Electrical resistivity recovery in cold-worked and electron-irradiated nickel

ELECTRICAL

RESISTIVITY

RECOVERY

IN

ELECTRON-IRRADIATED A.

SOSIN

J. A.

and

COLD-WORKED

AND

NICKEL* BRINKMAN

Pure nickel wires have been subjected to electron irradiation and cold work. Electrical resistivity recovery, starting at room temperature and extending to the recrystallization range, was studied. Recovery stages near 100°C (Stage III) and 27O’C (Stage IV) were found to occur by a diffusion process following cold work; dislocations are believed to be the defect sinks. Stage III was found to obey a second-order chemical rate equation following irradiation; Stage IV is essentially absent. An activation energy for defect migration of about 1.05 eV was found in Stage III following both irradiation and cold work; the energy associated with defect migration in Stage IV is not as well determined. These measurements plus other available data on nickel indicate that the defect migrating in Stage The close similarity between the recovery in nickel III is an interstitial atom in Stage IV a vacancy. and that in copper suggests a similar assignment in copper. RESTAURATION

DE

LA

RESISTIVITE ELECTRIQUE DANS PAR ELECTRONS ET DEFORME

LE

NICKEL

IRRADIE

Des fils de nickel purs ont et6 soumis a un bombardement d’electrons et deform&s a froid. Les auteurs ont Btudie la restauration de la resistivite Blectrique depuis la temperature ambiante jusqu’a celle de la recristallisation. 11s ont trouve que les stades de restauration aux environs de 100°C (3e stade) et 270°C (4e stade) resultent d’un mecanisme de diffusion provenant de la deformation; les auteurs pense que les dislocations servent de puits pour les autres defauts. Apres irradiation, le 3e stade de la restauration obeit a une equation du 2e ordre de la vitesse de la reaction chimique; le 4e stade n’existe pas. Les auteurs ont trouvi? que l’energie d’activation pour le deplacement des defauts Btait de 1,05 electrons volts au tours du 3e stade consecutif a l’irradiation et it la deformation; l’energie associee avec cette migration au tours du 4e stade n’est pas bien definie. Ces resultats, ainsi que d’autres, indiquent que le defaut se deplapant au tours du 3e stade est un atome interstitiel, tandis qu’au tours du 4e stade, il s’agit d’une lacune. La similitude entre la restauration du nickel et celle du cuivre suggere, pour ce dernier, une interpretation identique. ERHOLUNG

DES

ELEKTRISCHEN WIDERSTANDES UND ELEKTRONENBESTRAHLTEM

VON KALTVERFORMTEM NICKEL

Drahte aus reinem Nickel wurden der Elektronenbestrahlung und Kaltverformung unterworfen. Die Erholung des elektrischen Widerstandes wurde von Raumtemperatur bis zum Rekristallisationsbereich untersucht. Es ergab sich, dass den Erholungsstufen bei 100°C (Stufe III) und bei 270°C (Stufe IV) nach Kaltverformung ein Diffusionsprozess zugrunde liegt; vermutlich wirken Versetzungen als Senken fur die Fehlstellen. Nach Bestrahlung ergab sich fur Stufe III eine Reaktionsgleichung 2. Ordnung; Stufe IV fehlt im wesentlichen. Fur die Wanderung der Fehlstelle in Stufe III wurde nach Bestrahlung wie nach Kaltverformung eine Aktivierungsenergie von etwa 1,05 eV gefunden; die der Fehlstellenwanderung in Stufe IV entsprechende Energie liess sich nicht so gut bestimmen. Diese Messungen deuten in Verbindung mit anderen verfiigbaren Angaben tiber Nickel darauf hin, dass es sich bei der wandernden Fehlstelle in Stufe III urn Zwischengitteratome handelt, in Stufe IV urn Leerstellen. Die grosse Ahnlichkeit zwischen der Erholung von Nickel und der von Kupfer legt fur Kupfer eine ahnliche Zuordnung nahe.

1. INTRODUCTION

In the study of the production defects in metals it is desirable, examine

the behavior

one metal.

The

investigation. and motion of lattice if not necessary,

to

of these defects in more than

similarities

and differences

A comparison

of the results

The immediate found

in the

in

the

Michell and West.(1-3)

of

Clarebrough,

They measured

behavior in different metals offer a guide in the inter-

energy stored in pure copper, and moderately

the

defect

phenomena.

Among

the

metals, copper has received the greatest amount of attention. Nickel has been chosen for the present

pure nickel

results are shown in Figs. l-3. here are the following: (1) In pure copper

* Received July 21, 1958; in revised form October 1, 1958. t Atomics International, A Division of North American Aviation, Inc., Canoga Park, California. ACTA

METALLURGICA,

VOL.

7, JULY

1959

these

impetus for choosing nickel is to be work

pretation

of

in

two metals is given at the end of this paper.

(Fig.

arsenic-doped

l), the

about 290°C is associated

copper

by cold work. Their The points to be noted

energy released in the recovery 478

Hargreaves, the release of

majority

of the

stage centered at

with recrystallization.

SOSIN

AN,)

CLAREBROUGH,

BRINKMAN:

ELECTRICAL

ET. AL.

TEMPERATURE

i”C)

FIG. 1. Stored energy release, resistivity recovery, and Vickers hardness recovery of pure copper cold-worked at room temperature by Clarebrough et al.‘1-3)

There is, however, a definite ske-ness in the peak indicating that more than one recovery process is operating. (2) In arsenical copper (Fig. 2), the recrystallization peak is quite clearly defined and centered at about 330°C. The evidence for a- second process is less clear. (3) In nickel, two distinct stages exist. Clarebrough I

I

/

/

RESISTIVITY

47!4

RECOVERY

et al. have concluded on the basis of these measurements and associated measurements of electrical resistivity, density and lattice parameter, that the lower recovery &age is most probably associated with the migration and subsequent annihilation of vacancies; the upper stage is due to recrystallization. The purity of the nickel was 99.6 per cent. (4) Later work(*) on purer (99.85 per cent) nickel reveals some evidence for still a third process. From the available data, one can merely say that the “center temperature” for this stage is probably somewhere below 100°C. This later work was not known by us unt,il the present work work was nearly complete. The measurements of the recovery of stored energy, hardness, resistivity, lattice parameter and density changes following cold work, presented by Clarebrough et a.l., are extremely valuable. It was felt that an understanding of the recovery processes would be substantially aided by a detailed study of the kinetics of recovery. We have made such a study of the recovery of electrical resistivity in nickel following cold work and, to further aid the interpretation, we have also studied the recovery in nickel irradiated with 1.25 MeV electrons. The int~rpret~ationof the processes occurring during the various recovery stages is of utmost importance to imperfection studies in metals. Perhaps the most central point of disagreement has been the assignment

1 300 250

$

100

c

Cu+O.35% AS CLARERROUGH, ET. AL

z

i

E

AP

TEMPERATURE

Stored energy release and Vickers hardness recovery of arsenical-copper coldworked at room temperature by Clarebrough et aZ.‘l-s) l?m.

2.

(*c)

Fm. 3. Stored energy release, resistivity recovery and Vickern hardness recovery of moderately pure nickel cold-worked at room temperature by Clarebrough et al.‘---”

2 ..i ;

ACTA

480

of temperature vacancy

regions

and

and interstitial

activation

migration

the evidence for vacancy

METALLURGICA,

energies

in copper.

to

Since

VOL.

tivity

7,

1959

of annealed samples used in these experiments

varied

4 x 10e8 and 6 x 10ds !&cm.

between

Sub-

migration in nickel presented

stantially

by Clarebrough et al. seems quite conclusive, we have accepted this interpretation as our basic hypothesis.

occasions.

The cause was traced to faulty annealing

procedure,

as suggested

From the results of our recovery

rejected.

studies, we are then

able to make a definitive identification ture

range

in

which

interstitials

of the temperamigrate.

These

studies also allow us to make a compa.rison between the recovery

observed

found

these

that

sufficiently

well

regarding

in nickel

recoveries

to

allow

parallel

us to

the t.emperature

stitials and vacancies

and copper. each

draw

regions

It is other

conclusions

in which

inter-

migrate in copper.

It is obvious that a more straightforward

approach

toward studying defect migration in copper would be to work with copper itself. nature

Studies(5) of the present

have been made in copper

but have not been entirely migration

is found

for this purpose

satisfactory

to overlap

since defect

recrystallization,

as

shown in Fig. 1. We have chosen the more diverse route for three reasons: (1) The results of Clarebrough

et al. form a working

basis for interpretation, (2) point

defect

distinctly

recovery

separated

was shown from

to be more

recrystallization

in

nickel than copper, and (3) the results in nickel are important in themselves. Unless specifically stated otherwise, all the data presented were obtained using 99.98 per cent pure nickel.

All

samples

drawing through perature.

in wire

form

made

by

dies at or slightly below room tem-

Any pre-test annealing was done in vacua

at or above

700°C.

the experiments critical;

were

the

It is found during the course of

that annealing conditions

wires

were

extremely

were quite

susceptible

to

samples were mounted

on

contamination. The electron-irradiated lavite

holders

irradiation. lar

to

The experimental

that

Irradiations covery

and subsequently used

by

studies

The cold-worked

arrangement

Meechan

were carried

annealed and

at room

to

was simi-

90°K.

follows

that

temperature.

wires were also mounted

on lavite

of Meechan

and Brinkmanc6). with identical

wires were pre-annealed approximately

together

increase.

wire was prepared

to

In the

by drawing;

this wire was then cut into two parts, yielding

the

two required specimens. The

first specimen

successively vals.

was annealed

higher temperatures

at a series of

for equal time inter-

In the case of electron irradiation,

this specimen

was heated in fifteen degree intervals; each temperature

was five minutes.

the time at In the case of

cold work, the specimen reported here was heated in ten degree intervals;

the time at each temperature

was five minutes. The second specimen was annealed isothermally

at

a temperature recovery the

near the “center” of each of the main stages revealed by the first specimen. For

cold-worked

specimen,

were 82’ and 260°C; one isothermal

the

temperatures

was made at 100°C.

ing data may be analyzed recovery the

being monitored

annihilating

the result-

for several fact*ors. If the

obeys a chemical rate equation,

of the property with

used

in the case of electron irradiation,

As discussed by Meechan and Brinkman,

the part, p,

which is associated

defects,

should

follow

an

equation: dp = -Kf during an isothermal the reaction.

recovery.

Integration

pl-y

dt,

(1)

Here 1’ is the order of

of equation

(1) gives:

= c(t + M).

(2) constant and M is

Here C is a temperature

dependent

an integration

representing

constant

reduced, as a result of isothermal

temperatures up to 100°C and in a Fisher wax bath for temperatures between 100” and 350°C. Higher

initial value of p.

temperature

being

were performed

are

two distinct

and irradiated

the same resistivity work,

In this

histories

In the case of electron irradiation,

case of cold

were

ANALYSIS

the time which

would be required for the defect concentration

studies were made in a water bath for

studies

OF KINETICS

met.hod, two specimens used.

Such samples

of

of analysis used in the kinetics study

Re-

holders of various forms. Recovery

2. DISCUSSION

The method

above.

on a number

Brinkmanc6).

out at about

were started

prior

higher values were found

in

a furnace

annealing,

infinite value to that value corresponding measured

It is assumed

(resistivity)

to be

from an

to pO, the

that the property

is proportional

to the

where the samples were protected by an argon atmosphere. Electrical resistance measurements were

concentration

made in a liquid helium bath using the conventional

can therefore be made by plotting In p vs. In (t + M). If the chemical rate equation is valid, a value of M

four-probe

potentiometric

method.

The residual resis-

of the migrating

A test of the validity

defect.

of the chemical rate equation

SOSIN

AND

BRINKMAN:

ELECTRICAL

should exist so that this plot is a straight line.

The

Contrary to the implicit assumption for a chemical

obeyed in a solid-state discussed

below,

recovery

recovery

reaction.

it was found

stages failed to yield

often made, it

rate equation that

Indeed,

the

straight

cold-work

random

of infinite capacity is

finite

and

behavior

governing

migration

to see

the process was

of defects to sinks

or one in which the sink capacity

reduced

during

of p as a function

the

In equations

recovery.

The

of time over the entire

distance

(3b) and (3c), the

radius, a, is a measure of the size of the sink but is not intimately the defects.

related to the migration distance for D is the diffusion coeficient, presumed

to have the familiar temperature D = D

In these

data were re-analyzed

whether the rate equation one describing

as

the surface.

lines in the

ln p vs. In (t + M) plot for any value of M. cases, the isothermal

to be

481

RECOVERY

the surface of the sink, being the maximum from

slope of the line is then a measure of y. is not necessary

RESISTIVITY

where E,

--E&T

0e

is the activation

the defects. dependence

(4)

,

energy for migration

One might expect,

to determine E,

dependence,

therefore,

of

to be able

as well by studying the temperature

of 7.

The data have been analyzed more directly for E,. By comparing

the isothermal

curves with the tem-

length of the recovery stage for such a process depends

pering curves for identical

on the details of the model chosen.

mine the time 7i at which a value pi in the isothermal

We have investi-

gated three such models: (1) The volume

of point

(i.e.

grain

boundaries)

of spheres,

defects

boundaries

or

to the

the end ,of the ith pulse on the tempering

mosaic

carried out at a temperature procedure,

(2) the volume diffusion of point defects to internal (i.e. isolated dislocations),

and

-ri but

spheres (i.e. jogs, clusters, etc.).

the important

Ari E -ri -

obtained

(3) the volume diffusion of point defects to internal A dependence

one can deter-

curve is reached equal to the value of p measured at

diffusion

boundaries

cylinders

specimens,

Ti.

According

quantity Any

i--i.

to consider is not

straight

on a plot of In Ari vs. l/T,

by a unique activation

curve, to this

line section

is characterized

energy given by the expres-

sion:(Q

of p on time can be found for each of (5)

these models, although not necessarily in closed form. Since the models

are obviously

since the time dependence lar model,

oversimplified,

and

is sensitive to the particu-

there is usually

little hope of fitting the

entire recovery process by such an analysis. it can be shown that, in any model involving

random of point

of an initially uniform distribution

defects to a fixed array of infinite sinks, the dependence of p on time is the familiar t112associated phenomena

for sufficiently

3. PRESENTATION OF RESULTS AND INTERPRETATION

However,

migration

diffusion

where C’ is a constant.

with

small values of

3.1. Electron irradiation The resistivity,

p, vs. exposure

curve

for nickel

irradiated near 90°K with 1.25 MeV electrons is given in Fig. 4.

The damage rate is linear with a slope of

time.

8.5 x 1O-28 a-cm

A simple test of this model can be made by plotting We have done this for the Ap E (p,, - p) vs W.

curve for the same sample is given in Fig. 5. tempering

recovery

annealing stage centered at about 370°K is observed.

stages

observed

following

cold

work,

for

was

per electron/cm2. begun

at room

small values of t. The slopes of the straight lines one

Fig. 6 gives the isothermal recovery

expects

sample.

are equal to l/~l/~,

associated

where 7 is a “lifetime”

with the diffusion

process.

The values of

T for the three models are:(‘) 7E.z

respectively.

to be 1.03 eV f (3b)

.T = (64~~n%D)-~,

(3c)

concentration.

The An

at 100°C for this

and tempering

curves

are

to give a In Ari vs. l/T plot shown in

data, the activation

--

n2D ’

7 = (16a%%D)-1,

sink

then compared

temperature.

Fig. 7. The straight line criterion for a singly activated process is seen to hold. From a least squares fit of the

Here a is the radius of the sink and n is

the appropriate

The isothermal

The tempering

Note

that

in

equation (3a), the radius, a, is intimately related to the distance which a defect must migrate before reaching

energy for this stage was found

0.04 eV.

Returning

to the data for

the isothermal recovery, a plot of In Ap vs. In t (where Ap is the resistivitg change associated with a given recovery stage) is given in Fig. 8. The circled points are the original data.

It was then necessary to

choose a time, M, to add to all of the observed times, as explained

above.

M = 25 min was found to pro-

vide a best fit so that the readjusted

data would fit a

ACT-4

48%

METSLLURGICA,

VOL.

7,

1959

FIQ. 4. Electrical rosistivity as a function of integrated electron flux for 99,98 per cent pure nickel. Irradiation was carried out at about 90°K using I.25 rvIeV efectrons.

FIG. 5. Isochronal recovery of resistivity in pure nickel irradiated at about 90°K with 1.29 MeV electrons. The tempering rate is 3”K]min.

400

500

TEMPERATURE

600

C-K)

Frc. 6. Isothermal recovery at 100°C in 99.98 per cent pure nickel irradiated at about 90°K with 1.25 MeV electrons.

5.9:,“;

I IO

TIME

(

minutes)

1

t

1

SOSIN

BRINKMAN:

AND

ELECTRICAL

straight line.

The readjusted

by triangles.

The slope of t,his line is m = -1.01

0.01,

showing

The

data

recovery

f

obey

the

1 = 1.99 & 0.01. m

concerning

Stage III,

kinetics

with an order for the kinetics

y = 1-

called

this

recovery

are convincing

O

stage,

evidence

obeys a second order chemical

to

be

that the

rate process.

The bases for bhis confidence are the excellent straight line fits obtained

on the activation

on the

kinetics

order

important,

of

plot

IO

energy plot and

and,

perhaps

most

%

the fact that the order deduced is sensibly

integral and small. order

The interpretation

or one which

is greater

of a fractional

than

three,

say,

is

I

I

difficult. Taking

483

RECOVERY

data points are enclosed

that the recovery

chemical rate eyuation

RESISTIVITY

II

I

I

I

II

10

into

account

damage produced

the

be interpreted

of interstitial

(2) annihilation (3) divacancy

of vacancies production

(4) di-interstitial

nature

by electron irradiation,

data should, presumably, (1) annihilation

simple

the

the above in terms of

at vacancies,

at interstitial

atoms,

and rapid annihilation,

production

These interpretations

atoms

of

or

and rapid annihilation.

will be further discussed below.

In t

Guided by the work of Clarebrough

et al., an initial

study was made of cold work recovery

via a temper-

ing procedure.

The first results are shown in Fig. 9

are represented large

by

the

drop

circled

found

reading at room temperature prompted

points.

between

The first

the

and the one at 125°C

us to make another

study;

these results

are given in the same figure by the points enclosed

I

\

1000

3.2. Cold ulork

and

E= 1.03e.v.

Ii

FIG. 8. An analysis of the isothermal recovery data of Fig. 6 to determine the order of chemical kinetics governing the process in Stage III in 99.98 per cent pure nickel after electron irradiation.

unexpectedly

T

I

100

I\

with triangles.

These samples received a nominal

per cent area reduction. the recovery

observed

It may be significant near

100°C is larger in the

second sample than in the first.

It is believed

this difference is due to the additional exercised

in maintaining

the

-2 1

Fig.

10 gives the recovery

elongated

+

that

care which was

second

lower temperature during cold work.

C

40 that

sample

at a

For comparison,

of a sample

which

was

10 per cent.

In all cases, the existence of three recovery stages is found. These are Stage V, centered about 500°C; Stage

IV,

centered

about

270°C;

and

Stage

III,

centered about 90°C.

Guided by these data, a detailed study was made of Stages 111 and IV.

0

Before discussing the results of the detailed study,

\

two

0

L

2.5

2.7

2.6

1000/T

!.S

3.0

(“K)

FIG. 7. An analysis of the data of Figs. 5 and 6 to determine the energy of migration for the defect migrating in Stage III in 99.98 per cent pure nickel after electron irradiation.

should

in cold

unexpected

\

2.4

points

recovery

\

be work

in view

mentioned. found

The

of the fact

that

Clarebrough et al. fails to show it. this discrepancy are not known. possibilities

exist.

Their

Stage

III

here was somewhat

resistivity

the work

of

The reasons for A number of measurements

were made on a sample whose geometry

is far from

ACTA

484

METALLURGICA,

VOL.

7,

1959

FIG. 9. Resistivity

recovery of 99.98 per cent pure nickel following a nominal 40 per cent reduction in area by cold-drawing near room temperature.

;

0 6 __

99.98%NICKEL 40 “/o AREA

REDUCTION

0.6 04 0

300 TPC)

200

100

ideal for these measurements, the other

measurements

the measurements ments,

although

they

for

is greatly in

discrepancy

a better way of explaining

is completely

fact, the residual resistivity upon

annealing

in this

masked

this

purity

used

work.

It

We have found that by impurities.

In

has been found to increase temperature

sample of 99.4 per cent purity.

resistivity

IV.

by

Clarebrough

should

be noted

range

for

a

This is the range of et al. in their

further

that

earlier

a rise in

was also found in the corresponding

tem-

to be made concerning

sample

compared

sample.

The detailed

process

study

11-13 for a new sample, area reduction.

260°C.

recovery

In each case, the temperature

perature”

of recovery

below the “center

to make the time scale convenient.

given in Figs. 14 and 15. is found

temThe

from these figures are

A well defined activation

in Stage III;

64

E = 1.08 f

0.09 eV

i

62

w jp--+

5 N P

Fig. 13 is

curve for Stage IV taken at

was chosen to be somewhat

energy

curve, start-

Fig. 12 is the isothermal

curve for Stage III taken at 82°C.

the isothermal

in Figs.

to 56 per cent

Fig. 11 is the tempering

ing at room temperature. recovery

is presented

cold-drawn

amount of impurity.

The reason for this rise remains

in

further detail and will be discussed shortly.

In ari vs. l/T, plots deduced

Boas(*) suggests that it is due to

with the 10 per cent

This has been investigated

perature range for the arsenical copper with a similar to be determined;

Figs. 9

Stage III is enhanced in size for the 40 per cent

cold-drawn

by referring to the purity of the samples

used here and by Clarebrough(2).

away from their atmo-

and 10 is the relative sizes of recovery Stages III and

tensile-tested

this work. There is, perhaps,

of dislocations

Another observation

Our measure-

were made in a liquid

It seems fair to claim greater sensitivity

Stage III

the movement

spheres under thermal activation.

Furthermore,

helium bath where the thermal resistivity reduced.

600

500

excellent

made.

were made at 20°C.

as stated previously,

400

60

t

FIG. 10. Resistivity recovery of 99.98 per cent pure nickel following 10 per cent tensile strain near room temperature.

5 6 __

99.98%’ NICKEL 10 % EXTENSION

5.0 0

100

200

300 T PC)

400

500

600

Isochronal recovery of ra&in 99.98 per cent pure nickel followiag a nominal 40 per cent area redrrction by wire-drawing near soonl

FIG. Il. tivity

TEMPERATURE

SAMPLE

IOK)

At

NlCKEL - 99.98% ISOTHERMAL

PURE

- 355*K

STAGE III

FIG. 12. Isothermal recovery at 82°C in Stage IIS for a 99.98 per cent pure nickel wire with the identical history of the wire shown in Fig. 11 v Tha quantities Tzl 7-2and &tg, We r&&ed tr> $he methad of anal@. us& and explained in the text.

Li

otIO

* too

It 1 (TIME,

second%1

NlCKEL

TIME, (seconds)

- 99.98

% PURE

ACTA

486

METALLURGICA,

VOL.

7,

I959

\

I

\ NICKEL 99.98 STAGE IU

% PURE

\ lO,OOC 3-

\

-

a

IOOf3-

ini@

.-

2 IOCl-

IC )-

2.50

‘0

2.70

2.80

2.90

3.00

1000

TFIG. 14. An analysis of Figs. 11 and 12 to determine the energy of migration for the defect migrating in Stage III following cold-drawing of 99.98 per cent pure nickel.

3.2 :0

SOSIS

100,000

10.00c

AND BRINKMAN:

ELECTRICAL

r

,

f- -

-

RESISTIVITY

j

487

RECOVERY

/STAGE=

2.5

\ /

I

-

lOO()-

1

0

G

\

/

I.oev

tot )t \ 3

\

o\ 0

--

IC)-

~

--

\

, \

i 1.7

2.1

)

1000 T-

FIG. 15. An anctlysis of Figs. 11 and 13 to determine the activation energies ascribed to the recovery in Stage IV following cold-drawing of 99.98 per cent pure nickel.

2 .’4

ACTA

488

METALLURGICA,

VOL.

7,

1959

i.s-

FIG. 16. Replot of the data of Fig. 12 for short times t,o determine whether the process is one described by volume diffusionof defects to a random array of infinite capacity sinks.

s (as

determined

(seconds)“’

by a least squares fit of the data).

Two processes appear to be distinguishable IV

with activation

energies

in Stage

The conclusions Stage

and 2.5 eV. A plot of fn Ap vs. In t has also been made for each

defect

of these stages.

in Stage IV is not as simple to interpret.

case was it possible

obtain a straight line with adjustment parameter appearing in equation that the processes

operating

to

of M, the time

(2). This is evidence

are quite

infinite

sinks

but

values of activation

volume

diffusion

infinite sinks).

These plots are given in Figs. 16 and

27. In both cases straight lines were obtained. characteristic this amount

relaxation

to The

times for these stages and

of cold work are 3.9 x lo3 set in Stage

Evidently

infinite

the

the situation

The evidence of point defects to

presence

of

the picture.

two

are anomalous. A value of 1 eV in Stage IV seems difficult to understand, 1.08 eV having been found to characterize

the single

process

value of 2.5 eV is unreasonably it is reasonable

in Stage

to expect the activation

a”

I

I

KINETICS”

;I~ ,.o -

I 6

I 8 -h%?

10 (

12

seconds) “’

I 14

The

energies for

different processes to follow a pattern proportional

,^--I

4

III.

high, assuming that

S 1.20 m b 5 I.,

I 2

the

energies for these two processes

zu 1,‘~~ ’

0

activation

Furthermore,

“DIFFUSION

0.9

point

presumably

~nfo~unately,

I

FIG. 17. Replot of data of Fig. 13 for short times to determine whether the process is one described by volume diffusion of defects to R random array of infinite capacity sinks.

some

sinks,

suggests, once again, the migration

chemical rate equation. We have, therefore, plotted Ap vs. W for reasonably short times as a test of kinetics

to

related to dislocations.

energies complicates

diffusion-type

clear.

is migrating

by a

(i.e.

are not governed

III

to be drawn from these data for

1 eV

In neither

of approximately

III (at SS*C) and 4.8 x IO3 see in Stage IV (at 260’Cf.

16

I IS

to

SOSIX

ANL)

RRINKMAN:

K 9:

ELECTRICAL

I

r y

18. A resistivity vs. time1/2 plot for per cent pure nickel wires to deterthe effect of various amounts of work on the defect lifetime at 82°C. the amount of strain and 7 is a measure of the defect lifetime.

I

4s9

RECOVERY

,

STAGE m NICKEL (99.98%) EFFECT OF AMOVNT OF COLD-WORK

14.0

5

FIG. 99.98 mine cold E is

RESISTIVITY

E = 0.80

T=820C

13.0

m b

12.0

x

T = 4.5 X IO-3SEC

”

u

:

5

j

Ai I E=0.25

11.0

n

E iii s 10.0 T

=5.2

Xl03

I

SEC. I

A

<=0.09 9.0 8

4

12

PO

16

24

28

36

32

40

44

-(seconds)“”

the melting

temperature.

The experiment

peated to resolve this difficulty. activation

energies persisted,

ditional information If

however,

of the

the

“lifetime”

for

of the amount

these

shown in equations defect

concentration.

defects This

(3b) and (3~);

lifetime is inversely proportional Equation

of point

one would expect

of cold work,

mines the sink concentration.

would

be a

which deterexpectation

is

in both cases the

to the square of the (3e)

does

not

ex-

plicitly state such a dependence. To test these ideas, three more wires were colddrawn.

The area reductions

25 and 80 per cent.

These

annealed, first at 8S”C, later at 260°C.

were approximately

9,

wires were isothermally I

_

These results

are shown in Figs. 18 and 19. A dependence

of life-

time on amount of cold work is observed in the correct direction

migration

defects to infinite sinks is correct, that

with no ad-

being obtained.

the interpretation

function

was re-

The presence of two

in Stage III but the dependence

on the amount amount

of cold

work,

of area reduction,

was anticipated.

of lifetime

as expressed

for instance,

by the

is less than

The lifetime for the defects in Stage

IV is remarkable,

being independent

of the amount

of cold work for the samples tested. It is also interesting tivity

recovery

The magnitude

found

to note the amount

of resis-

in each stage for these wires.

of the recovery linearly

in Stage III is found

to depend

almost

on the amount

of area

reduction.

A fit of the present data gives Ap = E’.~,

where 8 is the amount of strain (i.e. area reduction). The uncertainty

in the amount

of strain and in the

I

STAGE Is? NICKEL 99.98% EFFECT OF AMOUNT OF COLD WORK T=xo”C

FIG. 19. A resistivity vs. timelI plot for 99.98 per cent pure nickel wires to determine the effect of various amounts of cold work on the defect lifetime at 260°C. F is the amount of strain. The lifetime is found to be independent of E.

ACTA

490

magnitudes

of the recovery

to be attributed

stage make this dependence tainty.

The magnitude

entirely clear. III

of the recovery

The magnitude

seems to be reasonable.

lifetime

in Stage IV is

of the amount

can be understood

of strain for

and the constancy in Stage IV are not

is only

slightly

accepted for

7,

in the noble metals and is expected

nickel

di-vacancy

as well.

It

migration

mechanism

with this interpretation is found

following

view of the observed

of

by the amount

of

The present

experiments

model.

is an interstitial the

defects

interstitials part,

and those

pertinent

The defect migrating atom;

IV is a vacancy.

to

in Stage III

the defect migrating

in Stage

In the case of electron irradiation,

produced

are

and vacancies.

by a bi-molecular

predominantly

isolated

These recombine,

in most

process

as di-vacancy

in Stage III.

The

forma-

The difficulty

irradiation

although

di-

in Stage III in

second order kinetics.

identity

of the dislocation

arrangements

infinite sinks for the migrating

or boundaries

nickel from X-ray in Stages

diffraction

data.

III

and IV

of

this

following

to dislocations

cold

sinks.

assumption

who has

of a given concentration

has almost

of

no effect on the

migration of further defects to dislocations; are potentially

The

is demon-

strated by the recent work of Thornson( shown that the migration

It is

model for

assumes infinite capacity

soundness

dislocations

of

found by Gay, Hirsch and Kelly(g) in

work explicitly

defects

as

These sinks

to point out that the proposed

the recovery physical

serving

defects.

are believed to be mosaic boundaries

pertinent

in most part at least, by the

the

The model presented thus far has not revealed the

cold-worked 4. DISCUSSION

to hold that

for Stage IV could

would have been produced

the “particles”

these can be understood,

be argued

is that no Stage IV recovery

electron

The small variation

by referring to equation

affected

might

apply if Stage III is interpreted

vacancies

cold work.

following

1959

of the recovery in Stage

one need only to assume that the spacing (3a); between boundaries serving as traps for the point defects

VOL.

tion in the case of electron irradiation.

the range of strains investigated. The behavior of these lifetimes of the magnitude

to the

subject to sizeable uncer-

of recovery

found to be independent

METALLURGICA,

therefore,

infinite sinks.

Nicholas@)

remaining portion which does not anneal in Stage III

is also led to this conclusion.

is to be associated

from the data, a value of Do/a2 = 5.5 x lo5 set-l for

irradiation

with point defects trapped

and Stage III

annealing.

In nominally

pure materials, impurities in low concentration adequate

trapping

sites for such a process.

case of cold work, the migrating

during provide In the

defects remain the

Stage IV.

Our analysis

gives D/a2 = l/n2r = 2 x Do and D are related as shown in equa-

lop4 set-l. tion

(4).

Taking

same but the effective trapping sites or sinks for these

of uncertainty ment

These interpretations

agree with the deductions

Clarebrough

et a1.(2) and the subsequent

Nicholas(s).

Nicholas

has analyzed

analysis

an activation

find Do/a2 = 6 x lo4 set-i.

defects are dislocation

arrangements.

involved

to an order

Nicholas’(*)

of

leads to a “particle”

size of about

in the peak due to different heating rates.

From this

to 0.04 p for 33 per cent rolling.

analysis,

energy

deduced

an activation

of

0.98 eV. He has concluded that the Stage IV recovery is due to vacancy

migration,

interstitial migration.

di-vacancy

Despite

of LeClaire(ll), 7 pu; our value

2 ,u. The observed

Gay Hirsch

agree-

seems reasonable.

value, using the analysis

leads to one of about

of 1 eV, we

in such calculations,

stored energy release in Stage IV, as well as the shift Nicholas

energy

With the large amount

of magnitude

of

the shape of the

He is able to deduce,

values of

and Kelly(g) were in the range of 1.9 p

the apparent

consistency

of the proposed

model, it is necessary to point out again that not all

migration

or

of the data are suitably

Referring to the calculations

of

It is particularly

accounted

for by the model.

difficult to understand

the pair of

Huntington on interstitial migration and to the calculations of Bartlett and Dienes on di-vacancy migration

some of the initial interest in nickel was due to the

in copper, and extending

evident

in a qualitative preference

manner,

for the vacancy

these calculations he has shown migration

to nickel a definite

interpretation.

He further points out that the density changes observed are not of the correct magnitude for interstitial annihilation. The interpretation of Stage IV in terms of interstitial migration is completely eliminated here by the bimolecular recovery found in Stage III, assuming that interstitials move at a lower temperature than vacancies. This assumption is generally

activation

energies

separation

found

IV.

Although

of Stages IV and V, the present

work and other associated have demonstrated

in Stage

work in this laboratory

that Stage V recovery

in nickel

does overlap Stage IV recovery to some extent. It is believed that the larger activation energy, about 2.5 eV, is more properly associated with Stage recovery. Further evidence for this interpretation

V is

the activation energy determined by Burgess and Smoluchowski(12) for self diffusion in nickel: 2.8 eV. Assuming

that the 2.5 eV energy can be accounted

SOSIN

BRINKMAN:

AND

ELECTRICAL

RESISTIVITY

for by a self diffusion process (presumably

the forma-

that by quenching

tion and motion

dislocation

concentration

climb),

of vacancies,

it remains

activation

difficult

initiating

to understand

the lower

energy, 1 eV, in light of the 1.08 eV found

in Stage III. anomaly

One way to account

for this apparent

is to assume that the ratio of the values of

the diffusion

D,, for the defects in Stage

coefficient,

III and Stage IV is approximately possible,

it does

explanation

not

seem

likely.

of this anomaly

the agreement

between

104. While this is Whatever

is, it must account

Recently,

the strain field around a dislocation D, for vacancies.

coefficient,

or less similarly depending properties to copper

His results indicate that

tive magnitude deuteron

much

activation

as 0.5 eV.

He also finds that the

energy

may

It is possible

be shifted

lation

for interstitials

altered,

however,

associated

should

show

of the effect

with

due

to

might

the

Such a calcusimilar

results;

be appreciably

large

the interstitial.

Stage III should also exhibit

as

that the difficulties

discussed above are due to this effect. the magnitude

by

elastic

strain

If this is correct,

the anomaly,

contrary

Still another difficulty

requiring

of the magnitude

in Stage IV mentioned

clarification

is the

and lifetime for recovery

earlier.

One might speculate

that these data are related to the nature of plastic flow.

At small deformations

amount

defects is controlled

by energy considerations

of vacancies

tion of interstitials. slip predominates, geometrical becomes

as compared

small

important.

Obviously

of the recovery

work in progress

interstitial

is

In Stage I, copper

intermediate

and

the

is just reversed in Stage III,

interrelationship

suggesting

The an

between the two stages.

The behavior

of copper has served as a guide in a

large part of our work in nickel. similarity

the most,

least.

should be expected.

Some

degree

of

The two atoms are of

nearly equal mass;

both structures are face-centered

cubic.

interesting

Particularly

the data

concerning

copper doped

to this comparison

the neutron

bombardment

is of

with as much as 1 per cent nickel.07)

This doped sample shows essentially the same behavior region between I and

III) as pure copper. There are also reasons to expect possible differences between nickel and copper.

The electronic

is, at first glance, significantly a 3&O 4s1 structure,

different.

accounting

structure

Copper has

for its simple elec-

structure.ls

hole in the d-band

production complete

should

help in

arriving at this understanding.

The

nickel’s ferromagnetic is ferromagnetic

behavior.

should

overemphasized.

be borne

In fact,

in mind

damage

of the

data, that this

in the discussion

or cold-work

for

but not

it is the opinion

has little, if any importance radiation

accounts

The fact that nickel

authors, on the basis of the avaiiable

effects

with

of the which

this paper is concerned. A comparison

5. A COMPARISON OF THE RECOVERY CHARACTERISTICS OF COPPER AND NICKEL

The theories of imperfections

recovers

gold

favoring

is lacking at this time.

on nickel

recovery

Metallic nickel has a 3d10-0.6 ~sO.~

is primarily a

following

These

tronic properties.

In a later stage of flow cross and

materials,

12°K.

of point

to the forma-

point defect production

in nature,

more

understanding Further

where a relatively

of cross slip occurs the production

the formation

at

is the rela-

stages near 40”Kf15)

three

in Stages I and II (temperature

to what is observed. constancy

for these

the

are impor-

of the deviations

bombardment

respectively. situation

apparent

it

stages are hereafter referred to as Stages I and III,

with respect

distance from the dislocation.

To some extent

of the recovery

240”Ku6)

silver

for an appreciable

In particular,

is realized, but the deviations

Most conspicuous

D is very sensitive to the polar position of the vacancy to the dislocation

it has

on how closely t,heir other

in their behaviors.

expectation

upon the diffusion

material,”

resemble those of copper.

tant.

the effect of

the simplest

was expected that silver and gold would be very close

and

Berghout(13) has calculated

achieve

In pursuing copper as a “standard

for

the present results and the

one would

of defects, an excess of astable vacancies.

been the hope that other meta,ls would behave more

the

analysis of Nicholas@).

49 1

RECOVERY

is presented

of the recoveries of copper and nickel

below.

electron irradiation

The

recovery

data

following

and cold work are sumnmrized in

Table 1.

in metals have leaned

very heavily on the data on copper. There are excellent reasons for this, both theoretical and

5.1. Stages I and II

experimental. It is, however, necessary to consider data on other metals. The most conspicuous example

been performed by the Oak Ridge group at 22.4”K.og)

of this point is the work on the quenching

the samples and $ is the integrated

of gold;(i4)

to date, no comprehensive work on the quenching of copper has been published. It has been the belief

Neutron bombardments

of copper and nickel have

The damage rates (dp/d& where p is the resistivity

of

neutron flux) are

1.1 x 1O-26 and 3.3 x 1O-26 !&cm per neutron/cm2, respectively. The recoveries up to 90°K are quite

ACTA

492

METALLURGICA,

VOL.

7,

1959

helium bath have also been reported.(20) cent extension

produced

a change

copper of 2.9 X lo-* !&cm;

An 18 per

in resistivity

in

a 14 per cent extension

produced a change in resistivity in nickel of 6.2 x IO-8 A-cm. The ratio of the resistivity changes, adjusted

for the slightly

work, is about 2.5.

amounts

of cold

Upon warming to 90”K,

different

about 2

per cent of the resistivity

change recovered

in each

wire. In neither case was a sharp recovery stage found in this temperature region: Stage I is absent in cold work. 5.2. Stages III,

IV and V

The most important

data for the present discussion

is given in Table 1. In addition, the two metals are compared

recovery

curves for

in Fig. 21 on a tempera-

ture scale reduced by the respective melting temperatures,

The details of the recovery in Stage IV follow-

ing cold work for copper are complicated ipcY 106’6ELECTRON

with Stage 77; ree~stallization

ICM21

PIG. 20. A comparison of electrical resistivity changes due to irradiation with 1 MeV electrons below 15% as a function of integrated flux. The dashed vertical lines indicate the extent of recovery following irradiation due to warming to about, 60°K for a short period of time.

even in Stage IV.21 Stage IV has not been clearly discerned irradiation

for copper.

about

recovers.

40 to 50 per cent of the resistivity

In both

region is found:

materials,

a dominant

recovery

Stage I is present after irradiation,

by Meeohan.(22) electron

We have also irradiated

copper

and nickel

(99.99

tures

LIP

15OK. with

The

samples

were

1 DnreV electrons.

irradiated

The damage

rates were found to be 3.6 x 10ez7 and 10.6 x 10m2’ Q-cm per electron/cm2.

Note that the damage rates

in both typos of bombardment

differ by a factor

three.

60 to 70 per cent of

Upon warming to 60°K,

the resistivity

recovers

in each.

Tbese

results

of are

given in Fig. 20.

‘FABLE

1.

to

occurs,

while in a liquid-

by the

annihilated

appreciable

e.g. 150°C.

allow dislocation

extent.

since the con-

The irradiation defects

do not

to resistivity;

climb and rearrangement,

decrease is observed.

they do and a net

Observation

be helpful

of this

in ~onfirmil~g this

and might shed some light on the Stage energy anomaly

is

where Stage IV recovery

Since the point

in nickel would

activation

at

than by

rather

annihilation,

remain, they do not contribute

effect

created

quickly

of point defects is never allowed to build

any

resistivity

of the latter is

the irradiation

carried out at, a temperature

model,

Similar data for wires elongated

during

are

direct interstitial-vacancy centration

below

for such

annealing reported

and interstitials

bombardment

per cent pure Cu, 99.98 per cent pure Ni) at temperasimultaneously

of radiation

The interpretation

that the vacancies dislocations

centered at about 40°K.

following

The only evidences

recovery are the “tail” of the recovery shown in Fig. 2 1 and the phenomenon

similar;

by overlap

is found to commence

IV

as well.

A~~~___ comparison of recovery following electron irradiation and cold-working of copper and nickel

._.~_

stage III

Stage IV ._~~~

Tc/Tm Copper Nickel

C.W.

0.18” i 0.20’

e0.23* 0.22c

Kinetics

Emi C.W. 0.7 1.08’

O&b

1.03c

c,w.

!

DifC

-.

I y=2’

‘_ .-__

!

Tc/Tm O.-a&‘.

O.3Od ! 0.31e

0% -

/

C.W.

l.lR” 1.0’

e--

1.38” -_:_

Kin&es

I

Em (eW

_.

C.W.

~

Dif” DifO ~~.

e-

- --

-..

a. see reference 21, 6. see reference 6, c. present work, d. see reference 5, e. see reference 22. !Z’JT, = ratio of the temperature at the “center” of the recovery stage t,o the melting temperature. E, = the activation energy for migration of the defect moving during the recovery. C.W. = results for coldwork. y = the order of the chemicatrate equation obeyed by the moving defect. e- = results for electron irradiation. Dif = indicates that the process occurs by a diffusion mechanism.

SOSIN

AND

BRINKMAN:

ELECTRICAL

The situation regarding Stage V in both copper and nickel, i.e. recrystallization vation

energy,

with a self-diffusion

is relatively

well understood

acti-

RESISTIVITY

migration

given previously

and

for the ACKNOWLEDGMENTS

The authors performing 5.3, Conclusions is of interest

for nickel is correct

applies as well to copper.

purpose of this paper.

express their thanks to H. Neely for

the experiments

to L. H. Rachal

In comparing

493

RECOVERY

the behaviors to propose,

of copper and nickel, it

following

a suggestion

by

cold-working

on radiation

for performing

effects.

Helpful

Meechan are also gratefully

effects and

the experiments

discussions

on

with C. J.

ack-iowledged.

06

Q

aa

Q-

FIG. 21. &4 comparison of electrical resistivity recovery in 99.99 per cent pure copper’6’ and 99.8 per cent pure nickel following 1.25 MeV electron irradiation near 90°K. pi is the total residual resistivity change due to bombardment. T, is the melting temperature.

A. Seegertz3), that the residual electrical resistivity the two metals should behave quite similarly. t,rue since resistivity

the

s-electrons

with

S-electrons d-band

portion

is determined

spin parallel

with

parallel

scattering.

and copper model,

residual

of nickel

suffer

If the differences expect

the

electrical

primarily

by the

to the d-band

spin

can be accounted

one would

of

of

This is

holes.

appreciable

between

nickel

for by such a simple

the conductivity

of nickel

at very low temperatures to be lower than the conductivity of copper in the ratio of 0.3 : 1 since the carrier concentration ratio.

Allowing

0.3 electrons,

is reduced

by essentially

for some contribution one might

vary by about one-third.

expect

this

from the other

the resistivities

to

This confirms the findings

as shown above and suggests that the defect configurations in the two metals following cold work and radiation damage may be quite similar. On the basis of the large amount of similarity, it seems fair to conclude that the data on copper and nickel reaffirm and supplement accepted,

one can conclude

each other.

If this is

that the model for defect

This work Btomic

was performed

Energy Commission

for the United

States

under Contract AT- 1 1- I-

GEN-8. REFERENCES 1. L. M. CLAREBROUGH, M. E. HARGREAVES, D. MICHELL and G. W. WEST, Pvoc. Roy. Sot., Lord. A215, 507 (1952). 2. L. M. CLAREBROUGH,M. E. HARGREAVES and G. W. WEST, Proc. Roy. SOL, Lond. A232, 252 (1955); Phil. Mag. 1, 528 (1956). 3. D. MICHELL, Phil. May. 1,584 (1956). BOAS, Dislocations and Mechanical Properties of 4. W. Crystals p. 333. Wiley, New York (1957). 5. J. A. BRINKMAN, C. E. DIXON and C. J. MEECHAN, Acta Met. 2, 38 (1954); D. B. BOWEN, R. R. EGGLESTON and R. H. KROPSCOT, J. AppZ. Phys. 23, 630 (1952). 6. C. J. MEECHAN and J. A. BRINKMAN, Phys. Rev. 103, 1193 (1956). I. R. M. BARRER, Diflusion in a.nd through Solids. Macmillan, New York (1941). 8. J. F. NICHOLAS, Phil. Meg. 46, 87 (1955). 9. P. GAY, P. B. HIRSCH and A. KELLY, Actn Met. 1, 315 (1953). 10. R. THOMSON, Acta Met. 6, 23 (1958). 11. A. D. LECLAIRE, Aetn Met. 1, 438 (1953). 12. H. BURGESS and R. SMOLUCHOWSKI, J. Appl. l’hys. 26, 491 (1955). 13. C. W. BERGHOUT, Thesis, de Technische Hogeschool te Delft; Acta Met. 6, 613 (1958) 14. J. E. BAUERLE and J. S. KOEHLER, Phys. Rw. 107, 14!)3 (1957).

ACTA

494 15. H.G.

METALLURGICA,

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94,496

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(1954).

16.J. W. MARX, H. G. COOPER and J. W. HENDERSON, Phyls. Rev. 89, 106 (1952). 17. T. H. BLEWITT, R. R. COLTMAN, D. E. KLABUNDE and T. S. NOGGLE, J. Appl. Phys. 28, 639 (1957). 18. N. F. MOTT and H. JONES, The Theory of the Properties

of Metals

and Alloys p. 222. Oxford University Press. (1936); R.J.WEISS and J.J.DEMARco, Rev.Mod. Phys.

30,59

(1958).

VOL.

7,

1959

19. T. H. BLEWITT, R. R. COLT&IAN,D. T. 8. NOGGLE ORNL-2188,(1956).

20. C. J. MEECHAN and A. SOSIN,J. A&.

K. HOLMES and Phys.

(1958).

21. R. R. EGGLESTON,ActaMet. 1, 679 (1953). 22. C. J. MEECHAN, J. A&. Phys. 29, 197 (1957). 23. A. SEEGER,2. Phys. 144,637 (1956).

29, 738