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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.
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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.
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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
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7500
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7300
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L -80
L -40
I 0
40
L 60
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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
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, A
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-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
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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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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.
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
ACTA
METALLURGICA,
VOL.
15,
1967
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,
VOL.
15,
1967
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
ACTA
532
METALLURGICA,
VOL.
15,
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.