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Journal of Alloys and Compounds 580 (2013) S109-S113

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Journal of Alloys and Compounds
journal h omepage: www.else vier.com/locate/jalcom

Neutron spectroscopy of nickel deuteride
V.E. Antonov a,, A.S. Ivanov b, M.A. Kuzovnikov a, M. Tkacz
a b c

c

Institute of Solid State Physics RAS, 142432 Chernogolovka, Moscow District, Russia Institut Laue langevin, 6, rue Jules Horowitz, BP 156, F-38042 Grenoble, France Institute of Physical Chemistry PAS, Kasprzaka 44/52, 01-224 Warsaw, Poland

article

info

abstract
A powder sample of fcc NiD synthesized under a deuterium pressure of 0.9 GPa at room temperature is studied at ambient pressure and 10 K by inelastic neutron scattering in the range of energy transfers 22-356 meV. The fundamental band of optical deuterium vibrations in NiD consists of a peak at 62 meV with a shoulder toward higher energies. The second and third optical bands demonstrate approximately harmonic behavior. The pffiffiffi spectrum of NiD is similar to that of NiH compressed along the energy scale by a factor of r = 1.43(2) % 2 characteristic of vibrations of D and H atoms in the same harmonic potential. Thermodynamic calculations using this value of r = 1.43 for optical vibrations in NiH and NiD accurately reproduce the experimental difference between the decomposition pressures of NiH and NiD near room temperature. ã 2013 Elsevier B.V. All rights reserved.

Article history: Available online 18 March 2013 Keywords: Metal hydrides Inelastic neutron scattering Phase equilibria

1. Introduction Nickel hydride belongs to a rather large family of hydrides of the group VI-VIII transition metals, in which hydrogen atoms occupy octahedral interstitial positions in the close-packed metal lattices with a fcc, hcp, or double hcp structure [1]. An occupancy of all octahedral positions gives an atomic ratio of H/Me = 1. The spectra of optical hydrogen vibrations in the monohydrides synthesized so far (fcc and hcp CrH, hcp MnH, dhcp FeH, fcc CoH, fcc NiH, hcp MoH, fcc RhH and fcc PdH) have earlier been studied by inelastic neutron scattering (see [2,3] and references therein). Irrespective of the type of the metal lattice, the first band of optical H vibrations in each of these hydrides consists of a strong peak with a broad shoulder extending toward higher energies. In all hydrides except for RhH [3], the second and the third optical H bands appear at energies approximately two and three times the energy of the first band, which is characteristic of harmonic vibrations. The effect of H substitution by D has earlier been investigated by inelastic neutron scattering (INS) for one of these monohydrides, PdH [4], and also for non-stoichiometric PdH0.63 [5]. The optical spectra of the deuterides proved to be very similar to the spectra of the hydrides compressed along the energy scale by factors of r = 1.51(2) and 1.49(2), pffiffiffi respectively. These values considerpffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ably differ from mH =mD % 2 % 1.41 for the H and D atoms vibrating in the same harmonic potential well. The factor r % 1.5 indicates that the force constants for H atoms in PdH are by %13% larger than those for D atoms in PdD.

In the present paper, we studied the spectrum of optical pffiffiffi vibrations in fcc NiD in order to examine if r > 2 is typical of hydrides and deuterides of other group VI-VIII transition metals. A comparison of this spectrum with the spectrum of fcc NiH meapffiffiffi sured earlier [6] gave a nearly ``harmonic'' value of r = 1.43(2) % 2 despite the fact that the Ni-H/D system is a close analog of the Pd- H/D system in many other respects. We also calculated the difference between the decomposition (equilibrium) pressures of NiH and NiD. The calculation using r = 1.43 well reproduced the experimental dependence of this difference in a rather wide temperature interval of Á100 ÀC around room temperature. Using r = 1.51 characteristic of the Pd-H/D system resulted in the dependence inconsistent with experiment.

2. Experimental details A 3 g batch of powdered nickel metal of 99.5 wt.% purity and a grain size of 3- 7 lm was loaded with deuterium in a D2 gas of 99.995 wt.% purity compressed to 0.9 GPa at room temperature using the high-pressure apparatus described in [7]. In view of the sluggish kinetics of the NiD formation under these conditions [8], the sample was first activated by exposing it to the high deuterium pressure for 24 h followed by degassing under ambient conditions for 30 min. In the second run, the sample was exposed to the 0.9 GPa deuterium pressure for another 24 h, cooled to Ð50 ÀC, decompressed and further stored in liquid nitrogen to prevent deuterium losses. An X-ray diffraction study of the obtained sample at ambient pressure and T = 85 K showed it to consist of 47 wt% of unreacted fcc Ni with the lattice parameter a = 3.517(3) Õ and 53 wt% of fcc NiD with a = 3.724(4) Õ. The INS spectrum from the powder Ni-D sample was measured at 10 K in the range of energy transfers, E, from 22 to 356 meV with an energy resolution of dE/ E % 5-8% using the IN1-BeF neutron spectrometer installed at the hot source of the high-flux reactor at the Institute Laue-Langevin in Grenoble. The E value was calculated by subtracting 3.5 meV, the mean energy of neutrons that passed through the cold Be filter, from the energy of the incoming neutrons selected with

Corresponding author. Tel.: +7 496 522 4027.
E-mail address: antonov@issp.ac.ru (V.E. Antonov). 0925-8388/$ - see front matter ã 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.jallcom.2013.03.021


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a focusing Cu(2 2 0) single crystal. The background spectrum from the cryostat and an empty flat sample holder made of thin aluminum foil was measured separately and then subtracted from the raw INS spectrum of the sample.

(a)
S ( Q, E ), arb. units
S S S
NiD NiH NiH

3. Results and discussion 3.1. Inelastic neutron scattering The obtained INS spectrum S(Q, E) of the NiD sample is shown in Fig. 1 together with the spectrum of NiH, which was measured earlier with the same neutron spectrometer IN1-BeF [6]. As one can see, the spectrum of optical vibrations in NiD is very similar to the NiH spectrum compressed along the energy scale. The first fundamental band of optical vibrations in NiD consists of a strong peak at E = 62 meV broadened toward higher energies. The second and the third optical bands resulting from multiphonon neutron scattering have a smoother intensity distribution and appear at energies approximately two and three times the energy of the fundamental band, respectively. The scattering intensity below 38 meV mostly results from the acoustic vibrations in NiD and also in the unreacted Ni remained in the sample. The acoustic spectra of NiH and, for comparison, of Ni were earlier measured by INS at energies down to 2 meV [9]. The acoustic spectrum of NiD should be very similar to that of NiH because pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiDffi for acoustic vibrations, the scaling factor EH/E ffiffi which equals to ?mNi ? mD î=?mNi ? mH î = 1.008 in the harmonic approximation, is close to unity due to the large mass mNi = 58.71 a.u. of the Ni atom compared to the masses mH = 1.008 a.u. and mD = 2.014 a.u. of the atoms of hydrogen isotopes. In the case of optical vibrations, the neutron scattering intensity is proportional to the neutron scattering cross-section r of the vibrating atom and inversely proportional to its mass m. As a result, the optical part of the INS spectrum from NiD well represents the density of states of the D vibrations, because the contribution from the Ni atoms does not exceed 5%. At the same time, a small impurity of less than 0.1 at.% H in NiD produces a parasitic feature of noticeable intensity - a peak of the H local modes - at energies of 86-106 meV (see Fig. 1) due to the anomalously large rH % 10.7rD [10] and mH % mD/2. As one can see, e.g., from Fig. 2b, the shape of the high-energy shoulder of the fundamental optical peak in NiD differs from that

(E ) (E Ç1.51) (E Ç2)

(b)
S ( Q, E ), arb. units

S S

NiD NiH

(E ) (E Ç1.43)

50

100

150

200

250

E, meV
Fig. 2. Comparison of the experimental INS spectrum of NiD (open circles) and the spectrum of pffiffiffi [6] compressed along the energy scale using the scaling factors NiH r = 1.51 and 2 (a) and the factor r = 1.43 (b).

IN1-BeF
S ( Q, E ), arb. units

T = 10 K
S S (E ) (E ) NiH
NiD

H impurity <0.1%

in NiH. The origin of this difference is not clear at the moment. In the case of NiD, the additional scattering intensity could result (at least, partly) from the band of covibrations of the H and D atoms. Such a band located at energies right above the main optical peak was recently observed in hydrogen-doped PdD samples [4]. As seen from Fig. 2a, the positions of the second and third optical bands in NiD are well represented by the INS spectrum offfiffiNiH pffi compressed along the energy scale by a `harmonic' factor r = 2.As shown in Fig. 2b, using a little larger factor of r = 1.43 additionally helps to better reproduce the position of the fundamental optical peak at 62 meV. Thus, in contrast to the Pd-H/D system, the force constants for D in the deuteride and for H in the hydride in the Ni-H/D system do not differ within the experimental accuracy. The density gNiH(E) of optical phonon states in NiH presented in Fig. 3 is derived from the experimental S(Q, E) spectrum of NiH measured in [6] and shown in Fig. 1. The method used is briefly described in [11]. Regretfully, this method is inapplicable to the S(Q, E) spectrum of NiD because of its contamination with scattering intensity from the H impurity. The density gNiD(E) of phonon states in NiD is calculated from gNiH(E) assuming that gNiD (E)= r Ñ gNiH(E Ñ r) and using r = 1.43.

0 0 100 200 300 400

E, meV
Fig. 1. The dynamical structure factors S(Q, E)of fcc NiD (open circles, present work, T = 10 K) and fcc NiH (thin solid curve [6], T = 5 K) as functions of the energy loss E of the inelastically scattered neutrons. The depicted spectrum of NiH [6] was measured for an angle w = 45À between the vector Q of neutron momentum transfer and the [1 0 0] axis of the (0 0 1)[1 0 0] texture of the bulk planar sample; this orientation made the spectrum virtually indistinguishable from the powder spectrum.

3.2. Isotope effect in the pressure of phase equilibrium The T-P phase diagrams shown in Fig. 4 gather together all available experimental data on the pressures of formation (solid symbols) and decomposition (open symbols) of nickel hydride [8,12-17] and deuteride [8,18,19]. The transition pressures determined in our works [14,19] are additionally corrected in accordance with our later, more accurate measurements of the mean


V.E. Antonov et al. / Journal of Alloys and Compounds 580 (2013) S109-S113

S111

0.08 g
-1
cal NiD

(E) = 1.43ÇgNiH(E Ç1.43)

0.06

0.04

gNiH(E)

0.02

0.00 50

60

70

80

90

100

110

120

130

E, meV
Fig. 3. Densities g(E) of phonon states for optical vibrations in NiH [6] (open circles R connected with a solid line) and NiD (solid line) normalized to give g ?EîdE = 1.

morphous phase transition from the hydrogen-poor c1 solid solution [20]. The equilibrium pressure of the c1 M c2 transformation is close to the pressure of the reverse c2 ? c1 transition of hydride decomposition (see [21] for discussion and explanation). At room temperature, the c2 ? c1 transition is accompanied by an abrupt decrease in the hydrogen solubility from an atomic H/Ni ratio of x % 1 to x 6 0.01 [20]. The compositions of the coexisting c1 and c2 phases get closer to each other with increasing temperature, and the line of the c1 M c2 equilibrium terminates in a critical point at 360 ÀC, 1.4 GPa and x % 0.5 [16,17]. The Curie temperature of the ferromagnetic c1 solutions decreases with hydrogen pressure due to the increase in the equilibrium hydrogen solubility [14]. The c2 phase is neither ferromagnetic, nor superconducting at temperatures down to 0.3 K [22]. The diagram of the Ni-D system is similar, only the critical point on the line of the c1 M c2 transformation is not yet located. Fig. 5 shows temperature dependences of the standard (at P0 = 0.1 MPa) Gibbs energies of the reactions Ni + ÍH2 ? NiH and Ni + ÍD2 ? NiD calculated using the equation

g(E ), meV

400

300

(a)

F 1



P 1

DG0 ?T î Ì NiH

Z
P

P

0

H eq

DVdP Ì
H eq

Z
P

P

0

H eq H eq

?V

NiH

ÐV

Ni

1 Ð V H2 îdP 2 ?1î

% ÐbH P

?

1 2

Z
P

P
0

V H2 dP

T, ÀC

200

Ni-H
100


0

P 2

[12] [13] [14] [15] [8] [16,17] [14]

300

(b)

F 1



P 1

T, ÀC

200

for the Ni-H system and a similar equation for the Ni-D system. In this equation, bH = VNiH - VNi % 1.25 cm3/mol % bD [23] is the difference between the molar volumes of NiH and Ni; V H2 ?T ; Pî is the molar volume of hydrogen and PH ?T î is the pressure of the c1 M c2 eq equilibrium, which we consider equal to the pressure of the c2 ? c1 transition. The molar volumes of H2 and D2 were calculated using equations of state from [24] at pressures above 1 MPa and the equation for ideal gases at 0.1 6 P 6 1 MPa. As seen from Fig. 5, the DG0 = DH0 - TDS0 dependences thus obtained are nearly linear in the studied temperature range. Such a linearity is typical of many metal-hydrogen systems (see, e.g., Ref. [25] discussing this phenomenon in the Pd-H system). The solid curves Peq(T) representing the c2 ? c1 transitions in Fig. 4a and b are obtained with the help of Eq. (1) from the straight lines DG0 ;fit ?T î and DG0 ;fit ?T î fitting the experimental DG0(T) NiH NiD

Ni-D
100
P 2
[18] [19] [8] [19]

T, ÀC
0 40 35
0 0.4 0.8 1.2 1.6 2.0
G H S
0 NiD 0

100
G
0 NiD 0 NiD

200

300

400

0



assuming D = 0

= H

0 NiD

- T Ç S

G0, kJ/g-atom H and D

P, GPa
Fig. 4. Experimental T-P phase diagrams of the Ni-H (a) and Ni-D (b) systems. The solid and open symbols show, respectively, the pressures of the c1 ? c2 transition (hydride formation) and c2 ? c1 transition (hydride decomposition). The open star stands for the critical point of the c1 M c2 transformation in the Ni-H system. The crosses indicate the transition temperatures of ferromagnetic cF solutions to the 1 paramagnetic cP state (the Curie points). The solid curves representing the c2 ? c1 1 transitions in Fig. 4a and b are obtained with the help of Eq. (1) from the straight lines fitted to the experimental DG0(T) dependences in Fig. 5. The diagram of the Ni-H system is also shown by thin lines in (b) for comparison with the Ni-D diagram.

30 25 20 15 10 5

NiD 0 NiD

= -6.59 kJ / g-atom D = -66.3 J / K / g-atom D

G H S

0 NiH 0

= H

0 NiH

- T Ç S

0 NiH

NiH 0 NiH

= -6.88 kJ / g-atom H = -62.9 J / K / g-atom H
500 600 700

temperature of the manganine pressure gauge positioned in the zone of strong temperature gradients near the steel obturator of the high-pressure chamber. At increasing H2 pressure, fcc nickel hydride (hydrogen-rich solid solution denoted as c2 phase in Fig. 4) is formed via an iso-

200

300

400

T, K
Fig. 5. Temperature dependences of the standard Gibbs energy DG0(T) for the reactions Ni + ÍH2 ? NiH and Ni + ÍD2 ? NiD calculated using Eq. (1). The symbols refer to the same experimental points as in Fig. 4.


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V.E. Antonov et al. / Journal of Alloys and Compounds 580 (2013) S109-S113

dependences in Fig. 5 and extrapolated down to -70 ÀC. We believe this extrapolation is trustworthy. The invariable values of the standard enthalpy, DH0, and entropy, DS0, resulting from the linear fits to the DG0(T) dependences in Fig. 5 are listed in Table 1. These values and also the values of DG0(298 K) are slightly different from previous estimates (see [8]) because of the term ÐbH P H taken into account in Eq. (1). eq Neglecting this term in the Ni-D system leads to the DG0(T) dependence shown in Fig. 5 by the dashed line. At temperatures below %100 ÀC, the hydrogen content of the c1 phase is very small and the composition of the c2 phase is close to NiH [17,19] therefore the DG0(T) dependences in Fig. 5 should describe the actual equilibrium in this temperature range. Using the gNiH(E) and gNiD(E) spectra allows establishing an interrelation between the lines of the Ni + ÍH2 M NiH and Ni + ÍD2 M NiD equilibria. If, e.g., the DG0 ;fit ?T î line in Fig. 5 is assumed to represent the NiD equilibrium between Ni and NiD, then the DG0 ?T î line can be calNiH culated. This is because the difference between the free energies of hydride and deuteride of a metal mostly results from the difference in the energies of optical vibrations, which can be written as

400


300 r = 1.43

1

600

500

T, ÀC

200


100 r = 1.51 0

2

400

300

0.0

0.4

0.8

1.2

1.6

2.0

200

P, GPa
Fig. 6. Temperature dependences of the decomposition pressures of c2 phases in the Ni-H and Ni-D systems. The experimental points fitted with the thin solid lines are taken from Fig. 4. The thick curves depict the dependences for the Ni-H system calculated from the experimental dependence for the Ni-D system using scaling factors of r = 1.43 and 1.51 (see Section 3.2).

G0 Ð G0 % 3NA kT NiH NiD Ðg
NiD

lnÍ1 Ð exp?ÐE=kT îÍg NiH ?Eî Z 3 ?EîdE ? NA EÍg NiH ?EîÐ g NiD ?EîdE; 2

Z

G0 Ð G0 % 3NA kT lnÍ?1 Ð exp?ÐEcg =kT îî=?1 NiH NiD H ? 2î 3 Ð exp?ÐEcg =kT îî ? NA ?Ecg Ð Ecg î: D H D 2 ?3î

where NA is the Avogadro number, k is the Boltzmann constant and R R g NiH ?EîdE Ì g NiD ?EîdE Ì 1. When this difference is known, the standard formation energy of NiH can be calculated as

DG0 ; NiH

calc

1 ?T î Ì DG0 ;fit ??G0 Ð G0 îÐ ?G0 2 Ð G0 2 î: NiD NiH NiD D 2H

Using Eq. (3) with the experimental value of Ecg = 96 meV and H the values of Ecg Ì Ecg =1:43 % 67 meV and Ecg =1:51 % 64 meV gives D H H temperature dependences of the NiH decomposition pressures coinciding within the line thickness with those calculated using Eq. (2) (thick lines in Fig. 6). 4. Conclusions An INS study of NiD has shown that the D atoms in NiD vibrate in virtually the same, approximately harmonic potential as the H atoms in NiH. A similar conclusion also follows from comparing the experimental and calculated differences in the decomposition pressures of NiD and NiH. This is a rather unexpected result because the Ni-H/D system is the closest analog of the Pd-H/D system and the force constants responsible for optical vibrations in PdH are significantly stronger than in PdD. Moreover, hydrides of some other d-metals of the VI-VIII groups are likely to have stronger force constants than the deuterides. In particular, a higher value of superconducting temperature for the compound with a heavier hydrogen isotope (the reverse isotope effect) was observed in hcp MoD (Tc = 1.11 K) and hcp MoH (Tc = 0.92 K) [27]. A higher Tc % 11 K of PdD compared to Tc % 9K of PdH is one of the most famous effects attributed to the difference in the force constants for optical vibrations in PdH and PdD [28,29]. By analogy, the reverse isotope effect in the Mo-H/D system could also be ascribed to the stronger force constants in MoH than in MoD. The reasons why the potential well for the H atoms in PdH is steeper than for the D atoms in PdD are not fully understood yet, and the effect for other metals cannot be predicted theoretically. We believe that inelastic neutron scattering will be most helpful in solving the problem. Acknowledgements This work was supported by Grant No. 11-02-00401 from the Russian Foundation for Basic Research and by the Program ``The Matter under High Energy Density'' of the Russian Academy of Sciences.

The difference G0 2 Ð G0 2 between the Gibbs energies of H2 and H D D2 gases at P0 = 0.1 MPa was calculated in [21] using tabulated data of [26] and proved to vary nearly linearly in a wide temperature interval of 200-1200 K:

G0 2 Ð G H

0 D2

% 7.4 + 0.01446ÑT [kJ/ mol H2 and D2]. Finally, the calculated values of DG0 ;calc ?T î should be NiH substituted in Eq. (1) to be resolved with respect to P H ?T î. eq If the above procedure is executed with gNiD(E) = 1.43ÑgNiH (EÑ1.43), this gives the P H ?T î dependence shown in Fig. 6 by the eq thick curve labeled `r = 1.43'. As one can see, the dependence thus calculated well represents the experimental curve of decomposition of the c2 phase in the Ni-H system at temperatures below $150 ÀC. As is also seen from Fig. 6, the calculated values of PH ?T î are very sensitive to the scaling factor r = EH/ED, and using eq gNiD(E) = 1.51ÑgNiH(EÑ1.51) leads to the P H ?T î dependence inconsiseq tent with experiment. Interestingly, the calculated difference between the decomposition pressures of NiH and NiD appears virtually insensitive to the shape of the gNiH(E) and gNiD(E) spectra. In fact, if we consider the extreme case of the Einstein model with gcg(E)= d(E - Ecg) narrowed to a d-function positioned at the center of gravity, Ecg, of the phonon density of states, then Eq. (2) reduces to

Table 1 Standard enthalpy DH0, entropy DS0 and Gibbs energy DG0(298 K) of formation of NiH and NiD resulting from linear fits to the DG0(T) dependences in Fig. 5. System Ni-H Ni-D

DH0 (kJ/mol Ni)
Ð6.9 Á 0.3 Ð6.6 Á 0.5

DS0 (J/K/mol Ni)
Ð62.9 Á 0.5 Ð66.3 Á 1.0

DG0(298 K) (kJ/mol Ni)
11.8 Á 0.3 13.2 Á 0.5

T, K


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