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The annealing of point defects in cold-worked molybdenum
THE ANNEALING
OF POINT DEFECTS
IN COLD-WORKED
MOLYBDENUM*
D. G. MARTINS The change in electrical resistance on annealing cold-worked moly~enum has been studied. It is proposed that a point defect, produced by cold-work, anneals at 150°C with an energy of migration of l-26 & 0.04 eV but that other more complex processes anneal simultaneously. LA DISPARITION
DES DEFAUTS
LOCAUX
DANS
LE MOLYBDENE
ECROUI
L’auteur a Btudiit la variation de la resistance Blectrique pendant 1% revenu de molybdene Bcroui. On propose qu’un defaut ponctuel produit par Bcrouissage, disparait a 150°C avec une energie de migration de 1,26 j, 0,4 eV mais que d’autres mecanismes plus complexes se deroulent simult&n~ment. D.4S AUSHEILEN
VON ATOMAREN
KALTBEARBEITETEM
FEHLSTELLEN
IN
MOLYBDAN
An kaltbearbeitetem Molybdan wurde die linderung des elektrischen Widerstands beim ,Snlassen untersueht. Es wird vorgeschlagen, dass bei 150°C eine bei der Kaltbearbeitung erzeugte atomare Fehlstelb mit einer Wander~senergie von 1,26 + 0,04 eV verschwindet, wahrend andere, komplexere Vorgange gleiehzeitig zur Erholung beitragen.
1. INTRODUCTION
tration of dislocations produced by cold-work should also be borne in mind when interpreting results. This paper describes a study of lattice defects produced by cold-working polyc~stalline mdybdenum wire. Molybdenum was chosen because (a) a parallel programme of irradiation effects in molybdenum had been started by Kinchin, (b) no systematic work had been done previously on a body-centr~ cubic metal, and (c) other work on noble metalsc5) indicated that thermal annealing of point defects occurred below room temperature. When this programme began, irradiations were only possible at pile temperature. It was hoped, therefore, by the choice of a high melting-point metal, that the comparable annealing stages would occur above room temperature. The method of comparing the damage produced by irradiation and cold-work is by annealing the point defects. If there is only one type of defect present, the annealing equation is
The irradiation of metals by fast neutrons and energetic charged particles may introduce vacancies and interstitial atoms in t*helattice. Much work has been done recently (l) to study the effect of these lattice defects on the fundamental physical properties of metals, with a view to giving us a more complete understanding of the solid state and, in particular, of interatomic forces. The data from irradiation effects are difficult to interpret theoretically; for example, the effects due to vacancies and interstitial atoms are difficult to discriminate. Consequently, a comparison between irradiation experiments and others which produce similar lattsicedefects may assist in interpreting the results. One method of introducing point defects is by coId-work, a possible explanation being that the motion of jogs formed by the intersection of dislocations leaves behind point defects.c2) Because theoretical considerations indicate that the energy of formation of a vacancy is smaller than that of an interstitial atom, some authors have tacitly assumed t’hat vacancies predominate when a metal is coldworked. However, by considering the way dislocations at right angles must move if slip is to take place, CottrelP) has pointed out that p~dominantly interstitial atoms may be produced, if in fact the mechanism for producing defects is the intersection of dislocations. In addition, the increased concen-
an dt-
* Received October 2, 1956. t Atomic Energy Research Establishment, Harwell, Berks, England. ACTA
METALLURGICA,
VOL.
5, JULY
1957
-y#(n)e-E@”
where n is the number of defects, E the activation energy for their migration, +(N) a function that varies mono~nically with n, T the absolute temperature, t the time, and Y the characteristic frequency of vibration of the atoms. It is possible to measure the changes in n by measuring the changes in electrical resistance, since, by analogy with dilute alloys,(“) the increase in residual resistivity is considered to be proportional to t,he
371
ACTA
372
number
of defects.
of a specimen equation
Consequently,
is measured
where
if the resistance
at constant
-
is the resistance
R,
defects
a.re present,
(2)
of the specimen
R the
resistance
when
n
when
R,) a function
was possible enabled
been
on specimens
or
heavily
strain
specimens
from
cold-worked
which
cold-worked. the Vat diameter
in vacua at 14OO”C, and subsequently
to a plastic
of 5%. the
The
heavily
Tungsten
Manu-
facturing Company were as received 0.020-in. diameter wire which had been drawn through dies to 0.015-in. diameter. Twelve
inches of the cold-worked
wrapped
on a specially
current and potential of the wire. Analysis
showed
designed
wire were then silica former
and
leads spot welded to the ends
that the two sorts of wire were
spectroscopically pure, shown in Table 1.
apart
from
the
elements
described
from the absolute below,
resistivity
Passing
all resistance the
measurements
same
were
specimen as a
current
through
the
specimens enabled the voltage drop across each to be measured on a potentiometer and hence the resistance ratio of the unknown to the standard to be determined. The specimens
were measured
in liquid
nitrogen
to
maintain a constant temperature ; this also increased the resistance 7 over
changes observed
room-temperature
TABLE 1. A spectrographic Diameter and source of wire
by a factor of about
measurements,
since
the
analysis of the specimens Impurities
Mg
1
0.001
the
this enables a comparison
to be made
different
Fe
1
Si
0.01
0.01
methods
specimens in
of
were
this
and
In the first method,
annealing
employed; the
the
these
succeeding
cola-
will
be
subsection.
all the anneals were performed
on a single specimen. An isothermal annealing curve of resistance against time was obtained, and then
the
temperature
was raised
by
when a similar curve was determined.
about
20°C,
This process
was repeated throughout the Since oxidation of molybdenum
temperature range. in air occurs within
the
study,
temperature
range
under
were performed in vacua. The cold-worked specimen, was placed
at the bottom
mounted
the
anneals
on its former,
of a long vertical
tube which was being continuously
evacuated
silica to a
pressure of 10M5 mm of mercury. To perform an anneal, a furnace which was temperature-controlled to O*l”C was raised and surrounded the silica tube. The temperature a
calibrated
of the specimen was measured with
platinum-platinum-rhodium
which made contact
thermo-
with the specimen.
when the specimen had cooled sufficiently danger
from oxidation,
At
was lowered,
and
to prevent
the silica tube was isolated
from the vacuum system and filled with helium. A Dewar of liquid nitrogen which also contained the standard
specimen
was then placed
round the tube
and the resistance ratio measured. One inevitable disadvantage of annealing in vacua is the length of time taken for the specimen to reach
the
annealing
sequent uncertainty
temperature
and
of the annealing time.
the
con-
However,
the effective time of anneal at the annealing temperature may be evaluated if the temperature time curve of the specimen
is known.
By effective
time
is meant the length of time of a square temperature pulse at the annealing t)emperature which, when
(wt. %) 1
Cu
0.008 in. Vao Tight Wire Co. 0.020 in. Tungsten Manufacturing Co.
below,
have been norma-
the end of an anneal the furnace
measurements
made relative to a similar molybdenum standard.
10M8V,
between different specimens.
couple
2.2. The measurement of electrical resistance Apart
reduced.
to
ratio to be evaluated
ratios before annealing
described
of specimens lightly
potentials
the resistance
lized to unity;
worked
cold-worked specimens from Company were of 0908-in.
wire annealed stretched
DETAILS
were performed
either
The lightly Tight Wire
measure
to 1 part in 105. In the results reported resistance
Two
had
to
2.3. The isochronal annealing experiments
2. EXPERIMENTAL
Experiments
1957
whose
propert’ies are similar to +(n).
2.1. The preparation
5,
thermal term in the resistance is considerably which
R,)e-*lkT
defects are present, and f(R -
VOL.
It
temperature,
(1) may be rewritten as o?R/clt= -vf(R
no
METALLURGICA,
0.005
applied to the specimen, produces the same decrease in resistance as is observed. From the resulting series of isothermal annealing curves, it is possible to evaluate the activation energy associated with the annealing. If the annealing curves are drawn for two adjacent temperatures, then at their point
of intersection
the specimen
is
MARTIN:
ANNEALING
OF
POINT
DEFECTS
IN
COLD-WORKED
MOLYBDENUM
373
By quenching the specimens in cold oil after an anneal it was possible to measure directly the effective time of annealing to about 1 set without resorting to calculations involving the temperature time history, as was necessary for the isochronal anneals. To evaluate E we assume that a certain value of R corresponds to an unambiguous state of the metal. Integrating equation (2), we have
I.0
3.g o.5 XE
g 2 0.3 aa 0.2
F(R - R,) = ----~te-~~k~ + constant /
I
I
I.090 RESISTANCE
I
1
1092 I.094 RATIO (NOT NORMALISED)
Frc. I. A series of isothermal annealing curves, showing the variation of rate of anneal with resistance. Activation energies may be calculated from these curves.
in the same state. Consequently, since f(R - R,) is the same in both annealing curves in equation (2),
Hence, if we draw lines of constant R, they will intersect the curves at points of constant tepElkT, and therefore E may be evaluated. From equations (2) and (4) it may be shown that ~~l~(ln t) is independent of time and temperature. Consequently, if the isothermals are plotted against the logarithm of the time, a series of identical curves displaced successively along the In t axis should be obtained. 3. THE
where subscripts 1 and 2 refer respectively to the two temperatures. Hence, a knowledge of the slopes and temperatures enables E to be determined at temperature (T1 -+ T,)/2. Since the slopes of the curves are rapidly changing at their point of intersection, their ratio was not determined geometrically. Instead, the slopes of the isothermals between the experimental points were computed and log dR/dt was plotted against the mean resistance between the points. A series of slowly varying curves, one for each isot‘hermal, resulted, and the change in ordinate required t,o fit one onto the continuation of an adjscent curve gave directly log (dR/dt),/(dR/cit),. A typical series of such curves is depicted in Fig. 1. 2.4. The ~~ot~~r~~ a~n~~ng
(4)
EXPERIMENTAL
RESULTS
The normalized resistance ratio curves for the isochronal anneals are shown in Fig. 2, for wires with different degrees of cold-work. Each point represents an anneal of 280 min at the corresponding temperature and is the total change in resistance of an isothermal annealing curve, obtained as described in Section 2.3. The noteworthy feature of these curves is the comparatively large drop in resistance between 100°C and lSO”C, with a maximum in slope for each curve at about 155°C. Also, in the neighbourhood of 180°C the slopes change abruptly.
~~e~~~~ent~
The results of the isochronal anneals, reported in Section 3, suggested that one type of point defect anneals in the neighbourhood of 160°C. It was decided therefore to investigate further this annealing process by a different technique. In the isot~hermal annealing method, a number of wires were heavily cold-worked the same amount and each specimen was annealed at different temperntrues, so producing a series of isothermal curves. The anneals were performed in a well stirred silicone oil-bath ; its temperature was controlled to 0.1% and was measured with a calibrated copper constantan t,hermocouple. Since oxidation of molybdenum does not occur below 250% and there was no evidence of chemical reaction with the oil, it was possible to immerse the specimens in the bath.
1
lObY
( 2ooOc 3&O% TEMPERATURE
I
,
400%
Fra. 2. Isochronal annealing curves for cold-worked molybdenum. (c) heavy cold-work. -. ^ . (a) and.(b) light cold-work, ^^^ Tune ot anneal at each temperature = MU mm.
ACTA
374
METALLURGICA,
VOL.
5, 1957
TABLE 2. Absolute resistivity measuremen& at liquid-nitrogen
temperature
_~__
~~
Initial Diameter of the wire (thou)
Resistivity
W cm)
20 Drawn from 0.0020 to 0.0015 in.
20
none
20
Drawn from 0.0020 to 0.0015 in.
20
8
none _
the deduced
TEMPERATURE FIG. 3. An isochronal annealing curve up to 900°C of a
heavily cold-worked molybdenum wire. Part of this cnrve is depicted in Fig. 2(c). Time of anneal at each temperature = 280 min. The calculated
activation
energies also reveal this
discontinuity at 180°C. Within the limits of experimental error they remain constant below this temperature,
with a value of 1.26 & 0.04 eV.
this temperature
the activation
Above
energy rises steadily
to 1.75 eV at 350°C. There is no significant difference in the values of these activation energies for specimens possessing The
annealing
different of the
(Fig. 2c) was continued isochronal
degrees heavily
of cold-work. cold-worked
wire
to 9OO”C, and the complete
annealing curve is shown in Fig. 3.
Isothermal
annealing
curves
at
10”
intervals
were obtained between 100°C and 2OO”C, and a few of these are depicted in Fig. 4. The shape of each curve is not identical; retical predictions
this disagrees with the theo-
of Section
2(d), and consequently
_
none
0.906 fO.005
none
0.974
annealed at 1400°C for 5 min
0.770
annealed at 1400°C for 5 min
0.590
annealed at 1400°C for 5 min
1.067 ~~_~ ~-
__~_..~
activation
energies possess no physical
meaning. (See next section.) Some electrical resistivity made at liquid-nitrogen
measurements
temperature
were
to supplement
the resistance measurements. Table 2 summarizes the results, together with the history of each specimen. The relative purity of the 0.008 in. and the 0.020 in. diameter
wires is reflected
of the former yR cm). Drawing increases ,uQ cm),
(l-067
from the
pfi
in the higher resistivity cm compared
@020 in.
resistivity
of which
just
to
by over
specimen
0.015 in.
7:/,
(O-906
0.770
diameter to
0.974
a half anneals
below
18O”C, using the data of Fig. 2(c). that an annealed
with
It is also apparent
possesses a lower resisti-
vity when it has been previously
cold-worked.
This
is in accord with observations that when a coldworked metal is annealed above the recrystallization temperature,
the resulting
grain size increases
with
the degree of cold-work.(‘) 4. DISCUSSION The evidence that a comparatively large decrease of resistance which anneals with a constant activation suggests
energy that
imperfection
occurs the
between
annealing
100°C of
a
and
18O’C
fundamental
such as a certain kind of point
defect
is being observed. Makin has shown that there is no measurable change in the yield point at room temperature when heavily cold-worked wires have been annealed for 280 min at 175°C. This indicates TtME (MINUTES)
FIQ. 4. Isothermal annealing curves for heavily cold-worked molybdenum
that little change in the number and position of dislocations have taken place, and therefore that the motion of dislocations is not responsible for the
MARTIN:
ANNEALING
OF
POINT
DEFECTS
large decrease in electrical resistance. The annealing above 180% with a rising activation energy is clearly
associated with no simple process. ~esumably, a relaxation of dislocations occurs over a broad spectrum of activation energies. Furthermore, the greater the degree of cold-work the larger is the IO&180% step compared with the rest of the annealing curve. This is what we would expect if the step is due to point defects, a~uming they are formed by the intersection of dislocations. These results may be compared with the annealing of neutron-irradiated molybdenum. Kinchinc4) has found that after neutron irradiation at 30% an annealing stage occurs up to 190°C with an activation energy of l-3 eV. A subst,antially similar resuIt has been found by Thompson(a) when the irradiation is performed at liquid-nitrogen temperature. It would appear reasonable to assume that the same point defect is responsible for the cold-work ~i.nnealingstage. It has already been pointed out that the shapes of the isothermal curves are not identical, and therefore that activation energies deduced from equation (4) have no physical meaning. Indeed, the apparent activation energies decrease linearly with the amount of resistance annealed. This, of course, is against expectation, but it was found that no limitations of the experimental method could explain this. The result of this experiment is to demonstrate that the effects of a low-temperature anneal for a long time and a short high-temperature anneal are not alike. In order to demonstrate this further experimentally, a heavily cold-worked wire was annealed at 120°C for 240 min and then annealed isothermally at lSO”C, When a correction for the 120°C anneal was added to the 180°C annealing times (this is not very critical), the 180°C isotherm did not correspond with the one shown in Fig. 4, but was uniformly displaced to the left. This displaced isotherm gave an activation energy of 1.25 eV, in agreement with the isochronal experiments. Hence we may appreciate that the objection to determining activation energies by the isothermal method is that a part,icular value of resistance does not correspond to a unique physical state of the metal. The isochronal method, however, is not susceptible to this objection, since the calculations are based on measurements taken when the specimen is in the same state. It is of considerable interest to form an estimate of the number of defects produced by cold-work. One method is by measuring the stored energy released by annealing and then, assuming the defects
IN
COLD-WORKED
MOLYBDENUM
375
are vacancies, to postulate that 3 eV are liberated when one point defect disappears. Unfortunately, no stored-energy measurements on cold-worked molybdenum have been done, but an estimate may be made by analogy with the work of Clarebrough, Hargreaves, and West,(l*) who observed the stored-energy release of a point defect in nickel as well as the energy released on recrystallization. Assuming the yield point of polycryst,alline molybdenum is 70 kg/mm2 and that no work-hardening occurs, the energy expended in a 40% deformation is 5.5 Cal/g. By analogy with nickel, we assume that 2% of this energy is stored in the lattice, of which one-fifth is in the form of point defects, Hence, 0.022 Cal/g are stored as point defects in molybdenum for 40% deformation, corresponding to 3.08 x 10m5 atomic concentration of defects, This is responsible for an increase of about O-035 ,u”cRcm in resistivity. Consequently, the stored energy to resistivity ratio is 0.6 cal/g/,uQ cm, and 1 at. o/0 of point defects will produce an increase of 11 ,UQcm in resistivity. This may be compared with Overhauser’@) experimental value of l-7 cal/g/pQ cm in copper after deuteron irradiation. If we assume that Overhauser was observing the annealing of vacancies and that the energy released per vacancy annealed is 1.3 eVs then 1 at. y. of defects in copper will produce an increase of 2.8 ,uln cm in resistivity. At present it is not possible to be certain of the nature of the point defect which anneals below 180%. Since the activation energies for cold-worked and irradiate1 specimens agree closely, it would appear that the defect is elementary. By plotting the activation energy against the temperature of anneal, both reduced by the melting-point (oorrections being made for different times of anneal), Thompson(i2) has shown that all activation energies so far determined in metals lie on a single curve. In particular, the 1*26-eV stage in molybdenum and the 0*7-eV stage in copper are superimposed on this curve. It would appear not unreasonable to assume that a similar defect is annealing in copper and molybdenum. The evidence we have to date(n) sugge&s that vacancies probably anneal at 0+7eV it is tentativeIy proposed that the in copper; 1.26 eV annealing stage in molybdenum is due to vacancies.
The helpful in the Stubbs
author is indebted to Dr. A. H. Cottrell for discussions, Mr. G. H. Kinchin for guidance initial stages of this work, and Miss M. J. for assistance in the experimental work.
376
ACTA
METALLURGICA,
REFERENCES J. W. GLEN Adwxncesin Physics 4, 381 (1955). F. SEITZ Advances in Phy8k.9 1,43 (1952). A. H. COTTRELL Private communication. G. H. KINCHIN See R. A. DUODALE, Report of Bristol Conferenceon Defects in Crwtdline Solid8 D. 249 (19551. 5. R. k. EQ*LESTO& J. Ap& Phys. 23, 1460 (195i) anh Acta Met. 1,679 (1953). 6. J. 0. LINDE Ann. Phys. 15, 219 (1950). 1. 2. 3. 4.
VOL.
5,
P. A. BECK
1957 Advances in Physics 3, 245 (1954).
i: M. J. MAKIN Private communication.
9. M. W. THOMPSON to be published. 10. L. M. CLAREBROUGH,M. E. HARGREAVES, and G. W. WEST Proc. Roy. Sot. A232, 252 (1955). 11. A. W. OVERHAUSER Phys. Rev. 94, 1551 (1954). 12. M. W. THO~~PSON to be published. 13. M. J. MAKIN British Report Atomic Energy Resestrch Establishment M/R 1852.
OF POINT DEFECTS
IN COLD-WORKED
MOLYBDENUM*
D. G. MARTINS The change in electrical resistance on annealing cold-worked moly~enum has been studied. It is proposed that a point defect, produced by cold-work, anneals at 150°C with an energy of migration of l-26 & 0.04 eV but that other more complex processes anneal simultaneously. LA DISPARITION
DES DEFAUTS
LOCAUX
DANS
LE MOLYBDENE
ECROUI
L’auteur a Btudiit la variation de la resistance Blectrique pendant 1% revenu de molybdene Bcroui. On propose qu’un defaut ponctuel produit par Bcrouissage, disparait a 150°C avec une energie de migration de 1,26 j, 0,4 eV mais que d’autres mecanismes plus complexes se deroulent simult&n~ment. D.4S AUSHEILEN
VON ATOMAREN
KALTBEARBEITETEM
FEHLSTELLEN
IN
MOLYBDAN
An kaltbearbeitetem Molybdan wurde die linderung des elektrischen Widerstands beim ,Snlassen untersueht. Es wird vorgeschlagen, dass bei 150°C eine bei der Kaltbearbeitung erzeugte atomare Fehlstelb mit einer Wander~senergie von 1,26 + 0,04 eV verschwindet, wahrend andere, komplexere Vorgange gleiehzeitig zur Erholung beitragen.
1. INTRODUCTION
tration of dislocations produced by cold-work should also be borne in mind when interpreting results. This paper describes a study of lattice defects produced by cold-working polyc~stalline mdybdenum wire. Molybdenum was chosen because (a) a parallel programme of irradiation effects in molybdenum had been started by Kinchin, (b) no systematic work had been done previously on a body-centr~ cubic metal, and (c) other work on noble metalsc5) indicated that thermal annealing of point defects occurred below room temperature. When this programme began, irradiations were only possible at pile temperature. It was hoped, therefore, by the choice of a high melting-point metal, that the comparable annealing stages would occur above room temperature. The method of comparing the damage produced by irradiation and cold-work is by annealing the point defects. If there is only one type of defect present, the annealing equation is
The irradiation of metals by fast neutrons and energetic charged particles may introduce vacancies and interstitial atoms in t*helattice. Much work has been done recently (l) to study the effect of these lattice defects on the fundamental physical properties of metals, with a view to giving us a more complete understanding of the solid state and, in particular, of interatomic forces. The data from irradiation effects are difficult to interpret theoretically; for example, the effects due to vacancies and interstitial atoms are difficult to discriminate. Consequently, a comparison between irradiation experiments and others which produce similar lattsicedefects may assist in interpreting the results. One method of introducing point defects is by coId-work, a possible explanation being that the motion of jogs formed by the intersection of dislocations leaves behind point defects.c2) Because theoretical considerations indicate that the energy of formation of a vacancy is smaller than that of an interstitial atom, some authors have tacitly assumed t’hat vacancies predominate when a metal is coldworked. However, by considering the way dislocations at right angles must move if slip is to take place, CottrelP) has pointed out that p~dominantly interstitial atoms may be produced, if in fact the mechanism for producing defects is the intersection of dislocations. In addition, the increased concen-
an dt-
* Received October 2, 1956. t Atomic Energy Research Establishment, Harwell, Berks, England. ACTA
METALLURGICA,
VOL.
5, JULY
1957
-y#(n)e-E@”
where n is the number of defects, E the activation energy for their migration, +(N) a function that varies mono~nically with n, T the absolute temperature, t the time, and Y the characteristic frequency of vibration of the atoms. It is possible to measure the changes in n by measuring the changes in electrical resistance, since, by analogy with dilute alloys,(“) the increase in residual resistivity is considered to be proportional to t,he
371
ACTA
372
number
of defects.
of a specimen equation
Consequently,
is measured
where
if the resistance
at constant
-
is the resistance
R,
defects
a.re present,
(2)
of the specimen
R the
resistance
when
n
when
R,) a function
was possible enabled
been
on specimens
or
heavily
strain
specimens
from
cold-worked
which
cold-worked. the Vat diameter
in vacua at 14OO”C, and subsequently
to a plastic
of 5%. the
The
heavily
Tungsten
Manu-
facturing Company were as received 0.020-in. diameter wire which had been drawn through dies to 0.015-in. diameter. Twelve
inches of the cold-worked
wrapped
on a specially
current and potential of the wire. Analysis
showed
designed
wire were then silica former
and
leads spot welded to the ends
that the two sorts of wire were
spectroscopically pure, shown in Table 1.
apart
from
the
elements
described
from the absolute below,
resistivity
Passing
all resistance the
measurements
same
were
specimen as a
current
through
the
specimens enabled the voltage drop across each to be measured on a potentiometer and hence the resistance ratio of the unknown to the standard to be determined. The specimens
were measured
in liquid
nitrogen
to
maintain a constant temperature ; this also increased the resistance 7 over
changes observed
room-temperature
TABLE 1. A spectrographic Diameter and source of wire
by a factor of about
measurements,
since
the
analysis of the specimens Impurities
Mg
1
0.001
the
this enables a comparison
to be made
different
Fe
1
Si
0.01
0.01
methods
specimens in
of
were
this
and
In the first method,
annealing
employed; the
the
these
succeeding
cola-
will
be
subsection.
all the anneals were performed
on a single specimen. An isothermal annealing curve of resistance against time was obtained, and then
the
temperature
was raised
by
when a similar curve was determined.
about
20°C,
This process
was repeated throughout the Since oxidation of molybdenum
temperature range. in air occurs within
the
study,
temperature
range
under
were performed in vacua. The cold-worked specimen, was placed
at the bottom
mounted
the
anneals
on its former,
of a long vertical
tube which was being continuously
evacuated
silica to a
pressure of 10M5 mm of mercury. To perform an anneal, a furnace which was temperature-controlled to O*l”C was raised and surrounded the silica tube. The temperature a
calibrated
of the specimen was measured with
platinum-platinum-rhodium
which made contact
thermo-
with the specimen.
when the specimen had cooled sufficiently danger
from oxidation,
At
was lowered,
and
to prevent
the silica tube was isolated
from the vacuum system and filled with helium. A Dewar of liquid nitrogen which also contained the standard
specimen
was then placed
round the tube
and the resistance ratio measured. One inevitable disadvantage of annealing in vacua is the length of time taken for the specimen to reach
the
annealing
sequent uncertainty
temperature
and
of the annealing time.
the
con-
However,
the effective time of anneal at the annealing temperature may be evaluated if the temperature time curve of the specimen
is known.
By effective
time
is meant the length of time of a square temperature pulse at the annealing t)emperature which, when
(wt. %) 1
Cu
0.008 in. Vao Tight Wire Co. 0.020 in. Tungsten Manufacturing Co.
below,
have been norma-
the end of an anneal the furnace
measurements
made relative to a similar molybdenum standard.
10M8V,
between different specimens.
couple
2.2. The measurement of electrical resistance Apart
reduced.
to
ratio to be evaluated
ratios before annealing
described
of specimens lightly
potentials
the resistance
lized to unity;
worked
cold-worked specimens from Company were of 0908-in.
wire annealed stretched
DETAILS
were performed
either
The lightly Tight Wire
measure
to 1 part in 105. In the results reported resistance
Two
had
to
2.3. The isochronal annealing experiments
2. EXPERIMENTAL
Experiments
1957
whose
propert’ies are similar to +(n).
2.1. The preparation
5,
thermal term in the resistance is considerably which
R,)e-*lkT
defects are present, and f(R -
VOL.
It
temperature,
(1) may be rewritten as o?R/clt= -vf(R
no
METALLURGICA,
0.005
applied to the specimen, produces the same decrease in resistance as is observed. From the resulting series of isothermal annealing curves, it is possible to evaluate the activation energy associated with the annealing. If the annealing curves are drawn for two adjacent temperatures, then at their point
of intersection
the specimen
is
MARTIN:
ANNEALING
OF
POINT
DEFECTS
IN
COLD-WORKED
MOLYBDENUM
373
By quenching the specimens in cold oil after an anneal it was possible to measure directly the effective time of annealing to about 1 set without resorting to calculations involving the temperature time history, as was necessary for the isochronal anneals. To evaluate E we assume that a certain value of R corresponds to an unambiguous state of the metal. Integrating equation (2), we have
I.0
3.g o.5 XE
g 2 0.3 aa 0.2
F(R - R,) = ----~te-~~k~ + constant /
I
I
I.090 RESISTANCE
I
1
1092 I.094 RATIO (NOT NORMALISED)
Frc. I. A series of isothermal annealing curves, showing the variation of rate of anneal with resistance. Activation energies may be calculated from these curves.
in the same state. Consequently, since f(R - R,) is the same in both annealing curves in equation (2),
Hence, if we draw lines of constant R, they will intersect the curves at points of constant tepElkT, and therefore E may be evaluated. From equations (2) and (4) it may be shown that ~~l~(ln t) is independent of time and temperature. Consequently, if the isothermals are plotted against the logarithm of the time, a series of identical curves displaced successively along the In t axis should be obtained. 3. THE
where subscripts 1 and 2 refer respectively to the two temperatures. Hence, a knowledge of the slopes and temperatures enables E to be determined at temperature (T1 -+ T,)/2. Since the slopes of the curves are rapidly changing at their point of intersection, their ratio was not determined geometrically. Instead, the slopes of the isothermals between the experimental points were computed and log dR/dt was plotted against the mean resistance between the points. A series of slowly varying curves, one for each isot‘hermal, resulted, and the change in ordinate required t,o fit one onto the continuation of an adjscent curve gave directly log (dR/dt),/(dR/cit),. A typical series of such curves is depicted in Fig. 1. 2.4. The ~~ot~~r~~ a~n~~ng
(4)
EXPERIMENTAL
RESULTS
The normalized resistance ratio curves for the isochronal anneals are shown in Fig. 2, for wires with different degrees of cold-work. Each point represents an anneal of 280 min at the corresponding temperature and is the total change in resistance of an isothermal annealing curve, obtained as described in Section 2.3. The noteworthy feature of these curves is the comparatively large drop in resistance between 100°C and lSO”C, with a maximum in slope for each curve at about 155°C. Also, in the neighbourhood of 180°C the slopes change abruptly.
~~e~~~~ent~
The results of the isochronal anneals, reported in Section 3, suggested that one type of point defect anneals in the neighbourhood of 160°C. It was decided therefore to investigate further this annealing process by a different technique. In the isot~hermal annealing method, a number of wires were heavily cold-worked the same amount and each specimen was annealed at different temperntrues, so producing a series of isothermal curves. The anneals were performed in a well stirred silicone oil-bath ; its temperature was controlled to 0.1% and was measured with a calibrated copper constantan t,hermocouple. Since oxidation of molybdenum does not occur below 250% and there was no evidence of chemical reaction with the oil, it was possible to immerse the specimens in the bath.
1
lObY
( 2ooOc 3&O% TEMPERATURE
I
,
400%
Fra. 2. Isochronal annealing curves for cold-worked molybdenum. (c) heavy cold-work. -. ^ . (a) and.(b) light cold-work, ^^^ Tune ot anneal at each temperature = MU mm.
ACTA
374
METALLURGICA,
VOL.
5, 1957
TABLE 2. Absolute resistivity measuremen& at liquid-nitrogen
temperature
_~__
~~
Initial Diameter of the wire (thou)
Resistivity
W cm)
20 Drawn from 0.0020 to 0.0015 in.
20
none
20
Drawn from 0.0020 to 0.0015 in.
20
8
none _
the deduced
TEMPERATURE FIG. 3. An isochronal annealing curve up to 900°C of a
heavily cold-worked molybdenum wire. Part of this cnrve is depicted in Fig. 2(c). Time of anneal at each temperature = 280 min. The calculated
activation
energies also reveal this
discontinuity at 180°C. Within the limits of experimental error they remain constant below this temperature,
with a value of 1.26 & 0.04 eV.
this temperature
the activation
Above
energy rises steadily
to 1.75 eV at 350°C. There is no significant difference in the values of these activation energies for specimens possessing The
annealing
different of the
(Fig. 2c) was continued isochronal
degrees heavily
of cold-work. cold-worked
wire
to 9OO”C, and the complete
annealing curve is shown in Fig. 3.
Isothermal
annealing
curves
at
10”
intervals
were obtained between 100°C and 2OO”C, and a few of these are depicted in Fig. 4. The shape of each curve is not identical; retical predictions
this disagrees with the theo-
of Section
2(d), and consequently
_
none
0.906 fO.005
none
0.974
annealed at 1400°C for 5 min
0.770
annealed at 1400°C for 5 min
0.590
annealed at 1400°C for 5 min
1.067 ~~_~ ~-
__~_..~
activation
energies possess no physical
meaning. (See next section.) Some electrical resistivity made at liquid-nitrogen
measurements
temperature
were
to supplement
the resistance measurements. Table 2 summarizes the results, together with the history of each specimen. The relative purity of the 0.008 in. and the 0.020 in. diameter
wires is reflected
of the former yR cm). Drawing increases ,uQ cm),
(l-067
from the
pfi
in the higher resistivity cm compared
@020 in.
resistivity
of which
just
to
by over
specimen
0.015 in.
7:/,
(O-906
0.770
diameter to
0.974
a half anneals
below
18O”C, using the data of Fig. 2(c). that an annealed
with
It is also apparent
possesses a lower resisti-
vity when it has been previously
cold-worked.
This
is in accord with observations that when a coldworked metal is annealed above the recrystallization temperature,
the resulting
grain size increases
with
the degree of cold-work.(‘) 4. DISCUSSION The evidence that a comparatively large decrease of resistance which anneals with a constant activation suggests
energy that
imperfection
occurs the
between
annealing
100°C of
a
and
18O’C
fundamental
such as a certain kind of point
defect
is being observed. Makin has shown that there is no measurable change in the yield point at room temperature when heavily cold-worked wires have been annealed for 280 min at 175°C. This indicates TtME (MINUTES)
FIQ. 4. Isothermal annealing curves for heavily cold-worked molybdenum
that little change in the number and position of dislocations have taken place, and therefore that the motion of dislocations is not responsible for the
MARTIN:
ANNEALING
OF
POINT
DEFECTS
large decrease in electrical resistance. The annealing above 180% with a rising activation energy is clearly
associated with no simple process. ~esumably, a relaxation of dislocations occurs over a broad spectrum of activation energies. Furthermore, the greater the degree of cold-work the larger is the IO&180% step compared with the rest of the annealing curve. This is what we would expect if the step is due to point defects, a~uming they are formed by the intersection of dislocations. These results may be compared with the annealing of neutron-irradiated molybdenum. Kinchinc4) has found that after neutron irradiation at 30% an annealing stage occurs up to 190°C with an activation energy of l-3 eV. A subst,antially similar resuIt has been found by Thompson(a) when the irradiation is performed at liquid-nitrogen temperature. It would appear reasonable to assume that the same point defect is responsible for the cold-work ~i.nnealingstage. It has already been pointed out that the shapes of the isothermal curves are not identical, and therefore that activation energies deduced from equation (4) have no physical meaning. Indeed, the apparent activation energies decrease linearly with the amount of resistance annealed. This, of course, is against expectation, but it was found that no limitations of the experimental method could explain this. The result of this experiment is to demonstrate that the effects of a low-temperature anneal for a long time and a short high-temperature anneal are not alike. In order to demonstrate this further experimentally, a heavily cold-worked wire was annealed at 120°C for 240 min and then annealed isothermally at lSO”C, When a correction for the 120°C anneal was added to the 180°C annealing times (this is not very critical), the 180°C isotherm did not correspond with the one shown in Fig. 4, but was uniformly displaced to the left. This displaced isotherm gave an activation energy of 1.25 eV, in agreement with the isochronal experiments. Hence we may appreciate that the objection to determining activation energies by the isothermal method is that a part,icular value of resistance does not correspond to a unique physical state of the metal. The isochronal method, however, is not susceptible to this objection, since the calculations are based on measurements taken when the specimen is in the same state. It is of considerable interest to form an estimate of the number of defects produced by cold-work. One method is by measuring the stored energy released by annealing and then, assuming the defects
IN
COLD-WORKED
MOLYBDENUM
375
are vacancies, to postulate that 3 eV are liberated when one point defect disappears. Unfortunately, no stored-energy measurements on cold-worked molybdenum have been done, but an estimate may be made by analogy with the work of Clarebrough, Hargreaves, and West,(l*) who observed the stored-energy release of a point defect in nickel as well as the energy released on recrystallization. Assuming the yield point of polycryst,alline molybdenum is 70 kg/mm2 and that no work-hardening occurs, the energy expended in a 40% deformation is 5.5 Cal/g. By analogy with nickel, we assume that 2% of this energy is stored in the lattice, of which one-fifth is in the form of point defects, Hence, 0.022 Cal/g are stored as point defects in molybdenum for 40% deformation, corresponding to 3.08 x 10m5 atomic concentration of defects, This is responsible for an increase of about O-035 ,u”cRcm in resistivity. Consequently, the stored energy to resistivity ratio is 0.6 cal/g/,uQ cm, and 1 at. o/0 of point defects will produce an increase of 11 ,UQcm in resistivity. This may be compared with Overhauser’@) experimental value of l-7 cal/g/pQ cm in copper after deuteron irradiation. If we assume that Overhauser was observing the annealing of vacancies and that the energy released per vacancy annealed is 1.3 eVs then 1 at. y. of defects in copper will produce an increase of 2.8 ,uln cm in resistivity. At present it is not possible to be certain of the nature of the point defect which anneals below 180%. Since the activation energies for cold-worked and irradiate1 specimens agree closely, it would appear that the defect is elementary. By plotting the activation energy against the temperature of anneal, both reduced by the melting-point (oorrections being made for different times of anneal), Thompson(i2) has shown that all activation energies so far determined in metals lie on a single curve. In particular, the 1*26-eV stage in molybdenum and the 0*7-eV stage in copper are superimposed on this curve. It would appear not unreasonable to assume that a similar defect is annealing in copper and molybdenum. The evidence we have to date(n) sugge&s that vacancies probably anneal at 0+7eV it is tentativeIy proposed that the in copper; 1.26 eV annealing stage in molybdenum is due to vacancies.
The helpful in the Stubbs
author is indebted to Dr. A. H. Cottrell for discussions, Mr. G. H. Kinchin for guidance initial stages of this work, and Miss M. J. for assistance in the experimental work.
376
ACTA
METALLURGICA,
REFERENCES J. W. GLEN Adwxncesin Physics 4, 381 (1955). F. SEITZ Advances in Phy8k.9 1,43 (1952). A. H. COTTRELL Private communication. G. H. KINCHIN See R. A. DUODALE, Report of Bristol Conferenceon Defects in Crwtdline Solid8 D. 249 (19551. 5. R. k. EQ*LESTO& J. Ap& Phys. 23, 1460 (195i) anh Acta Met. 1,679 (1953). 6. J. 0. LINDE Ann. Phys. 15, 219 (1950). 1. 2. 3. 4.
VOL.
5,
P. A. BECK
1957 Advances in Physics 3, 245 (1954).
i: M. J. MAKIN Private communication.
9. M. W. THOMPSON to be published. 10. L. M. CLAREBROUGH,M. E. HARGREAVES, and G. W. WEST Proc. Roy. Sot. A232, 252 (1955). 11. A. W. OVERHAUSER Phys. Rev. 94, 1551 (1954). 12. M. W. THO~~PSON to be published. 13. M. J. MAKIN British Report Atomic Energy Resestrch Establishment M/R 1852.