Hydrogen-related internal friction peak in the A15 compound Nb3Sn

Scripta METALLURGICA

Vol. 17, pp. 327-332 1983 Printed in the U.S'A.

Pergamon Press Ltd. All rights reserved

H Y D R O G E N - R E L A T E D I N T E R N A L F R I C T I O N P E A K IN T H E A15 C O M P O U N D Nb3Sn B.S. Berry and W.C. Pritchet IBM Thomas J. Watson Research Center, Yorktown Heights, New York, 10598, U.S.A. and J.F. Bussi~re Institut de Genie des Matdriaux, CNRC, 750 Bel-Air, Montrdal, Canada H4C 2K3 ( R e c e i v e d November 22, 1982) ( R e v i s e d D e c e m b e r 27, 1982) Introduction The Snoek relaxation associated with interstitial solutes in bce transitional metals is a well-known example of relaxation by stress-induced point-defect reorientation. (1) A n essential aspect of the Shock effect is that the solute atoms act as elastic dipoles due to occupancy of sites whose symmetry is lower (tetragonal) than that of the cubic host crystal. In terms of the widely-used h-tensor (1), the strength of a tetragonal dipole is represented by the difference in principal values X1-X2, whereas the overall dilatation is represented by the trace h 1+2h 2. Where measurements exist for the heavier interstitials (C, N, O), the tetragonality ratio h l / h 2 is of substantial magnitude (typically > 5 ) , with the consequence that the shape-factor ~ k l - h 2 and the volumetric size factor Al+2h 2 are not greatly different from each other. Typical values for both quantities are in the range 0.5 to 1.0. Despite a good deal of effort, the situation with respect to hydrogen and Shock relaxation remains clouded in mystery. F o r the relevant case of Nb, it has been inferred from the absence of a detectable relaxation that the hydrogen dipole strength is very small. (2) This cannot however be explained on the basis that h 1 and h 2 are both small quantities, since the size-factor ~'1 +2~'2 is known to have the quite substantial value of 0.17. (2) Rather, it must be presumed that for some reason the tetragonality ratio for hydrogen is substantially less than for the heavier interstitials.

F I G . 1. The tetrahedral sites occupied by hydrogen in Nb3Sn, numbered according to the orientation of the tetragonal axis. Note that the N b atoms occupy complementary tetrahedral sites on the faces of a bee cell of Sn atoms (shown shaded), an arrangement that produces orthogonal chains of N b atoms in the A 15 structure.

327 0036-9748/83/030327-06503.00/0 Copyright (c) 1983 Pergamon Press Ltd.

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Recently, a new perspective on the subject of the hydrogen Snoek relaxation has been provided by the discovery of a widespread and characteristic internal friction peak due to hydrogen in metallic glasses. (3-7) From detailed measurements on Pd-Si glasses (8,9), there is strong evidence that this relaxation is an analog of the Snoek relaxation, and that the tetragonality ratio hl//~2 is of the same substantial magnitude as for the heavier interstitials in bee metals. These findings point to the possibility that hydrogen may not necessarily be a weak elastic dipole in all crystalline environments, and encourages a search for Snoek-type hydrogen peaks in other crystal structures. In this paper, we first point out that compounds with the A15 structure are interesting candidates for studies of this type. We then report the discovery of a hydrogen-related peak in Nb3Sn, and discuss the present evidence concerning its possible identification as a Snoek-type relaxation. Remarks on A15 Compounds The A I 5 structure is shared by a group of brittle intermetallic compounds of A3B stoichiometry. These compounds have attracted widespread attention as a source of high-temperature superconductors, and Nb3Sn in particular is now of considerable technological importance. The structure is cubic, with atoms of the major constituent arrange d in three orthogonal chains (Fig. 1). The interatomic spacing along these chains is notably smaller than in the bee structure (e.g. 0.2645nm in Nb3Sn vs. 0.2852nm in Nb). The structure is subject to instability, and may exhibit a marked elastic softening which in some cases precedes a eubic-to-tetragonal phase transformation. (10-12) Hydrogenation of the A15 compounds has been obtained both by annealing in hydrogen and by acid immersion treatments. (13-15) While the diffusion kinetics do not appear to have been studied, the effects produced by brief a c i d immersions suggest an appreciable hydrogen mobility at room temperature. The solubility for hydrogen can be substantial; in the ease of Nb3Sn the measurements of Vieland et al. (15) indicate a solid-solution range extending to m o r e than 1 5 a / o H. The complementary lattice parameters reported by these workers provide an estimate of the size-factor h l + 2 x 2 of 0.13. This result appears preferable 4

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FIG. 2. Internal friction of the composite tape prior to deliberate hydrogenation, as measured at the first six tones of flexural vibration.

FIG. 3. The excess internal friction produced by a 600 sec immersion in 1:1 H F : H 2 0 , and the effect of a sequence of vacuum anneals. The background 6B is now the complete pre-immersion damping of Fig. 1. The data shown are for the second tone (312Hz).

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FRICTION

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329

to the much larger value indicated by the results of Ziegler. (16) Finally, the important question of hydrogen site-occupancy has been studied for Nb3Sn by Vieland et al. using neutron diffraction. They conclude that hydrogen atoms occupy the tetrahedral sites of Fig. 1, which "cross-link" orthogonal pairs of Nb atoms and provide a nearest-neighbor environment of remarkable similarity to that for hydrogen in bcc Nb. As may be found either by inspection or reference to the appropriate Tables (17), the symmetry of these sites is tetragonal. Consequently, relaxation of the S l l - S12 compliance is e x p e c t e d from the selection rules for anelasticity. (1) F o r a frequency of 100 Hz, the probable location of the corresponding internal friction peak is estimated to be somewhere in the range 45K to 250K, depending principally on the value assumed for the unknown activation energy for hydrogen diffusion. Procedure and Results The vibrating-reed technique (18) has been used to study a composite tape of a type used in superconducting windings. A f t e r etching off an outer silver coating, the cross-section of the tape consisted of polycrystaUine layers of Nb3Sn, each of 0.0008 cm thickness, on both sides of a 0.0045 cm thick substrate of the nickel-based alloy Hastelloy B. The internal friction behavior before hydrogenation is shown in Fig. 2 for the range 100K - 380K and for the first six flexural modes of the sample. A small peak near 250K is superposed on another contribution which can be shown to originate almost entirely from the transverse thermal current relaxation.(1) This can be demonstrated by separating out the small peak and replotting the remaining damping versus the logarithm of the frequency, for a series of different temperatures. The damping is then found to take the form of a Debye peak located at about 2kHz, whose height increases roughly in proportion to the absolute temperature. The location and magnitude of this peak are in satisfactory agreement with the thermoelastic peak calculated for a sample consisting entirely of Hastelloy B. F o r present purposes the damping of Fig. 2 is of interest only as a background damping to be subtracted from the results obtained after acid-immersion. Figs. 3 and 4 show the excess damping introduced after a 600 sec immersion in 1:1 H F : H 2 0 , a solution known to produce strong hydrogenation of the isostructural compound Nb3Ge. (14) The initial run of Fig. 3 was conducted about 1 hr after the acid immersion treatment. The data reveal a much stronger peak near 7.8 I

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FIG. 5. Comparison of the relative elastic stiffness after the 200°C and 300°C anneals (i.e. with and without the relaxation of Fig. 4). Note the composite relaxation strength A and the coincidence of the curves above thCe inflection. The data shown are for the third tone.

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260K, and a minor peak near 130K. After 3 days in vacuum at room temperature the 260K peak was found to have increased in height by about 4 0 % . This enhancement was removed by the 100°C vacuum anneal, which also modified the peak structure. A further anneal at 200°C had little effect on the peak height but caused the peak to become narrower and more symmetrical. Finally, the 300°C anneal removed the 260K peak completely and substantially reduced the minor peak at 130K. The frequency dependence of the 260K peak after the 200°C anneal is shown in Fig. 4. F o r purposes of analysis these data have been plotted against 1 / T with the ordinate (8-SB)T normalized to a peak height of unity. It should be noted, however, that the actual peak heights 8-8 B for all 3 tones were almost identical to each other. To complement the internal friction measurements, illustrative resonant frequency data after the 200°C and 300°C anneals are compared in Fig. 5. The overall downward trend of both curves with decreasing temperature reflects the elastic softening of Nb3Sn, which strongly outweighs the opposite trend expected for the Hastelloy substrate. In contrast to the monotonic variation exhibited after elimination of the peak by the 300°C anneal, the curve after the 2 0 0 ° C anneal shows a clear inflection centered on the temperature of the internal friction peak. F r o m the magnitude of the displacement indicated by the arrows of Fig. 5, the relaxation strength for the composite, Ac , is found to be 0.0076. One of the most striking features of Fig. 5, which we shall return to below, is the coincidence of the two curves above, rather than below, the relaxation. Discussion Based on present results and other supportive experiments, we believe that the 260K peak originates in the Nb3Sn layers of the composite and is associated with the presence of hydrogen. The present discussion is therefore centered on the question of whether the 260K peak can be identified as an analog of a hydrogen Snoek peak. We shall start with consideration of the peak strength. To convert the composite strength Ac of Fig. 5 to an intrinsic relaxation strength A appropriate to Nb3Sn alone, we use the following relation, derived from the theory of bending of a composite beam: A = Ac{1 + (b(1 + a ) 3 - 1 ) - 1 } ,

(1)

where a is the ratio of the total thickness of the outer Nb3Sn layers to that of the Hastelloy substrate, and b is the ratio of their Young's moduli. Inserting the values Ac ffi 0.0076, 0----0.358 and bffi0.75, we find A ffi 0.014. F o r a Snoek-type relaxation in a random polycrystalline aggregate, we also have

A ffi (4EOoC/45kT)(~tl-)t2)2,

(2)

where E is Young's modulus (taken as 132GPa for Nb3Sn), O0 is the volume per host atom (1.85 × 10-23cm3), C is the unknown mole fraction of hydrogen in solution, k is Boltzmann's constant, T the absolute temperature, and ()tl-~t2) is the dipole strength introduced earlier. Combining Eq. (2) with the result Affi0.014, we obtain 2 C(]kl--X2) ---- 2.4× 10 - 4 . (3) Although C is unknown in the present experiments, we do not expect it to exceed 0.1 (i.e. 1 0 a / o ) . Hence we conclude from Eq. (3) that (Xl--h2)_>0.05. This means that a Snoek-type mechanism is possible only if hydrogen acts as a relatively strong elastic dipole, in contrast to its apparent behavior in bcc Nb. We now return to an aspect of Fig. 5 that appears to weigh rather strongly against a Snoektype mechanism. As noted earlier, the curves for the 2 0 0 ° C and 3 0 0 ° C anneals are seen to be displaced from one another at low temperatures and to become coincident above the relaxation. Precisely the opposite behavior would have been expected for a point-defect relaxation. To reconcile t h e observed behavior with a Snoek-type mechanism, it is necessary to assume that hydrogen stiffens the unrelaxed elastic modulus by just the fight amount to reverse the expected behavior. While this cannot be ruled out at present, there is an alternative explanation of Fig. 5 which does not demand such a fortuitous circumstance. The alternative is that we abandon the Snoek-type mechanism, and presume

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instead that hydrggen at low temperatures is capable of pinning out a small fraction of defect that can be associated with the elastic softening of Nb3Sn. While the kinetics relaxation could thus remain associated with the motion of hydrogen atoms, the origin of strain would no longer depend on point-defect reorientation, and the necessity for a strength would be removed.

331

the modulus of the 260K the anelastic large dipole

We turn now to the kinetics of relaxation, and first examine the peak for dispersion. If, after the 200°C anneal, the peak were governed by a single relaxation time, the peak decrement expected from the composite sample would be (¢t/2)A c or 0.0119 using Fig. 5. In fact, the observed peak height is only 0.00285 (Fig. 3). The difference, a factor of 4.2, implies a much broader distribution of relaxation times than can be easily associated with a Snoek-type relaxation. Next, we examine the 1 / T shift between the peaks of Fig. 4 and the associated activation energy controlling the relaxation. Here we encounter a most unusual behavior. The 1 / T shift between the different peaks is not a constant, but systematically decreases with decreasing temperature. Moreover, the average shift taken at the peak temperature is surprisingly small and corresponds to an anomalously large apparent activation energy Q' of 1.4eV. The extent of the anomaly can be appreciated from a calculation of the apparent prefaetor TOp which appears in the usual expression for the relaxation time T. Writing T ffi TOp exp QP/kT, and using the condition that at the peak ¢ must also satisfy the condition T(T,) = 1/2~rf, where f is the measurement frequency, we find that a Qt of 1.4eV implies a Tot of 1.6x~10 -29 sec! F o r comparison, Snoek peaks in bec metals and the hydrogen peak in metallic glasses are associated with a prefactor of magnitude 10 -14 sec. Despite the unusual behavior represented by Fig. 4, there is a measure of P self-consistency in the data, in that a comparably high value of Q is obtained indepqndently from the peak width. F r o m Fig. 4 the peak width at half-maximum is /~(1000/T) ffi 0.73K ", which converts with the initial assumption of a single relaxation time to an energy of 0.312eV. To obtain an estimate of QP this result must now be multiplied by the dispersion factor of 4.2. The result (1.3eV) checks well enough with the 1.4eV obtained from the 1 / T shift of the peak maximum. A t first sight, it seems that the magnitude of T0' represents a clear proof against a Snoek-type mechanism. However, it has recently become apparent that seemingly anomalous frequency-shift behavior may have a relatively simple explanation in terms of a t e m p e r a t u r e - d e p e n d e n t activation energy. (19) F o r example, consider the mathematically simple situation in which a linearly-varying activation energy Q(T) = Q 0 ( 1 - a T ) governs a relaxation time T ffi TO exp Q(T)/kT where TO is taken to be of normal magnitude for a Snoek-type relaxation. We now have T = TO exp

(-aQo/k)

Qo/kT,

(4)

(-aQo/k).

(5)

exp

which leads to the relationships Q ' = Q0 and T0' -- T0 exp

With this i ~ r p r e t a t i o n of .,Fig. 4, we may evaluate a in Eqs. (5). b~ inserting TO -- 1.6× 1 0 - ' - s e c , T 0 = 1 0 - ~ 4 s e c and Q0ffi 1.4 eV. We find a f f i 2 . 1 x l 0 - a K - * , and thus estimate that the actual magnitude of the activation energy in the temperature range of the relaxation is about 0.6 eV. Based on this interpretation, we conclude that the unusual values of QP and TOt do not necessarily exclude a Snoek-type mechanism. We are however faced with the problem of explaining why the activation energy is temperature dependent. One obvious possibility is related to the pronounced elastic softening exhibited by Nb3Sn. Clearly, a comparison of the behavior of Nb3Sn with that of other hydrogenated A 15 compounds will form a n interesting subject for future work. Before leaving kinetic considerations, it is of interest to estimate the diffusion coefficient for hydrogen at room temperature, with the assumptions that the activation energy f o r ' d i f f u s i o n is 9~6eV and that the preexponential diffusion constant is 10"3em2/sec. The result, D ( 2 9 3 K ) = 6 x 1 0 - ' ~ em2/sec, in turn implies that diffusion - limited equilibration of the hydrogen concentration across the thickness of the Nb3Sn layers requires somewhat more than a day, and appears to be consistent with the slow growth

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noted in the peak height following the immersion treatment. We may also conclude from the annealing behavior that the subsequent desorption of hydrogen is a surface-controlled reaction which proceeds rapidly only above 200°C. Our main conclusions may now be summarized as follows. Some aspects of the hydrogen peak in polycrystalline Nb3Sn are similar to the hydrogen peak in amorphous Nb3Ge (4), which is believed to be of the Snoek type. The two peaks are found at similar temperatures, and are of a comparable magnitude. For both materials, the peaks can only be of a Snoek type if hydrogen atoms act as much stronger elastic dipoles than appears to be the case for bcc Nb. There are, however, important characteristics of the peak in Nb3Sn that are hard to reconcile with a Snoek-type mechanism. The most troublesome of these are (a) the behavior of the modulus, as discussed in connection with Fig. 5, and (b) the large dispersion associated with the peak, which is even greater than that for the hydrogen peak in glassy Nb3Ge. From the presently available evidence, therefore, we conclude that the 260K peak in Nb3Sn is probably not a hydrogen Snoek peak. Consequently, we may infer either that the dipole strength is small after all, or that a real and detectable Snoek-type peak has so far eluded discovery. One possibility is that untrapped hydrogen atoms may move in NbaSn with a much lower activation energy than the ~0.6eV presumed above, and hence may produce a Snoek peak below the temperature range explored here. If this were the case, however, the Gorsky peak associated with the long-range diffusion of hydrogen through the Nb3Sn layers would be expected in the temperature range of the present measurements, and this was not observed. Clearly, more experiments are needed to help clarify the situation. Regardless of the final outcome, we may remark in closing that the most important aspect of the present work seems simply to be the discovery of hydrogen-related anelasticity in a novel type of host, namely an intermetallic compound. This opens the door not only to future studies of hydrogenated Nb3Sn and other A15 compounds, but also to compounds with other crystal structures, such as those of interest for hydrogen - storage applications. (20) References 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20.

A.S. Nowick and B.S, Berry, .,inelastic Relaxation in Crystalline Solids, Academic, New York, 1972. H. Peisl, in Hydrogen in Metals, ed. by G. Alefeld and J. V01kl, Springer, Berlin, 1978, Vol. 1,p.53. B.S. Berry, W.C. Pritchet and C.C. Tsuei, Phys. Rev. Lett. 41,410 (1978). B.S. Berry and W.C. Pritchet, in Rapidly Quenched Metals III, edited by B. Cantor, The Metals Society, London, 1978, vol. 2, p.21. B.S. Berry and W.C. Pritchet, Scripta Met. 15,637 (1981). B.S. Berry and W.C. Pritchet, J. Physique 42, C5-1111 (1981). K. Agyeman, E. Armbruster, H.U. Ktlnzi, A. Das Gupta and H.-J. GUntherodt, J. Physique 42, C5-535 (1981). B.S. Berry and W.C. Pritchet, Phys. Rev. B, 24, 2299 (1981). B.S. Berry and W.C. Pritchet, In Rapidly Solidified Amorphou~ and Crystalline Alloys, edited by B.H. Kear, B.C. Giessen, and M. Cohen, North-Holland, New York, 1982, p.249. L.R. Testardi in Physical Acoustics, edited by W.P. Mason and R.N. Thurston, Academic Press, New York, 1973, Vol X, p,193; 1977, Vol. XIII, p.29. N. Nakanishi, Progress in Materials Science, 24, 143 (1980). J.F. Bussi~re, B. Faueher, C.L. Snead, Jr., and D.O. Welch, Phys. Rev. B 24, 4087 (1981). P.R. Sahm, Physics Letters, 26,4, 459 (1968). J.M. Rowell, P.H. Schmidt, E.G. Spencer, P.D. Dernier and D.C. Joy, IEEE Trans. Magn., MAG-13, 644 (1977). L.J. Vieland, A.W. Wicklund and J.G. White, Phys. Rev. B, 11, 3311 (1975). G. Ziegler, Helv. Phys, Acta. 41, 1267 (1968). International Tables for X-Ray Crystallography, Kynoeh Press, Birmingham, 1952. Vol. 1, p, 334. B.S. Berry and W.C. Pritehet, IBM J. Res. Dev., 19 334 (1975). B.S. Berry, Scripta Met., to be published. P.S. Rudman and G.D.Sandrock, Ann. Rev, Mater. Sci., 12,271 (1982).