Hydrogen in nonstoichiometric cubic niobium carbides: Neutron vibrational spectroscopy and neutron diffraction studies

Journal of Alloys and Compounds 478 (2009) 68–74

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Hydrogen in nonstoichiometric cubic niobium carbides: Neutron vibrational spectroscopy and neutron diffraction studies A.V. Skripov a,∗ , H. Wu b,c , T.J. Udovic b , Q. Huang b , R. Hempelmann d , A.V. Soloninin a , A.A. Rempel e , A.I. Gusev e a

Institute of Metal Physics, Ural Division of the Russian Academy of Sciences, S. Kovalevskoi 18, Ekaterinburg 620041, Russia NIST Center for Neutron Research, National Institute of Standards and Technology, 100 Bureau Drive, Gaithersburg, MD 20899-6102, USA Department of Materials Science and Engineering, University of Maryland, College Park, MD 20742-2115, USA d Physikalische Chemie, Universität des Saarlandes, Im Stadtwald, Geb. B22, 66123 Saarbrücken, Germany e Institute of Solid State Chemistry, Ural Division of the Russian Academy of Sciences, Pervomaiskaya 91, Ekaterinburg 620041, Russia b c

a r t i c l e

i n f o

Article history: Received 14 November 2008 Received in revised form 5 December 2008 Accepted 11 December 2008 Available online 24 December 2008 PACS: 61.66.Fn 61.05.fm 78.70.Nx Keywords: Hydrogen absorbing materials Crystal structure Inelastic neutron scattering Neutron diffraction

a b s t r a c t The vibrational spectra and positions of H(D) atoms in NbC1−y Hx (Dx ) (0.19 ≤ y ≤ 0.29, 0.04 ≤ x ≤ 0.30) have been studied by inelastic neutron scattering (INS) and neutron diffraction. The analysis of the neutron diffraction data for NbC0.76 Hx (Dx ) and NbC0.71 Hx (Dx ) has revealed a number of different structures depending on the carbon concentration and the presence of absorbed H(D) atoms: the partially ordered cubic ¯ structure for NbC0.76 , the partially ordered orthorhombic Pmmm structure for NbC0.76 D0.17 and Pm3m ¯ structure for NbC0.71 and NbC0.71 D0.30 , and the disordered tetragNbC0.76 H0.18 , the disordered cubic Fm3m onal I4/mmm structure for NbC0.71 H0.28 . The INS spectra of NbC0.81 Hx and NbC0.76 Hx (Dx ) in the energy transfer range 40–140 meV are found to consist of a single fundamental peak due to hydrogen optical vibrations (centered at 98 meV for H and at 65 meV for D) and a single peak due to carbon optical vibrations (centered at 78 meV). In addition to these peaks, the INS spectrum of NbC0.71 H0.28 exhibits a peak at 130 meV, suggesting that H atoms in this compound occupy the sites displaced from the centers of carbon vacancies. © 2008 Elsevier B.V. All rights reserved.

1. Introduction Cubic transition-metal carbides MC1−y are known to retain their stability up to high concentrations y of structural vacancies in the carbon sublattice [1]. Nonstoichiometric carbides MC1−y having the NaCl-type structure can absorb hydrogen from a gas phase forming ternary compounds MC1−y Hx . In the cubic carbides of Ti and Zr, hydrogen atoms are found to occupy mainly the vacancies in the carbon sublattice (octahedral sites) [2–6]. Neutron diffraction experiments [4] have also shown that hydrogenation facilitates the ordering of carbon vacancies in some titanium carbides. The cubic niobium carbides NbC1−y are stable in the y range from 0 to 0.30; at higher y, the Nb carbides adopt a hexagonal structure. There is no direct information on the positions of hydrogen atoms in the cubic Nb carbides. In addition to the centers of the vacancies with octahedral coordination, off-center sites in the vacancies and tetrahedral interstitial sites in the Nb sublattice should be consid-

∗ Corresponding author. Tel.: +7 343 378 3781; fax: +7 343 374 5244. E-mail address: [email protected] (A.V. Skripov). 0925-8388/$ – see front matter © 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.jallcom.2008.12.012

ered. A possibility of off-center hydrogen sites is suggested by the large volume of the vacancies; this volume considerably exceeds that of the regular interstitial sites in metals. A possibility of occupation of the tetrahedral sites by H atoms is suggested by the report [7] that, in cubic NbC1−y Hx compounds, x can be greater than y. The structure of the cubic carbides with carbon vacancies and tetrahedral interstitial sites is shown in Fig. 1. A nuclear magnetic resonance (NMR) study of NbC1−y Hx (0.01 ≤ y ≤ 0.29) [8] has shown that the hydrogen mobility in this system strongly depends on the concentration of carbon vacancies. For the samples with y ≤ 0.24, no significant motional contributions to the proton spinlattice relaxation rate R1 have been found up to 420 K. On the other hand, for NbC0.71 H0.28 , the measured R1 (T) exhibits a frequencydependent peak near 300 K [8]. Such a peak is consistent with the fast H jump motion with the characteristic rate of about 109 s−1 at 300 K. The spatial aspects of this motion and the origin of the strong dependence of H mobility on the vacancy concentration remain to be elucidated. The aims of the present work are to study the vibrational spectra and the positions of H(D) atoms in the cubic NbC1−y carbides using inelastic neutron scattering (INS) and neutron diffraction.

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295 K is shown in Fig. 2(a). In addition to the peaks expected for ¯ a NaCl-type structure (space group Fm3m), this pattern exhibits superstructure peaks suggesting an ordering of vacancies. The appearance of the superstructure peaks with the Miller indices h, k, l corresponding to the conditions h + k = 2n, k + l = 2n, and l + h = 2n ¯ allows us to conclude that the appropriate space group is Pm3m.

Fig. 1. The structure of cubic metal carbides. Gray spheres: metal atoms; black spheres: carbon atoms; open squares: carbon vacancies (octahedral sites); open circles: tetrahedral interstitial sites; crosses: the displaced 4e sites.

The results of the structure refinement for NbC0.76 are shown in Table 1. For the carbon/vacancy sublattice, the ordering is of the Cu3 Au type with the ideal stoichiometry of 3:1. This type of ordering prevents the formation of nearest-neighbor vacancy–vacancy pairs. As can be seen from Table 1, the ordering is not complete for our NbC0.76 sample, and carbon atoms are present in both 3d and 1c ¯ structure was sublattices. It should be noted that the ordered Pm3m first reported in the early neutron diffraction study of NbC0.75 [15]. However, the existence of such an ordered phase of NbC0.75 was not confirmed by subsequent studies [1,16,17]. It is likely that the vacancy ordering in our sample of NbC0.76 is facilitated by hydrogen absorption. As noted in Section 2, the NbC0.76 sample used in our neutron scattering experiments was prepared by removing hydrogen from NbC0.76 H0.19 , i.e., it was the product of at least one hydrogenation-dehydrogenation cycle. Hydrogen-induced

2. Experimental details Nonstoichiometric carbides of niobium were prepared by solid-state sintering of Nb and acetylene black powders, as described in Refs. [1,9,10]. The resulting powdered NbC1−y samples were charged with hydrogen at a pressure of about 1 bar using a Sieverts-type vacuum system. After annealing the carbide in vacuum at 973 K, H2 gas was admitted into the system at this temperature. The amount of absorbed hydrogen was determined from the pressure change in the calibrated volume of the system after slowly cooling down to room temperature. For these hydrogenation conditions, we did not find any hydrogen absorption in NbC1−y samples with y < 0.19. In NbC1−y Hx samples with 0.19 ≤ y ≤ 0.29, the concentration of absorbed hydrogen increased with increasing y, and at the upper end of this range, it was nearly the same as the concentration of vacancies, i.e., x ≈ y. Three hydrogenated samples, NbC0.81 H0.04 , NbC0.76 H0.19 and NbC0.71 H0.28 , were chosen as the basic materials for neutron scattering studies. Subsequently, hydrogen was partially or fully removed from these samples by heating them in vacuum, and the samples were charged with deuterium or a D2 –H2 mixture. For some experiments, the light hydrogen isotope was again substituted for deuterium; the final H concentrations (as determined volumetrically) slightly differed from those in the initially hydrogenated compounds. It should be noted that the same three basic samples were used in all manipulations related to H(D) absorption and desorption. According to X-ray diffraction analysis, the NbC0.81 and NbC0.76 samples were single-phase compounds with the cubic NaCltype structure, and the NbC0.71 sample contained about 5 wt.% of the hexagonal Nb2 C phase, in addition to the dominant NaCl-type phase. Neutron diffraction measurements at low temperatures (4–7 K) and at room temperature were performed on the high-resolution powder diffractometer BT1 [11] at the NIST Center for Neutron Research (Gaithersburg, MD, USA). This diffractometer used the Cu (3 1 1) monochromator; the neutron wavelength  was 1.5402 Å. Neutron diffraction patterns were recorded in the scattering angle range 3◦ ≤ 2 ≤ 165◦ with a step of 0.05◦ . Profile refinements of the diffraction patterns were made by Rietveld analysis using the GSAS code as implemented in EXPGUI [12,13]. Inelastic neutron scattering measurements of the H(D) vibrational spectra were performed on the time-focusing crystal analyzer spectrometer TFXA at the ISIS spallation neutron source (Rutherford Appleton Laboratory, Didcot, UK) and on the filter-analyzer neutron spectrometer (FANS) [14] at the NIST Center for Neutron Research. The range of the neutron energy loss ω measured on the TFXA was from 2 meV to 500 meV, with a full-width-at-half-maximum energy resolution of about 2% of ω. Typical ranges of ω measured on the FANS were 40–160 meV and 40–120 meV for the vibrational spectra of H and D, respectively, with an energy resolution of about 4–5% of ω. Vertical error bars associated with all INS spectra in this paper correspond to one standard deviation.

3. Results and discussion 3.1. Neutron diffraction For the studied systems NbC0.76 –H(D) and NbC0.71 –H(D), we have not found any signs of phase transitions between low temperatures (4–7 K) and room temperature. Therefore, in the following we shall focus on discussion of the room-temperature neutron diffraction data. The neutron diffraction pattern for NbC0.76 at

Fig. 2. The observed (circles) and calculated (solid lines) neutron diffraction patterns for NbC0.76 (a), NbC0.76 D0.17 (b) and NbC0.76 H0.18 (c). The solid lines below the data show the difference between the observed and calculated diffraction patterns. Vertical bars indicate the calculated positions of Bragg peaks. Uncertainties, not shown, are commensurate with the indicated scatter.

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Table 1 Structural parameters resulting from profile refinements for NbC0.76 Hx (Dx ) at 295 K. Calculated standard deviations for the last digit of parameters are given in parentheses. Sample, space group and lattice parameters

Atom

Site

x

y

z

Biso (10−2 Å2 )

Occupancy

NbC0.76 ¯ Pm3m, Z=4

Nb1 Nb2 C1 C2

1a 3c 3d 1b

0 0 0.5 0.5

0 0.5 0 0.5

0 0.5 0 0.5

0.77 (3) 0.75 (1) 0.87 (3) 0.52 (1)

1 1 0.824 (4) 0.557 (6)

NbC0.76 D0.17 Pmmm, Z = 2 a = 3.13752 (6) Å b = 3.14293 (5) Å c = 4.44557 (9) Å V = 43.838 (1) Å3

Nb1 Nb2 C1 C2 D1

1c 1f 1a 1h 1h

0 0.5 0 0.5 0.5

0 0.5 0 0.5 0.5

0.5 0 0 0.5 0.5

0.68 (3) 0.68 (3) 0.73 (4) 0.24 (4) 5.1 (1)

1 1 0.785 (6) 0.678 (6) 0.322 (6)

NbC0.76 H0.18 Pmmm, Z = 2 a = 3.14111 (9) Å b = 3.14552 (6) Å c = 4.4479 (1) Å V = 43.929 (1) Å3

Nb1 Nb2 C1 C2 H1

1c 1f 1a 1h 1h

0 0.5 0 0.5 0.5

0 0.5 0 0.5 0.5

0.5 0 0 0.5 0.5

0.64 (2) 0.61 (2) 0.68 (3) 0.91 (4) 7.05 (2)

1 1 0.871 (4) 0.639 (6) 0.349 (8)

a = 4.44123 (2) Å V = 87.601 Å3

Rietveld agreement factors: NbC0.76 : Rwp = 0.0711, Rp = 0.0567, 2 = 2.117. NbC0.76 D0.17 : Rwp = 0.0604, Rp = 0.0515, 2 = 2.028. NbC0.76 H0.18 : Rwp = 0.0343, Rp = 0.0264, 2 = 1.997.

ordering has been observed for metal atoms in a number of alloys [18–21] and for carbon vacancies in the Ti carbohydride [4]. The neutron diffraction patterns for NbC0.76 D0.17 and NbC0.76 H0.18 at 295 K are shown in Figs. 2(b) and (c). Our attempts to refine the structure of these compounds using the same cubic ¯ Pm3m cell have failed; they result in unreasonable H(D) and C occupancies exceeding 1. Furthermore, the lattice expansion due to hydrogenation is found to be slightly anisotropic. This suggests that the symmetry of NbC0.76 D0.17 and NbC0.76 H0.18 is lower than cubic. The first choice is the tetragonal space group P4/mmm. However, the corresponding structure refinement yields very large values of the isotropic thermal factor (Biso ≈ 11 × 10−2 Å2 ) for H atoms in 1d sites. In order to solve this problem, we have considered two models: (1) The 1d site for H may be split into two equivalent 2h positions forming a pair along the c direction. This model preserves the P4/mmm space group and results in a reasonable Biso value. (2) The unit cell may be distorted further to orthorhombic symmetry (space group Pmmm). This model improves the agreement R-factors and also leads to a reasonable Biso value. For NbC0.76 H0.18 , it is difficult to make a definite choice between these two models. However, for the deuterided sample NbC0.76 D0.17 , the Pmmm model is definitely preferable. Therefore, the Pmmm cell has been used for the final structural refinement; the corresponding results for NbC0.76 D0.17 and NbC0.76 H0.18 are included in Table 1. It should be noted that we have tested the possibility of H atoms occupying vacancies in both C1 and C2 sublattices. However, the refinements for both models (1) and (2) always result in negative H site occupancies in the C1 sublattice. Thus, although the vacancy ordering in NbC0.76 is not complete, and vacancies are present in both carbon sublattices, hydrogen atoms occupy only vacancies in one of these sublattices (C2). The ordered structure of NbC0.76 H0.18 and NbC0.76 D0.17 includes the C1 and C2/H(D) planes alternating along the c direction. The neutron diffraction pattern for NbC0.71 at 295 K is shown in Fig. 3(a). In addition to the peaks expected for NaCl-type structure, this pattern exhibits the peaks belonging to a minor hexagonal Nb2 C phase (space group P63 /mmc) and a number of weak peaks due to an unidentified phase that does not correspond to any reported Nb–C binary system. In contrast to the case of NbC0.76 , no superstructure peaks have been found for NbC0.71 . Therefore, the crystallographic

parameters for the dominant phase of NbC0.71 have been refined ¯ using a NaCl-type structure (space group Fm3m) with disordered carbon vacancies. The results of the refinement are shown in Table 2. Hydrogenation of NbC0.71 does not lead to the appearance of any superstructure peaks in the neutron diffraction patterns (Figs. 3(b) and (c) for NbC0.71 D0.30 and NbC0.71 H0.28 , respectively). Since our neutron vibrational spectroscopy data for NbC0.71 H0.28 (see below) suggest that H atoms in this compound can occupy additional sites, the first step is to check for the occupancy of the tetrahedral inter¯ cell, stitials in the Nb sublattice (see Fig. 1). For the cubic Fm3m these are 8c (1/4, 1/4, 1/4) sites. However, the corresponding refinement always results in negative H occupancies of these sites. The Fourier difference analysis of the neutron diffraction data has not revealed any extra scattering density at 8c sites. Thus, we can conclude that H(D) atoms do not occupy the tetrahedral interstitial sites in NbC0.71 H0.28 and NbC0.71 D0.30 . For NbC0.71 D0.30 , the satisfactory ¯ cell structure refinement has been obtained for the cubic Fm3m with D atoms occupying the centers of carbon vacancies. The results of this refinement are included in Table 2; the fitted values of Biso and the D site occupancy appear to be reasonable. The refinement of ¯ model using anisotropic thermal factors for D atoms leads the Fm3m to nearly spherical thermal ellipsoids. We have also considered the possibility of a tetragonal distortion of the unit cell (the corresponding space group is I4/mmm). However, the I4/mmm model results in ¯ model. Therefore, we conslightly worse R-factors than the Fm3m ¯ model provides the best description of the clude that the Fm3m structure of NbC0.71 D0.30 . In order to describe the structure of NbC0.71 H0.28 , we have ¯ model. However, for this model the also started with the Fm3m refinement does not lead to a satisfactory convergence because of unreasonable Biso values for the H atoms. This suggests that the structure of NbC0.71 H0.28 is more distorted than that of NbC0.71 D0.30 . For the case of tetragonal distortion (space group I4/mmm) with H atoms occupying the centers of carbon vacancies, the refinement converges, but the resulting value of Biso for H atoms is still very large (∼32 × 10−2 Å2 ). The refinement using anisotropic thermal factors for H atoms leads to thermal ellipsoids that are strongly elongated in the c direction. Therefore, we have assumed that the 2b site for H (corresponding to the center of a carbon vacancy) is split into two equivalent 4e positions forming a pair along the c direction. This model preserves the I4/mmm space group and results in

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Table 2 Structural parameters resulting from profile refinements for NbC0.71 Hx (Dx ) at 295 K. Calculated standard deviations for the last digit of parameters are given in parentheses. Sample, space group and lattice parameters

Atom

Site

x

y

z

Biso (10−2 Å2 )

Occupancy

NbC0.71 ¯ Fm3m, Z=4

Nb1 C1

4a 4b

0 0.5

0 0.5

0 0.5

0.56 (4) 0.62 (3)

1 0.75 (1)

Nb1 C1 D1

4a 4b 4b

0 0.5 0.5

0 0.5 0.5

0 0.5 0.5

0.61 (5) 0.63 (8) 1.90 (5)

1 0.71 (4) 0.30 (4)

Nb1 C1 H1

2a 2b 4e

0 0 0

0 0 0

0 0.5 0.685 (1)

0.50 (3) 0.81 (4) 6.4 (1)

1 0.700 (5) 0.125 (2)

a = 4.43382 (5) Å V = 87.163 (3) Å3 NbC0.71 D0.30 ¯ Fm3m, Z=4 a = 4.44135 (5) Å V = 87.608 (3) Å3 NbC0.71 H0.28 I4/mmm, Z = 2 a = 3.1393 (1) Å c = 4.4377 (4) Å V = 43.734 (1) Å3

Rietveld agreement factors, the abundance and lattice parameters of the secondary phase: NbC0.71 : Rwp = 0.0757, Rp = 0.0564, 2 = 2.473; FNb2C = 7.1(3) wt.%, a = 3.1251(22) Å, c = 4.982(5) Å. NbC0.71 D0.30 : Rwp = 0.0763, Rp = 0.0595, 2 = 1.941; FNb2C = 5.0(3) wt.%, a = 3.1326(8) Å, c = 5.048(2) Å. NbC0.71 H0.28 : Rwp = 0.0479, Rp = 0.0388, 2 = 1.305; FNb2C = 7.3(3) wt.%, a = 3.1230(8) Å, c = 5.022(2) Å.

the improved R-factors and a reasonable Biso value. The results of the corresponding refinement are included in Table 2. The displaced 4e sites are also shown in Fig. 1. The distance between two 4e positions forming a pair is 1.644 Å; since this distance is shorter than the ‘blocking’ radius of ∼2.1 Å [22], each pair of sites can be populated by only one H atom at any given moment. It is likely that H atoms rapidly jump between the 4e sites forming a pair. The appearance of the displaced H sites in NbC0.71 H0.28 suggests an explanation of the fast H jump motion observed in this compound [8]. We also cannot exclude the possibility that some H atoms remain in the centers of carbon vacancies, while the rest are displaced. 3.2. Neutron vibrational spectroscopy

Fig. 3. The observed (circles) and calculated (solid lines) neutron diffraction patterns for NbC0.71 (a), NbC0.71 D0.30 (b) and NbC0.71 H0.28 (c). The solid lines below the data show the difference between the observed and calculated diffraction patterns. Vertical bars indicate the calculated positions of Bragg peaks for the main phase (top) and the minor Nb2 C phase (bottom). Uncertainties, not shown, are commensurate with the indicated scatter.

For metal–hydrogen systems, INS spectra in the energy transfer range 50–160 meV are usually dominated by the fundamental modes of H optical vibrations. The simplest description of these vibrations is based on the model of a three-dimensional Einstein oscillator [23,24]. For the cubic point symmetry of H sites, this model predicts a single peak in an INS spectrum in the ω range of the fundamental modes. For lower point symmetries of H sites, this peak should be split into either two peaks with the intensity ratio 2:1 (for axial symmetry) or three peaks of nearly equal intensity (for symmetries lower than axial). Thus, if H atoms occupy the centers of carbon vacancies (octahedral sites) in the cubic NbC1−y , we should expect a single peak in the range of the fundamental modes. The initial INS measurements performed on the TFXA revealed a bimodal vibrational spectrum of NbC0.76 H0.19 in the energy transfer range 70–110 meV (see Fig. 4). However, subsequent INS experiments for the deuterium-substituted and outgassed NbC0.76 samples have demonstrated that the bimodal INS spectrum of NbC0.76 H0.19 cannot be attributed to H sites of non-cubic symmetry. The results of these experiments performed on the FANS are summarized in Fig. 5. Since the ratio of masses of D and H is 2, in the harmonic approximation, √ the vibrational energies of D should be shifted by a factor of 1/ 2 (0.707) compared to those of H. Comparison of the measured INS spectra for NbC0.76 H0.19 and NbC0.76 D0.17 (Fig. 5) shows that, while the peak centered at ∼96 meV shifts to ∼65 meV (i.e., by a factor of 0.68), the peak centered at ∼78 meV retains its position. The INS spectrum for the mixed-isotope compound NbC0.76 (H0.1 D0.9 )0.15 consists of three peaks centered at ∼65 meV (as for NbC0.76 D0.17 ), ∼96 meV (as for NbC0.76 H0.19 ), and

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Fig. 4. The low-temperature INS spectrum for NbC0.76 H0.19 measured on the TFXA. Time-of-flight channels are binned in groups of 3.

∼78 meV (as for both NbC0.76 D0.17 and NbC0.76 H0.19 ). Furthermore, as can be seen from Fig. 5, the peak centered at ∼78 meV is also observed for the hydrogen-free NbC0.76 ; its shape is similar to that of the corresponding peak for NbC0.76 H0.19 and NbC0.76 D0.17 , but its intensity is considerably lower than in the H- or D-loaded compounds. These observations indicate that the peak centered at 78 meV originates from optical vibrations of carbon atoms. In the H- and D-loaded carbides, the intensity of this peak is somewhat enhanced due to H or D vibrational coupling to these carbon-type normal modes. The position of this peak remains nearly unchanged for the other studied cubic carbides NbC1−y (see below). The INS spectrum of the stoichiometric carbide NbC (not shown) exhibits a peak centered at ∼74 meV. Taking into account the neutron diffraction data, the peaks centered at 96 meV for the hydrogenated compounds and at 65 meV for the deuterated compounds can be attributed to optical vibrations of H or D atoms located in the centers of carbon vacancies. The slight orthorhombic distortion of NbC0.76 Hx (Dx ) does not lead to a splitting of these peaks. The neutron vibrational spectroscopy of isotope-diluted hydrides is known as an effective tool for investigating the presence and degree of H–H interactions [25,26]. If the width of a certain INS peak for a pure hydride is predominantly due to H–H interactions, the width of this peak for the corresponding mixed-isotope hydride with a low H/D ratio should be consid-

Fig. 5. The low-temperature INS spectra for NbC0.76 H0.19 , NbC0.76 D0.17 , NbC0.76 (H0.1 D0.9 )0.15 and NbC0.76 measured on the FANS. The lines through the points are only guides to the eye.

Fig. 6. The low-temperature INS spectra for NbC0.71 H0.28 , NbC0.76 H0.19 and NbC0.81 H0.04 measured on the FANS. The lines through the points are only guides to the eye.

erably smaller, since the difference in mass between H and D effectively inhibits the dynamic coupling between each H atom and the nearest-neighbor D atoms. Comparison of the measured INS spectra for NbC0.76 H0.19 and NbC0.76 (H0.1 D0.9 )0.15 (Fig. 5) shows that both the shape and the width of the peak centered at 96 meV are nearly the same for the two compounds. This indicates that the effects of H–H interactions on the shape of INS spectra in these systems are small, so that a description in terms of local H vibrations seems to be reasonable. The low-temperature INS spectra for NbC0.81 H0.04 , NbC0.76 H0.19 and NbC0.71 H0.28 are compared in Fig. 6. It can be seen that all these spectra exhibit the peaks centered at 78 meV (due to carbon vibrations) and at 96 meV (due to vibrations of H atoms in the centers of carbon vacancies). For NbC0.81 H0.04 , the intensity of the peak at 96 meV is smaller than that of the peak at 78 meV because of the low H content in this sample. The INS spectrum for NbC0.71 H0.28 shows an additional peak at ∼130 meV which is not observed for NbC0.81 H0.04 and NbC0.76 H0.19 . This peak cannot be attributed to any high-order (two-phonon) transitions; its appearance suggests the existence of an additional H site in NbC0.71 H0.28 , in agreement with our neutron diffraction results. The shape of the INS spectrum for NbC0.71 H0.28 supports the idea that a part of H atoms in this compound are located at sites displaced from the centers of carbon vacancies. The low-temperature INS spectrum for the deuterium-substituted NbC0.71 D0.30 is shown in Fig. 7. Comparing

Fig. 7. The low-temperature INS spectrum for NbC0.71 D0.30 measured on the FANS. The lines through the points are only guides to the eye.

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peak at 130 meV drops dramatically with increasing temperature, so that already at T = 300 K this peak is strongly smeared out (Fig. 9). These results suggest very large mean-square displacements of H atoms in the additional sites responsible for the peak at 130 meV. Included in Fig. 7 is also the low-temperature INS spectrum for NbC0.71 H0.045 ; this sample has been obtained from NbC0.71 H0.28 by partial extraction of hydrogen. It can be seen that the peak at 130 meV for NbC0.71 H0.045 nearly completely disappears. This indicates that the additional H sites are preferably depopulated in the course of hydrogen desorption. 4. Conclusions

Fig. 8. The evolution of the INS spectrum for NbC0.76 H0.19 with the temperature. The lines through the points are only guides to the eye.

this spectrum with that for NbC0.71 H0.28 (Fig. 6), we see that the peak at 78 meV retains its position (as expected for the peak due to carbon vibrations), while the peak at 64 meV for D is shifted in energy by a factor of 0.67 with respect to the corresponding peak (96 meV) for H. Since the small peak at 125 meV is observed at the nearly doubled energy of the 64 meV peak, it is likely to represent the second-order transition. The obscure feature centered at ∼98 meV in the spectrum for NbC0.71 D0.30 can be ascribed to the D counterpart of the 130 meV peak for NbC0.71 H0.28 . It should be noted, however, that the relative intensity of this peak for D is considerably lower than that of the corresponding peak for H. These results are consistent with the effect of H ↔ D substitution on the structure of NbC0.71 Hx (Dx ), as revealed by our neutron diffraction measurements (see above). The evolution of INS spectra for NbC0.76 H0.19 and NbC0.71 H0.28 with temperature is shown in Figs. 8 and 9, respectively. In order to visualize the relative changes in peak intensities, the spectra are normalized to make the intensity of the peak at 78 meV nearly the same at all the temperatures studied. As can be seen from Fig. 8, the relative intensity of the peak at 96 meV for NbC0.76 H0.19 decreases considerably with increasing temperature. This is the natural consequence of the larger mean-square displacements for H vibrations corresponding to the peak at 96 meV. For NbC0.71 H0.28 , the relative changes in the intensity of the peak at 96 meV (Fig. 9) are nearly the same as in the case of NbC0.76 H0.19 . However, the intensity of the

The analysis of our neutron diffraction data for NbC0.76 Hx (Dx ) and NbC0.71 Hx (Dx ) has revealed a number of different structures depending on the carbon concentration and the presence of absorbed H(D) atoms. A partial ordering of carbon vacancies lead¯ structure has been found for NbC0.76 ; the ing to the cubic Pm3m ideal stoichiometry of this phase corresponds to NbC0.75 . Hydrogen absorption preserves the partially ordered state of carbon vacancies and results in the orthorhombic Pmmm structure of NbC0.76 H0.18 and NbC0.76 D0.17 where H(D) atoms occupy the vacancies in only one of the two carbon sublattices. In contrast to the case of NbC0.76 , we have not found any signs of ordering of carbon vacancies in NbC0.71 . Thus, NbC0.71 adopts the basic NaCl-type structure (space ¯ group Fm3m) with a disordered arrangement of carbon vacancies. The neutron diffraction pattern for the deuterated NbC0.71 D0.30 can ¯ structure with D atoms be described in terms of the same Fm3m occupying the centers of carbon vacancies. However, the isotopesubstituted compound NbC0.71 H0.28 appears to adopt the tetragonal I4/mmm structure where H atoms occupy the displaced 4e sites forming pairs along the c direction. Such a location of H atoms in NbC0.71 H0.28 is consistent with the inelastic neutron scattering results of the present work and with NMR data [8] indicating an enhanced H mobility in this compound. The inelastic neutron scattering spectra of NbC0.81 Hx and NbC0.76 Hx (Dx ) in the energy transfer range 40–140 meV exhibit a single fundamental peak due to optical hydrogen vibrations (centered at 96 meV for H and at 65 meV for D) and a single peak due to optical carbon vibrations (centered at 78 meV). In addition to these peaks, the high-intensity peak centered at 130 meV has been found in the low-temperature INS spectrum of NbC0.71 H0.28 . In agreement with our neutron diffraction results, this suggests that H atoms in NbC0.71 H0.28 occupy the sites displaced from the centers of carbon vacancies. The temperature dependence of the INS spectrum for this compound is consistent with very large mean-square displacements for H vibrations in the additional sites. Acknowledgements The authors are grateful to S.F. Parker for help with the TFXA measurements. This work was supported by the NATO Linkage Grant No. HTECH.LG 973890, the Russian Foundation for Basic Research (Grants No. 06-02-16246 and 09-03-00010) and the Priority Program “Basic energy problems” of the Russian Academy of Sciences. A.V. Skripov also acknowledges financial support from the NIST Center for Neutron Research and Universität des Saarlandes (Saarbrücken). References

Fig. 9. The evolution of the INS spectrum for NbC0.71 H0.28 with the temperature and the low-temperature INS spectra for NbC0.71 H0.045 and NbC0.71 . The lines through the points are only guides to the eye.

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