotates counterclockwise through an angle as plotted in Figure 58. This, then, is precisely the angle through which the diffraction pattern must be rotated (also counterclockwise) in order to make the two coincident. The rotation has been found to decrease slightly as the diffraction lens current increases. Position of the Tilt-Axis The Goniometer Stage has been designed so that the tilt axis is always defined by the direction of motion of the image when the left hand stage control knob is rotated. Therefore, the tilt axis can be determined quite accurately while the specimen is under observation. It can be measured photographically by double-exposing a plate, before and after moving the specimen stage with the left hand control only. The line joining a single feature in the doubleexposure is the tilt axis.

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162 (MOO S90j6'3p) UOIlDjO^ e5DLU|

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BIBLIOGRAPHY Ahlers, C. T. J., and Ba.lluffi, R. V] . , 1967, J. Appt. Fhijs., 38, 910. Amelinckx, S., 1964, The Direct Observation of Dislocations (New York: Academic Press). Ascoli, A., Asdente, M. , Germagnoli, E., and Manara , A., 1958, J. Phys. Chem. Solids, 6, 59. Ashby, M. F., and Brown, L. M. , 1963a, Phil. Mag., 8, 1083. Ashby, M. F., and Brown, L. M. , 1963b, Phil. Mag., 8, 1649. Bacchslla, G. L. , Germagnoli, E., and Granata, S., 1959, J. Appl. Phijs . , 30, 74 8 . Bauer, W., and Sosin, A., 1966, Phys. Rev., 147, 482. Bell, W. , Maher, D. M. , and Thomas, G., 1965, Latzice Defects in Quenched Metals (Nev; York: Academic Press) , p. 739. Bell, W. L., and Thomas, G., 1966, Phil. Mag., 13, 395. Bilby, B. A., Bullough, R. , and Smith, E., 1955, Proa. Roy. Soc. A, 231, 263. Blakely, J. M., and Mykura, H., 1962, Acta Met., 10, 565. Bowkett, K. M. , Hren, J., Ralph, B., 1964, Proc. Third Eur. Reg. Conf. for Elect. Micr . (Prague: Publishing House of the Czechoslovak Academy of Sciences) , p. 191. Bradshaw, F. J., and Pearson, S., 1956, Phil. Mag., 1, 812. Brandon, D. G., 1964, J. Sci. Inst., 41, 373. Brenner, S. S., 1962, Surfaces: Structure^ Energetics and Kinei-ics (Cleveland: American Society for Metals), p. 305. 163 -

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164 BIBLIOGRAPHY — Continued Bullough, R. , 1967, private communication. Chik, K. P., 1965, phijs. stat. sol., 10, 675. Cizek, A., 1967, Czech. J. Phys., B17 , 186. Clarebrough, L. M. , 1964, Phil. Mag., 9, 377. Clarebrough, L. M. , 1966, J. Austr. Inst. Metals, 11, 307. Clarebrough, L. M. , Humble, P., and Loretto, M. H., 1967, Acta Met., 15, 1007. Cottrell, A. H., 1953, Dislocations and Plastic Flow in Crystals (London: Oxford Univ. Press). Cottrell, A. H. , 1958, Vacancies and Other Point Defeats in Metals and Alloys (London: Institute of Metals), Monograph No. 23. Damask, A. C, and Dienes, G. J., 1963, Point Defeats in Metals (New York: Gordon and Breach). Darling, A. S., 1966, Plat. Met.' Rev., 10, 14. de Jong, M. , and Koehler, J. S., 1963, Phys. Rev., 129, 49." Doyama, M. , 1965, Lattice Defects in Quenched Metals (New York: Academic Press), p. 163. Drechsler, M. , and Miiller, E. W. , 1952, Zeit. fur Phys., 132, 195. Drechsler, M. , and Wolf, P., 1958, 4th Int. Congr. for Elect. Micr. (Berlin: Springer Verlag) . Edington, J. W. , and West, D. R. , 1966, 6th Int. Congr. for Elect. Micr. (Tokyo: Maruzen Co. Ltd.) Feltner, C. E., and Sefton, L. R. , 1964, Tech. Report SL 64-85, (Dearborn, Michigan: Ford Scientific Laboratories) . Fortes, M. A., and Ralph, B., 1966, 13th Field Emission Symposium, Cornell Univ., unpublished.

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165 BIBLIOGRAPPIY — Continued Frank, F. C, 1949, Proc. Phys. Soc . , A, 62, 202. Frank, F. C, 1951, Phil. Mag., 42, 809. Frenkel, J., 1926, Zeit. fur Phys., 35, 652. Friedel, J., 1964, Dislocations (New York: Pergamon Press) . Gevers, R. , 1963, Phil. Mag., 8, 769. Gomer , R. , 1961, Field Emission and Field Ionization (Cambridge, Massachusetts: Harvard Univ. Press). Groves, G. W. , and Whelan, M. J., 1962, Phil. Mag., 7, 1603. Hirsch, P. B., Howie, A., and Whelan, M. J., 1960, Phil. Trans. Roy. Soa. A, 252, 499. Hirsch, P. B., Silcox, J., Smallman, R. E., and Westmacott , K. H., 1958, Phil. Mag., 3, 897. Howie, A., and Whelan, M. J., 1961, Proc. Roy. Soc . A, 263, 217. Hren, J. J., 1967, private conununication . Hren, J. J., and Newman, R. W. , 1967, Rev. Sai. Inst . ^ 38, 869. Humble, P., Loretto, M. H., and Clarebrough, L. M. , 1967, Phil. Mag., 15, 297. Jackson, J. J., 1965a, Lattice Defects in Quenched Metals (New York: Academic Press), p. 467. Jackson, J. J., 1965b, Lattice Defects in Quenched Metals (New York: Academic Press), p. 479. Jackson, K. A., 1962, Phil. Mag., 7, 1117. Kiritani, M. , Shimomura, Y., and Yoshida, S., 1964, J. Phys. Soc. Japan, 19, 1624.

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166 BIBLIOGRAPHY — Continued Kuhlmann-Wilsdorf , D., 1958, Phil. Mag . ^ 3, 125. Kuhlmann-Wilsdorf , D., 1965, Acta Met.^ 13, 257. Kuhlmann-Wilsdorf, D., Maddin, R. , and Wilsdorf, H. G. F., 1960, Strengthening Mechanisms in Solids, (Cleveland: American Society for Metals), p. 137. Lazarev, B. G., and Ovcharenko, 0. N., 1955, Dokl. Akad. Nauk. S.S.S.R., 100, 875. Loretto, M. H., Clarebrough, L. M. , and Humble, P., 1966, Phil. Mag., 13, 953. Mclntyre, K. G., 1967, Phil. Mag., 15, 205. McLean, M. , and Mykura, H., 1966, Surface Sci., 5, 466. Moore, A. J. W. , 1962, J. Phys. Chem. Solids, 23, 907. Mukherjee, K. , 1966, Trans. Met. Soo. AIME , 236, 1324. Miiller, E. W. , 1951, Zeit. fur Phys., 131, 136. Mviller, E. W. , 1958a, Acta Met., 6, 620. Muller, E. W. , 1958b, 4th Int. Congr. for Elect. Mior . (Berlin: Springer Verlag) . Muller, E. W. , 1959, Structure and Properties of Thin Films, (New York: John V7iley and Sons, Inc.), p. 476. Muller, E. W. , 1960, Adv. Elect, and Electron Phys., 13, 83. Muller, E. W. , 1967, 14th Field Emission Symposium, Washington, D. C., unpublished. Muller, E. W. , Nakamura , S., Nishikawa, 0., and McLane , S. B., 1965, J. Appl. Phys., 36, 2496. . Newman, R. W. , Sanwald, R. C, and Hren, J. J., 1967, J. Sci, Inst., in the press.

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167 BlBL10GRAPliY--Continued Newman, R. w. , Sanwald, R. C, and Jenkins, E. J., 1967, submitted for publication. Pashley, D. W. , 1965, Rep. Prog. Phys., 28, 291. Pearson, S., and Bradshaw, F. J., 1957, Phil. Maa 2 1387. ^'' ' Piercy, G. R. , 1960, Phil. Mag., 5, 201. Pimbley, W. T., Speicher, C. A., Attardo, M. J., Galligan, J. M., and Brenner, S. S., 1966, 13th Field Emission Symposium, Cornell University, unpublished. Ranganathan, S., 1966a, J. Appl. Phys., 21, 4346. Ranganathan, S., 1966b, private communication. Ranganathan, S., Bowkett, K. M. , Hren, J. J., and Ralph, B. , 1965, Phil. Mag., 12, 841. Rao, P., and Thomas, G. , 1967, Acta Met., 15, 1153. Read, W. T., 1953, Dislocations in Crystals (New York: McGraw-Hill) . Ruedl, E., and Amelinckx, S., 1963, J. Phys. Soc. Japan, 18, Suppl. Ill, 195. Ruedl, E., Delavignette, P., and Amelinckx, S., 1962, J. Nual. Materials, 6, 46. Riihle, M. , and Wilkens, M. , 1967, Phil. Mag., 15, 1075. Sanwald, R. C., 1967, Ph.D. Dissertation, University of Florida. Sanwald, R. C, Ranganathan, S., and Hren, J. J., 1966, Appl. Phys. Letters, 9, 393. Seidman, D., 1967, private communication. Seitz, F., 1950, Phys. Rev., 79, 890.

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168 BIBLIOGRAPHY — Continued Silcock, J. M., and Tunstall, W. J., 1964, Phil. Mag . ^ 10, 361. Silcox, J., and Hirsch, P. B., 1959, Phil, Mag., 4, 72. Sraallman, R. E., and Ashbee , K. H. G., 1966, Modern Metallography (Oxford, England: Pergamon Press) . Southon, M. J., and Brandon, D. G., 1963, Phil. Mag., 8, 579. Swanson, L. W. , Reed, D. E., and Bell, A. E., 1967, 14th Field Emission Symposium, Washington, D. C, unpublished . Thomas, G., 1962, Transmission Electron Miarosaopy of Metals (New York: John Wiley and Sons, Inc.). van Landuyt, J., Gevers , R. , and Amelinckx, S., 1965, phys. stat. sol., 10, 319. Yoshida, S., Kiritani, M. , Shimomura, Y. , and Yoshimaka, A., 1965, J. Phys. Soc. Japan, 20, 628.

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BIOGRAPHICAL SKETCH Robert William Newman was born November 11, 1939, at Freeport, New York. In June, 1957, he was graduated from Freeport High School. In August, 1963, he received with Honors, the degree of Bachelor of Metallurgical Engineering from the University of Florida. In September, 1963, he enrolled in the Graduate School of the University of Florida. He worked as a graduate research assistant in the Department of Metallurgical and Materials Engineering while he pursued the degree of Doctor of Philosophy. Robert William Newman is married to the former Mary Katherine Pattillo and is the father of three children, He is a member of the American Institute of Mining, Metallurgical, and Petroleum Engineers, the American Society for Metals, Sigma Tau, Alpha Sigma Mu, and the Society of the Sigma Xi . . 169 -

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This dissertation was prepared under the direction of the chairman of the candidate's supervisory committee and has been approved by all members of that committee. It was submitted to the dean of the College of Engineering and to the Graduate Council, and was approved as partial fulfillment of the requirements for the degree of Doctor of Philosophy. December 19, 1967 Djean, College of Engineering Dean, Graduate School Supervisory Committee . ^A/ • ^-A^!^UJ ' ^A-