Cubic ZrW1.75Mo0.25O8 from a Rietveld refinement based on neutron powder diffraction data

Deng, X.; Cao, Y.; Tao, J.; Zhao, X.

doi:10.1107/S1600536809015281

inorganic compounds

CRYSTALLOGRAPHIC
COMMUNICATIONS

ISSN: 2056-9890

Volume 65| Part 5| May 2009| Pages i36-i37

doi:10.1107/S1600536809015281

Open

access

Cubic ZrW_1.75Mo_0.25O₈ from a Rietveld refinement based on neutron powder diffraction data

Xuebin Deng,^a Yilong Cao,^a Juzhou Tao ^b and Xinhua Zhao ^a ^*

^aCollege of Chemistry, Beijing Normal University, Beijing 100875, People's Republic of China, and ^bExperimental Physics Center, Institute of High Energy Physics, Chinese Academy of Sciences, Beijing 100049, People's Republic of China
^*Correspondence e-mail: xinhuaz@bnu.edu.cn

(Received 25 February 2009; accepted 23 April 2009; online 30 April 2009)

The solid solution in the system Zr–Mo–W–O with composition ZrW_1.75Mo_0.25O₈ (zirconium tungsten molybdenum octaoxide) was prepared by solid-state reactions as a polycrystalline material. Its structure has cubic symmetry (space group P2₁3) at room temperature. The structure contains a network of corner-sharing ZrO₆ octahedra (.3. symmetry) and MO₄ (M = W, Mo) tetrahedra (.3. symmetry). Along the main threefold axis of the cubic unit cell, the MO₄ tetrahedra are arranged in pairs forming M₂O₈ units in which the M1O₄ tetrahedra have larger distortions in terms of bond distances and angles than the M2O₄ tetrahedra. These units are disordered over two possible orientations, with the M—O_terminal vectors pointing to the [111] or [ $[\overline{1}]$ $[\overline{1}]$ $[\overline{1}]$ ] directions. The reversal of the orientations of the M₂O₈ units results from the concerted flips of these units. The time-averaged proportions of flipped and unflipped M₂O₈ units were determined and the fraction of unflipped M₂O₈ units is about 0.95. The order degree of the M₂O₈ 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

ZrW_1.75Mo_0.25O₈
M_r = 564.93
Cubic, P 2₁ 3
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
2θ_min = 53, 2θ_max = 145°

Refinement

R_p = 0.032
R_wp = 0.044
1893 reflections
58 parameters

Table 1
Selected geometric parameters (Å, °)

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) $[-z+{\script{1\over 2}}, -x, y-{\script{1\over 2}}]$ ; (ii) $[-z+{\script{1\over 2}}, -x+1, y-{\script{1\over 2}}]$ ; (iii) z, x, y.

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 $[Izumi, F. & Dilanian, R. A. (2005). Commission on Powder Diffraction, IUCr Newsletter, No. 32, pp. 59-63.]$ ); software used to prepare material for publication: GSAS.

Supporting information

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

checkCIF report

Comment top

Cubic ZrW₂O₈ type compounds have been attracting considerable interests due to their unusual isotropic negative thermal expansion properties (Mary et al., 1996). Many research groups have been studying isomorphism and polymorphism behaviors of this family (Evans et al., 2000; Deng et al., 2008; Huang et al., 2005; Lind et al.,1998), to investigate the structure-property relationships in detail, and to explore procedures for improving the properties of such materials. By means of Mo atoms partially substituting W atoms to form a cubic solid solution of the type ZrW_{2 -}_xMo_xO₈, we were able to extend the thermal stability range of cubic ZrW₂O₈ type compounds. Recently, we have reported the high-temperature synthesis of the solid solution ZrW_{2 -}_xMo_xO₈ series (Zhao et al., 2007), and found that the order-disorder phase transition temperature (T_tr) and the order degree of the ZrW_{2 -}_xMo_xO₈ series decrease with the increase of the Mo concentration. According to the X-ray diffraction patterns, these compounds (x < 0.9) adopt the ordered α-ZrW₂O₈structure at room temperature. However, the detailed average crystal structures are not reported.

In this paper, we describe the synthesis of cubic ZrW_1.75Mo_0.25O₈ and the average crystal structure as determined from neutron powder diffraction data using the Rietveld method. The crystal structure is presented in Fig.1 and plot of the Rietveld refinement is shown in Fig. 2.

The structure of ZrW_1.75Mo_0.25O₈ contains a network of corner-sharing ZrO₆ octahedra and MO₄ tetrahedra. Each octahedron shares all six corners with six separate MO₄ tetrahedra, but each MO₄ tetrahedron shares only three of its four oxygen corners with adjacent octahedra. In other words, each MO₄ tetrahedron has a 'terminal' oxygen atom. Along the main 3-fold axis of the cubic unit cell, the MO₄ tetrahedra are arranged in pairs forming condensed M₂O₈ units. The 'terminal' O atom of each MO₄ tetrahedron points in the same direction in the M₂O₈ unit, leading to an O4-M1···O3-M2 arrangement (Fig. 3). The M-O_terminal bond lengths are significantly shorter than the other M-O bond lengths. The second nearest M atom to terminal O4 atom lies at a distance of about 3.6 Å, so O4 atom is strictly one-coordinate. However, the distance to the terminal O3 atom is about 2.4 Å, indicating that it has one short and one long bond to the M atom. The existence of some interaction between M1 and the terminal O3 atom of the adjacent M2O₄ tetrahedron is proved by larger distortions in terms of bond angles and distances of M1O₄ tetrahedra than that of M2O₄ tetrahedra. The values of the bond length distortion index D (Baur, 1974), 0.02028, and of the bond angle variance σ² (Robinson et al., 1971), 58.12 °², of M1O₄ tetrahedra are both larger than that of M2O₄ tetrahedra in which D is 0.01355 and σ² is 0.0445. Moreover, the O1—O3 distance of 2.69Å is shorter than all other O—O distances, indicating there is a weak repulsive interaction between these two atoms. This is supported by bond angle values; O1—M1—O1 is larger than O2—M2—O2 and O1—M1—O4 is smaller than O2—M2—O3.

Based on the structure model of α-ZrW₂O₈ (Evans et al., 1996, 1999), some special conditions were constrained to match the 'ratcheting mechanism' described by Hampson et al. (2004, 2005) that considers the static (averaged) crystal structure determined by X-ray diffraction and the NMR observation of oxygen dynamics. The refinement results indicate that before and after the reversal process, the M atom site has a migration about a 0.93 Å, the O3 atom site has a 0.25Å migration, whereas the O1/O2 atom site migrate only a little (0.08 Å). The time-averaged proportion of flipped and unflipped M₂O₈ units was determined. The fraction of unflipped M₂O₈ units is about 0.95 and the order degree (defined as 2f-1, in which f is the site occupancy value of the unflipped part) is about 0.9.

Related literature top

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 cCubic 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 top

Cubic ZrW_1.75Mo_0.25O₈ was prepared using a similar procedure described previously (Zhao et al., 2007). Analytical-grade reagents ZrOCl₂^.8H₂O, (NH₄)₁₀W₁₂O₄₁^.5H₂O and (NH₄)₆Mo₇O₂₄^.4H₂O were dissolved in water and the solutions of Zr(IV) and Mo(VI) were simultaneously dropped into the slurry of the W(VI) compound to obtain a white precipitate. The precipitate was dried together with the mother liquor at 373 K and subsequently ground in an agate mortar to obtain a homogeneous powder. Then the powder was sintered at 873 K for 3 h. and then pressed into a pellet under a pressure of 4 MPa. Then the pellet was again sintered at 1403 K for 1 h and then quenched to room temperature to yield cubic ZrW_1.7Mo_0.3O₈. During the sintering process, the weight loss of this sample, which is attributed to the volatility of MoO₃, is 1.4 wt %, so the exact formula is ZrW_1.75Mo_0.25O₈. The trace of ZrO₂ as an impurity in the powder is undetectable by neutron diffraction.

Computing details top

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

Figures top

	Fig. 1. Polyhedral representation of cubic ZrW_1.75Mo_0.25O₈. ZrO₆ octahedra and MO₄ tetrahedra are shown as light-gray and dark-gray polyhedra. The bridging oxygen atoms and the terminal oxygen atoms are shown as red and pink balls, respectively. For clarity, the atoms related to the flipped part are removed from the figure.
	Fig. 2. Final Rietveld refinement neutron powder data plot and difference plot for cubic ZrW_1.75Mo_0.25O₈. The crosses are the observed data, the solid line is the calculated pattern, and the tick marks indicate the calculated reflection positions. The difference curve is plotted below. Only the 145° bank data is shown.
	Fig. 3. The schematic representation of the starting structural model for cubic ZrW_1.75Mo_0.25O₈. Black balls and circles represent 'unflipped' and 'flipped' atoms, respectively.

Zirconium tungsten molybdenum octaoxide top

Crystal data top

ZrW_1.75Mo_0.25O₈	D_x = 4.887 Mg m⁻³
M_r = 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

Data collection top

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

Refinement top

Least-squares matrix: full	? data points
R_p = 0.032	58 parameters
R_wp = 0.044	55 constraints
R_exp = ?	(Δ/σ)_max = 0.02
χ² = 2.341

Crystal data top

ZrW_1.75Mo_0.25O₈	Z = 4
M_r = 564.93	Time-of-flight radiation
Cubic, P2₁3	T = 298 K
a = 9.156880 (17) Å	cylinder, 30 × 10 mm
V = 767.79 (1) Å³

Data collection top

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

Refinement top

R_p = 0.032	χ² = 2.341
R_wp = 0.044	? data points
R_exp = ?	58 parameters

Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å²) top

	x	y	z	U_iso*/U_eq	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)

Atomic displacement parameters (Å²) top

	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)

Geometric parameters (Å, º) top

Zr1—O1ⁱ	2.038 (2)	O3—M2	1.729 (4)
Zr1—O1ⁱⁱ	2.038 (2)	O3—M1-1	2.659 (4)
Zr1—O1ⁱⁱⁱ	2.038 (2)	O3—M2-1	1.475 (4)
Zr1—O2^iv	2.092 (2)	O3—O3-1	0.254 (7)
Zr1—O2^v	2.092 (2)	O4—M1	1.711 (3)
Zr1—O2^vi	2.092 (2)	O4—M2-1	2.640 (3)
Zr1—O1-1^iv	2.026 (2)	M1-1—M2	0.930 (2)
Zr1—O1-1^v	2.026 (2)	M1-1—O2	1.7261 (18)
Zr1—O1-1^vi	2.026 (2)	M1-1—O2^vii	1.7261 (18)
Zr1—O2-1ⁱ	2.1037 (19)	M1-1—O2^viii	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	1.711 (3)
M1—O1^vii	1.8069 (18)	M1-1—O1-1	1.8069 (18)
M1—O1^viii	1.8069 (18)	M1-1—O1-1^vii	1.8069 (18)
M1—O3	2.405 (4)	M1-1—O1-1^viii	1.8069 (18)
M1—O4	1.711 (3)	M2-1—M1	0.929 (2)
M1—M2-1	0.929 (2)	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—O1^vii	1.8528 (18)
M1—O2-1^vii	1.7260 (18)	M2-1—O1^viii	1.8528 (18)
M1—O2-1^viii	1.7260 (18)	M2-1—O3	1.475 (4)
M2—O2	1.7933 (16)	M2-1—O4	2.640 (3)
M2—O2^vii	1.7933 (16)	M2-1—O3-1	1.729 (4)
M2—O2^viii	1.7933 (16)	M2-1—O2-1	1.7933 (16)
M2—O3	1.729 (4)	M2-1—O2-1^vii	1.7933 (16)
M2—M1-1	0.930 (2)	M2-1—O2-1^viii	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	2.640 (3)	O3-1—O3	0.254 (7)
M2—O1-1	1.8528 (18)	O3-1—M1-1	2.405 (4)
M2—O1-1^vii	1.8528 (18)	O3-1—M2-1	1.729 (4)
M2—O1-1^viii	1.8528 (18)	O4-1—M2	2.640 (3)
O1—Zr1^ix	2.038 (2)	O4-1—M1-1	1.711 (3)
O1—M1	1.8069 (18)	O1-1—Zr1^x	2.026 (2)
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—Zr1^x	2.092 (2)	O1-1—M1-1	1.8069 (18)
O2—M2	1.7933 (16)	O2-1—Zr1^ix	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)	O2^viii—M2—O3	109.28 (9)
O1ⁱ—Zr1—O1ⁱⁱⁱ	90.82 (10)	O2^viii—M2—M1-1	70.72 (9)
O1ⁱ—Zr1—O2^iv	178.37 (10)	O2^viii—M2—O3-1	109.28 (9)
O1ⁱ—Zr1—O2^v	87.64 (8)	O2^viii—M2—O1-1	110.24 (11)
O1ⁱ—Zr1—O2^vi	89.74 (8)	O2^viii—M2—O1-1^vii	110.90 (10)
O1ⁱ—Zr1—O1-1^iv	179.4968 (9)	O2^viii—M2—O1-1^viii	1.88 (12)
O1ⁱ—Zr1—O1-1^v	88.83 (7)	O3—M2—M1-1	180.0
O1ⁱ—Zr1—O1-1^vi	88.83 (7)	O3—M2—O1-1	107.43 (8)
O1ⁱ—Zr1—O2-1ⁱⁱ	92.01 (12)	O3—M2—O1-1^vii	107.43 (8)
O1ⁱ—Zr1—O2-1ⁱⁱⁱ	89.92 (10)	O3—M2—O1-1^viii	107.43 (8)
O1ⁱⁱ—Zr1—O1ⁱⁱⁱ	90.82 (10)	M1-1—M2—O3-1	180.0
O1ⁱⁱ—Zr1—O2^iv	89.74 (8)	M1-1—M2—O1-1	72.57 (8)
O1ⁱⁱ—Zr1—O2^v	178.37 (10)	M1-1—M2—O1-1^vii	72.57 (8)
O1ⁱⁱ—Zr1—O2^vi	87.64 (8)	M1-1—M2—O1-1^viii	72.57 (8)
O1ⁱⁱ—Zr1—O1-1^iv	88.83 (7)	O3-1—M2—O1-1	107.43 (8)
O1ⁱⁱ—Zr1—O1-1^v	179.4968 (9)	O3-1—M2—O1-1^vii	107.43 (8)
O1ⁱⁱ—Zr1—O1-1^vi	88.83 (7)	O3-1—M2—O1-1^viii	107.43 (8)
O1ⁱⁱ—Zr1—O2-1ⁱ	89.92 (10)	O1-1—M2—O1-1^vii	111.43 (8)
O1ⁱⁱ—Zr1—O2-1ⁱⁱⁱ	92.01 (12)	O1-1—M2—O1-1^viii	111.43 (8)
O1ⁱⁱⁱ—Zr1—O2^iv	87.64 (8)	O1-1^vii—M2—O1-1^viii	111.43 (8)
O1ⁱⁱⁱ—Zr1—O2^v	89.74 (8)	Zr1^ix—O1—M1	153.75 (12)
O1ⁱⁱⁱ—Zr1—O2^vi	178.37 (10)	Zr1^ix—O1—M2-1	174.36 (12)
O1ⁱⁱⁱ—Zr1—O1-1^iv	88.83 (7)	Zr1^ix—O1—O2-1	140 (2)
O1ⁱⁱⁱ—Zr1—O1-1^v	88.83 (7)	M1—O1—M2-1	29.39 (8)
O1ⁱⁱⁱ—Zr1—O1-1^vi	179.4984 (9)	M2-1—O1—O2-1	44 (2)
O1ⁱⁱⁱ—Zr1—O2-1ⁱ	92.01 (12)	Zr1^x—O2—M2	171.71 (13)
O1ⁱⁱⁱ—Zr1—O2-1ⁱⁱ	89.92 (10)	Zr1^x—O2—M1-1	155.98 (13)
O2^iv—Zr1—O2^v	91.81 (10)	M2—O2—O1-1	134 (2)
O2^iv—Zr1—O2^vi	91.81 (10)	M2—O2—M1-1	30.55 (8)
O2^iv—Zr1—O1-1^v	90.60 (12)	M1-1—O2—O1-1	163 (2)
O2^iv—Zr1—O1-1^vi	92.72 (10)	M2—O3—M2-1	179.972
O2^iv—Zr1—O2-1ⁱ	179.5134 (9)	M2-1—O3—O3-1	179.972
O2^iv—Zr1—O2-1ⁱⁱ	88.52 (6)	M2—M1-1—O2	78.73 (10)
O2^iv—Zr1—O2-1ⁱⁱⁱ	88.53 (6)	M2—M1-1—O2^vii	78.73 (10)
O2^v—Zr1—O2^vi	91.81 (10)	M2—M1-1—O2^viii	78.73 (10)
O2^v—Zr1—O1-1^iv	92.72 (10)	M2—M1-1—O4-1	179.972
O2^v—Zr1—O1-1^vi	90.60 (12)	M2—M1-1—O1-1	78.04 (9)
O2^v—Zr1—O2-1ⁱ	88.53 (6)	M2—M1-1—O1-1^vii	78.04 (9)
O2^v—Zr1—O2-1ⁱⁱ	179.5134 (9)	M2—M1-1—O1-1^viii	78.04 (9)
O2^v—Zr1—O2-1ⁱⁱⁱ	88.52 (6)	O2—M1-1—O2^vii	116.27 (6)
O2^vi—Zr1—O1-1^iv	90.60 (12)	O2—M1-1—O2^viii	116.27 (6)
O2^vi—Zr1—O1-1^v	92.72 (10)	O2—M1-1—O4-1	101.27 (10)
O2^vi—Zr1—O2-1ⁱ	88.52 (6)	O2—M1-1—O1-1^vii	115.68 (10)
O2^vi—Zr1—O2-1ⁱⁱ	88.53 (6)	O2—M1-1—O1-1^viii	116.42 (11)
O2^vi—Zr1—O2-1ⁱⁱⁱ	179.5122 (9)	O2^vii—M1-1—O2^viii	116.27 (6)
O1-1^iv—Zr1—O1-1^v	91.52 (10)	O2^vii—M1-1—O4-1	101.27 (10)
O1-1^iv—Zr1—O1-1^vi	91.52 (10)	O2^vii—M1-1—O1-1	116.42 (11)
O1-1^iv—Zr1—O2-1ⁱ	178.51 (10)	O2^vii—M1-1—O1-1^viii	115.68 (10)
O1-1^iv—Zr1—O2-1ⁱⁱ	87.63 (8)	O2^viii—M1-1—O4-1	101.27 (10)
O1-1^iv—Zr1—O2-1ⁱⁱⁱ	89.73 (9)	O2^viii—M1-1—O1-1	115.68 (10)
O1-1^v—Zr1—O1-1^vi	91.52 (10)	O2^viii—M1-1—O1-1^vii	116.42 (11)
O1-1^v—Zr1—O2-1ⁱ	89.73 (9)	O4-1—M1-1—O1-1	101.96 (9)
O1-1^v—Zr1—O2-1ⁱⁱ	178.51 (10)	O4-1—M1-1—O1-1^vii	101.96 (9)
O1-1^v—Zr1—O2-1ⁱⁱⁱ	87.63 (8)	O4-1—M1-1—O1-1^viii	101.96 (9)
O1-1^vi—Zr1—O2-1ⁱ	87.63 (8)	O1-1—M1-1—O1-1^vii	115.82 (6)
O1-1^vi—Zr1—O2-1ⁱⁱ	89.73 (9)	O1-1—M1-1—O1-1^viii	115.82 (6)
O1-1^vi—Zr1—O2-1ⁱⁱⁱ	178.51 (10)	O1-1^vii—M1-1—O1-1^viii	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—O1^vii	72.57 (8)
O2-1ⁱⁱ—Zr1—O2-1ⁱⁱⁱ	91.13 (9)	M1—M2-1—O1^viii	72.57 (8)
O1—M1—O1^vii	115.82 (6)	M1—M2-1—O3	179.9802
O1—M1—O1^viii	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—O2-1^vii	70.72 (9)
O1—M1—O2-1^vii	116.42 (11)	M1—M2-1—O2-1^viii	70.72 (9)
O1—M1—O2-1^viii	115.68 (10)	O1—M2-1—O1^vii	111.43 (8)
O1^vii—M1—O1^viii	115.82 (6)	O1—M2-1—O1^viii	111.43 (8)
O1^vii—M1—O4	101.96 (9)	O1—M2-1—O3	107.43 (8)
O1^vii—M1—M2-1	78.04 (9)	O1—M2-1—O3-1	107.43 (8)
O1^vii—M1—O2-1	115.68 (10)	O1—M2-1—O2-1^vii	110.90 (10)
O1^vii—M1—O2-1^viii	116.42 (11)	O1—M2-1—O2-1^viii	110.24 (11)
O1^viii—M1—O4	101.96 (9)	O1^vii—M2-1—O1^viii	111.43 (8)
O1^viii—M1—M2-1	78.04 (9)	O1^vii—M2-1—O3	107.43 (8)
O1^viii—M1—O2-1	116.42 (11)	O1^vii—M2-1—O3-1	107.43 (8)
O1^viii—M1—O2-1^vii	115.68 (10)	O1^vii—M2-1—O2-1	110.24 (11)
O4—M1—M2-1	179.9802	O1^vii—M2-1—O2-1^viii	110.90 (10)
O4—M1—O2-1	101.27 (10)	O1^viii—M2-1—O3	107.43 (8)
O4—M1—O2-1^vii	101.27 (10)	O1^viii—M2-1—O3-1	107.43 (8)
O4—M1—O2-1^viii	101.27 (10)	O1^viii—M2-1—O2-1	110.90 (10)
M2-1—M1—O2-1	78.73 (10)	O1^viii—M2-1—O2-1^vii	110.24 (11)
M2-1—M1—O2-1^vii	78.73 (10)	O3—M2-1—O2-1	109.28 (9)
M2-1—M1—O2-1^viii	78.73 (10)	O3—M2-1—O2-1^vii	109.28 (9)
O2-1—M1—O2-1^vii	116.28 (6)	O3—M2-1—O2-1^viii	109.28 (9)
O2-1—M1—O2-1^viii	116.28 (6)	O3-1—M2-1—O2-1	109.28 (9)
O2-1^vii—M1—O2-1^viii	116.28 (6)	O3-1—M2-1—O2-1^vii	109.28 (9)
O2—M2—O2^vii	109.66 (9)	O3-1—M2-1—O2-1^viii	109.28 (9)
O2—M2—O2^viii	109.66 (9)	O2-1—M2-1—O2-1^vii	109.66 (9)
O2—M2—O3	109.28 (9)	O2-1—M2-1—O2-1^viii	109.66 (9)
O2—M2—M1-1	70.72 (9)	O2-1^vii—M2-1—O2-1^viii	109.66 (9)
O2—M2—O3-1	109.28 (9)	M2—O3-1—O3	179.972
O2—M2—O1-1^vii	110.24 (11)	M2—O3-1—M2-1	179.972
O2—M2—O1-1^viii	110.90 (10)	Zr1^x—O1-1—M2	174.64 (11)
O2^vii—M2—O2^viii	109.66 (9)	Zr1^x—O1-1—O2	140 (2)
O2^vii—M2—O3	109.28 (9)	Zr1^x—O1-1—M1-1	153.95 (13)
O2^vii—M2—M1-1	70.72 (9)	Zr1^ix—O2-1—M1	155.76 (13)
O2^vii—M2—O3-1	109.28 (9)	Zr1^ix—O2-1—M2-1	171.56 (13)
O2^vii—M2—O1-1	110.90 (10)	M1—O2-1—O1	163 (2)
O2^vii—M2—O1-1^viii	110.24 (11)	O1—O2-1—M2-1	134 (2)

Symmetry codes: (i) −z+1/2, −x, y−1/2; (ii) y−1/2, −z+1/2, −x; (iii) −x, y−1/2, −z+1/2; (iv) −z+1/2, −x+1, y−1/2; (v) y−1/2, −z+1/2, −x+1; (vi) −x+1, y−1/2, −z+1/2; (vii) z, x, y; (viii) y, z, x; (ix) −z, x+1/2, −y+1/2; (x) −z+1, x+1/2, −y+1/2.

Experimental details

Crystal data
Chemical formula	ZrW_1.75Mo_0.25O₈
M_r	564.93
Crystal system, space group	Cubic, P2₁3
Temperature (K)	298
a (Å)	9.156880 (17)
V (Å³)	767.79 (1)
Z	4
Radiation type	Time-of-flight
Specimen shape, size (mm)	Cylinder, 30 × 10

Data collection
Diffractometer	GPPD diffractometer
Specimen mounting	Standard cylindrical vanadium sample holder
Data collection mode	?
Scan method	Time of flight
2θ values (°)	2θ_fixed = ?

Refinement
R factors and goodness of fit	R_p = 0.032, R_wp = 0.044, R_exp = ?, χ² = 2.341
No. of data points	?
No. of parameters	58
No. of restraints	?

Computer programs: IPNS local software (Worlton et al., 2006), GSAS (Larson & von Dreele (2000), GSAS (Larson & von Dreele, 2000), VICS-II (Izumi & Dilanian, 2005).

Selected geometric parameters (Å, º) top

Zr1—O1ⁱ	2.038 (2)	M1—O4	1.711 (3)
Zr1—O2ⁱⁱ	2.092 (2)	M1—M2-1	0.929 (2)
Zr1—O1-1ⁱⁱ	2.026 (2)	M2—O2	1.7933 (16)
Zr1—O2-1ⁱ	2.1037 (19)	M2—O3	1.729 (4)
M1—O1	1.8069 (18)	O1—O2-1	0.084 (4)
M1—O3	2.405 (4)	O3—O3-1	0.254 (7)

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

Symmetry codes: (i) −z+1/2, −x, y−1/2; (ii) −z+1/2, −x+1, y−1/2; (iii) z, x, y.

Acknowledgements

The work was supported by a grant from the National Science Foundation of China (NSFC 20471010) and the Institute of High Energy Physics, Chinese Academy of Sciences Innovation Grant H7515520U1.

References

Baur, W. H. (1974). Acta Cryst. B30, 1195–1215. CrossRef CAS IUCr Journals Web of Science Google Scholar
Deng, X., Tao, J., Yang, X., Ma, H., Richardson, J. W. & Zhao, X. (2008). Chem. Mater. 20, 1733–1740. Web of Science CrossRef CAS Google Scholar
Evans, J. S. O., David, W. I. F. & Sleight, A. W. (1999). Acta Cryst. B55, 333–340. Web of Science CrossRef CAS IUCr Journals Google Scholar
Evans, J. S. O., Hanson, P. A., Ibberson, R. M., Duan, N., Kameswari, U. & Sleight, A. W. (2000). J. Am. Chem. Soc. 122, 8694–8699. Web of Science CrossRef CAS Google Scholar
Evans, J. S. O., Mary, T. A., Vogt, T., Subramanian, M. A. & Sleight, A. W. (1996). Chem. Mater. 8, 2809–2823. CrossRef CAS Web of Science Google Scholar
Hampson, M. R., Evans, J. S. O. & Hodgkinson, P. (2005). J. Am. Chem. Soc. 127, 15175–15181. Web of Science CrossRef PubMed CAS Google Scholar
Hampson, M. R., Hodgkinson, P., Evans, J. S. O., Harris, R. K., King, I. J., Allen, S. & Fayon, F. (2004). Chem. Commun. pp. 392–393. Web of Science CrossRef Google Scholar
Huang, L., Xiao, Q.-G., Ma, H., Li, G.-B., Liao, F.-H., Qi, C.-M. & Zhao, X.-H. (2005). Eur. J. Inorg. Chem. pp. 4521-4526. Web of Science CrossRef Google Scholar
Izumi, F. & Dilanian, R. A. (2005). Commission on Powder Diffraction, IUCr Newsletter, No. 32, pp. 59–63. Google Scholar
Larson, A. C. & von Dreele, R. B. (2000). GSAS. Report LAUR-86-748. Los Alamos National Laboratory, New Mexico, USA. Google Scholar
Lind, C., Wilkinson, A. P., Hu, Z., Short, S. & Jorgensen, J. D. (1998). Chem. Mater. 10, 2335–2337. Web of Science CrossRef CAS Google Scholar
Mary, T. A., Evans, J. S. O., Vogt, T. & Sleight, A. W. (1996). Science, 272, 90–92. CrossRef CAS Web of Science Google Scholar
Robinson, K., Gibbs, G. V. & Ribbe, P. H. (1971). Science, 172, 567-570. CrossRef PubMed CAS Web of Science Google Scholar
Worlton, T., Hammonds, J., Mikkelson, D., Mikkelson, R., Porter, R., Tao, J. & Chatterjee, A. (2006). Physica B, 385–386, 1340–1342. Web of Science CrossRef CAS Google Scholar
Zhao, R. Q., Yang, X. J., Wang, H. L., Han, J. S., Ma, H. & Zhao, X. H. (2007). J. Solid State Chem. 180, 3160–3165. Web of Science CrossRef CAS Google Scholar

This is an open-access article distributed under the terms of the Creative Commons Attribution (CC-BY) Licence, which permits unrestricted use, distribution, and reproduction in any medium, provided the original authors and source are cited.