Anelastic relaxation in ZrV2Hx intermetallic compounds

Materials Science and Engineering A 442 (2006) 124–127

Anelastic relaxation in ZrV2Hx intermetallic compounds F. Trequattrini a,∗ , F. Cordero b , G. Cannelli c , R. Cantelli a , A. Coda d , A. Gallitognotta d a

Dipartimento di Fisica, Universit`a di Roma “La Sapienza”, P.le A. Moro, 2, I-00185 Roma, Italy b CNR, Istituto dei Sistemi Complessi, Via Fosso del Cavaliere 100, I-00133 Roma, Italy c Dipartimento di Fisica, Universit` a della Calabria, Arcavacata di Rende (CS), I-87036 Cosenza, Italy d Corporate R&D Labs, SAES Getters S.p.A., 20020 Lainate, Milan, Italy Received 28 July 2005; received in revised form 23 January 2006; accepted 9 February 2006

Abstract The anelastic spectrum of two intermetallic polycrystalline ZrV2 Hx samples (0 ≤ x ≤ 0.09) has been investigated from 1 to 600 K in the frequency range 2–50 kHz. Besides the well-known martensitic phase transformation around 120 K, two thermally activated peaks are detected in the H doped alloys around 230 and 410 K at a vibration frequency of about 3 kHz. The process at the lower temperature is due to the jumps of H atoms likely among tetrahedral interstitial sites in the cubic lattice of the Laves phase. The profile can be satisfactorily fitted with the superposition of two peaks, broader than single time Debye relaxations, with activation enthalpies of 0.33 and 0.41 eV. The peak above room temperature, which appears only on the sample containing impurity phases (primary solution phase of vanadium and zirconium), presents features which suggest a mechanism involving the interaction between point defects and dislocations. © 2006 Elsevier B.V. All rights reserved. Keywords: Metal–hydrogen systems; Laves phase; Phase transformations; H-dislocation interactions

1. Introduction The interest in intermetallic compounds arises from their relatively low densities and high melting temperatures, which render these materials attractive for high temperature structural applications. In addition, many of the Laves-phase compounds, which represent the largest group among the topologically closepacked ones, are able to absorb considerable amounts of hydrogen, and have been extensively studied as potential hydrogenstorage materials. A number of studies have evidenced unusual features in the dynamics of hydrogen isotopes in the cubic (C15type) AB2 compounds [1–4]. It is known that, in the cubic C15 structure, H occupies tetrahedral interstices of g-type (i.e., 2A2B: the tetrahedron is formed by two A atoms and two B atoms) or e-type (A3B). There are 96 g sites per unit cell (which has eight formula units) and 32 e sites. The g sites form linked hexagonal structures and each g site has three neighbouring g sites (two on its own hexagon and one on an adjacent hexagon) and one neighbouring e site. Each e site has three neighbouring g sites, each belonging to

∗

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a different hexagon.1 The g–g distances between neighbouring sites within a hexagon is usually shorter than the distance between neighbouring sites on different hexagons and the difference between the two distances is related to the atomic radii of the elements A and B. As a consequence, one could expect two different frequencies for interhexagon and intrahexagon H hopping and indeed there are experimental indications from NMR [2], quasi-elastic neutron scattering [3] and resonant ultrasound spectroscopy [4] in this sense. The two frequency scales appear to be widely different on TaV2 , for which the ratio of the atomic radii is anomalously low, so corroborating the hypothesized relation [4]. According to the same model, the two types of H motion are expected to have similar frequencies in compounds, which have this ratio of radii closer to the ideal value (1.225 for the Laves phases, as derived from the condition of the closest packing of hard spheres). That is the case of ZrV2 Hx , which easily absorbs hydrogen and forms an interstitial solid solution up to H concentration as high as x ≈ 6. It has been established that in ZrV2 Hx hydrogen occupies only g sites up to x ≈ 2.5 and both g and e sites at higher con-

1 For space reasons we do not include an illustration of the C15 structure with the interstitial sites (see, e.g., Ref. [3]).

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centrations. The main features of the composition–temperature (x, T) phase diagram of ZrV2 Hx have been understood [5] and the most peculiar aspect is a broad homogeneity region above room temperature with a continuous change of the lattice constants as a function of x. Nevertheless, the structures of the low temperature ordered phases are not well known, especially at low concentrations. Recently, an acoustic investigation of the ZrV2 Hx system over a wide H concentration range (even though rather coarse) has been reported [6], but the results are lacking at low concentrations. Besides, since the measurements were carried out only at one resonant frequency, a clear discrimination has not been shown between the thermally activated processes associated with the H dynamic and the effect due to hydride precipitation. The most intense anelastic effect in the ZrV2 system is due to a structural phase transformation [7,8], which occurs at about 120 K in H free materials and shifts towards higher temperature, decreasing its intensity, by increasing the H concentration [6]. In the present work, we report the anelastic spectra of two polycrystalline ZrV2 Hx samples in the concentration range 0 ≤ x ≤ 0.09. The samples were submitted to high temperature annealing of various durations. Only the sample which experienced shorter annealing showed an unexpected relaxation process above 300 K, probably connected with plastic phenomena due to the presence of the primary solution phase of zirconium and that of vanadium. Instead, below room temperature both the H-doped samples displayed a thermally activated process, which is certainly related to the H dynamics. No signs of hydride precipitation are found for the concentrations considered here.

2. Experimental Polycrystalline ingots of ZrV2 were prepared by SAES Getters S.p.A. by arc melting appropriate mixtures of high-purity constituent elements in an argon atmosphere. Each ingot was remelted many times to ensure homogeneity. Two rectangular bars (40 mm × 4 mm × 2 mm) were cut from the ingots by spark erosion. Samples 1 and 2 (S1 and S2) were then annealed at about 1273 K, for 20 and 36 h, respectively. Scanning electron microscopy images show residual grains of primary solution phase of zirconium and that of vanadium in sample S1, whereas sample S2 appears mostly single phase ZrV2 . To avoid sample disintegration and achieve phase homogeneity, the hydrogenation was carried out by heating the samples up to 1173 K in a quartz tube connected with an ultra high vacuum (UHV) system. A known amount of hydrogen was then slowly introduced and equilibrated at about 973 K. The dynamic compliance S = S − iS was measured by electrostatically exciting the samples on different flexural modes in the frequency range from 2 to 50 kHz. We will report the curves of the elastic energy loss coefficient Q−1 (ω, T) = S /S , which contain peaks in correspondence with phase transformations and at the temperatures Tm such that ωτ(Tm ) = 1, where ω is the angular vibration frequency and τ are relaxation times for various H diffusion processes, generally following the Arrhenius law τ = τ 0 exp(E/kB T).

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Fig. 1. Anelastic spectrum of “as received” sample S1 between 80 and 300 K at two vibration frequencies.

3. Results and discussion Fig. 1 presents results of the acoustic spectroscopy measurement carried out on the “as received” sample S1. The anelastic spectrum is dominated by the structural phase transformation (PT) from the cubic to the low-temperature rhombohedral symmetry. This phase instability, which manifest itself also as an anomaly in electrical resistivity [9], is peculiar of very few Laves phases (ZrV2 , HfV2 and few others) and seems to be related to the particular electronic properties of these compounds [10]. The anelastic spectra do not show any thermal hysteresis, supporting the hypothesis of a second order transformation [7]. A thermally activated peak around 240 K (PH) is also present, likely due to the presence of unwanted hydrogen. This hypothesis is corroborated by the observation that the subsequent annealing (1173 K for 2 h in UHV) of S1 produced a shift towards lower temperature of the frequency minimum (the difference in temperature is T ∼ = 7 K) and a reduction of the intensities of both PT and PH (not shown here). Indeed, it is known [6] that the increase of H concentration increases the phase transformation temperature and reduces the peak intensity. The latter effect seems to be in contradiction with our observation. However, the intensity of the elastic anomaly certainly depends on microstructure [9] and is affected by annealing at high temperature. The anelastic spectrum below room temperature of the “as received” sample S2 was qualitatively the same as for S1, but all the effects are much smaller, probably due to longer annealing time for S2 after alloying (see above). Marked differences in the anelastic spectra are found above room temperature; in fact, whilst S2 showed only a flat background, the spectrum for S1 presents a peak (PSK) having a complex phenomenology (see Fig. 2) which can be described as follows: (i) PSK appears only after cooling the sample from high temperature (several hundred kelvins): curve 1 is obtained after several hightemperature treatments in UHV; (ii) the peak is thermally activated as deduced from the peak shift with frequency (E = 0.8 eV and τ 0 = 1.1 × 10−14 s, about 25% broader than a single Debye peak); (iii) the peak intensity remains stable by heating up to

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Fig. 2. Anelastic spectrum of sample S1 after: annealing in UHV at 1173 K and heating up to 500 K (1), 550 K (2), 600 K (3), and after one month at room temperature (4). For comparison, the anelastic spectrum in the “as received” state is reported (dashed line).

about 450 K; (iv) rising the temperature over 450 K, PSK is progressively reduced and it almost disappears by heating the sample up to 600 K (curves 2 and 3); (v) ageing at room temperature for several days increases the intensity of the peak (curve 4). The absence of the peak in sample S2 suggests a correlation between PSK and the presence of the primary solution phases of zirconium and vanadium in sample S1. In particular, the misfit between cubic ZrV2 and hcp zirconium can produce plastic deformation during temperature variations [11]. Indeed, the anelastic relaxation in deformed zirconium has been extensively studied [12] and several anelastic peaks have been found. In addition, it is known that zirconium is a strong getter for gaseous impurity and as a consequence one can expect that part of the H is adsorbed by the precipitate particles of zirconium present in sample S1. We therefore identify PSK with the Snoek–K¨oster type relaxation arising from the interaction between dislocations and H atoms discussed in Ref. [12], although we cannot exclude that O impurities may also play a role. The effect of H charging on the anelastic spectrum of samples S1 and S2 is reported in Fig. 3. In both samples a clear anelastic process appears around 230 K and the dependence of its intensity on the H concentration, cH , indicates a direct involvement of H in the relaxation. The comparison between the peaks in the two samples clearly shows that PH is much more intense in S2 for the same H concentration. This is not surprising at all because, as already discussed, part of hydrogen in sample S1 is probably dissolved in the zirconium (and possibly vanadium) impurity phases. This fact prohibits an analysis of the peak intensity versus H concentration for S1 and we limit ourselves to observe that, as clearly indicated by Fig. 3 (upper part), the peak is quite broad and probably at least two separate relaxations contribute to it. We will concentrate on sample S2, where H should be almost completely dissolved among the interstitial g sites of ZrV2 . First of all we observe that PH becomes broader by increasing the H content and, as a consequence, it is difficult to analyse the dependence of the peak intensity on cH . In Fig. 4 we report the anelastic

Fig. 3. Anelastic spectrum of sample S1 (upper part) and sample S2 (lower part) containing controlled amounts of H.

spectrum for ZrV2 H0.07 measured at two frequencies, 3.8 and 49 kHz. Peak PH is characterised by a very broad distribution of the activation energies; the dashed curves in Fig. 4 are obtained assuming a unique value for the pre-exponential factor and by integrating a Debye peak over a Gaussian distribution centred at E0 /kB = 4900 K and width E/kB = 700 K.

Fig. 4. Peak PH (sample S2) at two vibration frequencies: the continuous lines are best fit to experimental points obtained using two broad Fuoss–Kirkwood peaks (dotted lines, see the text and Table 1); the dashed lines are obtained using a Gaussian distribution of the activation energy centred at 0.42 eV (E = 60 meV).

F. Trequattrini et al. / Materials Science and Engineering A 442 (2006) 124–127 Table 1 Parameters of the anelastic relaxations due to H in ZrV2 H0.07 (sample S2) PH1 PH2

τ 0 (s) 1.1 × 10−13 3.0 × 10−14

E (eV) 0.33 0.41

a (eV) 0.04 0

(two on one hexagon and one on an adjacent hexagon) should be very similar. α 0.85 0.52

For the definitions of the parameters, see the text.

The presence of at least two peaks contributing to PH is quite clear, especially from the Q−1 (T) of the higher frequency vibration mode. We can achieve a reasonable fit to the data of PH (continuous line) using the superposition of two peaks, PH1 and PH2 (dotted line). For both the peaks we used the following expression Q−1 =

1 Δ α T cosh (a/2kB T ) (ωτ) + (ωτ)−α 2

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(1)

where τ = τexp (E/kB T) sech (a/2kB T) is the relaxation time between two sites with energy separation a, the constant Δ is proportional to the H concentration, to the elastic modulus and to the change in the local distortion due to the H jump and α is the Fuoss–Kirkwood width parameter [13]. The relaxation parameters used for the fit are reported in Table 1. The fact that α < 1 indicates that both the peaks are broader than a Debye peak; the elastic energies of the H atoms are strongly affected by the long-range elastic interactions. Also, the shift of PH to lower temperature with increasing cH (Fig. 3, lower part) may be a consequence of a distribution of site energies; it is exhibited by the anelastic relaxation due to hopping of H trapped by substitutional atoms in bcc niobium and vanadium alloys [14] and also in amorphous alloys [15]. A semiquantitative model has been proposed to explain the shift [14] in terms of a potential-energy landscape with a distribution of the site energies due to disorder. The distribution is larger than that of the saddle points, so that smaller activation energies and therefore lower peak temperatures are associated with sites of higher energies. The latter tend to be populated at higher H contents, so contributing to the growth of the peak at the lower temperature. It seems quite natural to associate the two peaks with the two possible relaxations for the H atoms among the interstitial g sites. In fact, as already discussed in Section 1, the elastic dipole associated with H can reorient either because of the H jumps among the six g sites forming a hexagon or of the jumps (possibly via an e site) between g sites belonging to nearest hexagons. As expected for this material, the two frequencies for the H dynamics are quite close because, differently from the case of TaV2 , the distances between three neighbouring g sites

4. Conclusions Anelastic relaxation measurements in the kHz range on ZrV2 Hx (0 ≤ x ≤ 0.09) show a complicated spectrum. A broad peak around 230 K, whose intensity increases by increasing the H concentration, can be described as the sum of two broadened Debye peaks with activation energies of 0.33 and 0.41 eV. The two peaks should arise from different kind of H hopping among the tetrahedral g sites. The anelastic spectrum in H-free samples is dominated by the structural phase transformation occurring around 120 K. In one sample containing impurity phases (of alpha zirconium and alpha vanadium), a thermally activated peak around 410 K is also detected. This peak, which is suppressed by heating up to 600 K and is partially restored by ageing at room temperature for several days, could be associated with a Snoek–K¨oster type relaxation arising from the interaction between dislocations and H and possibly O atoms in the alpha zirconium precipitates. References [1] J. Shinar, D. Davidov, D. Shaltiel, Phys. Rev. B 30 (1984) 6331–6341. [2] A.V. Skripov, M.Yu. Belyaev, S.V. Rychkova, A.P. Stepanov, J. Phys. Condens. Matter 3 (1991) 6277–6291. [3] A.V. Skripov, J.C. Cook, D.S. Sibirtsev, C. Karmonik, R. Hempelmann, J. Phys. Condens. Matter 10 (1998) 1787–1801. [4] J.E. Atteberry, R.G. Leisure, A.V. Skripov, J.B. Betts, A. Migliori, Phys. Rev. B 69 (2004) 144110-1-6. [5] C. Geibel, W. Goldsacker, H. Heiber, V. Oestreich, H. Rietschel, H. W¨uhl, Phys. Rev. B 30 (1984) 6363–6367. [6] N.L. Arabajian, V.I. Serdobintsev, T.Sh. Kvirishvili, A.I. Naskidashvili, D.E. Tananashvili, J. Alloys Comp. 390 (2005) 1–8. [7] J.E. Doherty, D.F. Gibbons, Phys. Stat. Sol. B 44 (1971) K5–K8. [8] T.R. Finlayson, K.W. Thomson, T.F. Smith, J. Phys. F5 (1975) 225–229. [9] M. Levinson, C. Zahradnik, R. Bergh, M.L.A. MacVicar, J. Bostock, Phys. Rev. Lett. 41 (1978) 899–903. ˇ [10] F. Chu, D.J. Thoma, T.E. Mitchell, C.L. Lin, M. Sob, Philos. Mag. B 77 (1998) 121–136. [11] M.H. Youssef, P.G. Bordoni, Philos. Mag. A 67 (1993) 883–895. [12] L.T. Miyada-Naborikawa, R. De Batist, Phys. Stat. Sol. (a) 89 (1985) 191–198 and references therein. [13] A.S. Nowick, B.S. Berry, Anelastic Relaxation in Crystalline Solids, Academic Press, London, 1972. [14] G. Cannelli, R. Cantelli, F. Cordero, Phys. Rev. B 32 (1985) 3573–3579. [15] O. Yoshinari, M. Koiwa, A. Inoue, T. Masumoto, Acta Metall. 31 (1983) 2063–2072.