Electrical resistivity recovery of cold-worked high purity nickel

ELECTRICAL

RESISTIVITY

RECOVERY

H. KRESSEL,t$

OF COLD-WORKED

D. W. SHORT?

and

HIGH

PURITY

NICKEL*

N. BROWN?

The ekxtrical rcsistivity of high purity nickel deformed at - 196°C shows a stage II recovery with an activation energy of 0.54 eV, stage III with an activation energy of 0.86 eV and stage IV with an activation energy of 1.32 eV. The data are interpreted in terms of stage III recovery being due primarily to interstitials annihilating vacancies, and stage IV recovery being due to vacancies going to dislocations. The results suggest that during plastic deformation the number of vacancies generated is appreciably greater than the number of interstitials. RESTAURATIOX

DE LA RESISTIVITE ELECTRIQUE DU NICKEL DE HAUTE PWRETE DEFORME A FROID La r&istivit(! Blectriquedu nickel de haute purete deform6 a - 196°C montre un stade II de rest,auration avec une energie d’activation de 6,54 eV, un &ads III avec une Bnergie d’activation de Q,86 eV et un stsde IV avec nne irnergied’act,ivation de I,32 eV. Les don&es sont interpr&ees en considerant que le stade III de la restauration est dh essentiellement a l’annihilation des lacunes par les interstitiels, et clue le stade IV de la restauration provient du mouvement des lacunes vers les dislocations. Les resultats suggerent qu’au tours de la deformation plastique le nombre de lacunes creees est appreciablement plus grand que le nombre d’interstitiels. ERHOLU~G

DES ELE~TRIS~HE~ WIDERSTA~DES HOCHREINEM NICKEL

VON KALTVERFORM~E~l

Die Erholung das elektrischen Widerstandes von hochreinem Nickel zoigt nach Verformung bei - 196°C eine Stufe II mit einer Aktivierungsenergie von 0,54 eV, Stufe 111 mit 0,86 eV und Stxife IV mit 1,32 eV. Die Erholung in Stufe III wird hauptsachlioh der Annihilation von Zwischengitteratomen an Leer&hen mid Stufe IV der Wanderung von Leerstellen an Versetzungen zugeschrioben. Die Ergebnisse deuten an, da13 bei der plastischen Verformung wesentlich mehr Leerstellen als Zwischengitteratome erzeugt werden.

1. INTRODUCTION

Previous work concerning the recovery of cold worked nickel of moderate purityf1-5) has shown that the recovery process above room temperature, as determined by isochronal measurements, can be divided into three well defined stages: stage III centered at about 9O”C, stage IV centered at about 26O”C, and stage V above about 310°C. This last stage is clearly associated with recrystallization. The effect of ~purities on the recovery process is quite marked. In very impure nickel, stage III is absent; Simson and Sizmann have reported that stage IV is practically non-existent in very pure nickel.c4) Very little additional data are available concerning resistivity recovery in high purity nickel particularly with specimens deformed at sufficiently low temperatures to permit a study of the recovery process below room temperature. The presence or absence of appreciable stage IV recovery in very pure nickel has an important consequence with respect to the relative quantities of vacancies and in~rstitials present in the crystal after plastic deformation. The most probable explanation for stage 111 recovery in deformed and irradiated * Received March 21, 1966; revised July 8, 1066. t Metallurgy Department, Laboratory for Research on Structure of Matter, University of Pennsylvania, P~il~eiphia. $ Now at: RCA Laboratories, Princeton, New Jersey. ACTA METALLURGICA, 0

VOL.

15, MARCH

IQ67

525

nickel (and other noble metals) is that it is due to the recombination of interstitials with vacancies.(3J6) Since there is strong evidence which suggests that stage IV corresponds to the mi~ation of vacancies to dislocations or vacancy clusters,W) the absence of stage IV in very pure nickel, where the formation of interstitial-impurity complexes is minimized, implies that the number of interstitials and vacancies in the lattice after deformation is very nearly equal. The object of the present study was the investigation of the resistivity recovery process after deformation, above -196°C in general, and stage IV in particular, in the purest available nickel. A stage IV was found contrary to the investigation by Simson and Sizmann.(*) 2. EXPERIMENTAL

PROCEDURES

The three pass zone refined nickel as provided by the Materials Research Corporation, Orangeburg, New York was stated to contain the following impurities (ppm) C, 15; O,, 0.5; N, 0.3; Fe, 10; Si, 5. The initial material, in form of 0.25 mm dia. wire, was preannealed by the vendor at 800°C for 1 hr in a vacuum of better than 10v6 torr. The other nickel used was provided by Johnson and Matthey, Ltd. and was stated to be better than 99,99O/~pure. It was received in the form of (0.25 mm

526

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wires of identical initial length (7.5 cm) by an equal number of turns at constant temperature. As a check on the reproducibility of the amount of deformation, the resistance of the specimens was measured after mounting in the torsion apparatus and immediately after deformation. The resistance change, expressed as a fraction of the resistance prior to deformation, was found to be reproducible to within *lo/,. To simplify the comparison of the annealing data obtained on matching specimens, all of the resistance values of the isothermal specimens after deformation were normalized to correspond exactly to the resistance of the isochronal specimen after deformation by multiplying each isothermal resistance value by a constant factor. 3. EXPERIMENTAL

RESULTS

3.1 Isochronal annealing data

FIG. 1. Apparatus used for specimen annealing between - 130°C and room temperature.

dia.) wire and was preannealed in a vacuum of better than lO+j torr for 4 hr at 800°C. A spectroscopic analysis was made of this material (as received and after the preanneal) as well as of the zone refined nickel. Concentrations of less than 3 ppm of the following impurities were indicated Mg, Si, Cu, Ca and Fe. All other cations were below the limit of detention, No test was made for carbon. Unless noted otherwise, the specimens were deformed by torsion at -196°C with potential and current leads attached prior to deformation by spot welding. Recovery for these specimens could therefore begin at the deformation temperature. The resistance was measured at liquid nitrogen temperature by means of a Leeds and Northrup K-3 potentiometer and D.C. Null Detector. An annealed dummy specimen of the same material was used as a standard to compensate for temperature fluctuations in the liquid nitrogen bath. Annealing between - 130°C and room temperature was performed in the apparatus shown in Fig. 1. In the temperature ranges - 130°C to --5O”C, 40°C-2O”C, 3O”C-310°C and 31O”C-380°C, Freon 22, methanol, silicone oil and a salt solution were used, respectively. The method of M~chan and Brinkman was used to determine the activation energies of the various stages. This method involves the use of two specimens having similar histories, one annealed by the isochronal method, the other by the isothermal method. Such matched specimens were obtained by deforming

Two zone refined wires were deformed by torsion at -196’C so that the surface strain (~11) reached a value of 0.20 (specimen A) and 0.36 (specimen B), where ?E= number of turns, d = diameter and 1 = length (7.5 cm). The isochronal annealing data between -196’C and 370°C are given in Figs. 2 and 3. The resistivity change for the two specimens, plotted in terms of the fractional recovery of the total resistivity which annealed out between -196°C and 370°C, is shown in Fig. 4, to show general similarity in their behavior and the positive existence of stage IV. However, note that the recovery peaks, as determined from the Allah curves exhibit some differences in the two specimens. For example, a small peak near 0°C is more clearly defined in the more lightly deformed specimen. A third wire of the Johnson and Matthey nickel (specimen C), was also deformed at -196”C, but the

FIG. 2. Isochronal recovery showing stages II, III, IV and V in zone refined nickel deformed by torsion at - 196’C, ndjl = 0.2.

KRESSEL

;j 3

9850 -

y,

9750-

et ccl:

RESISTIVITY

RECOVERY

OF

COLD-WORKED

Ni

527

:

a

9950.

f

955094509x091509190-'.

FIQ. 3. Isochronal recovery and AR/AT showing stages II, III, IV and V in zone refined nickel deformed by torsion at -196”C, rid/Z = 0.36.

first resistance measurement was made after the specimen was held at room temperature for approximately 3 min. The isochronal recovery data between 20°C and 310°C are shown in Fig. 5. Finally, a fourth wire of zone refined nickel (specimen D) was rolled, after immersion in a liquid nitrogen bath, to a linear strain of approximately 120%. The isochronal recovery data between 20°C and 31O”C, are shown in Fig. 6. For specimens A and B, (Figs. 24) four main stages, are evident. The first, stage II, is centered at about -50°C; the second, stage III, at 90°C and the third, stage IV, in the vicinity af 240°C. Stage V, recovery starting about 310-330°C was not completed in these specimens. Stages III and IV are also quite well defined in specimens C and D. The large amount of deformation

Pm. 5. Isochronal recovery between 20°C and 310°C. Johnson and Matthey, Ltd., 99.990/, nickel deformed by torsion at -196”C, rid/Z = l/3.

D (Fig. 6) seems to have suppressed stage IV. It is evident from Fig. 4 that the separation between stages IV and V is more clearly defined in the more lightly deformed specimen A than in the more heavily deformed specimen B. in specimen

3.2 Activation energies Specimen B was chosen for a detailed study of stages II, III and IV. Stage IV was also studied in specimen D. On the basis of the minimum values of AR/AT (Fig. 3), the stage separations in specimen B are estimated to be as follows: stage II appears to end at -3O”C, stage III at about 14O”C, and stage IV at about 310”-330°C. This subdivision is not precise. Some structure is evident in the recovery data below 0°C. Note that a relatively large decrease in resistivity was observed in the first annealing step at - 130°C. While a peak is clearly observed at -50°C it is possible that an additional substage near 0°C is

;i

$

7500

$ YI

!+

7400

7300

001 L -120

L -80

L -40

I 0

40

L 60

I

,a

(

160 200

’ 240

I 280

’ 320

A’ 360 7200

1 ITI

FIG. 4. Fractional resistivity recovery between -196°C and 370°C. Zone refined nickel deformed by torsion at -196”C, rid/Z = 0.20and 0.36.

20

40

60

80

100

120

140 160

180 200

220 240 Es0 290 x0

320

FIG. 6. Isochronal recovery between 20°C and 310°C. Zone refined nickel deformed by rolling below O”C,E E 1.2.

M

ACTA

528

METALLURGICA,

FIG. 7. Isothermal recovery of zone refined nickel deformed by torsion at -196”C, rid/Z = 0.36 at various recovery temperatures. merged into stage III.

0°C is complex

The fact that recovery

below

and consists of a number of substages

was previously shown by the stored energy work of van den BeukelcB) in 99.999%

nickel deformed at - 196°C. by a series

Stages II, III and IV were investigated of isothermal

recovery

curves of specimens deformed

identically to specimen B. Figure 7 shows the stage II isothermal

recovery

at -6O”C,

stage III recovery

87°C and 100°C and stage IV recovery at, 270°C. activation

energy for each stage was determined

a comparison

at The

from

of the data of Fig. 3 with those of Fig. 7.

The resultant

Meechan-Brinkman

plots of stages

II, III and IV are shown in Fig. 8.

The activation

energies, as determined from the slope of the curves of AT versus l/T, are as follows: stage III,

stage II, 0.54 f

0.03 eV,

0.86 * 0.03 eV and stage IV, 1.32 5 0.02

eV.

”\

VOL.

15,

1967

FIG. 9. Isothermal recovery at 268°C of zone refined nickel rolled below O”C, E s 1.2.

Because question,

the existence it was decided

of stage IV recovery

is in

to also study in detail the

stage IV recovery of a specimen D which was deformed at a higher temperature specimen B. deformed

and by a different method than

For this reason the wire which had been

by rolling was cut into two equal sections.

The first was isochronally

annealed up to 310°C (Fig.

6), the second isochronally

annealed up to 140°C and

then isothermally activation

annealed

at 268°C (Fig. 9).

energy for stage IV was determined

The

from a

Meechan-Brinkman

plot (Fig. 10). The value obtained, 1.31 eV, is essentially the same as that obtained from

specimen B. 3.3 Annealing

kinetics

An analysis of the isothermal data was also made to determine the annealing kinetics.

Since frequent comparison between the isochronal and isothermal recovery

E~=0,54?.03eV -z

E586?.03sV

, A

. 0

2oLl.8

-6O.C 07* c 100. c 270. c 20

’

22

24

26

s

28

*

’

3.0

1000

32

I

34

L

36

38

c 42s

40

’

4.4

/T

FIQ. 8. Meechan-Brinkman plots for activation energies in stage II, III, and IV. Zone refined nickel deformed by torsion at -196”C, rid/Z = 0.36.

1000 IT

Fm. 10. Meeohan-Brinkman plot for stage IV activation energy. Zone refined nickel rolled near O”C, E e 1.2.

KRESSEL

et al:

RESISTIVITY

RECOVERY

OF

COLD-WORKED

Ni

529

are required for a given degree of deformation, we will denote the resistance of the isochronal specimen after annealing up to (and including) temperature T, by RTi.The isochronal recovery data are, of course, the basis for the subdivision of the recovery process into stages. As mentioned previously, this subdivision was determined by the estimated position on the temperature axis of the minima of the isochronal curve derivative (AR~AT). It was not possible to fit the stage II recovery data to a simple time dependence. As we shall see, the recovery processes for stages III and IV are not simple either. But for these stages, it was possible to divide

FIG. 11. Test of stage III annealing kinetics. Zone refined nickel deformed by torsion at -196°C. ndjl = 0.36. (a) W dependence. (b) t dependence,

Fra. 13. Test of stage IV annealing kinetics. Zone refined nickel deformed by rolling near O”C, E s 1.2. (a) Nz dependence. (b) exp --t/r dependence.

(b)

I

6

I

FIG. 12. Test of stage IV annealing kinetics. Zone refined nickel deformed by torsion at - 196”C, rid/l = 0.36. (a) W2 dependence. (b) exp -t/7 dependence.

the recovery into parts, each of which appeared to fit a simple time dependence. For stage III,l/(R - R,) shows a reasonably good linear fit when plotted as a function of t1i2 for the beginning of the recovery process [Fig. 11 (a)]. The same data plotted as a function of t, indicate a possible linear time dependence for intermediate times which suggests a b~olecular process, [Fig. 11 (bf]. However, the fit is rather uncertain. Marked deviation from linearity occurs for long times. Since the end of a recovery stage cannot be determined with precision, the value of R, for any one stage is not accurately known and estimated values of l/( R - R,) for t large are therefore not reliable. It is not possible, therefore,

ACTA

530

METALLURGICA,

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was deformed at a higher temperature A and B ; the magnitude not, therefore,

directly

than specimens

of its stage III recovery

comparable

is

to that of speci-

mens A and B. 4.1 Stage II The stage II recovery recovery

stage reported

and Matthey

observed

here is similar to a

by Reits et aZ.tg) in Johnson

high purity nickel deformed at - 196°C.

These authors did not, however, determine a value for the activation 20

60

100

140

160

220

260

TEMPERATURE

300 (‘C

340

360

420

be the migration

I

14. Microhmdness as a function of heat treatment for a three pass zone refined nickel rod reduced in area by & factor of four.

primarily to the motion of divacancies,

from this part of the curves

specimens, R,)

(D-2).

For both

R,,,O, = R,, a plot of l/(R of t112is linear for small t [Figs.

choosing

as a function

12 (a) and 13 (a)]. For longer times, AR is proportional to exp -

t/r suggesting

12 (b) and 13 (b)]. concerning

a first order process, of l/(R

-

R,)

that a definite indentification the results of extensive

but it is evident

of this stage must await

quenching

experiments.

The

complex process possibly involving more than one type of defect. Recent results have been obtained by Wuttig and Birnbaumol) the divacancy

in quenched nickel, but the value for

migration

energy was not determined.

[Figs. 4.2 Stage III

Here again the earlier comment

the uncertainty

by

results of van den Beukelt8) certainly suggest a very

Stage IV kinetics were analyzed in both a specimen specimen

in Cu (0.58

Schiile et uZ.(lO) It is possible that Stage II corresponds

at long times of anneal. of type B and a rolled

energies of divacancies

eV), Ag (0.57 eV) and Au (0.60 eV) as reported

FIG.

to draw any conclusions

energy.

Our Eal’ value is fairly close to what are believed to

values for

long times must be kept in mind.

The stage III similar

annealing

to the one

process observed

reported

after

here is

deformation

by

previous

authors. (3-5) The existing recovery data after irradiation, quenching and plastic deformation of

3.4 Mechanical properties To

check

location

whether

significant

changes

in

dis-

range where point defect annihilation

is believed

take place,

measurements

successive

microhardness

were made after annealing

steps between

nickel and the noble metals, as studied by following the

density or structure occur in the temperature to

changes

friction,

in

and Schiile.(6)

20°C and

electrical

has been reviewed

recovery

resistivity

and

internal et CAL(~)

by Schumacher

A significant fact is that a bimolecular

process

is also evident

in stage

III

after

380°C on a three pass zone refined rod reduced in area

electron irradiation,

by a factor of four at room temperature.

interstitials and vacancies are generated in appreciable

The results

where it is well known that only

are shown in Fig. 14. The hardness change is seen to be

quantities,

relatively

clusion reached by the above authors is that in general,

small even after 1 hr at 310°C.

men recrystallized

after 1 hr at 380°C

The speci-

resulting in a

and that stage IV is very small.

stage III in nickel and the noble metals corresponds to the annihilation

large decrease in hardness. of the same

with vacancies.

specimen were made after annealing for 1 hr at 128”C,

may, however,

200°C

process.

A number and

morphology

of electron 280°C.

No

micrographs differences

could be detected.

in

dislocation

Small scale rearrange-

ments cannot, however, be expected to be detected by such observations. 4. DISCUSSION

The resistivity

increments

for the various

defect recovery stages as estimated from the isochronal recovery data are shown in Table 1 for the three pass zone refined specimens.

We recall that specimen

D

of interstitials through recombination The recovery peak observed near 0°C be due to another

While this explanation recovery

defect or recovery

may account for most of the

process,

there is additional experimental evidence which suggested that a fraction of the interstitials migrate to dislocations. This is deduced from stress-strain

point

The con-

measurements

in the microstrain

region

which show that dislocations are effectively pinned at the end of stage III recovery.02) The P dependence of the initial part of the recovery similar conclusion.(l)

process suggests a

KRESSEL

et al:

RESISTIVITY

TABLE 1. Resistivity

A B D

recovery

RECOVERY

OF

COLD-WORKED

531

Ni

during stages II, III and IV in deformed zone refined Ni*

Degree of deformation

Temp. of deformation

rid/l = 0.2 rid/l = 0.36 B - 1.2

- 196°C - 196°C -0°C

stage II (- 196°C to -30°C) Ap&Q-cm)

stage III

Stage IV (140°C to 310°C Ap&fi-cm)

( - 30°C to 140°C) A,,,,(@-cm)

0.64 x 10m2 1.22 x IO-2 -

1.61 x 1O-2 2.68 x IO-2 3.40 x 10-Z

1.90 x 10-Z 2.23 x 10-Z 0.92 x 10-a

* Based on resistivity value of annealed nickel at - 196°C = 0.5 @-cm.

If the above observed

interpretation

is adopted,

then the

Ei” value of 0.86 eV should correspond

the migration observed

energy for interstitials.

activation

dependent.

For

have reported

However,

the

evident

from Table

mens A and B, deformed

to be impurity

lo-* Q-cm

Simson

and

larger plastic strain.

Sizmannc4)

a very similar value (0.92 5 0.04 eV)

for high purity Johnson Mattheynickel, for relatively impure 99.8% Ni.

but 1.0-l. 1 eV

Similar values in the

vacancy

would

appear, then, that because of defect-impurity

inter-

actions, the observed “effective”

migration

activation energy.

but only about near O”C, to a

nickel, it has been interpreted

dislocations, (3) although the formation

clusters is also likely.t5)

of

The nature of the

recovery process during stage IV observed in this work,

energy is actually an

as well as by previous investigators, supporbs this interpretation.

to

For diffusion of defects to a fixed array of

infinite sinks, the recovery

the Ei”

as being

The same applies

E,l”, as we shall see. By comparing

at -196”C, D deformed

due to the migration of vacancies to some type of sink, presumably

It

of

Since stage IV is the most significant recovery stage

vicinity of 1 .O eV were reported by others for medium (99.9%-99.98%).(1,3,5,12)

in specimen

in quenched

purity

nickel

1. Note that the magnitude

stage IV is of the order of 2 x 10-a Q-cm for speci-

appears

energy

example,

to

values in impure nickel to

process should show a PI2

dependence forsmall times and a exp -t/r

dependence

our value, an estimate may be obtained of the average

for longer times, where7 is a constant dependent on the

interstitial-impurity

diffusion coefficient and type and density of sinks.07)

order of 0.2 eV.

binding energy. This is of the Without further experiments with

specimens having controlled it is not possible

impurity

concentrations,

to say which impurity

affects the

recovery process most. Turning our attention

to the absolute values of the

increments

(Table

magnitude

of the stage III

1) we note recovery

that

the

is very much

on the degree of deformation.

Comparing

process fits this description

The present

EaIV value of 1.32 + 0.02 eV should

in pure nickel. dependent. nickel

Higher

of lower

99.97%‘12’

to the vacancy

Like Ek”, values

purity:

have

values

mens deformed

obtain a value of approximately

a well defined stage

are quite different from those of Simson

and Sizmann who found it essentially absent in specivalue of strain (up to 240%). disparity

estimate

of

the

in the impure

average

vacancy-impurity

from a comparison

temperature

to a large

We suggest that this

in results can be partially explained

by two

factors:

(a) as can be seen in Fig. 4, the separation

between

stages IV and

heavily deformed

V is much

specimens.

of EnIY

and zone refined nickel.

mation in niokel is approximately

The present results concerning

near room

for

Ni)t3) and

We

0.2 eV. If the present value of 1.32 eV is correct, the energy of vacancy for-

4.3 Stage II’

mens deformed

(99.9%

and 1.5 eV (99.8% Ni).t4)

was observed in a large number of 99.9774 pure speci-

IV recovery

purity

been reported

1.55 eV

binding may be obtained

An

migration energy

EalV is apparently

specimens A and B, the dependence appears to be very nearly linear. In fact, a linear relationship with strain by rolling.(i2)

as

we have shown earlier. therefore correspond

resistivity dependent

The stage IV recovery

less distinct

This is presumably

in due

to the earlier onset of recrystallization in more heavily deformed specimen. (b) Stage IV is apparently much more pronounced

after deformation

after deformation

closer to room temperature.

at -196°C

than This is

energy

of

self-diffusion

SmoluchowskP3) A

comment

1.5 eV, based on the

reported

by

Burgess

and

being 2.8 eV. concerning

the

separation

between

stages IV and V in the specimens shown in Figs. 2 and 3 is in order. While it appears from the positions of the minima in the AR/AT

values that the onset of stage

V occurs at a somewhat lower temperature in the more lightly deformed specimen, the more rapid change in AR/AT

with increasing temperature is clearly evident

in the heavily deformed

specimen

small apparent temperature significant in this case.

as expected.

The

shift is not believed to be

We next turn our attention

to the relative number

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1967

TABLE 2. Estimated vacancy and interstitial concentration after deformation in zone refined nickel

Specimen A B D

Degree of deformation

Temp of deformation

ndll = 0.20 ndjl = 0.36 e N 1.2

- 196°C - 196°C -0°C

c,*

c, ci

c”t 11.0 x 10-b 14.0 x 10-S 8.0 x 1W

1.6 x 10-S 2.7 x 10-S 3.4 x 10-b

6.9 5.2 2.4

* From equation (1) and Table 1. t From equation (2) and Table 1 (a = 0.5).

of vacancies

and interstitials

present

in the lattice

A

similar

quantitative

estimate

of stage

Simson and Sizmann suggested that

determine the vacancy

the concentrations

are very nearly equal and that in

that stage is difficult.

nickel

impurity

vacancies disappear entirely by absorption

after cold work. containing

sponds

to the diffusion

atoms,

stage IV

of vacancies

trapped by impurities.

According

corre-

to interstitials

to their argument

all, or nearly all, interstitials

are free to migrate

in

stage III in very pure nickel;

as a result interstitials

concentration

of dislocations

to make a contribution resistivity

contribution

therefore not be 4 @-cm,

small vacancy

residue to disappear in stage IV.

some constant less than one.

interpretation

was in agreement

This

In view

of the present

conflicting

correct.

It may, however,

the stage IV recovery nickel.

as being

explain

part of

process in relatively

impure

On the basis of the very appreciable

interstitials and vacancies present in the crystal after deformation

are not equal.

Vacancies

are left over

C, g

10-3Ap1,1 +

platinum

here;

deformed

recovery

at -196°C

is

in pure nickel as reported

stage IV is also very prominent.(4)

in stage

after deformation

4u

; (Ap in @Z&cm)

of interstitials

(2)

and vacancies (1) and (2) are

shown in Table 2 for the zone refined specimens (A, B

factor of 2.

that the resistivity

annealing out in

from Table 1 and equations

to note in this respect,

very similar to the recovery

10-2APlv

The concentrations estimated

the

process in 99.999%

concentration

should

where u is

can be estimated from

after stage III and these disappear by forming clusters in stage IV. It is of interest

or diffusing to dislocation

but 4cr @J-cm,

concentration

stage IV

recovery observed here, we suggest that the number of

The average

1 o/0 vacancies

(2)] to that disappearing

IV, the total vacancy

experimental

results, we cannot accept this interpretation generally

Adding the vacancy stage III [equation

mental results in high purity nickel.

and therefore continue

per

disappear in that stage leaving only a

at jogs and

clusters of remain

to the resistivity.

and vacancies

with their experi-

to

We do not know how many

how many become par of vacancy in the vicintiy

IV

annealing out in

and D), assuming u = 4. A choice of a = 1 decreases estimated

vacancy

concentration

by

In any case, the vacancy

appears to be appreciably

nearly

a

concentration

larger than the interstitial

concentration;

with increasing deformation,

C,/Ci becomes

progressively

the ratio

smaller, because C, does

not increase as rapidly with strain as Ci. This effect 4.4 Estimates of vacancy and interstitial concentrations Quantitative

estimates

concentrations The

of vacancy

resistivity

increment

per

increment

theoretically

vacancies

$l-cm.(15)

per 1% interstitials

calculated

the calculations

1%

in

has not been

for Cu, we shall assume

that it is not much larger than the value of vacancies, or -6

$&cm.

It follows,

then, that the resistivity

increment per interstitial-vacancy

pair annihilated

in

pairs. If we ignore the stage III is -10 $&cm/l% fact that some interstitials probably disappear in stage III as a result of their motion to dislocations,

as dis-

cussed earlier, the interstitial

can be

concentration

estimated from the relation Ci g

10-3AP111;

(1)

of

dealing with point defect generation

in shock deformed nickel. 5. SUMMARY

AND

CONCLUSIONS

The electrical resistivity of high purity zone refined nickel

deformed

stages (II-V).

at -196”C, Except

recovers

in four main

for lower activation

energies,

the stage III and IV recovery appears similar to that observed

in medium

purity

nickel

(99.9-99.8%)

in

that both stages are quite prominent. It does appear, however, that the temperature of deformation significantly influences the magnitude of state IV: recovery is relatively

less pronounced

0°C than after deformation It is tentatively

(Ap in $Lcm)

of specimens

nickel(12) and will be discussed in detail in a

The resis-

for nickel but on the basis of

of BlattP)

99.97%

future publication

can be made as follows:

nickel has been estimated as ~4 tivity

and interstitial

has been studied in a large number

responsible

suggested

after deformation

near

at -196°C. that the defect mainly

for stage II may be the divacancy.

It is

KRESSEL

et aE:

RESISTIVITY

RECOVERY

clear, however, that this stage is quite complex in nature. If this assignment is correct, its migration energy is -0.54 eV. The interstitial migration energy is believed to be ~0.86 eV, and that of the vacancy ~1.32 eV. These values are obtained from an analysis of stages III and IV, respectively. Higher values of the migration energies were reported earlier in less pure nickel where one observes an “effective” migration energy as a result of interaction with impurities. Also from an analysis of magnitudes of stages III and IV, it is concluded that the concentration of vacancies in the lattice after deformation is appreciably larger than the interstitial concentration. ACKNOWLEDGMENTS

This work was supported by the U.S. Atomic Energy Commission. Partial support was received from the Advanced Research Projects Agency of the Department of Defense through the Laboratory for Research on the Structure of Matter of the University of Pennsylvania. One of the authors (H. K.) expresses this thanks to the

OF

COLD-WORKED

Ni

533

Radio Corporation of America for a David Sarnoff Fellowship. A second author (D. S.) was a recipient of a National Science Foundation grant during the 196465 academic year. REFERENCES A. SOSIN and L. A. BRINKMAN,Acta Met. 7, 478 (1959). L. M. CLAREBROTJUN, M. E. HARGREAVES,M. H. LORETTO and G. W. WEST, Ada. Met. 8, 797 (1960). I). SCRUXIACHER, W. SCHULEand A. SEEGEB, 2. X&wf. 17a,228(1962). P, SIMSON and 12. SIZ;MANN,2. Natwf. 17a,596 (1962). F. BELL, Acta Met. 13, 363 (1965). W. SCHULE,J. phys. 8oc. Japan 18, suppl. III,%% (1963). C. J. MEECHANsnd J. A. BRINKMAN,Phys. Rev. 103, 1193 (1956). A, VAN DEN BEUKEL, Physica 27, 603 (1961). D. REITS, R. W. STARREYELDand H. J. DEWITT, Phys. Lett. 16, 13 (1965). W. SCHULE,A. SEEGER,F. RAMSTEINER,D. SCHU~~~CHER and K. KING, 2. Natullf. l&t, 323 (1962). M. WUTTIGand H. K. BIRNBAUM,Acta Met. 14,59 (1966). H. KRESSEL, Ph.D Thesis, University of Pennsylvania (1965). H. BITR~ESSand R. SMOLUCHOWSKI, ,7. appl. Phys. 20,491 (1955). L. C. MEN~WC, Phy&cca.30, 407 (1964). A. SEEOER,2. Phys. 144, 637 (1956). E. J. BLATT, Phys. Rev. 99, 1708 (1955). -4, C. DAMASKand G. J. DIE~ES, Point Defects in Metals. Gordon & Breech, New York (1963).

k: 3. 4. 5. 6. 7.

Ti 10. 11. 12. 13. 14. 15. 16. 17.