Äîêóìåíò âçÿò èç êýøà ïîèñêîâîé ìàøèíû. Àäðåñ îðèãèíàëüíîãî äîêóìåíòà : http://www.issp.ac.ru/lhpp/PapersAntonov/151.pdf Äàòà èçìåíåíèÿ: Fri Feb 10 18:35:22 2012 Äàòà èíäåêñèðîâàíèÿ: Tue Oct 2 06:35:09 2012 Êîäèðîâêà:

I

NSTITUTE OF

PHYSICS PUB

LISHING

JOUR

NAL OF

PHYSICS: C

ONDENSED

MATTER

J. Phys.: Condens. Matter 18 (2006) 1593­1599

doi:10.1088/0953-8984/18/5/012

Displacive ordering in the hydrogen sublattice of yttrium trihydride
V K Fedotov1,5 , V E Antonov1 ,I O Bashkin1 , T Hansen2 and I Natkaniec3,4
Institute of Solid State Physics, Russian Academy of Sciences, 142432 Chernogolovka, Moscow District, Russia 2 Institut Laue-Langevin, BP 156, 38042 Grenoble Cedex 9, France 3 Frank Laboratory of Neutron Physics, Joint Institute for Nuclear Research, 141980 Dubna, Moscow District, Russia 4 H Niewodniczanski Institute of Nuclear Physics, Polish Academy of Sciences, 31-342 Krakow, Poland E-mail: fedotov@issp.ac.ru
1

Received 31 August 2005 Published 17 January 2006 Online at stacks.iop.org/JPhysCM/18/1593 Abstract Powder samples of YH3 and YD3 have been studied by neutron diffraction (ND) with a much higher statistical accuracy than obtained previously. The profile analysis of the obtained ND patterns confirmed the high-symmetry HoH3 -type structure of YH3 and ruled out the `broken symmetry' structures proposed recently to explain the insulating properties and lattice dynamics of this compound. At the same time, it was demonstrated that the HoH3 type structure is only the structure of the mean lattice of YH3 . Large static displacements of H atoms from the symmetrical positions in this structure do occur, and ordering of these displacements on a short-range scale can settle the controversies between the crystal structure and physical properties of YH3 .

1. Introduction Yttrium trihydride has been intensely studied after the discovery [1] of a reversible metal­ insulator phase transition between the reflecting dihydride and optically transparent trihydride occurring in the Y­H system on varying the pressure of hydrogen gas. Not only did such a `switchable mirror' seem promising for applications, but the trihydride offered a challenge to both theorists and experimentalists as its insulating properties and lattice dynamics appeared inconsistent with the crystal structure (see e.g. [2] for discussion and references). In fact, powder neutron diffraction studies showed [3­5] that yttrium trihydride is ¯ isostructural with HoH3 . The unit cell of HoH3 , space group P 3c1, is a ( 3 â 3)R30
5 Author to whom any correspondence should be addressed.

0953-8984/06/051593+07$30.00 © 2006 IOP Publishing Ltd

Printed in the UK

1593


1594

V K Fedotov et al

expansion of the hexagonal unit cell of the hcp metal lattice in the basal plane [6]. Two thirds of the H atoms occupy distorted tetrahedral t-sites in the hcp metal lattice. 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 ofoctahedral sites toward the metal-defined basal planes. On the other hand, ab initio calculations demonstrated that significant features of the electronic band structure [7­9] and of the vibrational spectrum [10, 2] of YH3 cannot be ¯ explained if its structural symmetry is P 3c1. Instead, two other structures, P 63 cm and P 63 , were proposed [10, 2]. With the positional parameters for hydrogen atoms properly chosen ¯ (optimized), these new `broken symmetry' structures have lower total energy than the P 3c1 structure and allow a better explanation of the results of inelastic neutron scattering (INS) measurements [11, 12] and also of NMR [13, 14], Raman and IR [15, 16] studies of YH3 . All three structures proposed for yttrium trihydride are characterized by correlated placements of Ht and Hm atoms leading to a threefold increase in the parent hcp unit cell. Calculations [10, 2] renewed the discussion of the crystal structure of YH3 . The present paper reports on the results of a neutron diffraction (ND) investigation of YH3 and YD3 that was aimed at answering two questions:

· To what extent can the method of powder neutron diffraction discern the new `broken ¯ symmetry' structures P 63 cm and P 63 from the HoH3 -type P 3c1structure? · Is there a way to reconcile the results of the ND studies with the requirements of the symmetry of the YH3 structure arising from the data of the INS, NMR and some other experiments?
Compared to earlier ND studies of YH3 and YD3 , the diffraction patterns were measured with a much higher statistical accuracy in order to get smooth background and to establish the absence or the presence and intensities of weak reflections reliably. 2. Sample preparation and experimental details Yttrium trihydride and trideuteride were synthesized by gas-phase absorption in a Sievertstype apparatus using 99.9 wt% Y metal and hydrogen or deuterium produced by thermal decomposition of TiH2 or TiD2 , respectively. The compositions of the samples thus prepared were determined from the gained weight and proved to be close to YH3 and YD3 in agreement with [11]. A room-temperature x-ray diffraction examination (SIEMENS D-500 diffractometer, monochromated Cu K1 radiation) showed that the samples were single-phase hcp compounds ° ° with the lattice parameters a = 3.6712(5) A, c = 6.6068(8) A, c/a = 1.7996(4) for YH3 and ° ° a = 3.6712(5) A, c = 6.5968(8) A, c/a = 1.7969(4) for YD3 . Powdered samples of YH3 and YD3 , each weighing 5 g, were studied at 95 K by neutron diffraction using the high-luminosity D20 diffractometer at ILL, Grenoble. The diffraction patterns were recorded in steps of 0.1 in 2 . The sample was placed in a cylindrical, thinwalled vanadium can. The background was determined in a separate empty-can measurement and subtracted from the measured diffraction patterns. The resulting neutron spectra were analysed using the Rietveld profile refinement technique implemented in the DBWS-9411 computer program [17]. 3. Results and discussion The experimental ND patterns of YH3 and YD3 are shown by dots in figure 1. To compare ¯ the goodness of the fits achievable while modelling the patterns with the P 3c1, P 63 cm and


Displacive ordering in the hydrogensublattice of yttrium trihydride
â10
3

1595

55 50 15 10
1 0 1

(a)
01 1 0 01 1 1 20 1 2
2 0 1

1 1 2 2 0 2

YH3
2 1 1
1 0 3

D20 = 2.42 å T = 95 K
3 21 2 0 20 2 2 04 1
2 0 3

31 2 01 1 03 2

22 4 31 22 3 _ 1 1 2 0 1 {P 3c1} 1 2 0 43 2 14 24 2
4 0 1

Counts

{P 63}

5 0 0 0

_ P 3c1

P 63cm

0
P 63

40

60

80

100

120

140

2, degree
â10
3

(b)

225 200 50
01 10 01 11 20 12

YD3
1 1 2 2 0 2 2 1 1

3 0 0

1 1 3 2 1 2 3 21 2 0 20 2 2 04 1

D20 = 2.42 å T = 95 K
22 4 31 22 3 _ 1 1 2 0 1 {P 3c1} 1 2 0 43 2 14 24 2

Counts

25 0 0 0 0
1 0 1 2 0 1 1

P 63
_ P 3c1 P 63cm {P 63} 0
3 2 0 3

P 63

4 0 1

40

60

80

100

120

140

2, degree
Figure 1. Powder neutron diffraction patterns of YH3 (a) and YD3 (b) measured at 95 K with ° the D20 diffractometer at ILL, Grenoble, using neutrons with a wavelength of = 2.42 A (dots), and results of their Rietveld analysis (solid lines). A linear fit to the background is subtracted from the experimental spectra for better visualization of small diffraction features. Three lines at the bottom of each figure show the differences between the experimental spectrum and the spectra calculated assuming the indicated crystal structure of the sample. The calculated P 63 spectra are also superimposed on the corresponding experimental spectra. The rows of vertical bars labelled ¯ ¯ { P 3c1} in the upper part of each figure show the positions of reflections of the P 3c1 structure. The lower rows of bars labelled { P 63 } show the positions of additional reflections characteristic of the P 63 structure.

P 63 structure, we used the values of positional parameters optimized in [2] for structures to have the lowest total energy. These values are listed in table 1. The parameters of the fitting procedure were the thermal factors, BY and BH or BD was considered isotropic and independent of the site symmetry. The optimum

each of these only variable . Each factor values of the


1596

V K Fedotov et al

¯ Table 1. Optimized [2] positions ( xy z )of atoms in the YH3 unit cell modelled with the P 3c1, P 63 and P 63 cm structure, and displacements ( xy z ) of these positions in the P 63 and P 63 cm structures ¯ relative to those in the P 3c1 structure. ¯ P 3c1 x
Y Site xy z
xy z

P6 z
1/4 -- 0.093 --

3

P 63 cm z
0.250 0 0.093 0

y
6f 0 -- 12g 0.025 --

x
0.667 0.004 0.345 0.003

y
6c -0.003 -0.003 6c -0.015 -0.040 6c -0.042 -0.017 2a 0 0 2b 2/3 0 2b 2/3 0

x
0.669 0.006 0.306 -0.042

y
6c 0 0 6c 0 -0.025 6c 0 0.025 2a 0 0 4b 2/3 0

z
0.250 0 0.091 -0.002

0.663 -- 0.348 --

H1 (t)

Site xy z
xy z

H2 (t)

Site xy z
xy z

-0.308 0.040
0 -- 1/3 -- 2a 0 -- 4d 2/3 -- 1/4 -- 0.181 -- 0 0 1/3 0 1/3 0

-0.093 0 -0.316 -0.066
0.184 0.003

-0.354 -0.006
0 0 1/3 0

-0.092 0.001
0.324 0.074 0.200 0.019

H1 (m)

Site xy z
xy z

H2 (m)

Site xy z
xy z

H3 (m)

Site xy z
xy z

-0.216 0.035

Table 2. Thermal factors ( B ) and expected ( Rex ) and obtained ( Rp ) profile factors resulting from the Rietveld analysis of the neutron diffraction data for YH3 and YD3 (figure 1)using the positional parameters from table 1.

Rp (%)
Phase YH3 YD3 ° B Y (A ) 0.4 0.4
2

° BH ,BD (A ) 1.8 1.5

2

R

ex

(%)

¯ P 3c 1
5.6 5.8

P6
7.7 9.6

3

P 63 cm
14.5 22

2.6 1.1

thermal factors proved to be approximately the same for each of the analysed structures. These optimum B -values are presented in table 2 together with the values of the profile factors. As one can see from figure 1 and table 2, the P 63 structure is qualitatively inapplicable to modelling the ND patterns of both YH3 and YD3 . Not only are the resulting Rp factors unreasonably large for both compounds, but a series of rather intense additional lines (101), (201), (103) and (203) appears in the pattern of YD3 , while these lines are obviously missing in the experimental data (see figure 1(b)). Modelling with the P 63 cm structure does not directly contradict the experimental data, ¯ butthe resulting fit is noticeably worse than in the case of the P 3c1structure. This fact is most clearly seen for YD3 , from comparison of the Rp factors equal to 9.6% and 5.8%, respectively (see table 2). Varying the positional parameters and using different and reasonably anisotropic thermal ¯ factors for H or D atoms on different sites in the P 3c1, P 63 and P 63 cm structure did not result in a significantdecrease in the Rp values compared to those indicated in table 2. The positional parameters of each structure proposed in [2]appeared optimum for fitting the experimental ND


Displacive ordering in the hydrogensublattice of yttrium trihydride

1597

patterns. The analysis of the YH3 and YD3 patterns using these parameters therefore shows with certainty that neither of the P 63 and P 63 cm broken symmetry structures is consistent ¯ with the ND data. It is the HoH3 -type P 3c1 structure that agrees with the experimental data better thanother structures, in accordance with earlier results [3­5]. On the other hand, calculations [2] show that YH3 with the HoH3 -type structure is dynamically unstable and the `soft mode' moves in-plane Hm atoms out of the Y-defined planes. This is exactly how the alternative, broken symmetry structures P 63 cm and P 63 are formed (see lines ` xy z ' for the Hm atoms in table 1). The discrepancy can be eliminated by assuming that the short-range symmetry of hydrogen arrangements in YH3 is lower than the long-range ¯ P 3c1symmetry determined by such methods as neutron diffraction. In view of the small changes in the powder neutron diffraction pattern caused by any proposed type of long-range ordering in the hydrogen sublattice of YH3 and YD3 , there is no chance immediately to detect changes in the diffuse scattering resulting from the short-range ordering. Detecting such changes would be a difficult problem even with a good single crystal of YD3 , if it were ever grown. Nevertheless, some other experimental and theoretical findings suggest that a sort of displacive short-range ordering is very likely to occur in yttrium trihydride. The occurrence of large static hydrogen displacements, either chaotic or correlated on a short-range scale, is consistent with the available neutron diffraction data and explains the ¯ enormously large values of the thermal factors calculated for hydrogen atoms in the P 3c1 ¯ c1 is only the symmetry of the `mean' lattice structure (table 2). The assumption that P 3 of YH3 and YD3 also agrees with the large values of the Rp / Rex ratio reaching as much as 5.8/1.1 for YD3 (table 2). The problem of the too large Rp and BD values concomitant with ¯ modelling an ND pattern of YD3 with the P 3c1 structure was earlier encountered in [4] and it waspartly solved by allowing a `fractional disorder' in the occupancy of the two non-equivalent m-sites by deuterium atoms. Further NMR study of YD3 showed that D atoms on t-sites also `sit in a distribution of local environments' [13]. The displacements of both Dm and Dt atoms were considered chaotic [4, 13], but any short-range ordering of those displacements did not contradict the experiment data either. Meanwhile, the occurrence of a short-range order in the static hydrogen displacements ¯ from symmetrical positions in the P 3c1 structure can explain why the properties of YH3 measured by NMR [13, 14] and INS [11, 12], Raman and IR [15, 16] spectroscopy are better ¯ described with the P 63 cm or P 63 structure than with the P 3c1 structure. As a matter of fact, allthose methods are mostly sensitive to the local environment of the hydrogen atom, while the ¯ P 3c1structure characterizes the more symmetrical mean lattice. Moreover, the absence of the periodical structure corresponding to the lower short-range symmetry in the hydrogen placements suggests that such properties of YH3 as the hydrogen vibrational spectrum should be better described by a certain mixture of the spectra calculated for various `broken symmetry' periodical structures. This is illustrated in figure 2 where the average of the calculated P 63 cm and P 63 spectra represent the experimental feature near 57 meV better than the P 63 spectrum and the feature near 124 meV better than the P 63 cm spectrum. Interestingly, calculations [2] showed that subtle changes in the placements of H atoms in the YH3 structure led to drastic changes in the optical part (h > 35 meV) of the ¯ vibrational spectrum. At the same time, this part of the spectrum determined in the experiment (figure 2, [18]) is fine-structured and practically coincides with the spectrum of YH3 from [11] measured at h > 35 meV. The occurrence of the well-resolved and well-reproducible fine ¯ structure in the H vibrational spectrum of YH3 therefore implies a rather high degree of order in the hydrogen sublattice of this compound, since the spectrum would be smoothed and smeared if thedisplacements of H atoms were chaotic.


1598

V K Fedotov et al

0.20

S(Q,), arb. units

YH3
0.15 0.10

P 63

P 63cm
0.05

0.00 0.20

(P 63cm + P 63)/2

S(Q,), arb. units

0.15

0.10

Exp.

0.05

0.00

0

50

100

150

200

h, meV
Figure 2. The one-phonon inelastic neutron scattering spectrum S ( Q ,) of YH3 powder at 20 K [18](dots, bottom part of the figure) and the total phonon densities of states (lines) calculated in the broken symmetry structures P 63 cm and P 63 [2] (upper part of the figure) and their average (bottom part). The YH3 sample studied by ND in the present paper was the same as in [18].

This also suggests that the calculated P 63 cm and P 63 structures [2] reflect significant features of the short-range ordering in YH3 . Note in this connection that calculations [2] were carried out for relatively small supercells containing 192 atoms and therefore gave optimized parameters for the clusters rather than periodic structures. As seen from table 1,the largedisplacements of Hm atoms inthe P 63 cm or P 63 structures ¯ relative to their positions in the P 3c1 structure are accompanied by large displacements of Ht atoms. As long as the P 63 cm or P 63 structure represents the arrangement of hydrogen in YH3 , the displacements of Hm and Ht atoms in this trihydride should therefore be correlated. A similar short-range ordering of the hydrogen sublattice is likely to be inherent to many other trihydrides as well. Accurate powder neutron diffraction studies showed that trihydrides of heavy rare-earth metals (e.g., Tb, Dy, Ho, Er [11]) had the crystal structure of the HoH3 type. The INS investigation carried out in the same work of [11] demonstrated that the spectra of optical H vibrations in all these trihydrides were very similar to the spectrum of YH3 . In the light of results of the present paper, one can speculate that the fine structure in the spectra of those rare-earth trihydrides was also due to the occurrence of large static displacements of H ¯ atoms correlated on a short-range scale, while the P 3c1 symmetry only referred to the mean lattice.


Displacive ordering in the hydrogensublattice of yttrium trihydride

1599

Moreover, the optical H spectra of LuH3 [11] and ScH3 [18] proved to be similar to that of YH3 , while the neutron diffraction patterns of those trihydrides showed no distinct signs of displacive ordering in the hydrogen sublattice and rather indicated the P 63 / mmc symmetry of ¯ the crystal structure [11, 18]. The P 63 / mmc symmetry is higher than P 3c1and trihydrides of Lu and Sc have the smallest lattice parameters among trihydrides of the group III metals. This suggests an increase in the symmetry of the mean lattice of such trihydrides with decreasing atomic volume, the short-range order of the hydrogen sublattice remaining largely the same. 4. Conclusions

¯ The conflict between the P 3c1 structure of yttrium trihydride and some properties of this ¯ compound that are inconsistent with the high symmetry of the P 3c1 structure finds a non¯ c1 is the symmetry of the mean lattice contradictory solution under the assumption that (i) P 3 of YH3 ;(ii) the structure of YH3 is characterized by large static displacements of H atoms from ¯ symmetrical m- and t-positions of the P 3c1structure and these displacements are correlated on a short-range scale. The origin of the conflict was that the method of neutron diffraction used to determine the crystal structure was mostly sensitive to the averaged, long-range symmetry of the YH3 (or YD3 ) samples, while other their properties were measured by such techniques as NMR and INS, optical and IR spectroscopy that were mostly sensitive to the less-symmetrical local environments of hydrogen (or deuterium) atoms.
Acknowledgments This work was supported by grant No. 04-02-17269 from the Russian Foundation for Basic Research and by the Programme `Physics and Mechanics of Strongly Compressed Matter' of the Russian Academy of Sciences. References
[1] Huiberts J N, Griessen R, Rector J H, Wijngaarden R J, Dekker J P, de Groot D G and Koeman N J 1996 Nature 380 231­4 [2] van Gelderen P, Kelly P J and Brocks G 2003 Phys. Rev. B 68 094302-1­13 [3] Miron N F, Shcherbak V I, Bykov V N and Levdik V A 1972 Krystallografiya 17 404­6 Miron N F, Shcherbak V I, Bykov V N and Levdik V A 1972 Sov. Phys.--Crystallogr. 17 342­4 (Engl. Transl.) [4] Udovic T J, Huang Q and Rush J J 1996 J. Phys. Chem. Solids 57 423­35 Udovic TJ, Huang Q and Rush J J 1997 Phys. Rev. Lett. 79 2920 [5] Udovic T J, Huang Q, Lynn J W, Erwin R W and Rush J 1999 Phys. Rev. B 59 11852­8 [6] Mannsmann M and Wallace W E 1964 J. Physique 25 454­9 [7] Dekker J P, van Ek J, Lodder A and Huiberts J N 1993 J. Phys.: Condens. Matter 5 4805­16 [8] Wang Y and Chou M Y 1993 Phys. Rev. Lett. 71 1226­9 Wang Y and Chou M Y 1995 Phys. Rev. B 51 7500­7 [9] Kelly P J, Dekker J P and Stumpf R 1997 Phys. Rev. Lett. 78 1315­8 [10] van Gelderen P, Kelly P J and Brocks G 2001 Phys. Rev. B 63 100301-1­4 [11] Udovic T J, Huang Q and Rush J J 1998 Hydrogen in Semiconductors and Metals (MRS Symp. Proc. No. 513) ed N N Nickel, W B Jackson, R C Browman and R G Leisure (Pittsburgh, PA: Materials Research Society) p 197 [12] Udovic T J, Huang Q, Erwin R W, Hjorvarsson B and Ward R C 2000 Phys. Rev. B 61 12701­4 ¨ [13] Balbach J J, Conradi M S, Hoffmann M M, Udovic T J and Adolphi N L 1998 Phys. Rev. B 58 14823­31 [14] Zogal O J, Wolf W, Herzig P, VuorimakiA H, Ylinen EEand Vajda P 2001 Phys. Rev. B 64 214110-1­7 ¨ [15] Kierey H, Rode M, Jacob A, Borgschulte A and Schoenes J 2001 Phys. Rev. B 63 134109-1­11 [16] Schoenes J, Borgschulte A, Carsteanu A-M, Kierey H and Rode M 2003 J. Alloys Compounds 356/357 211­7 [17] Young R A, Sakthivel A, Moss T S and Paiva-Santos C O 1995 DBWS9411 User's Guide (Atlanta: Georgia Institute of Technology) [18] Antonov V E, Bashkin I O, Fedotov V K, Khasanov S S, Hansen T, Ivanov A S, Kolesnikov A I and NatkaniecI 2006 Phys. Rev. B at press