The recovery of cold-worked molybdenum

Physica 42 (1969) 165-178

THE

RECOVERY

o North-Holland

Publishilzg

OF COLD-WORKED

Co., Amsterdam

MOLYBDENUM

L. STALS and J. NIHOUL Departement

Fysica

van de vaste stof, S.C.K.-C.E.N.,

Mel,

Belgie”*

Received 30 August 1968

synopsis Molybdenum wires of 0.05 mm diameter were drawn at room temperature from an electron beam refined rod. These wires were subsequently subjected to isochronal and isothermal annealing treatments in a temperature range from 300 to 1200 K. The electrical resistivity is shown to decrease in four stages : stage III (300-500 K), stage IV (500-700 K), stage V (700-900 K) and stage VI (900-1200 K). These stages are associated with activation energies of 1.3 eV, 2.5 eV and 3.7 eV, respectively. The kinetics of the pronounced stage III recovery are compatible with a diffusion controlled bimolecular reaction. It is proposed that stage III is mainly due to free migration of interstitials to vacancies, stage IV to free migration of remaining vacancies, stage V to dislocation rearrangements and annealing and stage VI to recrystallization.

1. Introdzlction. In recent years, much effort has been paid to the study of structural defects in the transition metals having a b.c.c. structure. In spite of this a large number of questions remains unsolved. For a survey of the leading experiments and the current ideas about the interpretation of the recovery data we refer to some recent review papersr-a). Recovery experiments on cold-worked and irradiated b.c.c. metals (MO, W, Nb, Ta, V, . ..) with various degrees of purity have revealed recovery features at about O.l6T, (T, stands for the melting temperature expressed in K) 3). An exception is shown by alpha-iron for which a similar recovery stage has been observed at O.l2T,4) and O.Z?OT,5-7). Much controversy originated about the interpretation of this stage, which in all cases appears to be singly-activated and which occurs in the temperature range where reasonably the intrinsic stage III must be expecteds). Two main interpretations are put forward: a first group of authors ascribes the recovery to the migration of extrinsic defects (interstitial impurities) 5-7~s--21), whereas a second group explains this recovery stage as free migration of intrinsic point defects39 8922-34). The first group of authors has clearly shown that * This research has been performed in association with the Universities of Antwerpen and Leuven. 165

166

interstitial

L. STALS

impurities

AND

play an important

J. NIHOUL

role on the “stage III:’

deformed and neutron-irradiated b.c.c. metals, niobium119 14* 21), tantalum129 13), vanadiumi5)

recovery

of

at least for the Va metals and for irons-7). On the

other hand, they failed to observe a prominent purity materials either after neutron-irradiationzi)

recovery peak in highor after cold-workas).

The situation is rather different for the Via metals. Since the solubility of impurities in these metals is extremely low, the first group of authors suggest the possibility that the stage III recovery observed for molybdenum and tungsten may be caused by precipitation of impurities redistributed on an atomic scale within the lattice under the influence of plastic deformation or irradiationiiv 21). Th e experiments they performed on the Va metals, made these authors conclude that for these metals and most probably also for molybdenum and tungsten no intrinsic recovery stages occur above room temperature. Kuhlmann and Schultzs6), however, have demonstrated that in carefully decarbonized tungsten recovery occurs in the “stage III” temperature range after neutron-irradiation at 4.5 K. The observed effect is too large to be explained by carbon migration as it is the case for carbondoped tungsten after quenching 2% 36). Furthermore, to assume that no intrinsic point defect recovery occurs above room temperature in the Via metals, also implies that vacancies are mobile at temperatures below O.l6T, with a migration energy of only one fourth, or less, of the activation energy for self-diffusion. This is in contradiction with the conclusions drawn by Meakin et al. 37) from electron microscopic observation of n-irradiated MO and also with the fact that the formation energy of vacancies is widely assumed to be only 60% of the self-diffusion energy as). In contrast to the first group the second group of authors ascribes the stage III recovery to the migration of intrinsic point defects. Whereas some of them conclude from electrical resistivity measurements 49as) and electron microscopic observationssa) that vacancies are freely migrating and interact with dislocations at this temperature, others conclude from electrical resistivity measurementsap 8922--2%s6-28~ 35)) electron microscopics5) and field-ion microscopic observationssa-al) that self-interstitials are migrating and recombine with immobile vacancies. As far as molybdenum is concerned, the results available until now have been obtained on commercially pure materials> 3% 3593% 40). The present paper reports on recovery experiments performed on high purity molybdenum after plastic deformation at room temperature. 2. Exfierimerttal method. A high purity, electron beam refined molybdenum rod with a diameter of about 3 mm from Materials Research Corporation (USA), has been reduced to 0.05 mm diameter wire without any intermediate anneal. The resistivity ratio r = ~aaax/~4.z~ for the wire after annealing above 1200°C amounted to about 1000. After correcting for the

THE RECOVERY

scattering “bulk”

OF COLD-WORKED

of the conduction

r-values

electrons

MOLYBDENUM

167

at the surface of the thin wiredI),

of the order of 3000 were obtained

for the annealed poly-

crystalline wire. This can be compared with the r-value for the initial rod of about 10000. Specimens of about 5 cm length were cut from this wire in the cold-worked state and spiraled before mounting for electrical resistivity measurements. These measurements were performed at liquid helium temperature. The annealing experiments were carried out in an electric furnace either under vacuum or in a continuous flow of purified helium. The temperature of the furnace was controlled to within f0.2”C by means of a calibrated chromel-alumel thermocouple. 3. Exfierimental resdts. Fig. 1 shows the isochronal recovery curve between 300 K and 1200 K. Each point represents the electrical resistivity at 4.2 K after a pulse of 30 minutes at the indicated temperature. Three temperature-time programs were used, as indicated on the figure. Fig. 2 represents the corresponding results plotted as the resistivity decrease per temperature interval as a function of temperature. This annealing spectrum clearly shows four recovery stages, which can be labelleds*s) as: stage III between 300 K and 500 K, stage IV between 500 K and 700 K, stage Va between 700 K and 900 K, stage Vb between 900 K and 1200 K. Since the activation energies corresponding to stages Va and Vb are substantially different (see section 3) it might be more indicative to use the nomenclature of V and VI respectively.

I’_

‘._ :

AT=5K At : 30min

- 1.5. 6

*a. / --.

E ; Q 1.0.

*.

”

*.

I. AT=ZOK At = 30.min

. .

-./ 0.5.

03 300

. . *.*. **._....

I

.

.

600

I

I

I

900

I

ATr50K /ft =30min

I

I

1200 -

K

Fig. 1. Isochronal recovery curve of high-purity molybdenum plastically deformed at room temperature. Each point represents the electrical resistivity at 4.2 K after a heating pulse of 30 minutes at the indicated temperature. Notice also the change of heating program.

168

L. STALS AND J. NIHOUL

Fig. 2. Recovery

spectrum of cold-worked

molybdenum,

as derived from fig. 1.

0.6

0

200

400

600

800

lOOO---

tfmm)

Fig. 3. Isothermal recovery curves for stage III of cold-worked molybdenum; cr = (p - p;‘/(pfI - pg’) is the relative concentration of defects, with pA1’ and pi” the electrical resistivity at the beginning respectively at the end of stage III and p the electrical resistivity at time 1.

In the stage III region, we have performed some isothermal recovery experiments, the results of which are shown in fig. 3. From the recovery data of figs. 1 and 3 and using the Meechan-Brinkman methodas) and the cross-cut method43) we calculated the activation energy of stage III to be (1.29 f 0.03) eV. The data obtained by means of these methods lie satisfactorily on parallel straight lines, as shown in figs. 4 and 5.

THE RECOVERY

OF COLD-WORKED

MOLYBDENUM

169

1OOl E,,,=(1.26 f0.03)cV

.c E G

lOO( 1oc

.E :tE ; 100 10

IO 1 2.2

2.6 -

2.4

103

2.6

2.2

K-'

103

T

Fig. 4

Fig. 5

Ti

Fig. 4.

This indicates that the stage III process is essentially singly-activated. Fig. 6 shows the successive values of the activation energies as a function of temperature up to 1200 K as obtained by means of the Overhauser method**). This diagram too reflects the presence of four recovery stages occurring in the temperature regions already mentioned. According to this analysis the pre-

400

600

600

1000 .-1200 T(K)

Fig. 6. The spectrum of activation energies for cold-worked molybdenum determined between 300 K and 1200 K by means of the Overhauser method.

L. STALS

170

AND

J. NIHOUL

dominant activation energies in the various recovery stages are as follows: stage III: 1.3 eV; stage IV: 2.0 eV; stage V: 2.5 eV and stage VI: 3.7 eV. 4. Analysis

III

of stage

recovery.

As already mentioned

in section 3 the

present stage III recovery data point to a singly-activated process. Furthermore from figs. 7 and 8 one can deduce that the isothermal recovery in this stage follows a Jt-law in the beginning (~~-1 N Jt), and turns into a secondorder process (~~-1 N t) as recovery proceeds. This is in agreement with similar observations on other metalsss~ 2%45). To a first approximation these diagrams can be explained by assuming a diffusion-controlled bimolecular

Fig. 7. The isothermal

recovery

data of fig. 3 plotted

r

in a (c;l,

,,/2) - diagram.

P 445.7K 60

-

s

ID f

P

s

2.0-I

425.7_K_.c __--

/ 6' ,

50

E

40

5 ; -z

_*_--.

,.~~~J::::____~

1.5

__--

.df

.-

30

..a---

20

10

0 Fig. 8. The isothermal

200

recovery

400

600

600

data of fig. 3 plotted

--t (min)

100 0

in a (c;l,

0

t) -

diagram.

THE

reaction

RECOVERY

between

homogeneously described

two defect species present distributed

mathematically

1 -Cr.

OF COLD-WORKED

with respect

;;D

where C~ z C/CO,with COthe concentration at time t; ~0 = diffusion coefficients of both more mobile than the other,

171

with equal concentrations

to each other.

by the equation46)

1 = 47m)C~D t+ (

MOLYBDENUM

This

and

case can be

:

t J>

initial concentration of defect pairs and the “bound pair” radius; D = the sum reacting defects. If one defect species is the diffusion coefficient may be written

c the of the much as

D = Do e-E,,,lkT where DO is the diffusion constant of the mobile defect species and Em its migration energy. As shown in a previous paper47), the isothermal annealing equation (1) can be transformed into the isochronal annealing equation : 1

-

-

1 =

kof(q

+

hJf(T)

CT

with :

f(T) =

!?(,_2c)

ko

= 4x/_~rr,,D,-,co,

kr

= 87+~r;D~ca,

AT ,u = at

e-E,,,lkT

%(I

_

??!$)e-Em/kTc,,

= the heating rate (in this case AT = 5 K and At = 30 min.),

Do

= the diffusion constant

E,

= the migration vation

To

_

of the mobile defect species,

energy of the mobile defect species i.e. the acti-

energy of stage III

(in this case E,

= the temperature at the beginning this case To = 300 K).

= 1.29 eV),

of the annealing

treatment

(in

For more comments on the meaning of the various symbols of eqs. (1) and (2) and for restrictions on the validity of eq. (2), we refer to refs. 24 and 47. More particularly the condition AT < kTi/Em is fulfilled for the present case since kTi/Em = 6.0 K and T = 5 K. Figs. 9 and 10 show the theoretical curves calculated by means of eqs. (1) and (2). The value of COhas been estimated from the resistivity decrease in stage III and the Frenkel pair resistivity for MO reported by Lucasson and Walker-as) (Ap/l at. oh F.P. = = 4.5 @cm). A satisfactory agreement between the experimental points and the theoretical curves could be obtained for both the isochronal and

172

L. STALS

J. NIHOUL

J

O.*Fig. 9. Theoretical

AND

isothermal

400

600

annealing

curves

stage III isothermal

-

diffusion second 0

calculated

1000 -.-

t (min)

by

means

of eq.

(1) for

annealing.

kinetics order

experimental

points

450

400

350

.300F--

-

500 T(K)

Fig. 10. Theoretical the main

recovery

isochronal process

annealing

occurring

curves

for various

kinetics,

in stage III is a bimolecular reaction.

suggesting

that

diffusion-controlled

THE

RECOVERY

OF COLD-WORKED

MOLYBDENUM

173

the isothermal results. Fig. 10 shows furthermore that pure first- or secondorder kinetics are inadequate to explain the experimental results. From this analysis it turns out that the “bound pair” radius YOamounts to (10 f 3) lattice distances and that the diffusion coefficient of the molybdenum interstitial is given by the expression: DZ = (4 f

3) IOh exp(-(I

.29 5 0.03)}/kT

cm2/s.

These experimental data are in rather good agreement with the results of de Jong and Afman for electron irradiated molybdenums4). They found: Dg = 9 X 10-4*1 exp{-(I ~0 = (8 5 3) lattice

.29 f

0.04)}/kT

cma/s;

distances,

5. Discussiort 5.1. Stage III recovery. From the preceding analysis (section4) it turns out that stage III recovery in cold-worked molybdenum can be described rather well as a diffusion-controlled bimolecular reaction. This is in agreement with earlier observations on other Via metals as well after coldworkss) as after neutron-irradiation 39 3~ 3% 37) and electron-irradiations4). All these observations favour the two-interstitial recovery model in which intrinsic normal interstitials migrate freely in stage III and recombine with fixed vacancies. Some direct evidence supporting the latter model results from field ion microscopic observations by Attardo et al. 29) on neutron irradiated tungsten. The main objection against this model originates from the fact that the activation energy for interstitial impurity migration is very close to the measured activation energies for stage 1112). The most striking examples have been reported for the group Va metals and for a-iron as e.g. the migration of interstitial oxygen and nitrogen in niobium, tantalum and vanadiumrl-is$ 17-21) and of interstitial carbon in a-irons-T). For the group Via metals, molybdenum and tungsten, this possibility is less probable due to the low solubility of carbon in these metals 49-51). Furthermore, the hypothesis that stage III in these metals should be due to reprecipitation of impurities, put in solution in non-equilibrium concentration by irradiation or plastic deformation 119si), seems at the least improbable. Indeed, the presence of an intrinsic stage III in tungsten has been definitely demonstrated both after cold-work by Schultzss) and after neutron-irradiation by Kuhlmann and Schultzs6) and by Moteff and Smiths7). An intrinsic stage III has been found after neutron-irradiation both for commercially pure molybdenum 8) and for zone-refined molybdenums). Experiments by de Jong and Afmans4) on electron-irradiated molybdenum have revealed the existence of a well-defined singly-activated recovery peak in the stage III

174

L. STALS AND J. NIHOUL

zone. It seems rather unlikely that all these experiments might be explained by the precipitation of redissolved impurities. Moreover, Cuddy4) has recently shown that, as contrasted with earlier statements59 6) an intrinsic stage III does exist in plastically deformed LXiron provided the metal has been heavily cold-worked. This recovery stage, however, occurs at a somewhat lower temperature (-~0.12T,) than the stage which has been usually called “stage III” (~0.20T,) in this metal53 6). Cuddy explains the observed annealing results as stress-assisted vacancy migration to dislocations (Bullough-Newman kinetics529 53)). In this case the annealing kinetics are described by the equation: c = Q e-btP

(3)

-Waite

kinetics(A*:0.9)

------Bullough-Newman ExperImental

kinetics

(nz0.40)

points

Fig. 11. Comparison between Waite kinetics and Bullough-Newman kinetics for coldworked iron (reanalysis of the 210°K-isotherm of fig. 4 of ref. 4).

0.5 ; -

Waite

klnetlcs

Experimental

(A*=

0.9

1

points

100 annealing

time

( min

tool )

Fig. 12. Comparison between Waite kinetics and Bullough-Newman kinetics for the present results on molybdenum (425.7 K-isotherm of fig. 3).

THE

RECOVERY

where (Y = 010exp(--E,/kT). annealing

OF COLD-WORKED

He further

data for other cold-worked

b.c.c.

MOLYBDENUM

shows that

isothermal

metals can satisfactorily

175

stage

III

be de-

scribed by this type of kinetics. Recently, Balluffi and Seidman54), however, have shown that there is little theoretical basis for expecting a relation of the form of eq. (3) for describing the annealing kinetics of vacancies in the presence of dislocations. Furthermore a reanalysis of Cuddy’s results (2 10 Kisotherm in fig. 4 of ref. 4) shows that they are also consistent with bimolecular diffusion kinetics (fig. 11). This is also the case for the present results on cold-worked molybdenum (fig. 12). As also pointed out by Cuddy55) and by van den Beukel56), it is not surprising that both equations (1) and (3) can be fitted to the same recovery data, since the first term of the series expansion of eq. (3), for 1z = 4, reflects the same time dependence as eq. (1): 1 --

CT

1 = Ata + Bt + . . .

Whereas the coefficients A and B do not depend on the initial concentration, the coefficients of eq. (1) on the contrary, are proportional to the initial concentration. This may provide a way to decide between the two kinetics n recovery models. Indeed, for the case of Bullough-Newman should be independent of the initial concentration of defects and equal to 0.5, whereas if Waite kinetics should apply, the apparent n-value would depend on the initial concentration. By analyzing theoretical curves, we found for the latter case that n ~0.4 for A2 = 1 and n II 0.7 for A2 = 0.01 (A2 = 4r;co) 47157). There will not be any peak shift with point defect concentration for Bullough-Newman kinetics, whereas for Waite kinetics a peak shift has to occur. As a matter of fact Cuddy’s results (fig. 1 of ref. 4) suggest a peak shift of about 12 K for the highest and lowest deformation degree towards higher temperatures with decreasing deformation. This effect, however, could be explained on the basis of different dislocation densities which has to be reflected in the value of aa. On the other hand it follows from a simple calculation that the observed peak shift corresponds to what should be expected in the case of a diffusion-controlled bimolecular reaction with a mean reaction order y N 3. In a previous paperss) it has been shown that a reaction order of about 3 at 50% recovery occurs for A2 N_ 1. As already mentioned above, this value for A2 is also suggested by the value of n = 0.43, found by Cuddy for the highest deformation degree. Hence it follows that the possibility of a bimolecular recovery process governing stage III of cold-worked iron must not be excluded on the basis of Cuddy’s results. Nevertheless, it can not be ruled out that the high dislocation density of cold-worked metals plays a significant part even if the main recovery process is bimolecular. The striking similarity, however, of stage III re-

L. STALS

176

covery

after

irradiation

and after

AND

J. NIHOUL

plastic

that the influence of dislocations on stage portant. Some direct evidence for the latter Schultz for tungstenss).

deformation

seems

to indicate

III kinetics is not very imstatement has been given by

More direct evidence against vacancy migration in stage III results from field-ion microscopic observations on neutron-irradiated tungsten by Galligan and coworkerssa-31159)

who found that vacancies

are migrating

in the stage

IV range. 5.2. Higher recovery stages. Figs. 1, 2 and 6 show the presence of three more recovery stages above stage III in cold-worked molybdenum, labelled IV, V and VI. Stage IV at about 0.20T, emerges from the background recovery as a small peak associated with an activation energy of about 2 eV. This stage is most probably due to vacancy migration. As already mentioned above, field ion microscopic observations have in fact revealed the disappearance of the remaining single vacancies in neutron-irradiated tungsten in the corresponding temperature rangesg). From the magnitude of the present stage IV peak it can be estimated that the atomic concentration of single vacancies surviving stage III does not exceed about 10-S. This would confirm the assumption that during stage III annealing only a small fraction of interstitials disappears at sinks other than vacancies. X-ray diffraction patterns of specimens of the same material as used for the present resistometric investigations show the onset of recrystallization features between 500°C and 600°C. This is the temperature at which stage V (0.28T,) occurs. Since this peak is more pronounced in cold-worked than in neutron-irradiated molybdenum of the same purity a), we believe that it is caused by dislocation rearrangement and annealing. The activation energy of this stage is about 2.5 eV. Finally, stage VI at about 0.35T, having an activation energy of about 3.7 eV, is due to recrystallization and grain growth as confirmed by X-ray diffraction investigations. It is a well-known fact that the recrystallization temperature decreases as the metal has been previously

cold-worked489 49).

6. Conclusion. The presently available annealing data on Via metals are still unsufficient to propose a definite recovery model for these metals. The model outlined below for the high-temperature stages should therefore be considered as a tentative interpretation only: stage free migration of interstitials to vacancies, stage IV: free migration of remaining vacancies, dislocation rearrangements and annealing, stage V: stage VI : recrystallization. To contribute substantially to the experimental verification of this model,

rrr:

THE RECOVERY

especially

for stage III

OF COLD-WORKED

and IV, experiments

MOLYBDENUM

should be performed

mens (i) with at least one or two orders of magnitude

difference

177

on speciin degree

of deformation or irradiation dose and (ii) with different and known degrees of purity. Also quenching experiments on ultra pure material and subsequent annealing would be very helpful. Some of these experiments are in progress in our laboratory. Acknowledgements. The authors wish to thank Professor R. Gevers for reading the manuscript and for helpful discussions. Thanks are also due to Mr. J. Pelsmaekers, for the X-ray diffraction work. The technical assistance of Mr. F. Lafere (calculations), Mr. F. Biermans (drawings and cryogenics), Mr. J. Verreyt and Mr. M. George (electrical measurements) is also gratefully acknowledged.

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