Group Title: electron microscope and field ion microscope study of defects in quenched platinum
Title: An electron microscope and field ion microscope study of defects in quenched platinum
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Title: An electron microscope and field ion microscope study of defects in quenched platinum
Physical Description: xi, 169 leaves : ill. ; 28 cm.
Language: English
Creator: Newman, Robert William, 1939-
Publication Date: 1967
Copyright Date: 1967
Subject: Platinum -- Metallography   ( lcsh )
Electron microscopes   ( lcsh )
Microscope and microscopy   ( lcsh )
Metallurgical and Materials Engineering thesis Ph. D
Dissertations, Academic -- Metallurgical and Materials Engineering -- UF
Genre: bibliography   ( marcgt )
non-fiction   ( marcgt )
Thesis: Thesis - University of Florida.
Bibliography: Bibliography: leaves 163-168.
Additional Physical Form: Also available on World Wide Web
General Note: Manuscript copy.
General Note: Vita.
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Bibliographic ID: UF00097834
Volume ID: VID00001
Source Institution: University of Florida
Holding Location: University of Florida
Rights Management: All rights reserved by the source institution and holding location.
Resource Identifier: alephbibnum - 000559309
oclc - 13458609
notis - ACY4759


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December, 1967

1 11111111111111111111262 08552 33111111111111111111
3 1262 08552 3313

Dedicated to My Wife,

Mary Katherine


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-


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.






ABSTRACT . . . .



. . iii

. . V

. . vi

. . xi

. . 1







FURTHER STUDY . . . . . .





BIBLIOGRAPHY . . . . . . . . .


. . ,24

. . 49

. . 69

. . 81

. . 137

. . 144

. . 150

. . 157

* . 163

. . 169



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 .



. . . 19

. . . 47

. . . 48

. . 158


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


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



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




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 . . . . . .


. . Ill


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) . . .





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 . . . . . . . .


. . . 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



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

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.


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 -

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.



Defect Formation







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 -



Property Cu Ag Au Al Ni Pt

E (eV) 1.17 1.09 0.94 0.75 1.4 1.5

E (eV) 1.0 0.85 0.85 0.65 1.5 1.4

E (eV) 0.65 0.58 0.65 0.3 0.72 1.1

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-

Q (eV) 2.1 1.91 1.81 1.35 2.9 2.9

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

- energy

- energy

- energy

of formation

of motion of

of motion of

Sa vacancy



- binding energy between two vacancies

- concentration of vacancies at T






- 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


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


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 -



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

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- (- -) .

3 Q O '0 O'O 'O 1


- 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
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.



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

- 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)

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)

- 27 -

where K = g + s as in Figure 3b. Recognizing that g-r is
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

I() c sin rts (8)
Its) = 2 (8)

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




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 -



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

- 30 -


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 =
|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)

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


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 -




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 -



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 -


0I *I



o *

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


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 -


Q -P


o A

. .



-- 0


r >. r--

O --Q

0 0Q

t -
5o .0

4J m

I 00

(I M

**-1 F


o L
U, 0-


------ .

- 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.


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 -



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

1.8 t 0.2 N > P P
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 -



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

Assume x = st = 0.5.



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
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



Figure l1.--Schematic drawing of a field ion



- 51 -

applied voltage and the radius of the specimen (Muller

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

-H-H Cd

0 -4
S'-H .Q 0

0 Q)
-H H


0 W4-

4 -H .
-H H

s3 Er

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

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 -


ps C

B ,

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


/ O

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


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

- 56 -

Image Interpretation


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


--- [112]

b=- [Rio]


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],

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 -


.. 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-


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 -

Qc I
S-l 00

: ro o -A
n *--O 0


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

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

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)

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.



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 -

(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


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


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

liquid nitrogen baffled 2" oil diffusion pump, backed by
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
end of the 10 scale of the ion gauge.



23 a











0 4-P


H 0

s CL .g

- 72 -

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

Planes in Crystal

Axis of Microscope

Bright Field
(a )

Dark Field

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


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 -





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


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




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
than 1000 A in diameter, large enough to break through one

or both surfaces of the foil, while the majority were of
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
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
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 -

C d

0 *0

) f

>o 4P

(a 0

S ) (
Vi rm o

o r-

> 0 C0

$4 rj OH

4r U (1

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



c, 1
En 0 3

H -C N

0 0

*H aC) H


0~ 4


*H z)

Q) ruf

* 0- H


*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.

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