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PHYSICAL REVIEW B 73, 054107 2006

Crystal structure and lattice dynamics of high-pressure scandium trihydride
V. E. Antonov, I. O. Bashkin, V. K. Fedotov, and S. S. Khasanov
Institute of Solid State Physics RAS, 142432 Chernogolovka, Moscow District, Russia

T. Hansen and A. S. Ivanov
Institut Laue-Langevin, BP 156, 38042 Grenoble Cedex 9, France

A. I. Kolesnikov
Intense Pulsed Neutron Source Division, Argonne National Laboratory, Argonne, Illinois 60439, USA

I. Natkaniec
Frank Laboratory of Neutron Physics, Joint Institute for Nuclear Research, 141980 Dubna, Moscow District, Russia and H. Niewodniczanski Institute of Nuclear Physics PAS, 31-342 Krakow, Poland Received 8 July 2005; revised manuscript received 6 January 2006; published 21 February 2006 Powder samples of hcp ScH2.9 and ScD2.9 have been synthesized under a 1 GPa pressure of gaseous hydrogen or deuterium and studied at ambient pressure and 95 K by neutron diffraction. A profile analysis of the diffraction patterns indicated a crystal structure with P63 / mmc symmetry that differs from the structures of hcp trihydrides of yttrium and rare-earth metals by the absence of long-range order in the displacements of hydrogen atoms from high-symmetry positions. The lattice dynamics of scandium trihydride and, for comparison, yttrium trihydride were studied by inelastic neutron scattering at 20 K in the range of energy transfers 4 ­ 250 meV. The spectra of optical H vibrations in these two trihydrides proved to be similar, suggesting similar arrangements of hydrogen atoms on a short-range scale. DOI: 10.1103/PhysRevB.73.054107 PACS number s : 61.12. q, 78.70.Nx, 63.20.Dj

I. INTRODUCTION

Scandium is the lightest element of the group III transition metals. Similar to other group III metals--yttrium, lanthanum and most rare earths--scandium forms a fcc dihydride with a fluorite-type crystal structure at hydrogen pressures well below 1 atm.1 However, while trihydrides of other metals can also be formed at low hydrogen pressures, the synthesis of scandium trihydride requires pressures greater than 0.3 GPa.2,3 Samples of the high-pressure scandium trihydride are thermally unstable at ambient conditions. A room-temperature x-ray diffraction investigation of a partly decomposed sample showed it to be a mixture of fcc scandium dihydride with a = 4.874 å and hcp trihydride with a = 3.380 å, b = 6.135 å, c / a = 1.815.2 The lattice parameters of scandium trihydride are significantly smaller and its c / a ratio is larger than those of hcp trihydrides of other group III metals. Nonetheless, the values of the atomic volume of scandium trihydride and other trihydrides form a single smooth dependence if plotted as a function of the ionic radius of the metal.2 This suggests that all these trihydrides belong to the same family and, in particular, the coordination of H atoms in their hcp metal lattices is similar. The rather complex hydrogen sublattices and hydrogen vibrational spectra of hcp trihydrides of some rare-earth metals and yttrium were studied earlier by neutron scattering techniques see Refs. 4 ­ 6, and references therein . In the present paper, we studied the crystal structures of scandium trihydride and trideuteride by powder neutron diffraction and measured the H vibrational spectra of scandium trihydride and yttrium trihydride by inelastic neutron scattering INS .
1098-0121/2006/73 5 /054107 6 /$23.00

The INS spectrum of yttrium trihydride was measured mostly for comparison. In addition, this new spectrum involved the interval 4 ­ 35 meV of the low-energy "lattice" modes never examined earlier for YH3.
II. SAMPLE PREPARATION AND EXPERIMENTAL DETAILS

Bulk ingots of 99.8 wt% pure Sc and 99.9 wt% Y were used as starting materials. Scandium dihydride and dideuteride and yttrium trihydride were synthesized by gas-phase absorption in a Sieverts-type apparatus using hydrogen or deuterium produced by thermal decomposition of TiH2 or TiD2, respectively. The composition of the yttrium trihydride thus prepared was determined from the H2 uptake and proved to be close to YH3 in agreement with Ref. 4. A roomtemperature x-ray diffraction examination SIEMENS D-500 diffractometer, monochromated Cu K 1 radiation showed that the YH3 sample was a single-phase hcp compound with the lattice parameters a = 3.6712 5 å, c = 6.6068 8 å, c / a = 1.7996 4 . The scandium dihydride and dideuteride were powdered in an agate mortar and additionally loaded with hydrogen and deuterium, respectively, at a pressure of 1 GPa and a temperature of 250 ° C for 24 h. The hydrogenation technique is described elsewhere.7 The synthesized samples of scandium trihydride and trideuteride were then rapidly cooled under pressure to 150 K, the pressure was released, and the samples were removed from the high-pressure cell, and when not in use, stored in liquid nitrogen to prevent hydrogen/deuterium loss.
©2006 The American Physical Society

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Powdered samples of scandium trihydride and trideuteride, each weighing 1.2 g, were studied by neutron diffraction at 95 K with the D1B diffractometer at ILL, Grenoble, using neutrons with wavelengths of = 2.53 and 1.286 å. The diffractometer was equipped with a position-sensitive detector, covering 80° in 2 with 400 cells of 0.2° width. The sample was placed in a cylindrical, thin-walled vanadium can. The background was determined in a separate empty-can measurement and subtracted from the measured diffraction patterns. The resulting neutron spectra were analyzed using the Rietveld profile refinement technique implemented in the DBWS-9411 computer program.8 The same 1.2 g sample of scandium trihydride and a 7 g sample of powdered yttrium trihydride were investigated by INS at 20 K in the range of neutron energy transfers 4 ­175 and 4 ­ 300 meV, respectively, using the NERA-PR multicrystal inverted geometry time-of-flight neutron spectrometer at JINR, Dubna. The sample of scandium trihydride was additionally studied by INS at 10 K in the range of energy transfers 25 ­ 250 meV using the IN1-BeF neutron spectrometer installed at the hot source of the high-flux reactor at ILL, Grenoble. In the case of the IN1-BeF spectrometer, the energy lost by the neutrons was calculated by subtracting 3.5 meV, the mean energy of neutrons transmitted through the cooled Be filter, from the incident neutron energy. With both spectrometers, the background spectrum from an empty flat sample holder made of thin aluminium foil was measured separately and then subtracted from the raw INS spectrum of the sample.
III. RESULTS AND DISCUSSION A. Neutron diffraction

FIG. 1. Color online Neutron powder diffraction patterns of ScH2.9 and ScD2.9 measured at 95 K with the D1B diffractometer at ILL, Grenoble, using neutrons with a wavelength of = 1.286 å symbols and the profile fits calculated with the structure parameters listed in Table I solid lines and the differences between the experimental and calculated spectra two curves at the bottom . The upper row of vertical bars labeled P63 / mmc shows the positions of diffraction lines calculated for ScD2.9. The lower row of bars labeled P¯ c1 shows the positions of superstructure lines, which 3 would be observed in addition to the P63 / mmc lines the upper row if the structure of ScD2.9 were of the HoH3 type.

According to earlier neutron diffraction investigations see Ref. 1, and references therein , hcp trihydrides of rare earths are isostructural with HoH3. The unit cell of HoH3, 3 R30° expansion of the hcp space group P¯ c1, is a 3 3 unit cell in the basal plane.9 Two-thirds of the H atoms occupy distorted tetrahedral t sites. The remaining one-third of the H atoms occupy trigonal-like sites in or near the metal basal planes, referred to as m sites. The m sites can be considered as resulting from the vertical displacement of octahedral sites toward the metal-defined basal planes. Powder neutron diffraction studies showed10­12 that yttrium trihydride also has a P¯ c1 structure of the HoH3 type. 3 On the other hand, recent ab initio calculations13­15 demonstrated that significant features of the electronic band structure13 and the vibrational spectrum14,15 of YH3 cannot be explained if its structural symmetry is P¯ c1. Instead, two 3 other structures, P63 cm and P63, were proposed.14,15 These new "broken symmetry" structures allow a better explanation of the results of INS4,6 and also of nuclear magnetic resonance NMR ,16,17 Raman and IR18,19 studies of YH3. All three structures proposed for yttrium trihydride are characterized by correlated placements of Ht and Hm atoms leading to the threefold increase in the parent hcp unit cell. Neutron diffraction patterns of scandium trihydride and trideuteride are presented in Figs. 1 and 2. The patterns look

similar to those of other trihydrides except that they show no signs of long-range hydrogen ordering. As one can see, these patterns mostly consist of lines of the structure with the same P63 / mmc symmetry and the same lattice parameters as the hcp metal lattice of the scandium trihydride or trideuteride. There are also seen a few weak lines from an admixture of Sc2O3 oxide space group Ia3, a = 9.8672 å, the line in Fig.

FIG. 2. Color online Neutron powder diffraction patterns of ScH2.9 and ScD2.9 measured at 95 K with the D1B diffractometer at ILL, Grenoble, using neutrons with a wavelength of = 2.53 å symbols and the profile fits calculated with the structure parameters listed in Table I solid lines . Two rows of vertical bars show the line positions in the diffraction spectra calculated for ScD2.9 with the P63 / mmc structure and the hypothetical P¯ c1 structure of 3 the HoH3 type. The dashed curve shows the calculated profile of superstructure lines of the HoH3-type structure.

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TABLE I. Positional parameters X , Y , Z , thermal factors B and site occupancies for scandium trihydride and trideuteride according to a Rietveld profile refinement of the neutron diffraction data collected at 95 K with the D1B diffractometer at ILL, Grenoble. R p and Rex are the obtained and expected profile factors. Hexagonal structure, space group P63 / mmc No. 194 . Phase ScHx, x = 2.90 2 a = 3.373 1 å, c c / a = 1.815 1 ; R ScDx, x = 2.87 2 a = 3.361 1 å, c c / a = 1.815 1 ; R Atom Sc Ht Hm Sc Dt Dm Site 2 4 4 2 4 4 c f e c f e X 1 1 0 1 1 0 /3 /3 /3 /3 Y 2 2 0 2 2 0 /3 /3 /3 /3 Z 1/4 -0.088 0.210 1/4 -0.088 0.210 Bå 0.46 2.40 1.50 0.46 2.10 1.40
2

= 6.121 1 å p / Rex = 4.5 / 4.1 = 6.101 1 å p / Rex = 6.7 / 4.6

1.00 0.97 0.48 1.00 0.97 0.465

2 is marked with an asterisk and from an unidentified phase presumably, hydroxide; its line in Fig. 2 is marked with two asterisks . However, any "superstructure" lines resulting 3 from ordering of Hm atoms in the P¯ c1, P63 cm or P63 structure are missing. To illustrate the absence of additional lines 3 due to the HoH3-type P¯ c1 structure, hypothetical positions of these lines in the diffraction pattern of scandium trideuteride are indicated in Fig. 1 by the row of vertical bars labeled P¯ c1 , and hypothetical profiles of the two most 3 intense superstructure lines 202 and 211 are shown in Fig. 2 by the dashed curve. Profile analysis of the neutron diffraction patterns of scandium trihydride and trideuteride constrained to the P63 / mmc symmetry produced results presented in Tables I and II. The quality of the refinement is illustrated by the difference spectra at the bottom of Fig. 1. The resulting unit cell is schematically shown in Fig. 3. As seen from Table I, the profile refinement yields the compositions of the samples close to ScH2.9 and ScD2.9. The ScH2.9 composition agrees with the earlier estimate H / Sc 2.8 for samples of scandium trihydride synthesized under similar conditions.2 The structures of ScH2.9 and ScD2.9 are identical. The vertical displacements z = 0.210 · c 1.3 å of hydrogen m sites from the ideal octahedral positions 0,0,0 are of the same order of magnitude as in HoH3, but in contrast to the case of HoH3 these displacements are all equal. As a result, the m sites form dumbbells centered at the Sc-defined basal planes and oriented along the c axis. Because of the small distance 2 =2· 1/4- 0.210 · = 0.08 · c 0.5 å between the sites in a dumbbell, these positions cannot be occupied by hydrogen simultaneously due to the "blocking effect"20 requiring that the distance between hydrogen atoms in a metal should not be significantly less than 2 å. Only a half of the m sites are therefore accessible for hydrogen atoms. The occupancies = 0.48 and 0.465 of m sites in ScH2.9 and ScD2.9 Table I, the last column agree with this constraint and suggest a random distribution of H or D atoms over these sites in accordance with the P63 / mmc symmetry of the structure.
TABLE II. Interatomic distances in ScH Sc-H
t 2.9

The Ht atoms are displaced along the c axis from the ideal 1 positions with Zid =- 3 a / c 2 -0.101 away from the basal planes. The displacement z = Z - Zid · c -0.088 + 0.101 · 0.013 · c 0.08 å leads to the increase in the distance between the nearest Ht atoms from 1.82 to 1.98 å and between the nearest Hm and Ht atoms from 2.04 to 2.09 å. These distances exceed the blocking value of about 2 å and hydrogen can therefore occupy every Ht site regardless of the occupancy of the nearest Hm site, which is, in fact, observed t 1, see Table I . Assuming the P63 / mmc symmetry of the structure of scandium trihydride, the profile analysis thus gives a noncontradictory interpretation of the neutron diffraction data. However, the B factors for hydrogen atoms and especially those for t-hydrogen atoms see Table I are too large to be of purely dynamic origin. This suggests the occurrence of significant static displacements of hydrogen atoms away from the calculated positions.
B. Inelastic neutron scattering

Figure 4 shows the INS spectra S Q , of the ScH2.9 powder. The sample was first measured for two days with the

in angstroms .
m

Sc-H

m

Ht-H

t

Ht-H

Hm-H 2.57

m

2.185; 2.069

1.961

1.983

2.09

FIG. 3. Color online The hexagonal unit cell of scandium trihydride, space group P63 / mmc. The arrows show the vertical displacements of hydrogen atoms from the ideal tetrahedral positions solid circles and from the ideal octahedral positions crosses .

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FIG. 4. Color online The dynamical structure factor S Q , of ScH2.9 powder as a function of the energy loss q of the inelastically scattered neutrons. The horizontal bars show the energy resolution, respectively, of the two neutron spectrometers used, NERA-PR JINR, Dubna and IN1-BeF ILL, Grenoble . The lower thin solid line labeled "MPNS" presents the estimated multiphonon neutron scattering contribution.

FIG. 5. Color online The dynamical structure factor S Q , of ScH2.9 and YH3 powders as a function of the energy loss q of the inelastically scattered neutrons. The horizontal bars show the energy resolution. The lower thin solid line presents the estimated multiphonon contribution.

high-resolution NERA-PR spectrometer at T = 20 K in the range of neutron energy transfers starting from 4 meV. However, the mass 1.2 g of the sample was insufficient to get a spectrum with good statistics at neutron energies exceeding 100 meV, and the same ScH2.9 sample was additionally measured for 4 h with the high-luminosity IN1-BeF spectrometer at T = 10 K in the energy range 25 ­ 300 meV. As seen from Fig. 4, the two spectra agree with each other. The spectrum measured with the NERA-PR spectrometer is preferable at energies below 80 meV due to its better resolution, whereas the spectrum measured with IN1-BeF is more reliable at energies above 80 meV because of the better statistical accuracy. The vertical bars in the upper part of Fig. 4 indicate positions of the scattering maxima with due regard to this preference. Figure 5 shows the INS spectrum S Q , of a 7 g powder sample of YH3 measured for one day with the NERA-PR spectrometer. This spectrum includes the ranges of lattice 30 meV and optical H vibrations modes 40 meV . The optical part of the spectrum coincides well with the spectrum of YH3 from Ref. 4 measured at 35 meV. As seen from the inset to Fig. 5, the low-energy part of the vibrational spectrum of YH3, which is mainly determined by vibrations of the Y atoms, extends up to about 29 meV and shows features at 14.8, 16.8, 19.5, 22.8, and 25.8 meV. The low-energy part of the INS spectrum of ScH2.9 stretches to approximately 41 meV and demonstrates a more complex intensity distribution with peaks at 15.5, 18.3, 21.0, 23.8, 27.0, 30.0 and 36.0 meV. The ratio 41 / 30 1.41 of the highenergy cutoffs of the lattice modes in YH3 and ScH2.9 is close to the mass ratio mY / mSc 1.41, which points to nearly the same values of the Sc-Sc and Y-Y force constants in these trihydrides. As one can see from Fig. 5, the INS spectra of ScH2.9 and 40 meV of optical H viYH3 are similar in the range

brations. Most peaks in the spectrum of ScH2.9 are just shifted to higher energies due to the shorter hydrogen-metal distances and correspondingly stronger hydrogen-metal bonding. Discussing the optical vibrations in hydrides, however, it is usually more convenient to consider one-phonon INS spectra because they better reproduce the phonon density of states. The one-phonon spectra of ScH2.9 and YH3 are shown in Fig. 6. These spectra are obtained from the experimental INS spectra by subtracting the contributions from the multiphonon neutron scattering lower thin solid lines in Figs. 4 and 5, respectively estimated in a harmonic isotropic approximation using the iterative technique of Ref. 21. As seen from Fig. 6, the one-phonon spectrum of ScH2.9 reproduces every main feature of the YH3 spectrum in the range of the fundamental optical band from about 40 to 180 meV except the interval 60 ­ 75 meV, where the spectrum of ScH2.9 clearly shows additional intensity. Nevertheless, this difference can also be considered insignificant because of the anomalously high sensitivity of the optical H spectra of trihydrides to small changes in the arrangement of H atoms. By way of illustration, Fig. 7 shows the spectra for 3 YH3 calculated in Ref. 15 assuming the P¯ c1, P63cm and P63 structure. These structures differ in the magnitudes and directions of displacements of H atoms from symmetrical positions in the hcp metal lattice. The differences are small and the three structures can only be distinguished from each other in very sophisticated neutron diffraction experiments using specially prepared, nearly single-crystalline samples.6 Meanwhile, as seen from Fig. 7, the calculated optical H spectra of these very similar structures differ drastically. The difference between the INS spectra of ScH2.9 and YH3 at energies from 60 to 75 meV Figs. 5 and 6 is much smaller than the variation of the calculated vibrational intensity of YH3 in this energy interval and adjacent regions caused by subtle changes in the arrangement of H atoms in the P¯ c1, P63cm and P63 structures Fig. 7 . One could 3 therefore expect that the difference in the arrangements of H

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FIG. 6. Color online One-phonon spectra of ScH2.9 and YH3 obtained from the experimental INS spectra by subtracting the contributions from the multiphonon neutron scattering shown in Figs. 4 and 5, respectively, by the lower thin solid lines.

FIG. 7. Color online One-phonon INS spectrum of YH3 present paper and total phonon densities of states calculated for 3 YH3 in the P¯ c1, P63cm and P63 structure Ref. 15 .

atoms in ScH2.9 and YH3 is even less than in those three virtually indistinguishable crystal structures proposed for YH3. This implies, in particular, that the displacements of Hm atoms from the basal metal planes in ScH2.9 are not all equal and should be correlated as in YH3. At the same time, inasmuch as inelastic neutron scattering is mostly sensitive to the local environment of the scattering atom, these correlations in ScH2.9 may show no long-range order. The occurrence of large hydrogen displacements, either chaotic or correlated on a short-range scale, is consistent with our neutron diffraction results and explains the large values of B factors for hydrogen atoms Table I . One can speculate that the local symmetry of hydrogen arrangements in other hcp trihydrides is also lower than the long-range symmetry determined by such methods as neutron diffraction. This would explain, for example, why the "local" properties of YH3 measured by NMR,16,17 INS,4,6 Raman and IR18,19 spectroscopy are better described with the P63cm or P63 structure14,15 than with the higher symmetry P¯ c1 structure established10­12 by powder neutron diffrac3 tion. The occurrence of large hydrogen displacements correlated in a similar manner in all hcp trihydrides of the group III metals also explains why the spectrum of optical H vibrations in lutetium trihydride is similar to those in other rareearth trihydrides, while the crystal structure of LuH3 is more

symmetrical according to the neutron diffraction data LuH3 was studied by INS4 and LuD3 was studied by powder neutron diffraction4 and NMR22 . Interestingly, the structure of LuH3 is similar to the P63 / mmc structure of scandium trihydride and the presence of minor diffraction features only points to a more complex arrangement of hydrogen atoms.22 Lutetium trihydride has smaller lattice parameters than hcp trihydrides of other rare-earth metals and yttrium, and the parameters of scandium trihydride are smaller than those of lutetium trihydride. Therefore, there seems to be a tendency towards the increase in the long-range symmetry of the crystal structure of hcp trihydrides of the group III metals with decreasing atomic volume. The spectrum of H vibrations is likely to vary monotonically, too. In particular, the additional scattering intensity in the range 60 ­ 75 meV that makes the INS spectrum of ScH2.9 slightly different from that of YH3 see Figs. 5 and 6 is also observed only in the spectrum of LuH3. The similarity between the spectra of optical H vibrations in ScH2.9 and YH3 makes it possible to assign some portions of the ScH2.9 spectrum to certain modes of H vibrations using the phonon density of states14,15 calculated for YH3. Namely, the Hm vibrations polarized along the c axis have frequencies between 45 and 110 meV, whereas the abpolarized vibrations of Hm atoms have frequencies around 170 meV. The frequencies of the ab-polarized vibrations of Ht atoms lie in the interval 75 ­ 140 meV and those of the c-polarized vibrations in the interval 140 ­ 170 meV.

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PHYSICAL REVIEW B 73, 054107 2006

The INS investigation has shown that the spectrum of hydrogen vibrations in ScH2.9 is rather complex and its optical part has much in common with the spectra of hcp trihydrides of other group III metals, yttrium and rare earths. This suggests that the local environments of H atoms in ScH2.9 are similar to those in other hcp trihydrides characterized by large and correlated displacements of H atoms from symmetrical positions. At the same time, the neutron diffraction investigation of ScH2.9 and ScD2.9 revealed no long-range order in the H or D displacements and demonstrated that the crystal structure of scandium trihydride has a higher symmetry, P63 / mmc, than the structures of other hcp trihydrides. Inasmuch as INS is mostly sensitive to the local environment of the light atom,

the results of the neutron diffraction and INS investigation of scandium trihydride can be reconciled by assuming that hydrogen displacements characteristic of other trihydrides do occur in this compound, but they are not correlated on a long-range scale. This assumption also explains the large values of the Debye­Waller factors obtained for hydrogen atoms in scandium trihydride while modelling the neutron diffraction data with the P63 / mmc structure.
ACKNOWLEDGMENTS

This work was supported by Grant Nos. 01-02-16503 and 04-02-17269 from the Russian Foundation for Basic Research and by the Joint Project "Hydrogen Energy" of the Russian Academy of Sciences and MMC Norilsk Nickel.

1

2 3 4

5

6

7

8

9

10

P. Vajda, in Handbook on the Physics and Chemistry of Rare Earths, edited by K. A. Gschneider, Jr. and L. Eyring Elsevier, Amsterdam, 1995 , Vol. 20, Chap. 137, p. 207. I. O. Bashkin, E. G. Ponyatovskii, and M. E. Kost, Phys. Status Solidi B 87, 369 1978 . I. O. Bashkin, E. G. Ponyatovskii, and M. E. Kost, Izv. Akad. Nauk SSSR, Neorg. Mater. 14, 1615 1978 in Russian . T. J. Udovic, Q. Huang, and J. J. Rush, in: Hydrogen in Semiconductors and Metals, edited by N. N. Nickel, W. B. Jackson, R. C. Browman, and R. G. Leisure, MRS Symposia Proceedings No. 513 Materials Research Society, Pittsburgh, 1998 , p. 197. T. J. Udovic, J. J. Rush, Q. Huang, and I. S. Anderson, J. Alloys Compd. 253, 241 1997 . T. J. Udovic, Q. Huang, R. W. Erwin, B. HjÆrvarsson, and R. C. C. Ward, Phys. Rev. B 61, 12701 2000 . V. E. Antonov, I. O. Bashkin, S. S. Khasanov, A. P. Moravsky, Yu. G. Morozov, Yu. M. Shulga, Yu. A. Ossipyan, and E. G. Ponyatovsky, J. Alloys Compd. 330­332, 365 2002 . R. A. Young, A. Sakthivel, T. S. Moss, and C. O. Paiva-Santos, DBWS9411 User 's Guide Georgia Institute of Technology, Atlanta, 1995 . M. Mannsmann and W. E. Wallace, J. Phys. Paris 25, 454 1964 . N. F. Miron, V. I. Shcherbak, V. N. Bykov, and V. A. Levdik, Kristallografiya 17, 404 1972 Sov. Phys. Crystallogr. 17, 342 1972 .

11 12 13 14 15 16

17

18

19

20

21

22

T. J. Udovic, Q. Huang, and J. J. Rush, J. Phys. Chem. Solids 57, 423 1996 . T. J. Udovic, Q. Huang, J. W. Lynn, R. W. Erwin, and J. J. Rush, Phys. Rev. B 59, 11852 1999 . P. J. Kelly, J. P. Dekker, and R. Stumpf, Phys. Rev. Lett. 78, 1315 1997 . P. van Gelderen, P. J. Kelly, and G. Brocks, Phys. Rev. B 63, 100301 R 2001 . P. van Gelderen, P. J. Kelly, and G. Brocks, Phys. Rev. B 68, 094302 2003 . J. J. Balbach, M. S. Conradi, M. M. Hoffmann, T. J. Udovic, and N. L. Adolphi, Phys. Rev. B 58, 14823 1998 . O. J. Zogal, W. Wolf, P. Herzig, A. H. VuorimÄki, E. E. Ylinen, and P. Vajda, Phys. Rev. B 64, 214110 2001 . H. Kierey, M. Rode, A. Jacob, A. Borgshulte, and J. Schoenes, Phys. Rev. B 63, 134109 2001 . J. Schoenes, A. Borgschulte, A.-M. Carsteanu, H. Kierey, and M. Rode, J. Alloys Compd. 356­357, 211 2003 . V. A. Somenkov and V. P. Glazkov, Z. Phys. Chem., Neue Folge 117, 125 1979 . V. E. Antonov, I. T. Belash, A. I. Kolesnikov, J. Maier, I. Natkaniec, E. G. Ponyatovskii, and V. K. Fedotov, Fiz. Tverd. Tela Leningrad 33, 152 1991 Sov. Phys. Solid State 33, 87 1991 . V. D. Kodibagkar, C. D. Browning, T. J. Udovic, and M. S. Conradi, Phys. Rev. B 67, 174115 2003 .

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