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1H NMR study of local structure and proton dynamics in β-Ti1−yVyHx
Journal of
AILOY5 AND COMPOUND5 ELSEVIER
Journal of Alloys and Compounds 231 (1995) 226-232
1H NMR study of local structure and proton dynamics in
fl-Ti l_yVyHx Takahiro Ueda, Shigenobu Hayashi Department of Physical Chemistry, National Institute of Materials and Chemical Research, Tsukuba, lbaraki 305, Japan
Abstract
The local structure of the metal atoms around a hydrogen atom and the dynamics of hydrogen atoms in disordered metal hydrides fl-Ti 1 yVyHx (x - 1 and 0.2 ~
1. Introduction Alloys composed of Ti and V (Til_yVy) form cornpounds with hydrogen [1,2]. These alloys can absorb hydrogen until the ratio of hydrogen to metal atoms reaches a value of two. The hydrides have three phases depending on the degree of hydrogenation. In the dihydride (denoted as the 3,-phase), the metal atoms form a face-centred-cubic (f.c.c.) lattice and the hydrogen atoms occupy the tetrahedral site (T site) formed in the cubic lattice [3]. In hydrides with much lower hydrogen to metal ratios (i.e. x - 0), called the a-phase, the metal atoms form a body-centred-cubic (b.c.c.) lattice and the hydrogen atoms occupy the T site randomly [4-6]. In the monohydride (denoted as the /3-phase), although the metal atoms form a b.c.c, lattice similar to the a-phase, the nature of the hydrogen sites and the dynamic behaviour of the hydrogen atoms are not clearly understood. The concentration of hydrogen which results in a change from the a - to t h e / 3 - p h a s e is not known, In a previous paper, we studied the proton dynamics in the /3-phase using proton nuclear magnetic reso0925-8388/95/$09.50 © 1995 Elsevier Science S.A. All rights reserved SSDI 0925-8388(95)01820-4
nance (1H N M R ) through spin-lattice relaxation time (T 0 measurements, and tried to interpret the results using a local structural model [7]. In this model, the local structure of the metal atoms around a hydrogen atom is described by a binomial distribution. The hydrogen atoms have different activation energies depending on the local structure of the metal atoms, and it was assumed that the hydrogen atoms occupied only the T site. However, this model cannot describe the Ti I yVyH x system completely because the shortrange ordering of host metals should be present in binary alloys, and dual occupancy of T and octahedral (O) sites was reported in Ref. [8]. Brouwer et al., who studied diffusion and local structures in b.c.c, binary alloys, such as Nbl_yVy [9] and Til_yWy [10], with low hydrogen concentrations, derived formulae describing the composition dependence of the activation energy and enthalpy of solution in A l_yBy alloys on the basis of a local structual model taking into account the short-range ordering of metals [10]. They considered that Aa_iB i clusters represented the local structure of the metal atoms around a hydrogen atom. The clusters surround a
T. Ueda, S. Hayashi / Journal of Alloys and Compounds 231 (1995) 226-232
hydrogen atom tetrahedrally. By application of their formulae to enthalpy of solution data reported by other workers and to their diffusion data, they succeeded in determining the short-range order parameters for Ti l_yVy alloys. Thus a local structural model taking into account the slhort-range ordering of metals is necessary to describe the diffusion coefficients, apparent activation energy and enthalpy of solution for hydrogen in binary disordered alloys, From neutron inelastic scattering experiments, we found two kinds of hydrogen site in fl-Til_yVyHx (tetrahedral and octahedral sites) whose populations change with the composition of the alloys. The population of the T site is 91% for Tio.sVo.2Ho.94 and decreases monotonically to 6% for Tio.lVo.gHo.98; the population of the O site is 9% for Ti0.8Vo.2H0.94 and increases to 94% for Tio.lVo.9Ho.g8. Using a modified cluster model assuming Ti6_iV~ clusters as the local structure of the metal atoms around a hydrogen atom, the short-range order parameter was determined from an analysis of the dependence of the fraction of each hydrogen site on the alloy composition (0"=0.43_+ 0.05 [8]). In this paper, we re-analyse the temperature and frequency dependences of 1H T~ using the Bloembergen-Purcell-Pound (BPP) equations [11 ] considering the distribution of the correlation time, and determine the activation parameters for hydrogen diffusion in fl-Ti i_yvyHx . We take into account the fact that Til_yVy is disordered and exhibits large fluctuations in chemical and topological environments, such as crystal symmetry, hole radius, lattice distortion and the types of host metal. On the basis of neutron scattering experiments and the cluster model proposed by Brouwer et al. [9,10], the short-range order parameter and metal-hydrogen interactions are estimated from the dependence of the apparent activation energy on the alloy composition using a cluster model which assumes O site occupancy and therefore Ti6_iV/ clusters as the local structure of the metal atoms,
2. Experimental details Three of the Ti-V monohydride samples studied in this work were the same as those used in Ref. [6]: Tio.2Vo.sHo.83, Tio.4Wo.6n0.91 and Tio.6Vo.4Ho.91. These three samples had been confirmed to consist of the /3-phase only. Tio.sVo.2Ho.89 was synthesized by reaction between a Tio.8Vo.2 alloy and hydrogen gas. The details of the procedure have been described previously [7]. This hydride was a mixture of/3- and y-phases on the basis of the X-ray diffraction pattern, but the quantity of the y-phase was very small compared with that of the/3-phase. Therefore the contribution of the y-phase to the total relaxation time was negligible.
227
1H N M R measurements were carried out using a Bruker CXP100 pulsed spectrometer with an electromagnet. The proton spin-lattice relaxation times (T1) were measured in the temperature range 105-400 K at four frequencies (9, 22.5, 52 and 90 MHz) using the 90°-~--90 ° method. The width of the ¢r/2 pulse was adjusted in the range 2.3-3.5 /zs depending on the Larmor frequency. The experimental errors were less t h a n - 5 % . The temperature was controlled by a Bruker variable temperature unit (VT-1000) with an a c c u r a c y of-- 1 K, using the flow of cooled or heated nitrogen gas.
3. Results and analysis The magnetization recovery curves for Tio.aVo.2H0.89, Tio.6Vo.4Ho.9~, Tio.4Vo.6Ho.9~ and Tio.zVo.8Ho.83 are described by a single exponential decay over the entire temperature range. The IH T 1 values at the fourLarmorfrequenciesforTio.sVo.2Ho.89,Tio.6Vo.4Ho.91, Tio.4Vo.6Ho.91 and Tio.2Vo.sHo.83 are plotted as a function of the reciprocal temperature in Figs. l(a)-l(d) respectively. The frequency dependence of T~ is approximately described by a single exponential correlation function. In the region below the temperature of the T~ minimum, the T~ values are approximately proportional to the square of the frequency w 2, and the minimum values of T 1 a r e proportional to the frequency to. However, in the region above the temperature of the T~ minimum, the T 1 values depend on the frequency. For example, the T~ values at 364 K for Tio.2Vo.sH0.83are 40, 53, 73 and 85 ms at 9, 22.5, 52 and 90 MHz respectively. This behaviour cannot be described by a single exponential correlation function. In addition, it is clearly shown that 1H T 1 depends on the composition of the Ti-V alloys. For example, the temperature of the T 1 minimum at 9 MHz shifts to higher temperature with increasing content of Ti. The minimum temperatures are 174, 200, 215 and 217 K for Tio.2Vo.8Ho.83, Tio.4Vo.6Ho.91, Tio.6Vo.4Ho.91 and Tio.sVo.2Ho.89 respectively. These results show that the Ti atoms restrict the hydrogen motion more effectively than the V atoms. The minimum value of Tt decreases with increasing content of V. The values are 3.8, 5.2, 7.5 and 18 ms for Tio.2Vo.8Ho.83, Ti0.4Wo.6Ho.91, Tio.6Vo.4Ho.91 and Tio.8Vo.2Ho.89 respectively. These results show that the 1H-5~V dipolar interaction contributes significantly to the total relaxation time. On the basis of these results of the temperature and frequency dependences of 1H T1 for/3-Til_yVyHx, we analyse the relaxation data to obtain the activation parameters for hydrogen dynamics in the hydrides. The detailed procedure is described below. The total spin-lattice relaxation rates (T11) are
T. Ueda, S. Hayashi / Journal of Alloys and Compounds 231 (1995) 226-232
228
L
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-
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1/Z (10-aK-')
•
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°°~°"
-'.,
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,
.
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Fig. 1. Temperature and frequency dependences of the 1H spin-lattice relaxation times (Tl) for Tio.sVo.2Ho.89 (a), Tio.6Vo.aHo.91 (b), Tio.4Vo6Ho.9, (c) and Tio2Vo.8Ho.83 (d). The resonance frequencies are 9 MHz (O), 22.5 MHz (O), 52 MHz (A) and 90 MHz (A). Full lines are the results of data fitting and the top chain line shows the contribution of conduction electrons.
described by three components as follows [7] -
-a
-~
T1 1 = TI(HH) + TI(HV) + T1 ~
(1)
-1 where TI(HH ) is the contribution of the 1H-1H dipolar interaction, Tl(•v) -i • that of the 1H_5l V dipolar as interaction and Tie ~ is that of the interaction with conduction electrons which is independent of the frequency and satisfies the Korringa relation, Tle T = K (K is a constant) [12]. The contributions of the
47Ti-lH and 49Ti-lH dipolar interactions to the total T 1 are negligible. -1 The BPP relaxation equations for TI(HH) and -1 TI(HV), generalized to include a distribution F(S) of correlation times, are represented by [13-15] f+~ -1 TltHH ) = CHH and
_~
(
4% ,d S rc + --2 i F(S) 1 + o~r2c 1 + 4oJ0r c ]
(2)
T. Ueda, S. Hayashi / Journal of Alloys and Compounds 231 (1995) 226-232 f+°~
/
Tl(HV) = 2CHv_~_ F(S)
[
re --
\2
occupy the 0 and T sites and cannot occupy two sites within 2.1 ,~ distance simultaneously [20,21], we can calculate the lattice sum of H - H and H - V for each
2 2
t 1 + 4 ( 1 - a) to0rc
3rc
6re -] 2 2 -{'x2 2 2 J dS + 4to0"t~ 1 + 4(1 + a) OJorc where the variable S signifies S = ln(rc/rcm) -[-
1
(3)
(4)
In Eqs. (2) and (3), CHH and CHV are the dipolar strengths representing the magnitudes of those parts of the dipolar interactions which are averaged out when hydrogen diffusion takes place, too is the Larmor frequency of 1H and a is the ratio of the gyromagnetic ratios of 51Vand 1H (TV/TH). In Eqs. (2)-(4), rc is the correlation time describing the fluctuation of the 1H-1H dipolar interaction and r~r, is the mean correlation time. Using re, the correlation time describing the fluctuation of the XH-51V dipolar interaction is represented by 2r~. When the fluctuations occur by a simple thermally activated process, the temperature dependence of the mean correlation time is represented by the Arrhenius activation law using an apparent activation energy E a and a pre-exponential factor "tom "tcm= "tOmexp(Ea/RT)
229
(5)
where the apparent activation energy E a is the average activation energy of hydrogen for the several different types of site sampled by hydrogen when jumping in these materials. The relaxation constants C H H and CHV contain useful information on the arrangements of the nuclei, These constants are a function of both the internuclear distances of H - H and H - V pairs and the concentrations of the H and V nuclei. These constants are theoretically represented by [16-19] 4 4 2 CHH = ~ y H h I(I + 1)xEri -6 (6) i and 2 2 2 2 --6 C , v = -~yHYv h S(S + 1 ) y ~ r s (7) J on the basis of the structural model. The characters I and S are the nuclear spinquantum numbers for ~H ( I = 1/2) and 5aV (S = 7/2) respectively, r~ and r are the internuclear distances of ~H-~H and ~H~slV respectively, and the summations for r i and rj are performed over all the lattice points occupied by hydrogen and metal atoms, x and y are the probabilities of finding H and V at each lattice point respectively, which are equal to the x and y values in the composition of Til_yWyH.. Assuming a model structure of a b.c.c, unit cell with the lattice constant a o for the T i - V - H system, in which the hydrogen atoms
hydrogen site. The lattice sums ]~r1-6 for H - H for the T site and O site are 50,47ao 6 and 29.04ao 6 respectively. The lattice s u m s ]~rZ6 for H - V for the T site and O site are 146.53ao 6 and 169.56ao 6 respectively. In the actual system, the hydrogen atoms occupy the T and O sites simultaneously with fractions dependent on the composition of the Ti-V alloys [8]. The dipolar strength in the fl-Ti-V-H system is assumed to be the weighted average of the dipolar strengths of the T and O sites. According to this structural model, the calculated T 1 minimum values are smaller than the experimental values. The H - H dipolar interaction is considered to contribute to the relaxation as the theory predicts, since the calculated values of the T 1 minimum are in good agreement with the experimental values for hydrides such as Till x, ZrH x and HfH x [22]. Therefore the contribution of the H - V dipolar interaction is assumed to be suppressed and we introduce the reduction factor f. In the data fitting, we used the effective dipolar strength CHV, where CHV = fCHv(aV.). We used a gaussian or lognormal distribution for the distribution of the correlation times because it is the most general in nature; it is given by the following function [14,15]
F(S) = - ~ -1~ exp(-S2/fl 2)
(8)
As Eq. (5) is used to describe the temperature dependence of the correlation time, there are two origins of the distribution of the correlation times: the pre-exponential factor and the activation energy. Introducing the distribution parameters /30 and /3o to characterize the distribution of the pre-exponential factor and the activation energy respectively, the total distribution parameter/3 in Eq. (8) becomes temperature dependent and is represented by [23] /32 =/3~ +(/3o/RT)2
(9)
In the data fitting, we attempted to fix the preexponential factor "tom using the simplest assumption Z0m= 1/21)O~, which was assumed by Walstedt et al. [24] for the diffusion of Na + in Na-alumina. u0 is a local vibrational frequency of hydrogen atoms in the Ti-V alloy. These frequencies for each hydride were determined from neutron scattering experiments [8]. The frequencies of the most intense peak were used to calculate "to,,in each hydride: huo = 140 _ 2 meV ("to,, = 1.5 X 10 -14 S) for Tio.8Vo2Ho.89~ Ti0.6V0.aH0.91 and Wi0.nW0.6H0.91 , and hu o = 44 m e V ("tOm = 4.7 × 1 0 - ! 4 s) for Tio.2Vo.sH0.83. For the contribution of the conduction electrons in Eq. (1), we assume that the K value in
T. Ueda, S. Hayashi / Journal of Alloys and Compounds 231 (1995) 226-232
230
Table 1 Relaxation parameters determined from IHT~ data fitting Sample
C~.~. (109s 2) CHH
CHv
Tio 2Vo.sHos3 Tio.4W~.6Ho,gt Tio.6Vo.4Ho.gt Tio.sVo.2Ho.s9
3.90 3.98 3.83 3.62
10.0 6.58 3.98 1.82
f
E, (kJmol -~)
~,, (10 las)
fl,,
/30 (kJ mol ')
K (Ks)
0.6 0.6 0.6 0.1
17.5 21.8 23.5 24.0
4.7 1.5 1.5 1.5
2.7 2.4 2.1 1.8
2.9 4.2 4.6 4.9
93 83 74 69
the Korringa relation for fl-Til_yVyH x is given by the weighted average of the K values for Till x [25] and VH x [26]. The results of the data fitting are shown by the full lines in Figs. l(a)-l(d) and the activation parameters determined from the data fitting are listed in Table 1.
4. Discussion The composition dependence of the apparent activation energy E a in the Ti-V alloys reflects the degree of disorder in the arrangement of metal atoms. The metal composition dependence of E a is shown in Fig. 2, together with other literature data of the a - T i - V - H system [9]. E a gradually decreases from 24 kJ mo1-1 for y--0.2 to 21.8 kJ mol -t for y--0.6, and then rapidly decreases to 17.5 kJ mo1-1 for y--0.8. The absolute values of other data in the literature agree with our values very closely, although the phase and 30
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~ Tio.07Vo.93Ito.195 [] ri0.31V0.69F~0.o198 o Ti0.38V0.62H0.0158
0I V
,
,
~
.
.
.
.
.
.
1-y
Ea(y , tr)= Q - AH(y, or)
(10)
as a function of the metal composition y and the short-range order parameter tr. In Eq. (10), Q is the saddle-point energy; a constant value of -25.7 kJ mol -~ is used for the Ti-V alloy, the value used by Brouwer et al. [10]. AH(y,tr) is the enthalpy of solution of hydrogen, which is a function of the alloy composition and the short-range order parameter. This quantity can be calculated by
~ AH,(y)ci(y , tr) [1 - (s i/p(i, o'))c~(y, o-)] AH(y, o') = i ~ci(y,°')[1-(si/P(i,o'))ci(y, t r ) ] i (11)
v Tio.18Vo.a2Ho.0156
0
hydrogen concentrations are different. This result suggests that, in Ti-V alloys, the E a value of hydrogen diffusion is predominantly determined by the interaction between metal and hydrogen atoms. We tried to analyse the composition dependence of E, by means of the cluster model considering the short-range ordering of metal atoms. The cluster model adopted here assumes that the local structure of metal atoms around a hydrogen atom is Ti6_iVi, an octahedron with seven kinds of configuration depending on i. The bulk quantities were described by the statistical average of these clusters. Following Brouwer et al. [10], who considered the cluster Ti4_Y~ and tetrahedral sites of hydrogen atoms for the b.c.c, alloy with low hydrogen concentrations, the activation energy Ea(y,o-) of hydrogen diffusion in Ti-V alloys is represented by
I Ti
(atomic ratio of Ti to Ti+V) Fig. 2. Alloy composition dependence of the apparent activation energy E. for proton diffusion in Til_yVyHx. The full line shows the result of calculation using Eqs. (10)and (11).
as the long-range effective hydrogen-hydrogen interaction is neglected. In Eq. (11), AHi(y) is the site energy determined by the type of cluster occupied by the hydrogen atom, ci(y,tr) is the concentration of hydrogen on the type i sites represented by the FermiDirac distribution [27,28], s~ is the blocking factor which is equal to 4 [29] and p(i,tr) is the site fraction obtained by the method of Brouwer et al. [lO]. To calculate the activation energy theoretically, the variation of the site energy is considered to depend on the type of cluster. The model of the energy scheme
T. Ueda, S. Hayashi / Journal of Alloys and Compounds 231 (1995) 226-232
Type of cluster Ti rich 0
V rich 1
2
3
4
5
t
~I
I
t
t~
/
6 /
t
~- i
~/v ~
~T~ •m
231
Tio.4W0.6Ho.9t and Tio2V08Ho.83, whereas it is much smaller for Tio.8V0.2Ho.89. The fact that the reduction factor depends on the alloy composition should result f r o m the different arrangements of the metal atoms around a hydrogen atom. The inhomogeneous distribution of hydrogen atoms caused by the difference in the interactions between T i - H and V - H should result in a composition dependence of the reduction of the ~H-5~V dipolar interaction. As the affinity of a hydrogen atom to a Ti a t o m is stronger than that to a V atom, the hydrogen atoms have a tendency to gather around Ti-rich sites.
References Fig. 3. Schematic representation of the site energy, which depends on the type of clusters Ti 6 ~V.
describing the relation between the site energy and the type of cluster is shown in Fig. 3. A t Ti-rich compositions, the site energy is large and equal to the site energy of Tills, whereas at V-rich compositions, the site energy is relatively small and equal to that of V H x. The b o r d e r composition changing the site energy from T i l l x to VHx is derived from the results of neutron inelastic scattering [8]. The clusters with i = 0 - 4 have the same site energy as T i l l x, i.e. the T i - H interaction is dominant, whereas the clusters with i = 5 and 6 have the same site energy as V H x, i.e. the V - H interaction is dominant. Using this energy scheme, we fitted a theoretical curve to the experimental data as shown in Fig. 2, and obtained the m e t a l - h y d r o g e n interactions AnTi --50.5 kJ mo1-1 and A H v = - 3 4 kJ mol -~ and =
the short-range order p a r a m e t e r o-= 0.4. The m e t a l hydrogen interactions obtained are in good agreement with those in the pure,, metal hydrides, which have b e e n reported to be - 5 3 kJ mo1-1 at 573 K for T i - H [30] and - 3 2 kJ mo1-1 for V - H [31]. The difference
[1] H. Nagel and R.S. Perkins, Z. Metallkd., 66 (1975) 362. [2] S. Ono, K. Nomura and Y. Ikeda, J. Less-Common Met., 72 (1983) 159.
[3] s. Hayashi, K. Hayamizu and O. Yamamoto, J. Less-Common Met., 113 (1987) 1. [4] B. Nowak, Y. Chabre and R. Andreani, J. Less-Common Met., 130 (1987) 193. [5] B. Nowak, S. Hayashi, K. Hayamizu and O. Yamamoto, J. Less-Common Met., 123 (1986) 75. [6] S. Hayashi and K. Hayamizu, J. Less-Common Met., 161 (1990)
61. [7] T. Ueda, S. Hayashi and K. Hayamizu, Phys. Rev. B, 48 (1993) 5837.
[8] T. Ueda, S. Hayashi, Y. Nakai and S. Ikeda, Phys. Rev. B, in press. [9] R.C. Brouwer, E. Salomons and R. Griessen, Phys. Rev. B, 38
(1988) 10217. [lOl R.C. Brouwer, J. Rector, N. Koeman and R. Griessen, Phys. Rev. B, 40 (1989) 3546. [11] N. Bloembergen, E.M. Purcell and R.V. Pound, Phys. Rev., 73 (1948) 679+ [12] A. Abragam, The Principles of Nuclear Magnetism, Oxford
University Press, 1961, Chapter IX. [13] E.R. Andrew, D.J. Bryant and E.M. Cashell, Chem. Phys. Lett., 69 (1980) 551. [14] E.R. Andrew, D.J. Bryant, E.M. Cashell and Q.A. Meng, Phys.
Lett+ A, 88 (1982) 487.
in magnitude between the T i - H and V - H interactions is also reflected in the configurations of the clusters at which the site energy changes from A H x i to AH v. The Ti2V4 cluster has a site energy A n T i although it contains m o r e V atoms than Ti atoms. This is caused
[15] P.A. Fedders, Phys. Rev. B, 25 (1982) 78.
by the larger affinity of the Ti a t o m than the V a t o m for the hydrogen atom. T h e short-range order p a r a m e ter o" = 0.4 is also in good agreement with our previous value of or = 0.43 ___0.(15 determined from neutron
(1976) 3378. [20] A.C. Switendick, Z. Phys. Chem., Neue Folge, 117 (1979) 89. [21] B.K. Rao and P. Jena, Phys. Rev. B, 31 (1985) 6726.
inelastic scattering and 0.36 ~ or ~< 0.51 obtained by Brouwer et al. [10]. The relaxation constants of the ~H-5~V dipolar interaction, calculated using Eq. (7), are overestimated and we introduced the reduction factor f. The reduction factors determined from data fitting and the calculated values of the relaxation constants are listed in Table 1. The f value is constant for Wi0.6W0.aH0.9~,
[16] A. Abragam, The Principles of Nuclear Magnetism, Oxford
University Press, 1961, Chapter VIII. [17] C.A. Sholl, J. Phys. C: Solid State Phys., 7 (1974) 3378. [181 C.A. Sholl, J. Phys. C: Solid State Phys., 8 (1975) 1737. [19] W.A. Barton and C.A. Sholl, J. Phys. C: Solid State Phys., 9
[22] E.F. Khodosov and N.A. Shepilov, Phys. Status Solidi B, 47 (1971) 693. [23] A.S. Nowick and B.S. Berry, IBM J., O0 (1961) 297. [24] R.E. Walstedt, R. Dupree, J.P. Remeika and A. Rodriguer, Phys. Rev. B, 15 (1977) 3442. [25] C. Wert and C. Zener, Phys. Rev., 76 (1949) 1169. [26] J.C. Wang, M. Gaffari and Sang-il Choi, J. Chem. Phys., 63
(1975) 772. 1478. [28] E.H. Sevilla and R.M. Cotts, Phys. Rev. B, 37 (1988) 6813.
[27] S.J. Allen, Jr. and J.P. Remeika, Phys. Rev. Lett., 33 (1974)
232 [29] [30] [31] [32]
T. Ueda, S. Hayashi / Journal of Alloys and Compounds 231 (1995) 226 232
Y. Fukai and S. Kazama, Acta Metall., 25 (1977) 59. R. Kirchheim, Acta Metall., 30 (1982) 1069. R. Griessen, Phys. Rev, B, 27 (1983) 743. G. Boureau, J. Phys. Chem. Solids, 42 (1981) 743.
[33] E Dantzer, O.J. Kleppa and M.E. Melnichak. J. Chem. Phys. 64 (1976) 139. [34] O.J. Kleppa, E Dantzer and M.E. Melnichak, J. Chem. Phys. 61 (1974) 4048.
AILOY5 AND COMPOUND5 ELSEVIER
Journal of Alloys and Compounds 231 (1995) 226-232
1H NMR study of local structure and proton dynamics in
fl-Ti l_yVyHx Takahiro Ueda, Shigenobu Hayashi Department of Physical Chemistry, National Institute of Materials and Chemical Research, Tsukuba, lbaraki 305, Japan
Abstract
The local structure of the metal atoms around a hydrogen atom and the dynamics of hydrogen atoms in disordered metal hydrides fl-Ti 1 yVyHx (x - 1 and 0.2 ~
1. Introduction Alloys composed of Ti and V (Til_yVy) form cornpounds with hydrogen [1,2]. These alloys can absorb hydrogen until the ratio of hydrogen to metal atoms reaches a value of two. The hydrides have three phases depending on the degree of hydrogenation. In the dihydride (denoted as the 3,-phase), the metal atoms form a face-centred-cubic (f.c.c.) lattice and the hydrogen atoms occupy the tetrahedral site (T site) formed in the cubic lattice [3]. In hydrides with much lower hydrogen to metal ratios (i.e. x - 0), called the a-phase, the metal atoms form a body-centred-cubic (b.c.c.) lattice and the hydrogen atoms occupy the T site randomly [4-6]. In the monohydride (denoted as the /3-phase), although the metal atoms form a b.c.c, lattice similar to the a-phase, the nature of the hydrogen sites and the dynamic behaviour of the hydrogen atoms are not clearly understood. The concentration of hydrogen which results in a change from the a - to t h e / 3 - p h a s e is not known, In a previous paper, we studied the proton dynamics in the /3-phase using proton nuclear magnetic reso0925-8388/95/$09.50 © 1995 Elsevier Science S.A. All rights reserved SSDI 0925-8388(95)01820-4
nance (1H N M R ) through spin-lattice relaxation time (T 0 measurements, and tried to interpret the results using a local structural model [7]. In this model, the local structure of the metal atoms around a hydrogen atom is described by a binomial distribution. The hydrogen atoms have different activation energies depending on the local structure of the metal atoms, and it was assumed that the hydrogen atoms occupied only the T site. However, this model cannot describe the Ti I yVyH x system completely because the shortrange ordering of host metals should be present in binary alloys, and dual occupancy of T and octahedral (O) sites was reported in Ref. [8]. Brouwer et al., who studied diffusion and local structures in b.c.c, binary alloys, such as Nbl_yVy [9] and Til_yWy [10], with low hydrogen concentrations, derived formulae describing the composition dependence of the activation energy and enthalpy of solution in A l_yBy alloys on the basis of a local structual model taking into account the short-range ordering of metals [10]. They considered that Aa_iB i clusters represented the local structure of the metal atoms around a hydrogen atom. The clusters surround a
T. Ueda, S. Hayashi / Journal of Alloys and Compounds 231 (1995) 226-232
hydrogen atom tetrahedrally. By application of their formulae to enthalpy of solution data reported by other workers and to their diffusion data, they succeeded in determining the short-range order parameters for Ti l_yVy alloys. Thus a local structural model taking into account the slhort-range ordering of metals is necessary to describe the diffusion coefficients, apparent activation energy and enthalpy of solution for hydrogen in binary disordered alloys, From neutron inelastic scattering experiments, we found two kinds of hydrogen site in fl-Til_yVyHx (tetrahedral and octahedral sites) whose populations change with the composition of the alloys. The population of the T site is 91% for Tio.sVo.2Ho.94 and decreases monotonically to 6% for Tio.lVo.gHo.98; the population of the O site is 9% for Ti0.8Vo.2H0.94 and increases to 94% for Tio.lVo.9Ho.g8. Using a modified cluster model assuming Ti6_iV~ clusters as the local structure of the metal atoms around a hydrogen atom, the short-range order parameter was determined from an analysis of the dependence of the fraction of each hydrogen site on the alloy composition (0"=0.43_+ 0.05 [8]). In this paper, we re-analyse the temperature and frequency dependences of 1H T~ using the Bloembergen-Purcell-Pound (BPP) equations [11 ] considering the distribution of the correlation time, and determine the activation parameters for hydrogen diffusion in fl-Ti i_yvyHx . We take into account the fact that Til_yVy is disordered and exhibits large fluctuations in chemical and topological environments, such as crystal symmetry, hole radius, lattice distortion and the types of host metal. On the basis of neutron scattering experiments and the cluster model proposed by Brouwer et al. [9,10], the short-range order parameter and metal-hydrogen interactions are estimated from the dependence of the apparent activation energy on the alloy composition using a cluster model which assumes O site occupancy and therefore Ti6_iV/ clusters as the local structure of the metal atoms,
2. Experimental details Three of the Ti-V monohydride samples studied in this work were the same as those used in Ref. [6]: Tio.2Vo.sHo.83, Tio.4Wo.6n0.91 and Tio.6Vo.4Ho.91. These three samples had been confirmed to consist of the /3-phase only. Tio.sVo.2Ho.89 was synthesized by reaction between a Tio.8Vo.2 alloy and hydrogen gas. The details of the procedure have been described previously [7]. This hydride was a mixture of/3- and y-phases on the basis of the X-ray diffraction pattern, but the quantity of the y-phase was very small compared with that of the/3-phase. Therefore the contribution of the y-phase to the total relaxation time was negligible.
227
1H N M R measurements were carried out using a Bruker CXP100 pulsed spectrometer with an electromagnet. The proton spin-lattice relaxation times (T1) were measured in the temperature range 105-400 K at four frequencies (9, 22.5, 52 and 90 MHz) using the 90°-~--90 ° method. The width of the ¢r/2 pulse was adjusted in the range 2.3-3.5 /zs depending on the Larmor frequency. The experimental errors were less t h a n - 5 % . The temperature was controlled by a Bruker variable temperature unit (VT-1000) with an a c c u r a c y of-- 1 K, using the flow of cooled or heated nitrogen gas.
3. Results and analysis The magnetization recovery curves for Tio.aVo.2H0.89, Tio.6Vo.4Ho.9~, Tio.4Vo.6Ho.9~ and Tio.zVo.8Ho.83 are described by a single exponential decay over the entire temperature range. The IH T 1 values at the fourLarmorfrequenciesforTio.sVo.2Ho.89,Tio.6Vo.4Ho.91, Tio.4Vo.6Ho.91 and Tio.2Vo.sHo.83 are plotted as a function of the reciprocal temperature in Figs. l(a)-l(d) respectively. The frequency dependence of T~ is approximately described by a single exponential correlation function. In the region below the temperature of the T~ minimum, the T~ values are approximately proportional to the square of the frequency w 2, and the minimum values of T 1 a r e proportional to the frequency to. However, in the region above the temperature of the T~ minimum, the T 1 values depend on the frequency. For example, the T~ values at 364 K for Tio.2Vo.sH0.83are 40, 53, 73 and 85 ms at 9, 22.5, 52 and 90 MHz respectively. This behaviour cannot be described by a single exponential correlation function. In addition, it is clearly shown that 1H T 1 depends on the composition of the Ti-V alloys. For example, the temperature of the T 1 minimum at 9 MHz shifts to higher temperature with increasing content of Ti. The minimum temperatures are 174, 200, 215 and 217 K for Tio.2Vo.8Ho.83, Tio.4Vo.6Ho.91, Tio.6Vo.4Ho.91 and Tio.sVo.2Ho.89 respectively. These results show that the Ti atoms restrict the hydrogen motion more effectively than the V atoms. The minimum value of Tt decreases with increasing content of V. The values are 3.8, 5.2, 7.5 and 18 ms for Tio.2Vo.8Ho.83, Ti0.4Wo.6Ho.91, Tio.6Vo.4Ho.91 and Tio.8Vo.2Ho.89 respectively. These results show that the 1H-5~V dipolar interaction contributes significantly to the total relaxation time. On the basis of these results of the temperature and frequency dependences of 1H T1 for/3-Til_yVyHx, we analyse the relaxation data to obtain the activation parameters for hydrogen dynamics in the hydrides. The detailed procedure is described below. The total spin-lattice relaxation rates (T11) are
T. Ueda, S. Hayashi / Journal of Alloys and Compounds 231 (1995) 226-232
228
L
I
I
I
I
I
I
I
zooI" (a I
I'
i
i
.
-
t0-
10-2
i0 -z
i
I
l
~
r
I
f
i
5
I
i
.
I
[
I
10-3
-
t
r
i
l
l
i0
t
i
5
1/Z (10-aK-')
•
I
loO (b)
I0- ~
i0-2
I
I
i0
1/T (10"aK-')
°°~°"
-'.,
2-
,
.
t/it (10-aK-')
i//" (10--~K-')
Fig. 1. Temperature and frequency dependences of the 1H spin-lattice relaxation times (Tl) for Tio.sVo.2Ho.89 (a), Tio.6Vo.aHo.91 (b), Tio.4Vo6Ho.9, (c) and Tio2Vo.8Ho.83 (d). The resonance frequencies are 9 MHz (O), 22.5 MHz (O), 52 MHz (A) and 90 MHz (A). Full lines are the results of data fitting and the top chain line shows the contribution of conduction electrons.
described by three components as follows [7] -
-a
-~
T1 1 = TI(HH) + TI(HV) + T1 ~
(1)
-1 where TI(HH ) is the contribution of the 1H-1H dipolar interaction, Tl(•v) -i • that of the 1H_5l V dipolar as interaction and Tie ~ is that of the interaction with conduction electrons which is independent of the frequency and satisfies the Korringa relation, Tle T = K (K is a constant) [12]. The contributions of the
47Ti-lH and 49Ti-lH dipolar interactions to the total T 1 are negligible. -1 The BPP relaxation equations for TI(HH) and -1 TI(HV), generalized to include a distribution F(S) of correlation times, are represented by [13-15] f+~ -1 TltHH ) = CHH and
_~
(
4% ,d S rc + --2 i F(S) 1 + o~r2c 1 + 4oJ0r c ]
(2)
T. Ueda, S. Hayashi / Journal of Alloys and Compounds 231 (1995) 226-232 f+°~
/
Tl(HV) = 2CHv_~_ F(S)
[
re --
\2
occupy the 0 and T sites and cannot occupy two sites within 2.1 ,~ distance simultaneously [20,21], we can calculate the lattice sum of H - H and H - V for each
2 2
t 1 + 4 ( 1 - a) to0rc
3rc
6re -] 2 2 -{'x2 2 2 J dS + 4to0"t~ 1 + 4(1 + a) OJorc where the variable S signifies S = ln(rc/rcm) -[-
1
(3)
(4)
In Eqs. (2) and (3), CHH and CHV are the dipolar strengths representing the magnitudes of those parts of the dipolar interactions which are averaged out when hydrogen diffusion takes place, too is the Larmor frequency of 1H and a is the ratio of the gyromagnetic ratios of 51Vand 1H (TV/TH). In Eqs. (2)-(4), rc is the correlation time describing the fluctuation of the 1H-1H dipolar interaction and r~r, is the mean correlation time. Using re, the correlation time describing the fluctuation of the XH-51V dipolar interaction is represented by 2r~. When the fluctuations occur by a simple thermally activated process, the temperature dependence of the mean correlation time is represented by the Arrhenius activation law using an apparent activation energy E a and a pre-exponential factor "tom "tcm= "tOmexp(Ea/RT)
229
(5)
where the apparent activation energy E a is the average activation energy of hydrogen for the several different types of site sampled by hydrogen when jumping in these materials. The relaxation constants C H H and CHV contain useful information on the arrangements of the nuclei, These constants are a function of both the internuclear distances of H - H and H - V pairs and the concentrations of the H and V nuclei. These constants are theoretically represented by [16-19] 4 4 2 CHH = ~ y H h I(I + 1)xEri -6 (6) i and 2 2 2 2 --6 C , v = -~yHYv h S(S + 1 ) y ~ r s (7) J on the basis of the structural model. The characters I and S are the nuclear spinquantum numbers for ~H ( I = 1/2) and 5aV (S = 7/2) respectively, r~ and r are the internuclear distances of ~H-~H and ~H~slV respectively, and the summations for r i and rj are performed over all the lattice points occupied by hydrogen and metal atoms, x and y are the probabilities of finding H and V at each lattice point respectively, which are equal to the x and y values in the composition of Til_yWyH.. Assuming a model structure of a b.c.c, unit cell with the lattice constant a o for the T i - V - H system, in which the hydrogen atoms
hydrogen site. The lattice sums ]~r1-6 for H - H for the T site and O site are 50,47ao 6 and 29.04ao 6 respectively. The lattice s u m s ]~rZ6 for H - V for the T site and O site are 146.53ao 6 and 169.56ao 6 respectively. In the actual system, the hydrogen atoms occupy the T and O sites simultaneously with fractions dependent on the composition of the Ti-V alloys [8]. The dipolar strength in the fl-Ti-V-H system is assumed to be the weighted average of the dipolar strengths of the T and O sites. According to this structural model, the calculated T 1 minimum values are smaller than the experimental values. The H - H dipolar interaction is considered to contribute to the relaxation as the theory predicts, since the calculated values of the T 1 minimum are in good agreement with the experimental values for hydrides such as Till x, ZrH x and HfH x [22]. Therefore the contribution of the H - V dipolar interaction is assumed to be suppressed and we introduce the reduction factor f. In the data fitting, we used the effective dipolar strength CHV, where CHV = fCHv(aV.). We used a gaussian or lognormal distribution for the distribution of the correlation times because it is the most general in nature; it is given by the following function [14,15]
F(S) = - ~ -1~ exp(-S2/fl 2)
(8)
As Eq. (5) is used to describe the temperature dependence of the correlation time, there are two origins of the distribution of the correlation times: the pre-exponential factor and the activation energy. Introducing the distribution parameters /30 and /3o to characterize the distribution of the pre-exponential factor and the activation energy respectively, the total distribution parameter/3 in Eq. (8) becomes temperature dependent and is represented by [23] /32 =/3~ +(/3o/RT)2
(9)
In the data fitting, we attempted to fix the preexponential factor "tom using the simplest assumption Z0m= 1/21)O~, which was assumed by Walstedt et al. [24] for the diffusion of Na + in Na-alumina. u0 is a local vibrational frequency of hydrogen atoms in the Ti-V alloy. These frequencies for each hydride were determined from neutron scattering experiments [8]. The frequencies of the most intense peak were used to calculate "to,,in each hydride: huo = 140 _ 2 meV ("to,, = 1.5 X 10 -14 S) for Tio.8Vo2Ho.89~ Ti0.6V0.aH0.91 and Wi0.nW0.6H0.91 , and hu o = 44 m e V ("tOm = 4.7 × 1 0 - ! 4 s) for Tio.2Vo.sH0.83. For the contribution of the conduction electrons in Eq. (1), we assume that the K value in
T. Ueda, S. Hayashi / Journal of Alloys and Compounds 231 (1995) 226-232
230
Table 1 Relaxation parameters determined from IHT~ data fitting Sample
C~.~. (109s 2) CHH
CHv
Tio 2Vo.sHos3 Tio.4W~.6Ho,gt Tio.6Vo.4Ho.gt Tio.sVo.2Ho.s9
3.90 3.98 3.83 3.62
10.0 6.58 3.98 1.82
f
E, (kJmol -~)
~,, (10 las)
fl,,
/30 (kJ mol ')
K (Ks)
0.6 0.6 0.6 0.1
17.5 21.8 23.5 24.0
4.7 1.5 1.5 1.5
2.7 2.4 2.1 1.8
2.9 4.2 4.6 4.9
93 83 74 69
the Korringa relation for fl-Til_yVyH x is given by the weighted average of the K values for Till x [25] and VH x [26]. The results of the data fitting are shown by the full lines in Figs. l(a)-l(d) and the activation parameters determined from the data fitting are listed in Table 1.
4. Discussion The composition dependence of the apparent activation energy E a in the Ti-V alloys reflects the degree of disorder in the arrangement of metal atoms. The metal composition dependence of E a is shown in Fig. 2, together with other literature data of the a - T i - V - H system [9]. E a gradually decreases from 24 kJ mo1-1 for y--0.2 to 21.8 kJ mol -t for y--0.6, and then rapidly decreases to 17.5 kJ mo1-1 for y--0.8. The absolute values of other data in the literature agree with our values very closely, although the phase and 30
I
.
.
.
.
/ I-.
.
.
.
i
.
.
~ 6_
~
20
"7
"~
"~r.~
V 10
o VII0.006, T i l l 0 . 0 0 6
/
~ Tio.07Vo.93Ito.195 [] ri0.31V0.69F~0.o198 o Ti0.38V0.62H0.0158
0I V
,
,
~
.
.
.
.
.
.
1-y
Ea(y , tr)= Q - AH(y, or)
(10)
as a function of the metal composition y and the short-range order parameter tr. In Eq. (10), Q is the saddle-point energy; a constant value of -25.7 kJ mol -~ is used for the Ti-V alloy, the value used by Brouwer et al. [10]. AH(y,tr) is the enthalpy of solution of hydrogen, which is a function of the alloy composition and the short-range order parameter. This quantity can be calculated by
~ AH,(y)ci(y , tr) [1 - (s i/p(i, o'))c~(y, o-)] AH(y, o') = i ~ci(y,°')[1-(si/P(i,o'))ci(y, t r ) ] i (11)
v Tio.18Vo.a2Ho.0156
0
hydrogen concentrations are different. This result suggests that, in Ti-V alloys, the E a value of hydrogen diffusion is predominantly determined by the interaction between metal and hydrogen atoms. We tried to analyse the composition dependence of E, by means of the cluster model considering the short-range ordering of metal atoms. The cluster model adopted here assumes that the local structure of metal atoms around a hydrogen atom is Ti6_iVi, an octahedron with seven kinds of configuration depending on i. The bulk quantities were described by the statistical average of these clusters. Following Brouwer et al. [10], who considered the cluster Ti4_Y~ and tetrahedral sites of hydrogen atoms for the b.c.c, alloy with low hydrogen concentrations, the activation energy Ea(y,o-) of hydrogen diffusion in Ti-V alloys is represented by
I Ti
(atomic ratio of Ti to Ti+V) Fig. 2. Alloy composition dependence of the apparent activation energy E. for proton diffusion in Til_yVyHx. The full line shows the result of calculation using Eqs. (10)and (11).
as the long-range effective hydrogen-hydrogen interaction is neglected. In Eq. (11), AHi(y) is the site energy determined by the type of cluster occupied by the hydrogen atom, ci(y,tr) is the concentration of hydrogen on the type i sites represented by the FermiDirac distribution [27,28], s~ is the blocking factor which is equal to 4 [29] and p(i,tr) is the site fraction obtained by the method of Brouwer et al. [lO]. To calculate the activation energy theoretically, the variation of the site energy is considered to depend on the type of cluster. The model of the energy scheme
T. Ueda, S. Hayashi / Journal of Alloys and Compounds 231 (1995) 226-232
Type of cluster Ti rich 0
V rich 1
2
3
4
5
t
~I
I
t
t~
/
6 /
t
~- i
~/v ~
~T~ •m
231
Tio.4W0.6Ho.9t and Tio2V08Ho.83, whereas it is much smaller for Tio.8V0.2Ho.89. The fact that the reduction factor depends on the alloy composition should result f r o m the different arrangements of the metal atoms around a hydrogen atom. The inhomogeneous distribution of hydrogen atoms caused by the difference in the interactions between T i - H and V - H should result in a composition dependence of the reduction of the ~H-5~V dipolar interaction. As the affinity of a hydrogen atom to a Ti a t o m is stronger than that to a V atom, the hydrogen atoms have a tendency to gather around Ti-rich sites.
References Fig. 3. Schematic representation of the site energy, which depends on the type of clusters Ti 6 ~V.
describing the relation between the site energy and the type of cluster is shown in Fig. 3. A t Ti-rich compositions, the site energy is large and equal to the site energy of Tills, whereas at V-rich compositions, the site energy is relatively small and equal to that of V H x. The b o r d e r composition changing the site energy from T i l l x to VHx is derived from the results of neutron inelastic scattering [8]. The clusters with i = 0 - 4 have the same site energy as T i l l x, i.e. the T i - H interaction is dominant, whereas the clusters with i = 5 and 6 have the same site energy as V H x, i.e. the V - H interaction is dominant. Using this energy scheme, we fitted a theoretical curve to the experimental data as shown in Fig. 2, and obtained the m e t a l - h y d r o g e n interactions AnTi --50.5 kJ mo1-1 and A H v = - 3 4 kJ mol -~ and =
the short-range order p a r a m e t e r o-= 0.4. The m e t a l hydrogen interactions obtained are in good agreement with those in the pure,, metal hydrides, which have b e e n reported to be - 5 3 kJ mo1-1 at 573 K for T i - H [30] and - 3 2 kJ mo1-1 for V - H [31]. The difference
[1] H. Nagel and R.S. Perkins, Z. Metallkd., 66 (1975) 362. [2] S. Ono, K. Nomura and Y. Ikeda, J. Less-Common Met., 72 (1983) 159.
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(1988) 10217. [lOl R.C. Brouwer, J. Rector, N. Koeman and R. Griessen, Phys. Rev. B, 40 (1989) 3546. [11] N. Bloembergen, E.M. Purcell and R.V. Pound, Phys. Rev., 73 (1948) 679+ [12] A. Abragam, The Principles of Nuclear Magnetism, Oxford
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in magnitude between the T i - H and V - H interactions is also reflected in the configurations of the clusters at which the site energy changes from A H x i to AH v. The Ti2V4 cluster has a site energy A n T i although it contains m o r e V atoms than Ti atoms. This is caused
[15] P.A. Fedders, Phys. Rev. B, 25 (1982) 78.
by the larger affinity of the Ti a t o m than the V a t o m for the hydrogen atom. T h e short-range order p a r a m e ter o" = 0.4 is also in good agreement with our previous value of or = 0.43 ___0.(15 determined from neutron
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inelastic scattering and 0.36 ~ or ~< 0.51 obtained by Brouwer et al. [10]. The relaxation constants of the ~H-5~V dipolar interaction, calculated using Eq. (7), are overestimated and we introduced the reduction factor f. The reduction factors determined from data fitting and the calculated values of the relaxation constants are listed in Table 1. The f value is constant for Wi0.6W0.aH0.9~,
[16] A. Abragam, The Principles of Nuclear Magnetism, Oxford
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232 [29] [30] [31] [32]
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Y. Fukai and S. Kazama, Acta Metall., 25 (1977) 59. R. Kirchheim, Acta Metall., 30 (1982) 1069. R. Griessen, Phys. Rev, B, 27 (1983) 743. G. Boureau, J. Phys. Chem. Solids, 42 (1981) 743.
[33] E Dantzer, O.J. Kleppa and M.E. Melnichak. J. Chem. Phys. 64 (1976) 139. [34] O.J. Kleppa, E Dantzer and M.E. Melnichak, J. Chem. Phys. 61 (1974) 4048.