The Snoek-köster relaxation transient period in cold-worked niobium

THE

SNOEK-KijSTER RELAXATION TRANSIENT PERIOD IN COLD-WORKED NIOBIUM C. OYTANA

and D. VARCHON

Laboratoire de Mecanique Appiiquee associe au C.N.R.S.. Facuiti des Sciences de Besancon. 25030 Besanqon Cedex:. France (Received 15 December 1977: in revised ,(orm 27 April 1978) so-called S-K peak observed in internal friction experiments on cold-worked b.c.c. metals has been studied through relaxation tests in order to lengthen the measurable relaxation times and to lower the temperatures. We could then show the existence of a transient period during which the relaxation time TV),increases in a very large proportion while the relaxation strength remains constant. The results agree qualitatively with Schoeck’s theory and with an aging due to the migration of interstitiais towards the dislocations. But the study of the aging kinetics together with that of yield point return conveys the idea that the disiocatton mechanism is more complex and can be compared to that leading to the ;’ peak. Abstract-The

R&urn&Le pit de frottement interne dit pit S-K observi sur ies cubiques cent& tcrouis est Ctudie en relaxation afin d’aiionger ies temps de relaxation mesurabies et d’abaisser ies tempiratures. On peut ainsi mettre en Cvidence i’existence d’une phase transitoire au tours de iaqueiie ie temps de relaxation rsL croit dans de trts grandes proportions tandis que i’amphtude de relaxation reste constante. Les rtsuitats sont en accord quaiitatifs avec la thiorie de Schoeck et un vieiiiissement dQ g la migration des mterstitieis vers ies dislocations. Mais I’ttude conjomte de la cinetique du vieiilissement et du retour de iimite eiastique donne B penser que ie mecanisme est plus compiexe et pourrait itre compare g ceiui du pit ;‘.

Zusammenfassung-Das sogenannte S-K-Maximum der inneren Reibung an krz. verformten Metaiien wurde mit Reiaxationsversuchen studiert, urn die me5baren Relaxationszeiten zu veriingern und die Temperaturen abzusenken. Wir konnten damit die Existenz einer ubergangsperiode nachweisen. wlhrend der sich die Reiaxationszeit rs). sehr stark vergr65ert. wohmgegen die Reiaxationssttirke konstant bieibt. Diese Ergebnisse stimmen quaiitativ mit Schoecks Theorie iiberein und mit einer Aitaung durch die Wanderung von Zwischengitteratomen zu den Versetzungen. Jedoch iegt die Untersuchung der Alterungskinetik und der FiieDpunktumkehr nahe. da5 der Versetzungsmechanismus kompiexer ist und mit demjenigen des ;-Maximums vergieichbar ist.

1. INTRODUCTIOlV

ally admitted that Schoeck’s model of the diffusion controlled bowing of pinned dislocation segments is the most realistic [S]. This theory assumes that the anelastic strain is due to the gliding of dislocation segments dragging their bound solute atoms. The migration of the interstitials controls the motion of dislocation segments, and then, the strain rate. This leads to a relaxation strength A which must depend on the pinned dislocations density .I and on the average segment length I between immobile locking points. Schoeck’s calculation gives

Cold-worked b.c.c. containing some interstitial impurities exhibit an internal friction peak termed SnoekKGster peak (or S-K peak). Its activation energy is higher than that for the free lattice migration of interstitial atoms [l]. Other properties have been reported: influence of the amount of cold work, increase of the peak height with the interstitial content [Z]. heat treatment sensitivity [2. 33. but these experimental aspects, are not found in every case and seem to depend on particular metallurgical transformations produced by the thermal excursion required to trace out the peak. Especially. in iron alloys. on which most studies have been pursued. Petarra and Beshers [3] then Ferron er al. [4] have established that N forms Cottrell atmospheres around the dislocations and is so responsible for the S-K peak. while C can produce a drastic reduction of it through a precipitation on the dislocations. Several mechanisms have been proposed to explain this relaxation phenomenon. but presently it is gener\\, I’ 1 It

A = j9,11*

(II

where B is a geometrical parameter. The relaxation time should depend on Cd (the interstitial concentration at the dislocation) and on the diffusion coefiicient of the bound interstitial atoms. The result derived by Schoek is stkTCJ2

(21

where LYY is also a constant. the other letters having their usual meaning. 17

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With regards to the activation energy Ws, of the S-K peak, Schoeck suggests that: ws, = w, + Ebr

(3)

where W, is the bulk diffusion energy as given for instance by the Snoek peak while E, is approximately the binding energy of the interstitial to the dislocation. If the S-K peak is related to the dislocation-interstitial interaction. there should exist a transition period corresponding to the migration of point defects towards the dislocations (according to the relationship (2), ask should increase with C,). Transient phenomena have already been reported. for instance. that due to carbon in Fe [4]. But in this case, the evolution of the relaxation must not be attributed to that of Cd but to a specific effect of annealing. In the same way Boone and Wert [2] observed in niobium that Tp, the temperature of the S-K peak due to nitrogen, decreases during successive tracing out of the peaks, but this cannot be attributed to a variation of Cd, the effect of which should be the opposite of the observed one. They actually explain their observations by a background effect. If such a transient phase in the S-K peak could be pointed out, it should allow us to define the nature and the mechanism of the corresponding relaxation more accurately. 2. EXPERIMENTAL

METHOD

If a transient phase exists, the reason why it is not observed in internal friction experiments obviously comes from the fact that too high temperatures are needed to trace out the peak. Cottreli’s atmosphere formation gives rise to several macroscopic phenomena: yield point return [6], recovery of Granate Hikata-Liicke internal friction [l]. . . . The temperatures at which the aging due to this formation is observable through them, in a time of the same order as that of an internal friction excursion (from a few minutes to some hours), are much lower than the S-K peak temperature Tp for the usual frequencies. For instance, in the tantalum-oxygen system. the study of Cottrell’s atmosphere formation through the yield point return technique is possible at temperatures about 330 K [6] while the corresponding Tp is 423 K for a frequency of 0.6 Hz. In the same way in ironcarbon, different studies of yield point return [S] and of internal friction recovery [9. lo] show that at the temperatures where the S-K peak is measured, the aging time is much too short to be observed. To lower the temperature at which the anelastic phenomenon corresponding to the S-K peak is observed it is necessary to increase the relaxation time rsk and, therefore, either to achieve internal friction experiments at very low frequencies, or to use direct relaxation tests; two methods requiring sophisticated equipment. We used the second one, the measurements being performed on a torsion apparatus de-

scribed elsewhere [ll]. With regards to the curves analysis a method has been set on [12. 131, which starts from Schwartz1 and Staverman’s approximations [I]. Let H(ln T) be the relaxation spectrum to which we have to go back from the experimental relaxation curves: then. the equation of these curves is : I oft) = CT,+ Ac H(ln 7) e-’ ’ d(ln r). (4) s0 The spectrum H(in r) can be approximated functions : H,(ln t) =

(- 1)P Aa(p - l)!

by the

dPa(r)

&)PsP-L c

d(ln tV I ,_pr’

(5)

The H&r T) are approached functions of H(lnr), the accuracy of which increases with p. Their main advantage is that they only need a derivative of a(r), so that it is possible to get H,(lnr) in a finite range of ~5:(ri, r2) starting from the experimental curve a(r) which must be obtained only in a limited interval of time: (t,, r2) and not from r = 0 to c = x, as in the case where the standard methods of inversion of a Laplace integral would be used. Quite a lot of results can be obtained from the first approximation P = 1, especially the values of the relaxation times in the case of a discrete spectrum with eventually some dispersion around them [11, 121, which is the most common one in internal friction studies. The qualities of this method, as compared with those of internal friction, have been discussed and it has been possible to show that Schwartz1 and Staverman’s first approximations lead to an accuracy of the same order as internal friction experiments [13]. Tantalum and Niobium exhibit an S-K peak, produced by oxygen interstitial atoms. and which is poorly known [7]. This lack of knowledge is due to the fact that the peak is vanishing during the thermal excursion required to describe the peak: but, according to Delamotte and Wert’s experiments, one can foresee that the relaxation time should lie between 10 and lo4 s (values open to the relaxation test) in a temperature range of about 370-470 K. For these temperatures, yield point return experiments have shown that Cottrell’s atmosphere formation is important for aging time ranging from an hour to several days [14]. Besides, these alloys are simpler than the Fe-N or Fe-C ones. These miscellaneous remarks account for the choice of the niobium oxygen alloys. The samples are 0.6mm diameter wires, alloyed with oxygen through an anneal in a vacuum with a residual pressure of 10s3 to IO-‘Torr at 1270 K and cold worked by wire drawing at room temperature. During the relaxation test, they are heated in air by an oil circulating furnace which allows a constant temperature within a O.l”C oscillation. The oxygen Snoek peak has been measured before and after such a heating to check that the oxygen content does not change during the experiments.

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s

7,

Fq. 1. Relaxation test at 418 K on niobium cold worked 4”,, and annealed at 418 K. tat Normalised relaxation function. (bt First-order approximation H, of the relaxation spectrum. (cl Background. (dl H, after correction of the background.

3. EXPERIMENTAL

RESULTS

?.I T/w S-K peak On Figure 1. a result obtained at 418 K is shown. The oxygen content is 125 p.p.m.. the cold work amount 4”” and the sample has been aged at 418 K for 70 h. Curve (a) represents the normalised relaxation function Y(r) = [a(O) - a(r)]/a(O) where a(O) is the first measured value of a(r) (after the end of the sample straining): the numerator is u(O) - o(t). so as to obtain positive values for Y(r). (Actually, the test is a torsion one. so that a torque instead of a stress has been measured.) Curve (b) represents the first approximate function H, of the spectrum H(ln T) calculated from (5) with p = 1. Curve (dt is obtained from

1000

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(bl by removing the background (cl. To this extent. we have to notice that (bt or (cl are approximate curves and that their width is not equal to that of H. Nevertheless. the observed width of HI is larger than that which would be obtained from a single relaxation time. Comments about the problems arising from this width as compared with those of mternal frictton can be found tn Ref. 13. The peak of Fig. I can be identified with the S-K peak for two reasons: (al Its strength depends on the amount of cold work (the height of H, rises to 5.1O-9 when the cold work deformation is j?““t. (b) Let 7sk,( 3~. 7) be the value of 7 corresponding to the maximum of H, (and then of HI. for a test performed at a temperature T after a very long aging at a temperature 7; > 400 K. The Arrhenius diagram of In rs,.( X. T) vs T- ’ leads to a straight line (Fig. 2. curve It. The S-K internal friction peak of de Lamotte and Wert [7] gives a point which is also located on the same straight line. The parameters of the S-K peak of niobium oxygen which had been but roughly estimated by Lamotte and Wert can then be determined: activation energy I+&( z I = 2.05 eV. frequency factor r&( I I = 5.2 x lo-” s. Taking into account the relationship (31 this gives a binding energy Eb 1 1 eV. 3.2 Transient period In 3.1 the samples had been aged for a long time before testing. Figure 3 shows three curves of H, obtained on the same sample after three different aging times before test r? at 398 K. i.e. for 1: r, = 5000s. for 2: 1,. = 8.104s. for 3: 1,. = 1.8 x 10’s. The relaxation tests have been done at the same temperature as aging: T = 398 K. The experiment has been done in the following way: the cold-worked sample is maintained at temperature T in the relaxation machine during 5000s before the first test (actually the minimum time needed to pet the temperature stability required by the experiments is 2400s): these 5000s add to the

/T’K

Fig. 2. Arrhenms plot. Curve 1: plot of rsk (I_. 71 as measured on aged samples (point L-W: result obtained in internal friction by de Lamotte and Wert). Curve 2: plot of I,,(O) as deduced from Fig. 5 and relationship (11t. Curvje 3: low temperature measurements of the oxygen Snoek peak as obtained through relaxation tests.

Fig. 3. Influence of aging on the S-K relaxation. The curves represent the first approxrmation of the relaxation spectrum. (1) after holding at 398 K during 40 mn before the test: (2) same sample. Recovery consecutive to relaxation test (It: (3) relaxation test consecutive to (2). e:,, =j‘(rl: straining cycle.

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time of the 1st relaxation test to constitute the aging time of the second test which is a recovery one (after the 1st relaxation test performed with a constant strain E,,,,e,,, is brought back to zero and the resulting recovery is treated through equations (4) and (5) to give curve 2). In the same way. the aging of the 3rd test is due to the first SooOs and to the 2 previous tests. It has been checked that the same results are obtained when a different sample is used for each aging time, a single relaxation test being then performed on each sample. One can observe. in these experiments, the existence of a peak shifting towards longer times when the aging time r,. increases. Consecutive experiments show that the asymptotic value of the corresponding relaxation time when t,. becomes very large is rSK(x, 77. i.e. the limit value for large aging time of this shifting peak is the S-K one. Therefore the existence of a transient period of the S-K relaxation has been shown: and we shall call ~sk(t,, T) the relaxation time of this shifting peak obtained after aging during t, at temperature T. The main difficulties arising when one wants to show that this shifting peak has got the S-K one as a limit are: on the one hand, at the lower temperatures (for instance in the case of Fig. 3, at 398 K), rSK(X, T) is too long and it is not possible to observe it (curve 3 of Fig. 3 represents a sort of a limit case for slow relaxations): on the other hand at the highest temperatures used, the shortest aging time of 2400s becomes important and the first t,,(r,, T) measurable is close to rsx( X, T). It is, anyway, easy to show that the limit position of the shifting peak is the rsI( one, but some difficulties will arise when the kinetics will be considered. With regards to the amplitude of the variation of tsk during aging, to this extent. it is possible to determine it for the lowest experimental temperatures. In fact, at 328 K, the peak migration is very slow and it is actually possible to get rsK(O,328 K). The extrapolation of the Arrhenius plot (Fig. 2, curve 1) gives T& 1,328 K). At this temperature one gets 5:; ’ (01= rsI;

1.2 x 106

which is quite a large value. Another important feature to be pointed out is that during this important increase of rsy the relaxation strength does not show any significant change (Fig. 3). Unlike Fig. 3. it is often observed that the shape of the spectrum is changed by aging, chiefly at elevated temperatures. where the maximum in H, decreases while it becomes wider. But, within the experimental error range, the strength A does not change. 3.3 Kinrrics of rhr increase of‘5sk:(t,, 77 The study of the S-K peak has been carried out between 328 K and 438 K. Figure 4 shows 4 examples of the variations of ~~~ vs the aging time t,. The fact that some curves are intersecting demands an explanation: the position of the curves is the result

IN COLD-WORKED

NlOBlUM

II -

IO -

398-K x 38l’K

0

. 36S.K 0 344.K

68-1 ‘0g

t,

Fig. 4. Examples of aging at 4 experimental temperatures. Evolutton of rsK.

of two opposite phenomena: first, the aging which shifts T&., T) upwards with a kinetics which is enhanced by a rise in T and, second, the thermal activation I+&( x ) which results in an important decrease of the asymptotic value of each curve when T is increased. If we refer to equations (2) and (3) we must expect the increase of ~~~ with aging to be due to the variations of C, from the bulk concentration to a saturation value (see further in Discussion of the Results). Figure 4 shows that an ordinary Bilby Cottrell’s law cannot account for the results and this is not surprising as Cd is reaching saturation values. If more general laws are used. such as the extensions to long aging time of Bilby Cottrell’s law [IS] (which allow an interpretation of yield point return experiments on niobium [ 141):

Ts~

%C

then T is found to have a 2eV activation energy. To determine this it is necessary to have T&O, T): as we saw before, this value can be obtained at our lowest experimental temperature. Starting from this result, 2 extreme cases have been considered: either r,,(O, T) has the same activation energy as rsa( X. T) or T,,(O. 77 and 5SK(x, 77 have the same frequency factor. Both cases lead to a 2 eV value for the activation energy of 5. More generally, it must be noticed that aging can be observed in the whole temperature range of our experiments. Now, these tests are longer than the corresponding 5sK but of the same order (5 times longer, Fig. 3): consequently, temperature induces variations in the kinetics of the aging of r,,(t,,, T) of the same order as those induced in rSK(x , T) and therefore this kinetics if thermally activated should have an activation energy about I&( x ) = 2.05 eV very different from the oxygen diffusion one which should be

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expected if the shifting of the transient peak had to be attributed to a mere increase in C,,. 4. DISCUSSION

OF THE RESULTS

If these observations are compared with the relationships (2) or (3). a qualitative agreement is found if aging only produces a variation in Cd: I and A remaining constant. At these temperatures. the main observed aging effects are due to Snoek’s or Cottrell’s atmospheres formation [6, 8. 10, 143. which. at the strain rates met in S-K relaxation experiments are but soft pinning points dragged along when dislocations are moving. The constancy of I and A ma) therefore be a reasonable assumption. Now. E, is of the order of several tenths of an eV. this gives a very large ratio

Cd” Cd(O) [C,,(O) is the bulk concentration] large, values of T& ’

and explains

the

ALL l 376'K

AU'

* 381 "K 1398°K

C 344'K > 355-K * 365'K

FIB. 5. A vs (Aa),Aq/. A IS defined in (91 and is a monotonic function of y. The curve shows that y can be a function of (Aat,An only. independent of 7 and r,.. when ~~(0) is such that r&(01 = I.8 x IO--s and IX;,(O) = 0.65 eV. A good fitting of a single monotonic curve can be obtained for values of &(OI until 0.9eV with their correspondmg &01.

TS);fO)’ Actually Cd( YZI is not. in our case. an equilibrium value defined by the binding energy E,, but rather a saturation value. If this was not so. C,(X) would depend on Cd(O) and then on the previous vacuum anneal. As all our ?sK(z. T) values fit the same Arrhenius straight line together with Lamotte and Wert’s result it can be inferred that. actually. for rsn( x I the dislocation segments are saturated with interstitials. 4.2 Comparison

wiril Ao t$ecr

The comparison with Schoek’s theor) shows that it is very likely that the shifting of the transient peak is induced by oxygen migration to dislocations. However. as we saw in 3.3. no correlation can be found between this migration and the activation of the peak displacement. To precise the S-K aging mechanism. we should find the relation r,,(C,). Cd being an equilibrium concentration. This could be obtained by fixing an oxygen average content Co low enough. in order that Cd( z T) = Co exp(E,)/I, T < C;: C; corresponding to the saturation of the dislocation segments (as we saw it. in the present case Cd( x ) = C;). This experiment is a rather complicated one. Another way has been chosen. Let us define Cd(fJ - Cd(O) (7) y1 = C&Xl--Cd(O)‘ where C,(r,.). C,(O) and C,( x I respectively represent the oxygen concentration on the dislocations for aging times r,.. 0. and x at the aging temperature 7. One has q, = y,(r,.. 77. This parameter is not available during a relaxation test. However. there exist measurable physical quantities which are monotonic

functions of q,. for instance the yield poinr return (or Aa effect). It has been shown that the yield point return due to oxygen in niobium can be written as

$= ($),[I -exp(ff)i3].

(81

Au/a and (Au.@, being the relative increases of the elastic limit at the temperature T for aging times r, and I [12]. The temperature becomes involved in the relation essentially through the activation energy of T (which is checked to be IQ’, = I. 1eV) and through the parameter (Au;u)~[~~]. It could then be inferred that

is actually a function of q, only [13]. It is then possible to compare q to Au,‘Aul instead of ql. That is to say. we have to look for a possible thermically activated function ~~~(0)such that: Ts~(f,1 - T,,(o) 4=

be a monotonic

function of $

TsK(%) -T,,(O)

I

Figure 5 shows that this is possible when Q,(O) is such that its two parameters have got the ver! rough values: ws,(0) = 0.65eV and T~~(O~= IO--s (this ~~~(0)is plotted on Fig. 2). Whatever values are given for I,. and T,.. every experimental point fits a single curve. 4.3 Ahernarir’e

irrrerprettrrior7

The above analysis leads to the relationship (91

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This involves that %,(L) =

WsdYlt

7$&q,)exp -

kT

with

and WS&) = ws,to) + 8”: /I = Wsk(x ) - cVs,(O)2. 1.4 eV .

(11)

It is obvious that the q,(tJ variations as given by (10) and (1 II come from the chosen form of (I. But this choice agrees with Schoeck’s assumption of a relaxation mechanism related to the diffusion controlled bowing of pinned dislocation. In this case, to a given value of C,, and then of qi (obtained for instance by long time aging of samples with different weak oxygen contents), corresponds a value of rsk: ss,(y,, Tk To this value are attached a frequency factor &qi) and an activation energy B&&i) independent of T. The proposed analysis aliows a rough estimate of the variations of these two parameters with 41.

The proposed model will have to account for the following points: (a) The S-K peak is certainly related to the oxygendislocation interaction. (b) A transient phase does exist during which iSK can increase on a very large scale. (c) Meanwhile, the relaxation strength remains constant. (d) To relate this transient phase to the long range migration of interstitiais it is necessary to admit large variations in activation energy together with the frequency factor. The property c shows that the anelastic strain comes from dislocation segments bowed by the applied stress. the pinning points of which are insensitive to aging, We must notice, too, that r,k(O) depends on the samples. rs,(O) corresponds to a zero aging time and then to Cd = Co and not to Cd = 0. If the average oxygen content decreases, ~~(0) will decrease too and tend to an intrinsic dislocation mechanism. Due to the large imprecision in the calculations of r&(O) and Pi&(O)it is diecult to say to which intrinsic mechanism the S-K peak has to be compared. Nevertheless. the value of W&(O) is closed to that of the 7 peaks to which Seeger and Sestak associate the double kinks formation on screw dislocations (111 j [16].If the activation energy of 7 peaks (i.e. about 0.8 eV) is prescribed to W&(O) (which still is in the error range of the determination of Fig. 5) then the frequency factor comes to 2.3 x IO-‘OS (when assuming that r,,(O) = rs the Snoek relaxation time, at 320 K), which is a value about IO* times larger than the estimated one for the 7 peaks r!?[16]. EIeyond the large imprecision in the det~mina~ion of both r&(O) and 7p, this gap comes from the very

IN COLD-WORKED

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nature of these two relaxation phenomena. While in the Seeger and Sestak’s interpretation of the ;’ peak (formerly applied to the Bordoni I peak1 we have a maximum damping when the applied stress frequency is related to that of a jump of a dislocation length from one valley to the next one. the S-K(O) should be considered as a long-range motion of a dislocation segment to its equilibrium position corresponding to the applied stress. and this needs a great number of elementary mechanisms of the ;’ type to operate. This point demonstrates the difference between the S-K(O) relaxation mechanism and the See.ger and Sestak’s one for 7 peaks. The long-range dislocation motion can be impeded either by Snoek’s and Cottrell’s atmospheres dragging, or by the core solute atoms [173. In the former case, a practically constant activation energy as given by (3) can be expected. The latter one would correspond to a combined “extended-core-impurity” model for screw dislocations in b.c.c. [IS]. For very small values of Cd the strain rate would be controlled by kinks pairs formation (as described before! and gradually, when Cd increases. this control would come from the kinks pairs formation and/or their diffusion modified by the presence of core impurity atoms. In the present state of our experimental knowledge an improvement of the model does not seem worthwhile. CONCLUSION The main feature of the above study is the existence of a transient period in the S-K relaxation. In the case of niobium with oxygen as an interstitial, during this period, the relaxation time shifts towards higher values while the relaxation strength does not undergo any drastic change. This phenomenon cannot be observed in internal friction experiments for frequencies around 1 Hz, the experimental temperature being too high. These observations seem to be confirmed on tantalum-oxygen system [13] and are different from the transient phases sometimes observed on several alloys which are actually related to specific metallurgical transformations and not to a Bilby-Cottrell type aging [I]. Another important feature has to be pointed out: the experimental observations are in a qu~itative agreement with Schoeck’s mechanism [5]. The gliding of dislocation segments controlled by the diffusion of interstitials must then be accepted. It is not, however, possible to explain the observed kinetics through a (3) type relationship if the variations of rSK have to be related to the interstitial migration to the dislocations, which is a very likely assumption. An analysis has been proposed to enforce this migration as the origin of the evolution of rsk( X) with t,. But the precision in the determination of s,,(O) is not good enough to altow a comparison of the S-K peak, at zero aging time and at very low C,(O), to intrinsic internal friction mechanisms in a definite way: the 9 peak seems. however, to be the

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best candidate. In this regard. it must be noticed that at 323 K the rs,, increase is very slow so that at lower temperatures this evolution will not be observable except if aging temperature 7; is larger than the test one: Tr. So that this peak would look stable in r during an internal friction experiment. Again. when the ;’ peak appears at much higher temperatures than the Snoek one. aging is too rapid and cannot be observed. then the peak is observable onl! on htph purit! metals. It may be concluded that it is not surprising that no migration of an intrinsic peak has been observed. In the case of relaxation. it IS not possible to extend the tests under 320 K because the relaxation times become too long and because the separation from the Snoek peak is rather difficult. A further progress in this problem seems to require materials with different Cd( 7.. Tt and then very small interstitial contents. REFERENCES 1. A. S. Nowick and B. S. Berr!. .4w/asric Relarnrioa irt Cr!srul/iw So/iris. Academic Press. New York f 19721.

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2. D. H Boone and C A. Wert. J. pltt,.~.Sot,. Jmpan 18,

141 (19631. 3. D. P Petarra and D. N;. Beshers. Acre merdl. 12, 791 (19671 F. Ferron. J. Parisot and J. De Fouquet. ScripI