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Low-temperature deuterium ordering in the cubic Laves phase derivative α-ZrCr2D0.66
Journal of Alloys and Compounds 327 (2001) L4–L9
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Letter
Low-temperature deuterium ordering in the cubic Laves phase derivative a-ZrCr 2 D 0.66 a, b b c c a H. Kohlmann *, F. Fauth , P. Fischer , A.V. Skripov , V.N. Kozhanov , K. Yvon b
a ` , CH-1211 Geneva 4, Switzerland Laboratoire de Cristallographie, Universite´ de Geneve ¨ and Paul Scherrer Institute, CH-5232 Villigen PSI, Switzerland Laboratory for Neutron Scattering, ETH Zurich c Institute of Metal Physics, Urals Branch of the Academy of Sciences, Ekaterinburg 620219, Russia
Received 26 April 2001; accepted 3 May 2001
Abstract The solid solution of the cubic Laves phase derivative a-ZrCr 2 D x undergoes a structural phase transition at low temperature that leads to a novel type of deuterium atom ordering. Neutron powder diffraction at 50 and 2 K reveals a monoclinic structure of composition ZrCr 2 D 0.66 (space group P21 /n, Z58; a5894.11(3) pm, b5513.72(2) pm, c5890.50(4), b 5109.563(3)8 at 2 K) in which deuterium occupies four (out of 24) sorts of [Zr 2 Cr 2 ] type interstices with occupancies in the range 23–40%. The ordering differs from that in the more deuterium rich monoclinic low temperature structure of a9-ZrCr 2 D 3.8 (space group C2 /c) and leads to the lowest deuterium-to-metal ratio known among Laves phase derivative structures undergoing order–disorder transitions. A list of known compositions for ordered (or partially ordered) cubic Laves phase hydride derivative structures is given. 2001 Elsevier Science B.V. All rights reserved. Keywords: Hydrogen absorbing materials; Transition metal compounds; Crystal structure; Phase transition; Neutron diffraction
1. Introduction The Laves phase compound ZrCr 2 crystallizes with the hexagonal C14 (MgZn 2 ) type structure at high temperature and the cubic C15 (MgCu 2 ) type structure at low temperature. Both modifications absorb considerable amounts of hydrogen (up to approximately four H atoms per formula unit). According to a tentative ZrCr 2 -D phase diagram [1] the C15 type hydride derivative ZrCr 2 D x shows an aphase at low (x,0.9) and an a9-phase at high (2.4,x# 3.8) hydrogen contents. Neutron diffraction studies [2,3] on the deuterium rich a9-phase revealed an ordering of deuterium atoms at low temperature that leads to a monoclinic structure of composition ZrCr 2 D 3.8 (T5250 K, space group C2 /c [3]). On the other hand, little is known about a possible deuterium ordering in the deuterium poor a-phase. Usually, metal–hydrogen systems at low hydrogen contents show phase separation and the precipitation of a concentrated hydride phase. In a-ZrCr 2 H x (x#0.5) nuclear magnetic resonance (NMR) data have revealed no phase separation down to 11 K [4,5]. On the other hand,
specific heat measurements on ZrCr 2 H x (x#0.5) [6,7] and neutron diffraction experiments on a-ZrCr 2 D 0.7 below 100 K [1], indicated the occurrence of a structural phase transition in the temperature range 55–70 K which could possibly be of the order–disorder type. Order–disorder transitions at such low hydrogen contents are relatively rare. They have been reported for binary a-phases of YHx (D x ) and related systems [8,9] in which hydrogen (deuterium) shows quasi-one-dimensional short-range order. In ternary a-phases of C15 type derivatives, threedimensional long-range order of deuterium is known to occur at deuterium-to-metal ratios down to D/ M50.38 (monoclinic ZrV2 D 1.14 [10]). The aim of the present study is to show that a similar ordering already occurs in aZrCr 2 D x at D/ M|0.22. It leads to a structure of monoclinic symmetry that differs from those of the more deuterium rich phases a9-ZrCr 2 D 3.8 and ZrV2 D 1.14 .
2. Experimental
2.1. Synthesis *Corresponding author. Present address: High Pressure Science and Engineering Center, Department of Physics, University of Nevada, Las Vegas, Las Vegas, NV 89154-4002, USA.
An alloy of nominal composition ZrCr 2 was prepared by arc melting appropriate amounts of metal constituents in a
0925-8388 / 01 / $ – see front matter 2001 Elsevier Science B.V. All rights reserved. PII: S0925-8388( 01 )01565-1
H. Kohlmann et al. / Journal of Alloys and Compounds 327 (2001) L4 –L9
helium atmosphere. The ingot obtained showed the presence of a hexagonal C14-type structure having the cell parameters a5509.0(5) pm and c5827.0(5) pm. After annealing under argon at 1570 K for 3 h, the sample was single-phase and showed a cubic C15-type structure with cell parameter a5720.5(3) pm. Small pieces of the annealed alloy were put into a Sieverts-type apparatus and charged with deuterium gas at a pressure of 40 kPa while heating the sample to a temperature of 973 K and subsequent slow cooling to room temperature. The absorbed deuterium content was determined from the pressure change in the calibrated volume of the system and found to be ZrCr 2 D 0.70( 4) .
2.2. Neutron diffraction A powder sample (mass 6 g) of composition ZrCr 2 D 0.7 was filled under He gas into a cylindrical vanadium container (8-mm diameter, sample height |18 mm, sealed by an indium wire) and mounted on the neutron powder diffractometer D1A at ILL (Grenoble, France). Four data sets were collected at the temperatures 2, 50, 150 and 293 K by using an ILL type cryostat (neutron wavelength l5191.1 pm, maximum diffraction angle 2u 51588, step size D2u 50.058, 12-h data collection per temperature). Measurements of the transmission factor yielded m r5 0.110 ( m, linear absorption coefficient; r, sample radius). The patterns observed at the various temperatures are represented in Fig. 1.
2.3. Crystal structure refinements The neutron diffraction patterns at 293 and 150 K confirmed the cubic Laves phase type derivative structure in which deuterium atoms occupy at random tetrahedral [Zr 2 Cr 2 ] type interstices. A possible occupancy of [ZrCr 3 ]
Fig. 1. Neutron powder diffraction patterns of ZrCr 2 D 0.66 at 2, 50, 150 and 293 K (from bottom to top), l5191.1 pm. Note the occurrence of additional reflections due to formation of a superstructure at low temperatures.
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type interstices could be excluded after preliminary structure refinements by the Rietveld method (FullProf.98 programme [11]) had shown that the population parameter of the corresponding site (0.7(2)%) did not differ significantly from zero. The background of the patterns was described by a linear interpolation of 19 points, and a pseudo-Voigt function was used for modeling reflection profiles. The following 15 parameters were allowed to vary in the final refinements: one scale factor, three halfwidth, one mixing, two asymmetry, one lattice, two positional parameters, three Debye-Waller factors, one occupancy factor and one zeropoint shift in 2u. For the T5293 K data, observed and calculated powder patterns are shown in Fig. 2a and refinement results are listed in Table 1. The refined composition ZrCr 2 D 0.66( 1) is in good agreement with the results of the volumetric measurements. For the 150 K data, similar refinements yielded structure parameters that did not differ significantly from those obtained at 293 K except for the cell parameter that was somewhat smaller (Table 1). The diffraction data collected at T550 and 2 K showed additional reflections indicative for the occurrence of a structural phase transition (Fig. 1). They were indexed on a monoclinic cell using the same metrical relationships (a mono ¯c mono ¯(3 / 2)1 / 2 a cubic , b mono ¯(2)1 / 2 / 2 a cubic , 1/2 bmono ¯2 arctan (2) ¯109.478) as those used to describe the monoclinic low-temperature structure of more deuterium rich ZrCr 2 D 3.8 [3]. Unlike the latter, however, the systematically absent reflections suggested space group P21 /n rather than C2 /c. A structure model was constructed by transforming all atom positions of the cubic to the monoclinic cell (Table 1). This required splitting of the eightfold Zr position in the cubic cell into two fourfold positions in the monoclinic cell, and of the 16-fold Cr and the 96-fold D positions into four and 24 fourfold positions, respectively. A stepwise refinement of the occupancy factors of the D sites revealed that only four (out of 24) positions were significantly occupied (Table 2). The background of the low-temperature patterns was described by a linear interpolation of 12 points and a pseudo-Voigt function was used for modeling reflection profiles. The following 49 parameters were allowed to vary in the final refinements: one scale factor, three halfwidth, one mixing, two asymmetry, four lattice, 30 positional parameters, three Debye-Waller factors, four occupancy factors and one zeropoint shift in 2u. Debye-Waller factors were constrained to have the same value for atoms of the same kind. The observed and calculated powder patterns are shown in Fig. 2b and refinement results are listed in Table 2. The refined deuterium content (ZrCr 2 D 0.61( 2) ) is somewhat lower than that obtained at room temperature (ZrCr 2 D 0.66( 1) ). The difference, however, is not significant. Refinement of the T550 K data yielded structure parameters not significantly different from those at T52 K, except for bigger cell parameters (Table 2). Note that some of the metal atom sites have negative B values which indicates that the structure model still needs to be improved, for
H. Kohlmann et al. / Journal of Alloys and Compounds 327 (2001) L4 –L9
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Fig. 2. Observed (crosses), calculated (solid line) and difference neutron powder diffraction pattern ( l5191.1 pm) of ZrCr 2 D 0.66 at (a) T5293 K, (b) T52 K. Intensity in total detector counts.
Table 1 ] Crystal structure data for cubic ZrCr 2 D 0.66 (space group Fd3 m) at T5293 K as refined from neutron powder diffraction data Atom
Site
Zr Cr D
8a 16d 96g
Symmetry ] 43m ] 3m ..m
x /a
y /b
z /c
B a / 10 4 pm 2
Occupancy
1/8 1/2 0.0686(4)
1/8 1/2 x
1/8 1/2 0.8711(5)
0.41(3) 0.40(3) 1.2(2)
1 1 0.055(1)
Cell parameters:
a (293 K)5729.18(1) pm; a (150 K)5728.11(4) pm
Agreement indices:
R p 52.8%, R wp 53.4%, R Bragg 52.5% (R p 5S uy i (obs)2y i (calc)u / S y i (obs); R wp 5[S w i ( y i (obs)2y i (calc))2 / S w i y i (obs)2 ] 1 / 2 ; R Bragg 5S uIB (‘obs’)2IB (calc)u / S IB (‘obs’))
a
Form of the temperature factor: T5exp[2Biso (sin u /l)2 ].
H. Kohlmann et al. / Journal of Alloys and Compounds 327 (2001) L4 –L9
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Table 2 Crystal structure data for monoclinic ZrCr 2 D 0.66 (space group P21 /n) at T52 K as refined from neutron powder diffraction data Atom
Site
Symmetry
x /a
y /b
z /c
B a / 10 4 pm 2
Occupancy
Zr1 Zr2 Cr1 Cr2 Cr3 Cr4 D1 D2 D3 D4
4e 4e 4e 4e 4e 4e 4e 4e 4e 4e
1 1 1 1 1 1 1 1 1 1
0.4358(7) 0.0639(7) 0.258(1) 0.231(1) 0.987(1) 0.248(2) 0.061(3) 0.087(2) 0.489(3) 0.278(3)
0.250(1) 0.254(2) 0.995(3) 0.519(3) 0.255(3) 0.248(3) 0.116(4) 0.031(5) 0.456(4) 0.256(7)
0.0671(7) 0.9358(7) 0.252(2) 0.751(2) 0.241(1) 0.500(2) 0.442(3) 0.140(2) 0.884(3) 0.851(4)
0.08(3) B(Zr1) 20.25(4) B(Cr1) B(Cr1) B(Cr1) 0.5(2) B(D1) B(D1) B(D1)
1 1 1 1 1 1 0.40(2) 0.30(1) 0.29(2) 0.23(1)
Cell parameters:
T52 K: a5894.11(3) pm, b5513.72(2) pm, c5890.50(4), b 5109.563(3)8 T550 K: a5894.08(4) pm, b5513.84(3) pm, c5890.54(6) pm, b 5109.565(4)8
Agreement indices:
R p 54.8%, R wp 53.7%, R Bragg 56.2%
a
Form of temperature factor and agreement indices as in Table 1.
example by collecting data of higher resolution. This would allow a decrease the correlation between displacement parameters and occupancy factors and presumably would yield more reliable values for both types of parameters.
3. Discussion At room temperature a-ZrCr 2 D x has cubic symmetry ] (space group Fd3 m) and contains deuterium only in [Zr 2 Cr 2 ] type interstices, in agreement with a recent inelastic neutron scattering study [12]. The refined occupancy (5.5(1)%) corresponds to the composition ZrCr 2 D 0.66 . As the temperature is lowered to 150 K no
significant structural changes occur except for a contraction of the lattice. In particular, no long-range order is observed. Upon further lowering the temperature to T550 and 2 K additional, relatively sharp peaks appear in the diffraction patterns that are due to three-dimensional longrange order of the deuterium atoms. The onset temperature of ordering has not been determined, but from previous studies [6,7] it is likely to be in the range 55–70 K. As shown by the structure refinements, the low-temperature phase of ZrCr 2 D 0.66 has monoclinic symmetry (space group P21 /n) and its deuterium atoms occupy only four (out of 24 possible) sorts of [Zr 2 Cr 2 ] interstices with an occupancy in the range 23–40%. Note that the metric distortion of the monoclinic lattice is very small, corresponding to ,0.5% with respect to cell edges and ,0.18
Fig. 3. Structures of disordered cubic ZrCr 2 D 0.66 (T5293 K, left) and ordered, monoclinic ZrCr 2 D 0.66 (T52 K, right) in a projection along cubic [110] and along monoclinic [010], respectively (chromium atom tetrahedra outdrawn; deuterium site occupancies in parentheses). Note that only one sixth of the D positions of the disordered, cubic modification (left) are occupied in the ordered, monoclinic modification (right), with accordingly higher occupancies.
H. Kohlmann et al. / Journal of Alloys and Compounds 327 (2001) L4 –L9
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Table 3 Metal–deuterium and deuterium–deuterium distances shorter than 230 pm in monoclinic ZrCr 2 D 0.66 at 2 K (in pm) Zr1
–D1 –D1 –D3 –D3 –D4
188(2) 195(2) 213(3) 165(2) 197(3)
D1
–Zr1 –Zr1 –Cr3 –Cr4 –D1 –D3 –D3
188(2) 195(2) 184(2) 171(3) 211(3) 77(4) 193(4)
Zr2
–D2 –D2 –D4
210(2) 195(3) 228(3)
D2
–Zr2 –Zr2 –Cr1 –Cr3
210(2) 195(3) 154(2) 186(3)
Cr1
–D2
154(2)
D3
Cr2
–D3 –D4 –D4
224(3) 159(4) 151(4)
–Zr1 –Zr1 –Cr3 –Cr2 –D1 –D1 –D3 –D4
213(3) 165(2) 167(3) 224(3) 77(4) 193(3) 205(4) 208(4)
Cr3
–D1 –D3 –D2
184(2) 167(3) 186(3)
D4
–Zr1 –Zr2 –Cr2 –Cr2 –D3
197(3) 228(3) 159(4) 151(4) 208(4)
Cr4
–D1
171(3)
with respect to cell angles. As can be seen in Fig. 3, noticeable changes in the metal atom positions occur only with the chromium sites Cr1 and Cr2. The low-temperature structure of a-ZrCr 2 D 0.66 is closely related to that of a9-ZrCr 2 D 3.8 [3] which derives also from an order–disorder phase transition at low temperature. According to the crystallographic group–subgroup ¨ relationships introduced by Barnighausen [13] both are
related by a transition of index 2 (klassengleich) in which the C centering is lost: C2 /c (ZrCr 2 D 3.8 , T52 K)2 k2→P21 /n (ZrCr 2 D 0.7 , T52 K). The four eightfold D positions in C2 /c split up into eight fourfold positions in P21 /n, only two of which are occupied in ZrCr 2 D 0.66 (D1, D3). The two other positions (D2, D4) correspond to [Zr 2 Cr 2 ] sites that are not occupied in ZrCr 2 D 3.8 . Thus monoclinic a-ZrCr 2 D 0.66 and a9-ZrCr 2 D 3.8 are two ordered variants of the same cubic aristotype and differ only in the ordering scheme of the D atoms. As to their atomic environments they are similar, except that the metal sites in the D-poor composition generally have a smaller number of deuterium ligands than in the D-rich composition. Some Cr atoms, for example, have only one deuterium ligand (Cr1, Cr4) in ZrCr 2 D 0.66 . The metal–deuterium distances in monoclinic ZrCr 2 D 0.66 (Table 3) are consistent with those in monoclinic ZrCr 2 D 3.8 except that the former are generally shorter than the latter which is presumably due to the lower D site occupancies in ZrCr 2 D 0.66 (#40%) compared to ZrCr 2 D 3.8 ($85%). Note that the deuterium order in ZrCr 2 D 0.66 is still not complete and that the proximity of some deuterium sites (D1–D3577 pm) excludes them from being fully occupied. Finally, the order–disorder transition in a-ZrCr 2 D 0.66 is consistent with previous NMR and specific heat studies [4–7]. Altogether these studies show that hydrogen ordering may also occur in a-phases of ternary metal hydrides at rather low hydrogen-to-metal ratios. In the present system ordering occurs at H / M50.22 and is clearly longrange and three-dimensional in character. This is the lowest deuterium-to-metal ratio known among Laves phase derivative structures showing order–disorder transitions. Numerous other order–disorder transitions have been reported in such structures at higher H / M ratios. They are summarized in Table 4 and show a great variety of compositions and symmetries. At least ten different order-
Table 4 Ordered modifications of deuterium containing C15 type Laves phase derivatives a Compound
T (K)
Space group
D positions
D occupancies (%)
Ref.
HfV2 D 4 ZrV2 D 3.9 ZrV2 D 3.6 HfV2 D 1.9 ZrCr 2 D 3.8 ZrCr 2 D 0.7 ZrV2 D 3 ZrV2 D 2.8 ZrV2 D 2.3 ZrV2 D 1.8 ZrV2 D 1.5 ZrV2 D 1.1 YFe 2 D 1.3 b YFe 2 D 1.8 YMn 2 D 4.3
77 90 230 100 2 2 77 90 100 100 100 100 293 293 300
I41 /a I41 /a I41 /a C2 /c C2 /c P21 /n P21 /c P21 /c C2 /c C2 /c C2 /c C2 /c ] I4 ] I43 m R3 m
1 1 1 4 4 4 4 4 5 3 3 3 7 9 3
100 98 91 14–100 85–100 23–40 51–93 50–90 33–71 33–100 27–100 20–61 36–81 17–76 50–94
[17] [16] [15] [10] [3] This work [14] [16] [10] [10] [10] [10] [18] [18] [19]
a
Only those phases are included that undergo temperature dependent order–disorder transitions and are structurally characterized by neutron diffraction. Bold formula refer to new ordering patterns and indented formula to the ordering pattern of the preceding line. ] b YFe 2 D 1.9 has probably a similar structure with space group I4 and a tripled c-axis [18].
H. Kohlmann et al. / Journal of Alloys and Compounds 327 (2001) L4 –L9
ing patterns occur in systems such as ZrCr 2 D x [1–3], ZrV2 D x [10,14–16], HfV2 D x [10,17], YFe 2 D x [18] and YMn 2 D x [19], and they have cubic, tetragonal, rhombohedral and monoclinic symmetry. Note that four different ordering patterns occur with space group C2 /c and two with P21 /c. The latter include the currently studied aZrCr 2 D 0.66 and ZrV2 D x (1.1,x,2.3). They have distinctly different ordering patterns and are related by the common minimal supergroup I2 /m. Altogether these ordering patterns underline the very rich crystal chemistry of metal hydrides in general and the subtle balance between hydrogen content, atomic size and electronic effects on the ordering behavior of hydrogen in cubic Laves phase derivative structures in particular.
Acknowledgements This work was supported by the Russian Foundation for Basic Research (grant No. 99-02-16311) and the Swiss National Science Foundation (grant No. 20-53642.98).
References [1] V.A. Somenkov, A.V. Irodova, J. Less-Common Met. 101 (1984) 481.
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[2] A.V. Irodova, O.A. Lavrova, G.V. Laskova, L.N. Padurets, Sov. Phys.-Solid State 24 (1982) 22. [3] H. Kohlmann, F. Fauth, K. Yvon, J. Alloys Comp. 285 (1999) 204. [4] A.V. Skripov, M.Yu. Belyaev, A.P. Stepanov, Solid State Commun. 78 (1991) 909. [5] A.V. Skripov, M.Yu. Belyaev, J. Phys. Condens. Matter. 5 (1993) 4767. [6] A.V. Skripov, A.V. Mirmelstein, J. Phys. Condens. Matter. 5 (1993) L619. [7] A.V. Skripov, A.E. Karkin, A.V. Mirmelstein, J. Phys. Condens. Matter. 9 (1997) 1191. [8] M.W. McKergow, D.K. Ross, J.E. Bonnet, I.S. Anderson, O. Scharpf, J. Phys. C 20 (1987) 1909. [9] O. Blaschko, J. Less-Common Met. 172–174 (1991) 237. [10] H. Kohlmann, K. Yvon, J. Alloys Comp. 309 (2000) 123. [11] J. Rodriguez-Carvajal, FullProf.98, 1998, LLB (unpublished). ´ ´ [12] J.F. Fernandez, M. Kemali, D.K. Ross, C. Sanchez, J. Phys. Condens. Matter. 11 (1999) 10353. ¨ [13] H. Barnighausen, MATCH 9 (1980) 139. [14] A.V. Irodova, I.I. Borisov, Phys. Solid State 36 (1994) 960. [15] J.J. Didisheim, K. Yvon, P. Fischer, P. Tissot, Solid State Commun. 38 (1981) 637. [16] A.V. Irodova, G. Andre, F. Boure, J. Alloys Comp. 302 (2000) 159. [17] A.V. Irodova, V.P. Glazkov, V.A. Somenkov, S.S. Shilstein, J. LessCommon Met. 77 (1981) 89. ´ M. Latroche, A. Percheron-Guegan, J. [18] V. Paul-Boncour, L. Guenee, Solid State Chem. 142 (1999) 120. [19] I.N. Goncharenko, I. Mirebeau, A.V. Irodova, E. Suard, Phys. Rev. B 56 (1997) 2580.
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Letter
Low-temperature deuterium ordering in the cubic Laves phase derivative a-ZrCr 2 D 0.66 a, b b c c a H. Kohlmann *, F. Fauth , P. Fischer , A.V. Skripov , V.N. Kozhanov , K. Yvon b
a ` , CH-1211 Geneva 4, Switzerland Laboratoire de Cristallographie, Universite´ de Geneve ¨ and Paul Scherrer Institute, CH-5232 Villigen PSI, Switzerland Laboratory for Neutron Scattering, ETH Zurich c Institute of Metal Physics, Urals Branch of the Academy of Sciences, Ekaterinburg 620219, Russia
Received 26 April 2001; accepted 3 May 2001
Abstract The solid solution of the cubic Laves phase derivative a-ZrCr 2 D x undergoes a structural phase transition at low temperature that leads to a novel type of deuterium atom ordering. Neutron powder diffraction at 50 and 2 K reveals a monoclinic structure of composition ZrCr 2 D 0.66 (space group P21 /n, Z58; a5894.11(3) pm, b5513.72(2) pm, c5890.50(4), b 5109.563(3)8 at 2 K) in which deuterium occupies four (out of 24) sorts of [Zr 2 Cr 2 ] type interstices with occupancies in the range 23–40%. The ordering differs from that in the more deuterium rich monoclinic low temperature structure of a9-ZrCr 2 D 3.8 (space group C2 /c) and leads to the lowest deuterium-to-metal ratio known among Laves phase derivative structures undergoing order–disorder transitions. A list of known compositions for ordered (or partially ordered) cubic Laves phase hydride derivative structures is given. 2001 Elsevier Science B.V. All rights reserved. Keywords: Hydrogen absorbing materials; Transition metal compounds; Crystal structure; Phase transition; Neutron diffraction
1. Introduction The Laves phase compound ZrCr 2 crystallizes with the hexagonal C14 (MgZn 2 ) type structure at high temperature and the cubic C15 (MgCu 2 ) type structure at low temperature. Both modifications absorb considerable amounts of hydrogen (up to approximately four H atoms per formula unit). According to a tentative ZrCr 2 -D phase diagram [1] the C15 type hydride derivative ZrCr 2 D x shows an aphase at low (x,0.9) and an a9-phase at high (2.4,x# 3.8) hydrogen contents. Neutron diffraction studies [2,3] on the deuterium rich a9-phase revealed an ordering of deuterium atoms at low temperature that leads to a monoclinic structure of composition ZrCr 2 D 3.8 (T5250 K, space group C2 /c [3]). On the other hand, little is known about a possible deuterium ordering in the deuterium poor a-phase. Usually, metal–hydrogen systems at low hydrogen contents show phase separation and the precipitation of a concentrated hydride phase. In a-ZrCr 2 H x (x#0.5) nuclear magnetic resonance (NMR) data have revealed no phase separation down to 11 K [4,5]. On the other hand,
specific heat measurements on ZrCr 2 H x (x#0.5) [6,7] and neutron diffraction experiments on a-ZrCr 2 D 0.7 below 100 K [1], indicated the occurrence of a structural phase transition in the temperature range 55–70 K which could possibly be of the order–disorder type. Order–disorder transitions at such low hydrogen contents are relatively rare. They have been reported for binary a-phases of YHx (D x ) and related systems [8,9] in which hydrogen (deuterium) shows quasi-one-dimensional short-range order. In ternary a-phases of C15 type derivatives, threedimensional long-range order of deuterium is known to occur at deuterium-to-metal ratios down to D/ M50.38 (monoclinic ZrV2 D 1.14 [10]). The aim of the present study is to show that a similar ordering already occurs in aZrCr 2 D x at D/ M|0.22. It leads to a structure of monoclinic symmetry that differs from those of the more deuterium rich phases a9-ZrCr 2 D 3.8 and ZrV2 D 1.14 .
2. Experimental
2.1. Synthesis *Corresponding author. Present address: High Pressure Science and Engineering Center, Department of Physics, University of Nevada, Las Vegas, Las Vegas, NV 89154-4002, USA.
An alloy of nominal composition ZrCr 2 was prepared by arc melting appropriate amounts of metal constituents in a
0925-8388 / 01 / $ – see front matter 2001 Elsevier Science B.V. All rights reserved. PII: S0925-8388( 01 )01565-1
H. Kohlmann et al. / Journal of Alloys and Compounds 327 (2001) L4 –L9
helium atmosphere. The ingot obtained showed the presence of a hexagonal C14-type structure having the cell parameters a5509.0(5) pm and c5827.0(5) pm. After annealing under argon at 1570 K for 3 h, the sample was single-phase and showed a cubic C15-type structure with cell parameter a5720.5(3) pm. Small pieces of the annealed alloy were put into a Sieverts-type apparatus and charged with deuterium gas at a pressure of 40 kPa while heating the sample to a temperature of 973 K and subsequent slow cooling to room temperature. The absorbed deuterium content was determined from the pressure change in the calibrated volume of the system and found to be ZrCr 2 D 0.70( 4) .
2.2. Neutron diffraction A powder sample (mass 6 g) of composition ZrCr 2 D 0.7 was filled under He gas into a cylindrical vanadium container (8-mm diameter, sample height |18 mm, sealed by an indium wire) and mounted on the neutron powder diffractometer D1A at ILL (Grenoble, France). Four data sets were collected at the temperatures 2, 50, 150 and 293 K by using an ILL type cryostat (neutron wavelength l5191.1 pm, maximum diffraction angle 2u 51588, step size D2u 50.058, 12-h data collection per temperature). Measurements of the transmission factor yielded m r5 0.110 ( m, linear absorption coefficient; r, sample radius). The patterns observed at the various temperatures are represented in Fig. 1.
2.3. Crystal structure refinements The neutron diffraction patterns at 293 and 150 K confirmed the cubic Laves phase type derivative structure in which deuterium atoms occupy at random tetrahedral [Zr 2 Cr 2 ] type interstices. A possible occupancy of [ZrCr 3 ]
Fig. 1. Neutron powder diffraction patterns of ZrCr 2 D 0.66 at 2, 50, 150 and 293 K (from bottom to top), l5191.1 pm. Note the occurrence of additional reflections due to formation of a superstructure at low temperatures.
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type interstices could be excluded after preliminary structure refinements by the Rietveld method (FullProf.98 programme [11]) had shown that the population parameter of the corresponding site (0.7(2)%) did not differ significantly from zero. The background of the patterns was described by a linear interpolation of 19 points, and a pseudo-Voigt function was used for modeling reflection profiles. The following 15 parameters were allowed to vary in the final refinements: one scale factor, three halfwidth, one mixing, two asymmetry, one lattice, two positional parameters, three Debye-Waller factors, one occupancy factor and one zeropoint shift in 2u. For the T5293 K data, observed and calculated powder patterns are shown in Fig. 2a and refinement results are listed in Table 1. The refined composition ZrCr 2 D 0.66( 1) is in good agreement with the results of the volumetric measurements. For the 150 K data, similar refinements yielded structure parameters that did not differ significantly from those obtained at 293 K except for the cell parameter that was somewhat smaller (Table 1). The diffraction data collected at T550 and 2 K showed additional reflections indicative for the occurrence of a structural phase transition (Fig. 1). They were indexed on a monoclinic cell using the same metrical relationships (a mono ¯c mono ¯(3 / 2)1 / 2 a cubic , b mono ¯(2)1 / 2 / 2 a cubic , 1/2 bmono ¯2 arctan (2) ¯109.478) as those used to describe the monoclinic low-temperature structure of more deuterium rich ZrCr 2 D 3.8 [3]. Unlike the latter, however, the systematically absent reflections suggested space group P21 /n rather than C2 /c. A structure model was constructed by transforming all atom positions of the cubic to the monoclinic cell (Table 1). This required splitting of the eightfold Zr position in the cubic cell into two fourfold positions in the monoclinic cell, and of the 16-fold Cr and the 96-fold D positions into four and 24 fourfold positions, respectively. A stepwise refinement of the occupancy factors of the D sites revealed that only four (out of 24) positions were significantly occupied (Table 2). The background of the low-temperature patterns was described by a linear interpolation of 12 points and a pseudo-Voigt function was used for modeling reflection profiles. The following 49 parameters were allowed to vary in the final refinements: one scale factor, three halfwidth, one mixing, two asymmetry, four lattice, 30 positional parameters, three Debye-Waller factors, four occupancy factors and one zeropoint shift in 2u. Debye-Waller factors were constrained to have the same value for atoms of the same kind. The observed and calculated powder patterns are shown in Fig. 2b and refinement results are listed in Table 2. The refined deuterium content (ZrCr 2 D 0.61( 2) ) is somewhat lower than that obtained at room temperature (ZrCr 2 D 0.66( 1) ). The difference, however, is not significant. Refinement of the T550 K data yielded structure parameters not significantly different from those at T52 K, except for bigger cell parameters (Table 2). Note that some of the metal atom sites have negative B values which indicates that the structure model still needs to be improved, for
H. Kohlmann et al. / Journal of Alloys and Compounds 327 (2001) L4 –L9
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Fig. 2. Observed (crosses), calculated (solid line) and difference neutron powder diffraction pattern ( l5191.1 pm) of ZrCr 2 D 0.66 at (a) T5293 K, (b) T52 K. Intensity in total detector counts.
Table 1 ] Crystal structure data for cubic ZrCr 2 D 0.66 (space group Fd3 m) at T5293 K as refined from neutron powder diffraction data Atom
Site
Zr Cr D
8a 16d 96g
Symmetry ] 43m ] 3m ..m
x /a
y /b
z /c
B a / 10 4 pm 2
Occupancy
1/8 1/2 0.0686(4)
1/8 1/2 x
1/8 1/2 0.8711(5)
0.41(3) 0.40(3) 1.2(2)
1 1 0.055(1)
Cell parameters:
a (293 K)5729.18(1) pm; a (150 K)5728.11(4) pm
Agreement indices:
R p 52.8%, R wp 53.4%, R Bragg 52.5% (R p 5S uy i (obs)2y i (calc)u / S y i (obs); R wp 5[S w i ( y i (obs)2y i (calc))2 / S w i y i (obs)2 ] 1 / 2 ; R Bragg 5S uIB (‘obs’)2IB (calc)u / S IB (‘obs’))
a
Form of the temperature factor: T5exp[2Biso (sin u /l)2 ].
H. Kohlmann et al. / Journal of Alloys and Compounds 327 (2001) L4 –L9
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Table 2 Crystal structure data for monoclinic ZrCr 2 D 0.66 (space group P21 /n) at T52 K as refined from neutron powder diffraction data Atom
Site
Symmetry
x /a
y /b
z /c
B a / 10 4 pm 2
Occupancy
Zr1 Zr2 Cr1 Cr2 Cr3 Cr4 D1 D2 D3 D4
4e 4e 4e 4e 4e 4e 4e 4e 4e 4e
1 1 1 1 1 1 1 1 1 1
0.4358(7) 0.0639(7) 0.258(1) 0.231(1) 0.987(1) 0.248(2) 0.061(3) 0.087(2) 0.489(3) 0.278(3)
0.250(1) 0.254(2) 0.995(3) 0.519(3) 0.255(3) 0.248(3) 0.116(4) 0.031(5) 0.456(4) 0.256(7)
0.0671(7) 0.9358(7) 0.252(2) 0.751(2) 0.241(1) 0.500(2) 0.442(3) 0.140(2) 0.884(3) 0.851(4)
0.08(3) B(Zr1) 20.25(4) B(Cr1) B(Cr1) B(Cr1) 0.5(2) B(D1) B(D1) B(D1)
1 1 1 1 1 1 0.40(2) 0.30(1) 0.29(2) 0.23(1)
Cell parameters:
T52 K: a5894.11(3) pm, b5513.72(2) pm, c5890.50(4), b 5109.563(3)8 T550 K: a5894.08(4) pm, b5513.84(3) pm, c5890.54(6) pm, b 5109.565(4)8
Agreement indices:
R p 54.8%, R wp 53.7%, R Bragg 56.2%
a
Form of temperature factor and agreement indices as in Table 1.
example by collecting data of higher resolution. This would allow a decrease the correlation between displacement parameters and occupancy factors and presumably would yield more reliable values for both types of parameters.
3. Discussion At room temperature a-ZrCr 2 D x has cubic symmetry ] (space group Fd3 m) and contains deuterium only in [Zr 2 Cr 2 ] type interstices, in agreement with a recent inelastic neutron scattering study [12]. The refined occupancy (5.5(1)%) corresponds to the composition ZrCr 2 D 0.66 . As the temperature is lowered to 150 K no
significant structural changes occur except for a contraction of the lattice. In particular, no long-range order is observed. Upon further lowering the temperature to T550 and 2 K additional, relatively sharp peaks appear in the diffraction patterns that are due to three-dimensional longrange order of the deuterium atoms. The onset temperature of ordering has not been determined, but from previous studies [6,7] it is likely to be in the range 55–70 K. As shown by the structure refinements, the low-temperature phase of ZrCr 2 D 0.66 has monoclinic symmetry (space group P21 /n) and its deuterium atoms occupy only four (out of 24 possible) sorts of [Zr 2 Cr 2 ] interstices with an occupancy in the range 23–40%. Note that the metric distortion of the monoclinic lattice is very small, corresponding to ,0.5% with respect to cell edges and ,0.18
Fig. 3. Structures of disordered cubic ZrCr 2 D 0.66 (T5293 K, left) and ordered, monoclinic ZrCr 2 D 0.66 (T52 K, right) in a projection along cubic [110] and along monoclinic [010], respectively (chromium atom tetrahedra outdrawn; deuterium site occupancies in parentheses). Note that only one sixth of the D positions of the disordered, cubic modification (left) are occupied in the ordered, monoclinic modification (right), with accordingly higher occupancies.
H. Kohlmann et al. / Journal of Alloys and Compounds 327 (2001) L4 –L9
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Table 3 Metal–deuterium and deuterium–deuterium distances shorter than 230 pm in monoclinic ZrCr 2 D 0.66 at 2 K (in pm) Zr1
–D1 –D1 –D3 –D3 –D4
188(2) 195(2) 213(3) 165(2) 197(3)
D1
–Zr1 –Zr1 –Cr3 –Cr4 –D1 –D3 –D3
188(2) 195(2) 184(2) 171(3) 211(3) 77(4) 193(4)
Zr2
–D2 –D2 –D4
210(2) 195(3) 228(3)
D2
–Zr2 –Zr2 –Cr1 –Cr3
210(2) 195(3) 154(2) 186(3)
Cr1
–D2
154(2)
D3
Cr2
–D3 –D4 –D4
224(3) 159(4) 151(4)
–Zr1 –Zr1 –Cr3 –Cr2 –D1 –D1 –D3 –D4
213(3) 165(2) 167(3) 224(3) 77(4) 193(3) 205(4) 208(4)
Cr3
–D1 –D3 –D2
184(2) 167(3) 186(3)
D4
–Zr1 –Zr2 –Cr2 –Cr2 –D3
197(3) 228(3) 159(4) 151(4) 208(4)
Cr4
–D1
171(3)
with respect to cell angles. As can be seen in Fig. 3, noticeable changes in the metal atom positions occur only with the chromium sites Cr1 and Cr2. The low-temperature structure of a-ZrCr 2 D 0.66 is closely related to that of a9-ZrCr 2 D 3.8 [3] which derives also from an order–disorder phase transition at low temperature. According to the crystallographic group–subgroup ¨ relationships introduced by Barnighausen [13] both are
related by a transition of index 2 (klassengleich) in which the C centering is lost: C2 /c (ZrCr 2 D 3.8 , T52 K)2 k2→P21 /n (ZrCr 2 D 0.7 , T52 K). The four eightfold D positions in C2 /c split up into eight fourfold positions in P21 /n, only two of which are occupied in ZrCr 2 D 0.66 (D1, D3). The two other positions (D2, D4) correspond to [Zr 2 Cr 2 ] sites that are not occupied in ZrCr 2 D 3.8 . Thus monoclinic a-ZrCr 2 D 0.66 and a9-ZrCr 2 D 3.8 are two ordered variants of the same cubic aristotype and differ only in the ordering scheme of the D atoms. As to their atomic environments they are similar, except that the metal sites in the D-poor composition generally have a smaller number of deuterium ligands than in the D-rich composition. Some Cr atoms, for example, have only one deuterium ligand (Cr1, Cr4) in ZrCr 2 D 0.66 . The metal–deuterium distances in monoclinic ZrCr 2 D 0.66 (Table 3) are consistent with those in monoclinic ZrCr 2 D 3.8 except that the former are generally shorter than the latter which is presumably due to the lower D site occupancies in ZrCr 2 D 0.66 (#40%) compared to ZrCr 2 D 3.8 ($85%). Note that the deuterium order in ZrCr 2 D 0.66 is still not complete and that the proximity of some deuterium sites (D1–D3577 pm) excludes them from being fully occupied. Finally, the order–disorder transition in a-ZrCr 2 D 0.66 is consistent with previous NMR and specific heat studies [4–7]. Altogether these studies show that hydrogen ordering may also occur in a-phases of ternary metal hydrides at rather low hydrogen-to-metal ratios. In the present system ordering occurs at H / M50.22 and is clearly longrange and three-dimensional in character. This is the lowest deuterium-to-metal ratio known among Laves phase derivative structures showing order–disorder transitions. Numerous other order–disorder transitions have been reported in such structures at higher H / M ratios. They are summarized in Table 4 and show a great variety of compositions and symmetries. At least ten different order-
Table 4 Ordered modifications of deuterium containing C15 type Laves phase derivatives a Compound
T (K)
Space group
D positions
D occupancies (%)
Ref.
HfV2 D 4 ZrV2 D 3.9 ZrV2 D 3.6 HfV2 D 1.9 ZrCr 2 D 3.8 ZrCr 2 D 0.7 ZrV2 D 3 ZrV2 D 2.8 ZrV2 D 2.3 ZrV2 D 1.8 ZrV2 D 1.5 ZrV2 D 1.1 YFe 2 D 1.3 b YFe 2 D 1.8 YMn 2 D 4.3
77 90 230 100 2 2 77 90 100 100 100 100 293 293 300
I41 /a I41 /a I41 /a C2 /c C2 /c P21 /n P21 /c P21 /c C2 /c C2 /c C2 /c C2 /c ] I4 ] I43 m R3 m
1 1 1 4 4 4 4 4 5 3 3 3 7 9 3
100 98 91 14–100 85–100 23–40 51–93 50–90 33–71 33–100 27–100 20–61 36–81 17–76 50–94
[17] [16] [15] [10] [3] This work [14] [16] [10] [10] [10] [10] [18] [18] [19]
a
Only those phases are included that undergo temperature dependent order–disorder transitions and are structurally characterized by neutron diffraction. Bold formula refer to new ordering patterns and indented formula to the ordering pattern of the preceding line. ] b YFe 2 D 1.9 has probably a similar structure with space group I4 and a tripled c-axis [18].
H. Kohlmann et al. / Journal of Alloys and Compounds 327 (2001) L4 –L9
ing patterns occur in systems such as ZrCr 2 D x [1–3], ZrV2 D x [10,14–16], HfV2 D x [10,17], YFe 2 D x [18] and YMn 2 D x [19], and they have cubic, tetragonal, rhombohedral and monoclinic symmetry. Note that four different ordering patterns occur with space group C2 /c and two with P21 /c. The latter include the currently studied aZrCr 2 D 0.66 and ZrV2 D x (1.1,x,2.3). They have distinctly different ordering patterns and are related by the common minimal supergroup I2 /m. Altogether these ordering patterns underline the very rich crystal chemistry of metal hydrides in general and the subtle balance between hydrogen content, atomic size and electronic effects on the ordering behavior of hydrogen in cubic Laves phase derivative structures in particular.
Acknowledgements This work was supported by the Russian Foundation for Basic Research (grant No. 99-02-16311) and the Swiss National Science Foundation (grant No. 20-53642.98).
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