Cubic ZrW(1.75)Mo(0.25)O(8) from a Rietveld refinement based on neutron powder diffraction data.

The solid solution in the system Zr-Mo-W-O with composition ZrW(1.75)Mo(0.25)O(8) (zirconium tungsten molybdenum octa-oxide) was prepared by solid-state reactions as a polycrystalline material. Its structure has cubic symmetry (space group P2(1)3) at room temperature. The structure contains a network of corner-sharing ZrO(6) octa-hedra (.3. symmetry) and MO(4) (M = W, Mo) tetra-hedra (.3. symmetry). Along the main threefold axis of the cubic unit cell, the MO(4) tetra-hedra are arranged in pairs forming M(2)O(8) units in which the M1O(4) tetra-hedra have larger distortions in terms of bond distances and angles than the M2O(4) tetra-hedra. These units are disordered over two possible orientations, with the M-O(terminal) vectors pointing to the [111] or [] directions. The reversal of the orientations of the M(2)O(8) units results from the concerted flips of these units. The time-averaged proportions of flipped and unflipped M(2)O(8) units were determined and the fraction of unflipped M(2)O(8) units is about 0.95. The order degree of the M(2)O(8) unit orientation is about 0.9. During the reversal process, the M-atom site has a migration about 0.93 Å, one of the O-atom sites has a 0.25 Å migration distance, whereas two other O-atom sites migrate marginally (≃ 0.08 Å). The results prove the constraint strategy to be a reasonable approach based on the ratcheting mechanism.

Related literature

For a general description of the structures and properties of unsubstituted ZrW2O8, see: Mary et al. (1996 ▶); Evans et al. (1996 ▶, 1999 ▶). Details on the ratcheting mechanism have been described by Hampson et al. (2004 ▶, 2005 ▶). For the synthesis of the title compound, see: Zhao et al. (2007 ▶). For a detailed description of polyhedral distortion parameters, see: Baur (1974 ▶); Robinson et al. (1971 ▶). For isomorphism and polymorphism in cubic ZrW2O8 type compounds, see: Evans et al. (2000 ▶); Lind et al. (1998 ▶); Huang et al.(2005 ▶); Deng et al. (2008 ▶). For their unusual isotropic negative thermal expansion properties, see: Mary et al. (1996 ▶).

Experimental

Crystal data

ZrW1.75Mo0.25O8

M = 564.93

Cubic,

a = 9.156880 (17) Å

V = 767.79 (1) Å3

Z = 4

Time-of-flight radiation

λ = 0.5–4.4 Å

T = 298 K

Specimen shape: cylinder

30 × 10 × 10 mm

Data collection

GPPD diffractometer

Specimen mounting: standard cylindrical vanadium sample holder

Scan method: time of flight

2θmin = 53, 2θmax = 145°

Refinement

R p = 0.032

R wp = 0.044

1893 reflections

58 parameters

Data collection: IPNS local software (Worlton et al., 2006 ▶); cell refinement: GSAS (Larson & von Dreele (2000 ▶); data reduction: IPNS local software; program(s) used to solve structure: GSAS; program(s) used to refine structure: GSAS; molecular graphics: VICS-II (Izumi & Dilanian, 2005 ▶); software used to prepare material for publication: GSAS.

Crystal structure: contains datablocks global, I, DXB-W1.75_p_01, DXB-W1.75_p_02. DOI: 10.1107/S1600536809015281/wm2222sup1.cif

Rietveld powder data: contains datablocks I, I, I. DOI: 10.1107/S1600536809015281/wm2222Isup2.rtv

Additional supplementary materials: crystallographic information; 3D view; checkCIF report

ZrW1.75Mo0.25O8	Dx = 4.887 Mg m−3
Mr = 564.93	Time-of-flight radiation
Cubic, P213	T = 298 K
a = 9.156880 (17) Å	white
V = 767.79 (1) Å3	cylinder, 30 × 10 mm
Z = 4

GPPD diffractometer	Scan method: time of flight
Specimen mounting: standard cylindrical vanadium sample holder

Least-squares matrix: full	? data points
Rp = 0.032	58 parameters
Rwp = 0.044	55 constraints
Rexp = ?	(Δ/σ)max = 0.02
χ2 = 2.341

	x	y	z	Uiso*/Ueq	Occ. (<1)
Zr1	0.00068 (14)	0.00068 (14)	0.00068 (14)	0.01044
W1	0.34038 (14)	0.34038 (14)	0.34038 (14)	0.01449	0.8339 (22)
W2	0.60102 (13)	0.60102 (13)	0.60102 (13)	0.01048	0.8339 (22)
O1	0.20648 (18)	0.4373 (2)	0.4482 (2)	0.02634	0.9530 (26)
O2	0.78912 (16)	0.5691 (2)	0.55685 (18)	0.01893	0.9530 (26)
O3	0.4920 (2)	0.4920 (2)	0.4920 (2)	0.02679	0.9530 (26)
O4	0.23253 (13)	0.23253 (13)	0.23253 (13)	0.03851	0.9530 (26)
Mo1	0.34038 (14)	0.34038 (14)	0.34038 (14)	0.01449	0.11913 (32)
Mo2	0.60102 (13)	0.60102 (13)	0.60102 (13)	0.01048	0.11913 (32)
W1-1	0.65963 (14)	0.65963 (14)	0.65963 (14)	0.01449	0.0411 (22)
W2-1	0.39898 (13)	0.39898 (13)	0.39898 (13)	0.01048	0.0411 (22)
Mo1-1	0.65963 (14)	0.65963 (14)	0.65963 (14)	0.01449	0.00587 (32)
Mo2-1	0.39898 (13)	0.39898 (13)	0.39898 (13)	0.01048	0.00587 (32)
O3-1	0.5080 (2)	0.5080 (2)	0.5080 (2)	0.02679	0.0470 (26)
O4-1	0.76747 (13)	0.76747 (13)	0.76747 (13)	0.03851	0.0470 (26)
O1-1	0.79352 (18)	0.5627 (2)	0.5518 (2)	0.02634	0.0470 (26)
O2-1	0.21088 (16)	0.4309 (2)	0.44315 (18)	0.01893	0.0470 (26)

	U11	U22	U33	U12	U13	U23
Zr1	0.0104 (2)	0.0104 (2)	0.0104 (2)	−0.0002 (3)	−0.0002 (3)	−0.0002 (3)
W1	0.0145 (5)	0.0145 (5)	0.0145 (5)	0.0080 (6)	0.0080 (6)	0.0080 (6)
W2	0.0105 (5)	0.0105 (5)	0.0105 (5)	0.0006 (4)	0.0006 (4)	0.0006 (4)
O1	0.0198 (9)	0.0272 (12)	0.0320 (11)	0.0083 (8)	0.0142 (8)	−0.0013 (8)
O2	0.0054 (7)	0.0272 (10)	0.0242 (10)	0.0057 (6)	0.0016 (7)	0.0058 (7)
O3	0.0268 (5)	0.0268 (5)	0.0268 (5)	−0.0090 (6)	−0.0090 (6)	−0.0090 (6)
O4	0.0385 (6)	0.0385 (6)	0.0385 (6)	−0.0119 (6)	−0.0119 (6)	−0.0119 (6)
Mo1	0.0145 (5)	0.0145 (5)	0.0145 (5)	0.0080 (6)	0.0080 (6)	0.0080 (6)
Mo2	0.0105 (5)	0.0105 (5)	0.0105 (5)	0.0006 (4)	0.0006 (4)	0.0006 (4)
W1-1	0.0145 (5)	0.0145 (5)	0.0145 (5)	0.0080 (6)	0.0080 (6)	0.0080 (6)
W2-1	0.0105 (5)	0.0105 (5)	0.0105 (5)	0.0006 (4)	0.0006 (4)	0.0006 (4)
Mo1-1	0.0145 (5)	0.0145 (5)	0.0145 (5)	0.0080 (6)	0.0080 (6)	0.0080 (6)
Mo2-1	0.0105 (5)	0.0105 (5)	0.0105 (5)	0.0006 (4)	0.0006 (4)	0.0006 (4)
O3-1	0.0268 (5)	0.0268 (5)	0.0268 (5)	−0.0090 (6)	−0.0090 (6)	−0.0090 (6)
O4-1	0.0385 (6)	0.0385 (6)	0.0385 (6)	−0.0119 (6)	−0.0119 (6)	−0.0119 (6)
O1-1	0.0198 (9)	0.0272 (12)	0.0320 (11)	0.0083 (8)	0.0142 (8)	−0.0013 (8)
O2-1	0.0054 (7)	0.0272 (10)	0.0242 (10)	0.0057 (6)	0.0016 (7)	0.0058 (7)

Zr1—O1i	2.0384 (21)	O3—M2	1.729 (4)
Zr1—O1ii	2.0384 (21)	O3—M1-1	2.659 (4)
Zr1—O1iii	2.0384 (21)	O3—M2-1	1.475 (4)
Zr1—O2iv	2.0915 (20)	O3—O3-1	0.254 (7)
Zr1—O2v	2.0915 (20)	O4—M1	1.7105 (32)
Zr1—O2vi	2.0915 (20)	O4—M2-1	2.6400 (29)
Zr1—O1-1iv	2.0261 (21)	M1-1—M2	0.9295 (23)
Zr1—O1-1v	2.0261 (21)	M1-1—O2	1.7261 (18)
Zr1—O1-1vi	2.0261 (21)	M1-1—O2vii	1.7261 (18)
Zr1—O2-1i	2.1037 (19)	M1-1—O2viii	1.7261 (18)
Zr1—O2-1ii	2.1037 (19)	M1-1—O3	2.659 (4)
Zr1—O2-1iii	2.1037 (19)	M1-1—O3-1	2.405 (4)
M1—O1	1.8069 (18)	M1-1—O4-1	1.7105 (32)
M1—O1vii	1.8069 (18)	M1-1—O1-1	1.8069 (18)
M1—O1viii	1.8069 (18)	M1-1—O1-1vii	1.8069 (18)
M1—O3	2.405 (4)	M1-1—O1-1viii	1.8069 (18)
M1—O4	1.7105 (32)	M2-1—M1	0.9294 (23)
M1—M2-1	0.9294 (23)	M2-1—M2	3.204 (4)
M1—O3-1	2.659 (4)	M2-1—O1	1.8528 (18)
M1—O2-1	1.7260 (18)	M2-1—O1vii	1.8528 (18)
M1—O2-1vii	1.7260 (18)	M2-1—O1viii	1.8528 (18)
M1—O2-1viii	1.7260 (18)	M2-1—O3	1.475 (4)
M2—O2	1.7933 (16)	M2-1—O4	2.6400 (29)
M2—O2vii	1.7933 (16)	M2-1—O3-1	1.729 (4)
M2—O2viii	1.7933 (16)	M2-1—O2-1	1.7933 (16)
M2—O3	1.729 (4)	M2-1—O2-1vii	1.7933 (16)
M2—M1-1	0.9295 (23)	M2-1—O2-1viii	1.7933 (16)
M2—M2-1	3.204 (4)	O3-1—M1	2.659 (4)
M2—O3-1	1.475 (4)	O3-1—M2	1.475 (4)
M2—O4-1	2.6399 (29)	O3-1—O3	0.254 (7)
M2—O1-1	1.8528 (18)	O3-1—M1-1	2.405 (4)
M2—O1-1vii	1.8528 (18)	O3-1—M2-1	1.729 (4)
M2—O1-1viii	1.8528 (18)	O4-1—M2	2.6399 (29)
O1—Zr1ix	2.0384 (21)	O4-1—M1-1	1.7105 (32)
O1—M1	1.8069 (18)	O1-1—Zr1x	2.0261 (21)
O1—M2-1	1.8528 (18)	O1-1—M2	1.8528 (18)
O1—O2-1	0.084 (4)	O1-1—O2	0.084 (4)
O2—Zr1x	2.0915 (20)	O1-1—M1-1	1.8069 (18)
O2—M2	1.7933 (16)	O2-1—Zr1ix	2.1037 (19)
O2—M1-1	1.7261 (18)	O2-1—M1	1.7260 (18)
O2—O1-1	0.084 (4)	O2-1—O1	0.084 (4)
O3—M1	2.405 (4)	O2-1—M2-1	1.7933 (16)
O1i—Zr1—O1ii	90.82 (10)	O2viii—M2—O3	109.28 (9)
O1i—Zr1—O1iii	90.82 (10)	O2viii—M2—M1-1	70.72 (9)
O1i—Zr1—O2iv	178.37 (10)	O2viii—M2—O3-1	109.28 (9)
O1i—Zr1—O2v	87.64 (8)	O2viii—M2—O1-1	110.24 (11)
O1i—Zr1—O2vi	89.74 (8)	O2viii—M2—O1-1vii	110.90 (10)
O1i—Zr1—O1-1iv	179.4968 (9)	O2viii—M2—O1-1viii	1.88 (12)
O1i—Zr1—O1-1v	88.83 (7)	O3—M2—M1-1	180.0
O1i—Zr1—O1-1vi	88.83 (7)	O3—M2—O1-1	107.43 (8)
O1i—Zr1—O2-1ii	92.01 (12)	O3—M2—O1-1vii	107.43 (8)
O1i—Zr1—O2-1iii	89.92 (10)	O3—M2—O1-1viii	107.43 (8)
O1ii—Zr1—O1iii	90.82 (10)	M1-1—M2—O3-1	180.0
O1ii—Zr1—O2iv	89.74 (8)	M1-1—M2—O1-1	72.57 (8)
O1ii—Zr1—O2v	178.37 (10)	M1-1—M2—O1-1vii	72.57 (8)
O1ii—Zr1—O2vi	87.64 (8)	M1-1—M2—O1-1viii	72.57 (8)
O1ii—Zr1—O1-1iv	88.83 (7)	O3-1—M2—O1-1	107.43 (8)
O1ii—Zr1—O1-1v	179.4968 (9)	O3-1—M2—O1-1vii	107.43 (8)
O1ii—Zr1—O1-1vi	88.83 (7)	O3-1—M2—O1-1viii	107.43 (8)
O1ii—Zr1—O2-1i	89.92 (10)	O1-1—M2—O1-1vii	111.43 (8)
O1ii—Zr1—O2-1iii	92.01 (12)	O1-1—M2—O1-1viii	111.43 (8)
O1iii—Zr1—O2iv	87.64 (8)	O1-1vii—M2—O1-1viii	111.43 (8)
O1iii—Zr1—O2v	89.74 (8)	Zr1ix—O1—M1	153.75 (12)
O1iii—Zr1—O2vi	178.37 (10)	Zr1ix—O1—M2-1	174.36 (12)
O1iii—Zr1—O1-1iv	88.83 (7)	Zr1ix—O1—O2-1	139.9 (22)
O1iii—Zr1—O1-1v	88.83 (7)	M1—O1—M2-1	29.39 (8)
O1iii—Zr1—O1-1vi	179.4984 (9)	M2-1—O1—O2-1	44.3 (21)
O1iii—Zr1—O2-1i	92.01 (12)	Zr1x—O2—M2	171.71 (13)
O1iii—Zr1—O2-1ii	89.92 (10)	Zr1x—O2—M1-1	155.98 (13)
O2iv—Zr1—O2v	91.81 (10)	M2—O2—O1-1	133.9 (22)
O2iv—Zr1—O2vi	91.81 (10)	M2—O2—M1-1	30.55 (8)
O2iv—Zr1—O1-1v	90.60 (12)	M1-1—O2—O1-1	162.9 (23)
O2iv—Zr1—O1-1vi	92.72 (10)	M2—O3—M2-1	179.972
O2iv—Zr1—O2-1i	179.5134 (9)	M2-1—O3—O3-1	179.972
O2iv—Zr1—O2-1ii	88.52 (6)	M2—M1-1—O2	78.73 (10)
O2iv—Zr1—O2-1iii	88.53 (6)	M2—M1-1—O2vii	78.73 (10)
O2v—Zr1—O2vi	91.81 (10)	M2—M1-1—O2viii	78.73 (10)
O2v—Zr1—O1-1iv	92.72 (10)	M2—M1-1—O4-1	179.972
O2v—Zr1—O1-1vi	90.60 (12)	M2—M1-1—O1-1	78.04 (9)
O2v—Zr1—O2-1i	88.53 (6)	M2—M1-1—O1-1vii	78.04 (9)
O2v—Zr1—O2-1ii	179.5134 (9)	M2—M1-1—O1-1viii	78.04 (9)
O2v—Zr1—O2-1iii	88.52 (6)	O2—M1-1—O2vii	116.27 (6)
O2vi—Zr1—O1-1iv	90.60 (12)	O2—M1-1—O2viii	116.27 (6)
O2vi—Zr1—O1-1v	92.72 (10)	O2—M1-1—O4-1	101.27 (10)
O2vi—Zr1—O2-1i	88.52 (6)	O2—M1-1—O1-1vii	115.68 (10)
O2vi—Zr1—O2-1ii	88.53 (6)	O2—M1-1—O1-1viii	116.42 (11)
O2vi—Zr1—O2-1iii	179.5122 (9)	O2vii—M1-1—O2viii	116.27 (6)
O1-1iv—Zr1—O1-1v	91.52 (10)	O2vii—M1-1—O4-1	101.27 (10)
O1-1iv—Zr1—O1-1vi	91.52 (10)	O2vii—M1-1—O1-1	116.42 (11)
O1-1iv—Zr1—O2-1i	178.51 (10)	O2vii—M1-1—O1-1viii	115.68 (10)
O1-1iv—Zr1—O2-1ii	87.63 (8)	O2viii—M1-1—O4-1	101.27 (10)
O1-1iv—Zr1—O2-1iii	89.73 (9)	O2viii—M1-1—O1-1	115.68 (10)
O1-1v—Zr1—O1-1vi	91.52 (10)	O2viii—M1-1—O1-1vii	116.42 (11)
O1-1v—Zr1—O2-1i	89.73 (9)	O4-1—M1-1—O1-1	101.96 (9)
O1-1v—Zr1—O2-1ii	178.51 (10)	O4-1—M1-1—O1-1vii	101.96 (9)
O1-1v—Zr1—O2-1iii	87.63 (8)	O4-1—M1-1—O1-1viii	101.96 (9)
O1-1vi—Zr1—O2-1i	87.63 (8)	O1-1—M1-1—O1-1vii	115.82 (6)
O1-1vi—Zr1—O2-1ii	89.73 (9)	O1-1—M1-1—O1-1viii	115.82 (6)
O1-1vi—Zr1—O2-1iii	178.51 (10)	O1-1vii—M1-1—O1-1viii	115.82 (6)
O2-1i—Zr1—O2-1ii	91.13 (9)	M1—M2-1—O1	72.57 (8)
O2-1i—Zr1—O2-1iii	91.13 (9)	M1—M2-1—O1vii	72.57 (8)
O2-1ii—Zr1—O2-1iii	91.13 (9)	M1—M2-1—O1viii	72.57 (8)
O1—M1—O1vii	115.82 (6)	M1—M2-1—O3	179.9802
O1—M1—O1viii	115.82 (6)	M1—M2-1—O3-1	179.972
O1—M1—O4	101.96 (9)	M1—M2-1—O2-1	70.72 (9)
O1—M1—M2-1	78.04 (9)	M1—M2-1—O2-1vii	70.72 (9)
O1—M1—O2-1vii	116.42 (11)	M1—M2-1—O2-1viii	70.72 (9)
O1—M1—O2-1viii	115.68 (10)	O1—M2-1—O1vii	111.43 (8)
O1vii—M1—O1viii	115.82 (6)	O1—M2-1—O1viii	111.43 (8)
O1vii—M1—O4	101.96 (9)	O1—M2-1—O3	107.43 (8)
O1vii—M1—M2-1	78.04 (9)	O1—M2-1—O3-1	107.43 (8)
O1vii—M1—O2-1	115.68 (10)	O1—M2-1—O2-1vii	110.90 (10)
O1vii—M1—O2-1viii	116.42 (11)	O1—M2-1—O2-1viii	110.24 (11)
O1viii—M1—O4	101.96 (9)	O1vii—M2-1—O1viii	111.43 (8)
O1viii—M1—M2-1	78.04 (9)	O1vii—M2-1—O3	107.43 (8)
O1viii—M1—O2-1	116.42 (11)	O1vii—M2-1—O3-1	107.43 (8)
O1viii—M1—O2-1vii	115.68 (10)	O1vii—M2-1—O2-1	110.24 (11)
O4—M1—M2-1	179.9802	O1vii—M2-1—O2-1viii	110.90 (10)
O4—M1—O2-1	101.27 (10)	O1viii—M2-1—O3	107.43 (8)
O4—M1—O2-1vii	101.27 (10)	O1viii—M2-1—O3-1	107.43 (8)
O4—M1—O2-1viii	101.27 (10)	O1viii—M2-1—O2-1	110.90 (10)
M2-1—M1—O2-1	78.73 (10)	O1viii—M2-1—O2-1vii	110.24 (11)
M2-1—M1—O2-1vii	78.73 (10)	O3—M2-1—O2-1	109.28 (9)
M2-1—M1—O2-1viii	78.73 (10)	O3—M2-1—O2-1vii	109.28 (9)
O2-1—M1—O2-1vii	116.28 (6)	O3—M2-1—O2-1viii	109.28 (9)
O2-1—M1—O2-1viii	116.28 (6)	O3-1—M2-1—O2-1	109.28 (9)
O2-1vii—M1—O2-1viii	116.28 (6)	O3-1—M2-1—O2-1vii	109.28 (9)
O2—M2—O2vii	109.66 (9)	O3-1—M2-1—O2-1viii	109.28 (9)
O2—M2—O2viii	109.66 (9)	O2-1—M2-1—O2-1vii	109.66 (9)
O2—M2—O3	109.28 (9)	O2-1—M2-1—O2-1viii	109.66 (9)
O2—M2—M1-1	70.72 (9)	O2-1vii—M2-1—O2-1viii	109.66 (9)
O2—M2—O3-1	109.28 (9)	M2—O3-1—O3	179.972
O2—M2—O1-1vii	110.24 (11)	M2—O3-1—M2-1	179.972
O2—M2—O1-1viii	110.90 (10)	Zr1x—O1-1—M2	174.64 (11)
O2vii—M2—O2viii	109.66 (9)	Zr1x—O1-1—O2	140.0 (22)
O2vii—M2—O3	109.28 (9)	Zr1x—O1-1—M1-1	153.95 (13)
O2vii—M2—M1-1	70.72 (9)	Zr1ix—O2-1—M1	155.76 (13)
O2vii—M2—O3-1	109.28 (9)	Zr1ix—O2-1—M2-1	171.56 (13)
O2vii—M2—O1-1	110.90 (10)	M1—O2-1—O1	162.9 (23)
O2vii—M2—O1-1viii	110.24 (11)	O1—O2-1—M2-1	133.9 (22)

Zr1—O1i	2.0384 (21)
Zr1—O2ii	2.0915 (20)
Zr1—O1-1ii	2.0261 (21)
Zr1—O2-1i	2.1037 (19)
M1—O1	1.8069 (18)
M1—O3	2.405 (4)
M1—O4	1.7105 (32)
M1—M2-1	0.9294 (23)
M2—O2	1.7933 (16)
M2—O3	1.729 (4)
O1—O2-1	0.084 (4)
O3—O3-1	0.254 (7)

O1—M1—O1iii	115.82 (6)
O1—M1—O4	101.96 (9)
O2—M2—O2iii	109.66 (9)
O2—M2—O3	109.28 (9)

M = Mo, W. Symmetry codes: (i) ; (ii) ; (iii) .