Nucleation and growth of stacking fault tetrahedra in gold

NUCLEATION

AND

GROWTH

OF STACKING

W. WESTDORPt,

FAULT

TETRAHEDRA

IN GOLD*

and R. MADDINS

H. KIMURAJ

The formation of stacking fault tetrahedra in quenched gold foils was observed by transmission electron microscopy. The density of tetrahedra was found to be about 6 x lOi cm-8 for quenches from 890°C and independent of the annealing time and temperature beyond the early stage of armealing. The growth of the tetrahedra was confirmed; their nucleation was found to be completed in the very early stages of annealing. These results imply that condensation of vacancies occurs, to some extent, during quenching and that the binding energy of a divacancy is about 0.4 eV. NUCLEATION

ET CROISSANCE TERAHEDRALES

DES FAUTES DANS L’OR

D’EMPILEMENT

La formation de fautes d’empilement tetrahedrales dans des feuilles d’or trempe a 6te observee par microscopic Qlectroniquede transmission la densite de tetrahh6dralestrouvee a Bte d’a peu pres 6 x 1014 cm-8 pour lea trempes a 89O’C et independante du temps de recuit et de la temperature. La croissanoe des tetrahedrales a Qtt5conflrmee; on a trouve que leur nucleation est terminee dans lea tout premiers stades du recuit. Ces resultats impliquent que la condensation de lacunes a lieu, dens une certaine mesure, durant la trempe et que l’energie de liaison d’une bilacune eat d’environ 0.4 eV. KEIMBILDUNG

UND

WACHSTUM

VON

STAPELFEHLERTETRAEDERN

IN GOLD

Mit Hilfe von Durchstrahlungsaufnahmen im Elektronenmikroskop wurde die Bildung von Stapelfehlertetraedern in abgesohreckten Goldfolien beobachtet. Die Dichte der Tetraeder ergab sich su etwa 6 x lOi cm-8 bei einer Abschrecktemperatur von 89O”C, unabhiingig von der Anlafizeit und der Anl& temperatur. Das Wachsen der Tetraeder wurde bestatigt. Die Keimbildung wurde in den Anfangsstadien des Anlessens bereits abgeschlossen. Diese Ergebnisse deuten an, da6 Leerstellenkondensation su einem gewissen Grade schon wiihrend des Abschreckens erfolgt und da9 die Bindungsenergie einer Doppelleerstelle etwa 0.4 eV ist.

INTRODUCTION

Gold, quenched

gested

from above a critical

temperature

that

product

the

tetrahedron

was a transformation

of a sessile dislocation

loop.

In this regard,

(about SOO”C),exhibits a characteristicS-shapeddecay

Czjzek, Seeger and Maderc4) suggested

the possibility

curve of quenched-in

of tetrahedron

absorption

annealing, tivity

resistivity

with about

remaining Maddin

explained

this decay

tivity

in terms

dislocation

10% of the quenched-in

after

Kimura,

a low temperature

and

condensation

loops upon annealing, Silcox

general validity

of the vacancy

that the secondary

of For

the

tetrahedra

example,

Silcox

vacancy

and Maddin

condensation

the

mecha-

resistivity

It

recently

and Hirsch@)

been sug-

States Atomic Energy Commission. t Part of a thesis submitted by W. Westdorp to the Graduate School of Arts & Sciences, University of Pennsylvania, in partial fulfillment of the requirements for the Ph.D. degree. Presently, DuPont Experimental Station, Bldg. 356, Wilmington, Delaware, U.S.A. $ School of Metallurgical Engineering, University of Pennsylvania. On leave from the Institute of Physical and Chemical Research, Komagome, Bunkyo-Ku, Tokyo, Japan. 5 School of Metallurgical Engineering and Laboratory for Research on the Structure of Matter, University of Pennsylvania, Philadelphia, Pennsylvania. 4

is the

VOL. 12, MAY 1964

495

by successive

in their attempt

decay curve.

for the growth

to explain the

Kimura,

from energetic

Kuhlmannand atomistic

mechanism

no attempt

of a tetra-

has been made

to decide

whether or not a tetrahedron

can grow.

purpose

of the

present

answer the question of tetrahedron An

with the

* Received September 23, 1963. Sponsored by the United

ACTA METALLURGICA,

considerations

experimentally

in

for the growth

of

proposed

hedron modified the model by de Jong and Koehler. Nevertheless,

and showed

concerned have

mechanism of vacancies

S-shaped

fault tetrahedron.

investigations

absorption Wilsdorf

new sinks

by successive

De Jong and Koehlerc5) recently

resis-

confirmed

as well as for the remaining

growth

into sessile

creating

Hirschc3)

vacancies. a particular

first

defect responsible for the annealing

Many theoretical published.

and

electron microscopy

gold was the stacking formation

anneal.(l)

curve and the remaining

of vacancy

nism by transmission

resis-

Kuhlmann-Wilsdorf(2)

for vacancies.

phenomenon

upon low temperature

additional

nucleation

unsolved

of the S-shaped

decay

sessile dislocation

curve

to

growth.

problem

of the tetrahedron.

Kuhlmann-Wilsdorf’2)

investigation concerns

the

In their explanation Kimura,

Maddin

and

assumed that the nucleation

of

loops takes place during quenching

or in the very early stage of annealing,

and showed

that this assumption would be possible if the binding energy of a divacancy is about 0.4 eV. De Jong and KoehleiJ5) concluded that the number of tetrahedra should increase gradually upon annealing and level off after reaching the half decay time if the binding energies

of a divacancy

0.1 eV and

<0.3

and

trivacancy

eV, respectively.

are

low,

It is hoped that

ACTA

496

the direct quenched

observation

of tetrahedron

gold annealing

will provide

METALLURGICA,

VOL.

12,

1964

formation

in

tion

information

to

measuring the edge length of at least 1000 tetrahedra.

for each

experimental

point

was obtained

by

help solve this problem. RESULTS EXPERIMENTAL

PROCEDURE

It was generally

One cm pieces of gold wire (99.999%, were carefully an average

rolled down in hand rolls to sheet with

final thickness

(8 x 20 mm) annealed

were

cut

of 0.07 mm.

from

at 800°C for

the

A

sandwich

loaded

of

platinum

36 hr to obtain

alternating boat,

gold

of TQ = 890°C

to be 10-l cm. specimens

was quenched

quenching

experiments.

cies quenched-in

a short,

To fix one

quenching

satisfactory. quenching

including

the

of vacanand

by Simmons was

time

bath was up to 2 min. intentionally

constituted

for

a pre-annealing

of importance

all

and

considered

spent

into

in

the

The time was kept quenches,

treatment

since

it

which could be

in the early stage of vacancy

condensa-

tion. Specimens

from

each

quench

A striking only

in size of tetrahedra

characteristic

in annealing

Figs. 1, 2 and 3. Analyzing distribution

in Fig. 4.

were annealed

for

next

time.

See, for example,

annealing

time.

The background

to larger

This background increase

in tetrahedra

ones for short

experiments,

density

nealing time was previously size, however,

with

increasing

an an-

size was used.

is almost the same for all at least for the

at room temperature.

from various quenches from 890°C and temperatures varying from 50°C to 200°C

are compiled

in Fig. 5. This figure shows a constant

tetrahedra

density

error

all

beyond

was not hence,

reported,cg) nor was any

times and temperatures,

case of pre-anneal

annealing

be noticed.

size effect since the maximal tetrahedron The maximal

This result

of very small

of very small tetrahedra

in the preliminary

for

can be

areas of specimens

the results in terms of size-

detected

Results annealing

of

shows that the peak of largest tetrahedra

increases with increasing

annealing

density

in agreement

of Cotterill.@)

difference

noted by comparing

is shown

low

and no resolved tetrahedra,

with the observations

differing

that foils immediately a very

times (Fig. 1) should especially

The transfer time of the specimens

nitrogen

dislocations

observed

contained

tetrahedra

of the

with the thermal

technique

quenching

temperature

from the density

and compared

after

most

As shown below, the agreement is good and

present

constant

for

value at 890°C obtained

Balluffi.“)

from

The concentration

is calculated

size of tetrahedra, equilibrium

constant

and

in a spring

the quenching

was kept

bulk

a uniform,

furnace into iced brine.

of the many parameters,

liquid

and

paper discs (used as separators)

vertical induction

the

Specimens

sheet

stable grain-size, which was determined asbestos

1 mm dia.)

within the experimental

investigated

annealing

range of

temperatures

the early stages of annealing.

times ranging from 2 set to 8 hr in a silicone oil bath at one of the following 200°C.

temperatures:

A series of experiments

temperature

50, 100, 150,

varying

the annealing

and time was carried out with specimens

from the same quench. Specimens ture bath

were electro-polished

to avoid

any

heating to the annealing

in a low tempera-

contribution

of local

bath

process. *

Small pieces of the polished specimens were observed by transmission least 20 pictures point

electron

(2 specimens)

determine

including

the thickness

traces were observed. was obtained

microscopy

were taken

at 100 kV.

diffraction

of the foil

patterns

whenever

The average tetrahedron

by direct counting

At

for each experimental to slip

density

and the size distribu-

* Initial fast polish at -3O”C, 30 V and 1.5 A/cm2 35 % ethyl alcohol 15 % glycerine 50 o$ cone. HCl and the final slow polish at O”C, 22 V and 0.8 A/cm2 133 ml glacial acetic acid in 25 g Cr,O, 7 ml water

in

FIG. 1. Characteristic area of a specimen quenched from 890°C and annealed at 50°C for 60 min.

WESTDORP

et al:

STACKING

FAULT

TETRAHEDRA

IN

497

GOLD

(5) The density of tetrahedra remains constant throughout low temperature annealing except for the very early stage of annealing. The density is also independent of the annealing temperature. DISCUSSION I.

Growth of tetrahedra

A constant tetrahedw density within the limits of experimental error for various annealing times after constant pre-annealing of 2 min at room temperature was observed in our investigation for each annealing temperature. This fact, together with the increase of the maximum size peak (see Fig. 4) can be taken as evidence of growth of the stacking fault tetrahedra

Fra. 2. Charae~ristic area. of a specimen quenched from 890°C rendannealed at 50°C for 2 hr.

loo

606

so0

edge lengthlil

-

FIG. 4. Density and size distribution of tetrahedra versus annealing time at 50°C after quenching from 899°C.

FIQ. 3. Characteristic area of a specimen quenched from 890°C and annealed at 50°C for 4 hr.

The experimental results may be summarized as follows: (1) For the freshly quenched state-after 2 min at room temperature-there are no observable tetrahedra. (2) After a short annealing (e.g. 1 hr at 50°C) time, there are a few large tetrahedra (about 800 A in size) and many tetrahedra close to 100 A. (3) These tetrahedra grow on annealing. (4) Generally, they do not grow beyond 800 A in edge length for the present experimental conditions. (A few of them grow beyond 1000 A.)

Annealing

time

~lminl

-

FIG. 5. Density of tetrahedra versus annealing time after quenching from 890°C. (For clarity, duplicating experiments with equal annealing temperature have been omitted as well as the exact experimental points.)

ACTA

498

through

absorption

of vacancies

of the annealing.

METALLURGICA,

during the progress

The difference

in average

tetra-

VOL.

12, 1964

during the pre-annealing temperature)

and/or

treatment

hedron size for short and long annealing times can be

annealing.

seen directly from the electron micrographs

able tetrahedra in the as-quenched

of Figs. 1,

The observation

rule out the possibility

2 and 3. Moreover,

no

sessile

dislocation

stacking faults were observed. that a tetrahedron

loops

enclosing

We take this to mean

grows as a tetrahedron

without

vacancy

clusters.

that there are no resolvspecimens does not

of the existence of unresolvable

The rapid completion

has been definitely They

(2 min at room

during the very early stage of

confirmed

pre-annealed

the

specimen

for

of time at various temperatures

quenched

and

passing though an intermediate

stage of sessile disloca-

various periods

tion loops

We consider

found that 3 min at room temperature

of resolvable

growth mechanism and modified Maddin

size.

proposed

by Kimura,

is the active

Kuhlmann-Wilsdorf

process.

however, the possibility formed to a tetrahedron. smallest

to

is first formed and trans-

in their first attempt

can be drawn

is

observed

that

and not by the

tetrahedra

greater

should be energetically

unstable according

formation

Tetrahedra

which

of a sessile loop,

than

Moreover,

number of tetrahedra

to Hirsch’s

tetrahedra

is based

upon

the

is formed by the transwhich apparently

is not

from

of

quenched-in

the density

vacancies

is

and size of tetrahedra,

the low binding

be 2.7 x 10-4. all vacancies long

Simmons

This agreement

condensed annealing remains

period

annealing,

(except

the

existing

means

number small.

constant

of

that

tetrahedra

that almost and that

unresolvable

throughout early

vacancies

stage of

vacancy

migrate

a constant

by annealing an initial

and at -10°C which

of

value

for less than 1 hr, was found

of the number of

time,

as well

as the

decay curve, is based upon

energy

tried to measure

-35”C, decay.

annealing

from

for the divacancy, the binding

energy

experiments

slight

near 0°C.

decrease

They

in resistivity

after quenching

was followed

0.1 eV. of a diat

from 1000°C to

by the usual S-shaped

They also found that the initial decrease was

suppressed when the specimen was quenched to + 18°C

the an-

of visible tetrahedra (or

to

Since the density

for the very

where the number

it is concluded

and

to visible tetrahedra

clusters is negligibly

of tetrahedra

already

by

at 900°C

and the

that the density

calculation

of the vacancy

-3°C

result

vacancies

resistivity

reached

calculation

Balluffi(7)

the

small),

already

versus

observed

nealing

had

It was found

tetrahedra

They

time.

was made with specimens

(0.6 x lOi cm-3) after annealing

vacancy

of

the half decay

while the half decay time for the resistivity to be about 2 hr at 50°C.

is calculated

vacancy

off after reaching

in the present research a direct comparison

of the decay curve of quenched-in

concentration

after

that the number

and leveled

Fig. 4, to be 2 to 3 x 10m4. The thermal equilibrium from

by de Jong and Koehler,@)

the same quench.

2. Constant density of tetrahedra concentration

the S-

agree with the

De Jong and Koehler’s

calculated

to explain

does not

of this size

the case.

The

but

it

Frank sessile loops, it is

that a tetrahedron

curve,

conclusion

of vacancies

size calculation,

decay

of tetrahedra increased with annealing time from zero

exist.

critical

shaped

about the size of the

1000 A in edge length

assumption

This result of constant density of tetrahedra throughout almost the whole range of annealing supports the made by Kimura, Maddin and Kuhlmann-

Since

that

was sufficient

of tetrahedra.

assumption

of observable

understand

the nucleation

Wilsdorfc2)

No conclusion

sizes by the absorption

to complete

void

about 100 d in edge length grow to larger

transformation easy

It does not rule out,

investigation

tetrahedron.

tetrahedra

and

that a small unresolvable

of several tens of vacancies from the present

that the

by de Jong and Koehler

of nucleation

by Mori and MeshiPO.

is to

clusters).

instead of to -35°C. when the specimen after

completion

They attributed of divacancies: concentration

The initial decrease reappeared was pulse-heated

of the

initial

these phenomena immediately

of divacancies

at about

decrease

at

150°C -3°C.

to the formation

after

quenching

the

is less than that required

These tetrahedra (or clusters) may have been formed prior to determining the first annealing data. We

when

consider that new nuclei do not form at a later stage since the density remains constant. This conclusion

in equilibrium with single vacancies at an annealing temperature is built up during the initial decay period.

is further supported by the fact that the concentration of vacancies calculated from the tetrahedra density is in agreement with the concentration of vacancies

These phenomena, however, can also be understood as an interaction of divacancies with impurity atoms.

according to Simmons and Balluffi. The nucleation of tetrahedra should be completed during quenching,

divacancies

vacancies,

are

in

equilibrium

and hence a concentration

with

single

of divacancies

It is likely that an impurity decreases the electrical resistivity of both the impurity atom and vacancy when they combine with each other.(11-14) During the

WESTDORP

et al.:

STACKING

initial decay period, divaoancies may combine with impurity atoms to attain a divacancy-impurity equilibrium which may have a lower resisti~ty than the sum of the resistivities of separated divacancies and impurity atoms. It will be seen from the following consideration that this is a plausible mechanism for the initial decay. The number of jumps made by an average divacancy during the initial decay, 30 minutes at -10°C (the half decay time taken from their figure), is calculated to be about 7 x 105 taking the migration energy of a divacancy to be 0.6 eV. This means that the concentration of the effective impurity is about 1.5 x lo-*, which is quite reasonable for the purity of s~cimens used. It may be noted that a similar effect was found in a dilute alloy of AI-Sn.(la) On the other hand, the single vacancy divacancy reaction does not yield a proper value for the number of jumps. The number of jumps an average single vacancy makes during the initial decay period is calculated to be about 50 taking the migration energy to be 0.82 eV. Since the coneentration of vacancies is about 5 x lo-* for a quench from lOOO’C, an average vacancy needs about 2000 jumps to establish equilibrium between single and divacancies. The number 50 calculated from the experiment seems to be too small to establish the equilibrium. Hence, we consider de Song and Koehler’s reasoning from which they conclude the low binding energy of a divacancy not to be justified. Therefore, we consider that the disagreement between de Jong and Koehler’s calculated curve and the present observations in the number of tetrahedra versus annealing time stems probably from their assumed low binding energy for a divacancy. 3. Nucleation of tetrahedra Since nucleation of the tetrahedra is completed during the early stage of annealing (during the preannealing stage according to Mori and MeshiP)) no nucleus is formed during the later low temperature annealing. Vacancies have ample opportunity to collide during the annealing (the number of jumps made by a vacancy during annealing is about 108, whiie the concentration of vacancies is about lo-*), yet the formation of nuclei by collision of the migrating vacancies is prevented by some mechanism below 200°C during the later annealing. Therefore, it is reasonable to consider that vacancy clusters capable of absorbing additional vacancies are formed during quenching, that is, until the temperature falls below 200°C. We do not know as yet what mechanism prevents nucleation at low temperatures nor what is the critical size of a vacancy cluster capable of

FAULT

TETRAHEDRA

IN

GOLD

499

absorbing vacancies. Kimura, Maddin and KuhlmannWilsdorf(2) assumed a repulsive potential between two single vacancies about two atomic distances apart inhibiting the formation of divacancies during annealing after quenching from below 700°C. A similar mechanism might act to prevent divacancies combining with other divacancies. ~though we cannot calculate the number and size of the vacancy clusters formed during quenching without proper values of the binding energies for vacancy clusters of various size, it is quite likely that some vacancy olusters larger than divacancies are formed during quenching as considered by Kimura, Maddin and Ku~ma~-W~sdorf.(2) They showed that more than half of the vacancies become divacancies; some larger clusters may even be formed during quenching if the binding energy of a divacancy is about 0.4 eV. The repulsive potential, if any is not effective in preventing the formation of divacancies and larger clusters because of thermal energy at temperatures above 400°C. A large binding energy, 0.3 eV, was also proposed by Meshii, Mori and Kauffman.05) During pre-annealing (1 min at room temperature), some of the clusters formed during quenching absorb vacancies, grow and are converted to tetrahedra. We consider these are the nuclei. Some of the clusters are too small to grow and to be converted to tetrahedra. We may call the clusters, which become nuclei during pre-annealing, embryos. We can estimate the number of vacancies absorbed by the embryos during preannealing, in the following manner: The number of jumps made by a divacancy with migration energy 0.6 eV during pre-annealing is about 3 x 105. Hence, in average about half of the concentration of divacancies in a volume 3 x lo5 atomic sites surrounding an embryo have a chance to meet it. Since the concentration of quenched-in vacancies is 2.6 x 10m4, the number of divacancies in this volume is about 30. Therefore, an average of about 60 vacanciey can meet an embryo. Although we do not know the size of the embryo, we may consider the nucleus of the tetrahedra formed during pre-annealing to be about 60 vacancies, which is about 35 A in edge length. As discussed by Kimura, Kuhlmann-Wilsdorf and Maddin,f6) a tetrahedron can be dissolved by successive evaporation of vacancies, if a 70.5” ledge of full length is formed. For a tetrahedron of 35 A in side length, the energy of this ledge is about 1.5 eV, and the activation energy for the dissolution is about 2.5 eV (including the migration energy of a single vacancy). This energy is sufficiently large to stabilize the tetrahedron at 200°C.

ACTA

500

METALLURGICA,

4. Growth rate of tetrahedra and the S-shaped

throughout

of tetrahedra

the annealing

remains

period,

the growth

constant

the characteristic

S-shaped decay curve should be explained rate of the tetrahedra.

because

does not proceed

of

the

statistical

Although

tetra-

with the same rate

fluctuation

of

vacancy

arrival.

Hence, the exact shape of the observed decay curve is a superposition of the growth of tetrahedra of various sizes. the vacancy

Nevertheless,

the character of

decay curve should reflect the nature of

the growth curve of the single tetrahedron. shown qualitatively

It will be

here that the growth of a tetra-

hedron results in a type of S-shaped curve, although a mathematical

derivation

the discussion

S-shaped

Maddin

The growth rate is proportional

the number of vacancies on a tetrahedron.

to

in larger

annealing,

We may expect more

tetrahedra.

At

there is a maximum

but the size of a tetrahedron of sinks is a minimum; will be small.

the

beginning

number

of

of vacancies

of low temperature hedra

remains

independent

the rate of growth

Soon after, a tetrahedron

grows and

the number of sinks increases, but many vacancies are still available.

The growth rate will be high.

later stage of annealing,

In the

the number of sinks is large

annealing;

constant

when

the number

during

of tetra-

annealing,

and

is

of the annealing temperature.

(2) The tetrahedra of vacancies,

grow by successive

although

their

minimum

absorption size is not

known as yet. These observations (a) Vacancy

lead to the following conclusions:

clusters, which can act as embryos

the nucleation

of tetrahedra,

during quenching. the binding

energy

for

should be formed

This conclusion

implies that

of a divacancy

should

be

may

be

about 0.4 eV. (b) The

S-shaped

explained

vacancy

decay

curve

in terms of only the growth

rate of

tetrahedra. ACKNOWLEDGMENT

The authors would like to thank Dr. M. Meshii for making available to us their results before publication as well as for his valuable

and, hence, the number

therefore,

missed

CONCLUSIONS

of sinks on a tetra-

plus 4 (the number of corners).

is often

strain is introduced.

hedron is the number of 70.5” ledges in a tetrahedron ledges

curve

vacancies

why the initial slow

(1) Nucleation of stacking fault tetrahedra is a very rapid process. It is completed in the very early stages

and to the number of sinks

The number

of

quenching

is similar in nature to

given by Kuhlmann-Wilsdorf,

and Kimura.(16)

of quenched-in

portion

of the growth curve will not

explanation

10%

This would explain

be given. The qualitative

about

decay fast.

in terms of

hedra of similar size are formed during pre-annealing, their growth

12, 1964

of tetrahedra,

decay curve Since the number

VOL.

discussion.

REFERENCES 1. J. E. BAUERLE and J. S. KOERLER, Phys. Rev. 107, 1493 (19.571. \--- , 2. H. KIMURA, R. MADDIN and D. KUHLMANN-WILSDORF, Acta Met.

7,

145 (1959).

3. J. SILCOX and P. B. HIRSCH, Phil. Mag. 4, 72 (1959). 4. G. CZJZEK, A. SEEGER and S. MADER, Phys. Stat. Sel. 2, 558 (19621.

but vacancies

are few, and the growth

rate is again

slow. The

_ 0. M. DEJON~ and J. S. KOEHLER, Phys. Rev. 129,49 (1963). and R. MADDIN, 6. H. KIMURA, D. KUHLMANN-WILRDORF

model

existence

7. R. 0. SIMMONS and R. W. BALLUFI,

above

abnormally

can

explain

large tetrahedra

the

while the majority

still quite small (Pig. 1). These large tetrahedra be nucleated

during

quenching

and grow

of are may

to their

large size during annealing because of the increasingly large numbers of sinks on them. Upon low temperature annealing, these tetrahedra grow much faster than others and cease to grow when all the vacancies volume

surrounding

them are depleted.

nism for their fast nucleation known, but quenching

8. 9. 10. 11. 12. 13.

in a

The mecha-

during quenching

Appl.

14.

is not

strains may play an important

role. Since the number of these fast growing tetrahedra was found to be about 10% of the total number

15.

Phys.

Letters

3, 4 (1963).

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125, 1239 (1962).

16. D. KUHLMANN-WILSDORF, 2. Metallk. 49, 584 (1958).

R. MADDIN

and H. KIMURA,