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Acta Crystallogr Sect E Struct Rep Online. 2009 May 1; 65(Pt 5): i36–i37.
Published online 2009 April 30. doi:  10.1107/S1600536809015281
PMCID: PMC2977542

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


The solid solution in the system Zr–Mo–W–O with composition ZrW1.75Mo0.25O8 (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 M 2O8 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—Oterminal vectors pointing to the [111] or [An external file that holds a picture, illustration, etc.
Object name is e-65-00i36-efi1.jpg An external file that holds a picture, illustration, etc.
Object name is e-65-00i36-efi1.jpg An external file that holds a picture, illustration, etc.
Object name is e-65-00i36-efi1.jpg] directions. The reversal of the orientations of the M 2O8 units results from the concerted flips of these units. The time-averaged proportions of flipped and unflipped M 2O8 units were determined and the fraction of unflipped M 2O8 units is about 0.95. The order degree of the M 2O8 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 ([similar, equals] 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 [triangle]); Evans et al. (1996 [triangle], 1999 [triangle]). Details on the ratcheting mechanism have been described by Hampson et al. (2004 [triangle], 2005 [triangle]). For the synthesis of the title compound, see: Zhao et al. (2007 [triangle]). For a detailed description of polyhedral distortion parameters, see: Baur (1974 [triangle]); Robinson et al. (1971 [triangle]). For isomorphism and polymorphism in cubic ZrW2O8 type compounds, see: Evans et al. (2000 [triangle]); Lind et al. (1998 [triangle]); Huang et al.(2005 [triangle]); Deng et al. (2008 [triangle]). For their unusual isotropic negative thermal expansion properties, see: Mary et al. (1996 [triangle]).


Crystal data

  • ZrW1.75Mo0.25O8
  • M r = 564.93
  • Cubic, An external file that holds a picture, illustration, etc.
Object name is e-65-00i36-efi4.jpg
  • 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
  • min = 53, 2θmax = 145°


  • R p = 0.032
  • R wp = 0.044
  • 1893 reflections
  • 58 parameters

Data collection: IPNS local software (Worlton et al., 2006 [triangle]); cell refinement: GSAS (Larson & von Dreele (2000 [triangle]); 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 [triangle]); software used to prepare material for publication: GSAS.

Table 1
Selected geometric parameters (Å, °)

Supplementary Material

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


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.

supplementary crystallographic information


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 ZrW2 - xMoxO8, 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 ZrW2 - xMoxO8 series (Zhao et al., 2007), and found that the order-disorder phase transition temperature (Ttr) and the order degree of the ZrW2 - xMoxO8 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-ZrW2O8 structure at room temperature. However, the detailed average crystal structures are not reported.

In this paper, we describe the synthesis of cubic ZrW1.75Mo0.25O8 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 ZrW1.75Mo0.25O8 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-Oterminal 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.


Cubic ZrW1.75Mo0.25O8 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 ZrW1.7Mo0.3O8. 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 ZrW1.75Mo0.25O8. The trace of ZrO2 as an impurity in the powder is undetectable by neutron diffraction.


The starting structure model for refinement is based on the crystal structure of α-ZrW2O8 (Evans et al. 1999). The schematic representation of the starting structure model is shown in Fig. 3. During the refinement sets of constraints of structure parameters were used to match the 'ratcheting mechanism' (Hampson et al., 2004, 2005). The W sites of the original model are statistically occupied by W and Mo atoms (denoted with M). The corresponding atomic coordinates of flipped and unflipped M2O8 units are set to be centrosymmetric through the imaginary inversion center of the unit cell. The corresponding anisotropic atomic displacement parameters are constrained to be equal for each site. The initial occupancy fractions of the original atomic sites were set to 1 (the occupancy fraction sum of M1 and M2 were set to unity) while those of the derived atomic sites were set to 0. During the refinement process, the occupancy fraction of the atoms as a parameter in either unflipped or flipped part is constrained to maintain the chemical composition. Two histograms (bank 1 and bank 5) of data from GPPD were used in the refinement. The given reliability factors (see Tables) are the result of the combined refinement based on bank 1 and bank 5 data.


Fig. 1.
Polyhedral representation of cubic ZrW1.75Mo0.25O8. 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, ...
Fig. 2.
Final Rietveld refinement neutron powder data plot and difference plot for cubic ZrW1.75Mo0.25O8. The crosses are the observed data, the solid line is the calculated pattern, and the tick marks indicate the calculated reflection positions. The difference ...
Fig. 3.
The schematic representation of the starting structural model for cubic ZrW1.75Mo0.25O8. Black balls and circles represent 'unflipped' and 'flipped' atoms, respectively.

Crystal data

ZrW1.75Mo0.25O8Dx = 4.887 Mg m3
Mr = 564.93Time-of-flight radiation
Cubic, P213T = 298 K
a = 9.156880 (17) Åwhite
V = 767.79 (1) Å3cylinder, 30 × 10 mm
Z = 4

Data collection

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


Least-squares matrix: full? data points
Rp = 0.03258 parameters
Rwp = 0.04455 constraints
Rexp = ?(Δ/σ)max = 0.02
χ2 = 2.341

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

xyzUiso*/UeqOcc. (<1)
Zr10.00068 (14)0.00068 (14)0.00068 (14)0.01044
W10.34038 (14)0.34038 (14)0.34038 (14)0.014490.8339 (22)
W20.60102 (13)0.60102 (13)0.60102 (13)0.010480.8339 (22)
O10.20648 (18)0.4373 (2)0.4482 (2)0.026340.9530 (26)
O20.78912 (16)0.5691 (2)0.55685 (18)0.018930.9530 (26)
O30.4920 (2)0.4920 (2)0.4920 (2)0.026790.9530 (26)
O40.23253 (13)0.23253 (13)0.23253 (13)0.038510.9530 (26)
Mo10.34038 (14)0.34038 (14)0.34038 (14)0.014490.11913 (32)
Mo20.60102 (13)0.60102 (13)0.60102 (13)0.010480.11913 (32)
W1-10.65963 (14)0.65963 (14)0.65963 (14)0.014490.0411 (22)
W2-10.39898 (13)0.39898 (13)0.39898 (13)0.010480.0411 (22)
Mo1-10.65963 (14)0.65963 (14)0.65963 (14)0.014490.00587 (32)
Mo2-10.39898 (13)0.39898 (13)0.39898 (13)0.010480.00587 (32)
O3-10.5080 (2)0.5080 (2)0.5080 (2)0.026790.0470 (26)
O4-10.76747 (13)0.76747 (13)0.76747 (13)0.038510.0470 (26)
O1-10.79352 (18)0.5627 (2)0.5518 (2)0.026340.0470 (26)
O2-10.21088 (16)0.4309 (2)0.44315 (18)0.018930.0470 (26)

Atomic displacement parameters (Å2)

Zr10.0104 (2)0.0104 (2)0.0104 (2)−0.0002 (3)−0.0002 (3)−0.0002 (3)
W10.0145 (5)0.0145 (5)0.0145 (5)0.0080 (6)0.0080 (6)0.0080 (6)
W20.0105 (5)0.0105 (5)0.0105 (5)0.0006 (4)0.0006 (4)0.0006 (4)
O10.0198 (9)0.0272 (12)0.0320 (11)0.0083 (8)0.0142 (8)−0.0013 (8)
O20.0054 (7)0.0272 (10)0.0242 (10)0.0057 (6)0.0016 (7)0.0058 (7)
O30.0268 (5)0.0268 (5)0.0268 (5)−0.0090 (6)−0.0090 (6)−0.0090 (6)
O40.0385 (6)0.0385 (6)0.0385 (6)−0.0119 (6)−0.0119 (6)−0.0119 (6)
Mo10.0145 (5)0.0145 (5)0.0145 (5)0.0080 (6)0.0080 (6)0.0080 (6)
Mo20.0105 (5)0.0105 (5)0.0105 (5)0.0006 (4)0.0006 (4)0.0006 (4)
W1-10.0145 (5)0.0145 (5)0.0145 (5)0.0080 (6)0.0080 (6)0.0080 (6)
W2-10.0105 (5)0.0105 (5)0.0105 (5)0.0006 (4)0.0006 (4)0.0006 (4)
Mo1-10.0145 (5)0.0145 (5)0.0145 (5)0.0080 (6)0.0080 (6)0.0080 (6)
Mo2-10.0105 (5)0.0105 (5)0.0105 (5)0.0006 (4)0.0006 (4)0.0006 (4)
O3-10.0268 (5)0.0268 (5)0.0268 (5)−0.0090 (6)−0.0090 (6)−0.0090 (6)
O4-10.0385 (6)0.0385 (6)0.0385 (6)−0.0119 (6)−0.0119 (6)−0.0119 (6)
O1-10.0198 (9)0.0272 (12)0.0320 (11)0.0083 (8)0.0142 (8)−0.0013 (8)
O2-10.0054 (7)0.0272 (10)0.0242 (10)0.0057 (6)0.0016 (7)0.0058 (7)

Geometric parameters (Å, °)

Zr1—O1i2.0384 (21)O3—M21.729 (4)
Zr1—O1ii2.0384 (21)O3—M1-12.659 (4)
Zr1—O1iii2.0384 (21)O3—M2-11.475 (4)
Zr1—O2iv2.0915 (20)O3—O3-10.254 (7)
Zr1—O2v2.0915 (20)O4—M11.7105 (32)
Zr1—O2vi2.0915 (20)O4—M2-12.6400 (29)
Zr1—O1-1iv2.0261 (21)M1-1—M20.9295 (23)
Zr1—O1-1v2.0261 (21)M1-1—O21.7261 (18)
Zr1—O1-1vi2.0261 (21)M1-1—O2vii1.7261 (18)
Zr1—O2-1i2.1037 (19)M1-1—O2viii1.7261 (18)
Zr1—O2-1ii2.1037 (19)M1-1—O32.659 (4)
Zr1—O2-1iii2.1037 (19)M1-1—O3-12.405 (4)
M1—O11.8069 (18)M1-1—O4-11.7105 (32)
M1—O1vii1.8069 (18)M1-1—O1-11.8069 (18)
M1—O1viii1.8069 (18)M1-1—O1-1vii1.8069 (18)
M1—O32.405 (4)M1-1—O1-1viii1.8069 (18)
M1—O41.7105 (32)M2-1—M10.9294 (23)
M1—M2-10.9294 (23)M2-1—M23.204 (4)
M1—O3-12.659 (4)M2-1—O11.8528 (18)
M1—O2-11.7260 (18)M2-1—O1vii1.8528 (18)
M1—O2-1vii1.7260 (18)M2-1—O1viii1.8528 (18)
M1—O2-1viii1.7260 (18)M2-1—O31.475 (4)
M2—O21.7933 (16)M2-1—O42.6400 (29)
M2—O2vii1.7933 (16)M2-1—O3-11.729 (4)
M2—O2viii1.7933 (16)M2-1—O2-11.7933 (16)
M2—O31.729 (4)M2-1—O2-1vii1.7933 (16)
M2—M1-10.9295 (23)M2-1—O2-1viii1.7933 (16)
M2—M2-13.204 (4)O3-1—M12.659 (4)
M2—O3-11.475 (4)O3-1—M21.475 (4)
M2—O4-12.6399 (29)O3-1—O30.254 (7)
M2—O1-11.8528 (18)O3-1—M1-12.405 (4)
M2—O1-1vii1.8528 (18)O3-1—M2-11.729 (4)
M2—O1-1viii1.8528 (18)O4-1—M22.6399 (29)
O1—Zr1ix2.0384 (21)O4-1—M1-11.7105 (32)
O1—M11.8069 (18)O1-1—Zr1x2.0261 (21)
O1—M2-11.8528 (18)O1-1—M21.8528 (18)
O1—O2-10.084 (4)O1-1—O20.084 (4)
O2—Zr1x2.0915 (20)O1-1—M1-11.8069 (18)
O2—M21.7933 (16)O2-1—Zr1ix2.1037 (19)
O2—M1-11.7261 (18)O2-1—M11.7260 (18)
O2—O1-10.084 (4)O2-1—O10.084 (4)
O3—M12.405 (4)O2-1—M2-11.7933 (16)
O1i—Zr1—O1ii90.82 (10)O2viii—M2—O3109.28 (9)
O1i—Zr1—O1iii90.82 (10)O2viii—M2—M1-170.72 (9)
O1i—Zr1—O2iv178.37 (10)O2viii—M2—O3-1109.28 (9)
O1i—Zr1—O2v87.64 (8)O2viii—M2—O1-1110.24 (11)
O1i—Zr1—O2vi89.74 (8)O2viii—M2—O1-1vii110.90 (10)
O1i—Zr1—O1-1iv179.4968 (9)O2viii—M2—O1-1viii1.88 (12)
O1i—Zr1—O1-1v88.83 (7)O3—M2—M1-1180.0
O1i—Zr1—O1-1vi88.83 (7)O3—M2—O1-1107.43 (8)
O1i—Zr1—O2-1ii92.01 (12)O3—M2—O1-1vii107.43 (8)
O1i—Zr1—O2-1iii89.92 (10)O3—M2—O1-1viii107.43 (8)
O1ii—Zr1—O1iii90.82 (10)M1-1—M2—O3-1180.0
O1ii—Zr1—O2iv89.74 (8)M1-1—M2—O1-172.57 (8)
O1ii—Zr1—O2v178.37 (10)M1-1—M2—O1-1vii72.57 (8)
O1ii—Zr1—O2vi87.64 (8)M1-1—M2—O1-1viii72.57 (8)
O1ii—Zr1—O1-1iv88.83 (7)O3-1—M2—O1-1107.43 (8)
O1ii—Zr1—O1-1v179.4968 (9)O3-1—M2—O1-1vii107.43 (8)
O1ii—Zr1—O1-1vi88.83 (7)O3-1—M2—O1-1viii107.43 (8)
O1ii—Zr1—O2-1i89.92 (10)O1-1—M2—O1-1vii111.43 (8)
O1ii—Zr1—O2-1iii92.01 (12)O1-1—M2—O1-1viii111.43 (8)
O1iii—Zr1—O2iv87.64 (8)O1-1vii—M2—O1-1viii111.43 (8)
O1iii—Zr1—O2v89.74 (8)Zr1ix—O1—M1153.75 (12)
O1iii—Zr1—O2vi178.37 (10)Zr1ix—O1—M2-1174.36 (12)
O1iii—Zr1—O1-1iv88.83 (7)Zr1ix—O1—O2-1139.9 (22)
O1iii—Zr1—O1-1v88.83 (7)M1—O1—M2-129.39 (8)
O1iii—Zr1—O1-1vi179.4984 (9)M2-1—O1—O2-144.3 (21)
O1iii—Zr1—O2-1i92.01 (12)Zr1x—O2—M2171.71 (13)
O1iii—Zr1—O2-1ii89.92 (10)Zr1x—O2—M1-1155.98 (13)
O2iv—Zr1—O2v91.81 (10)M2—O2—O1-1133.9 (22)
O2iv—Zr1—O2vi91.81 (10)M2—O2—M1-130.55 (8)
O2iv—Zr1—O1-1v90.60 (12)M1-1—O2—O1-1162.9 (23)
O2iv—Zr1—O1-1vi92.72 (10)M2—O3—M2-1179.972
O2iv—Zr1—O2-1i179.5134 (9)M2-1—O3—O3-1179.972
O2iv—Zr1—O2-1ii88.52 (6)M2—M1-1—O278.73 (10)
O2iv—Zr1—O2-1iii88.53 (6)M2—M1-1—O2vii78.73 (10)
O2v—Zr1—O2vi91.81 (10)M2—M1-1—O2viii78.73 (10)
O2v—Zr1—O1-1iv92.72 (10)M2—M1-1—O4-1179.972
O2v—Zr1—O1-1vi90.60 (12)M2—M1-1—O1-178.04 (9)
O2v—Zr1—O2-1i88.53 (6)M2—M1-1—O1-1vii78.04 (9)
O2v—Zr1—O2-1ii179.5134 (9)M2—M1-1—O1-1viii78.04 (9)
O2v—Zr1—O2-1iii88.52 (6)O2—M1-1—O2vii116.27 (6)
O2vi—Zr1—O1-1iv90.60 (12)O2—M1-1—O2viii116.27 (6)
O2vi—Zr1—O1-1v92.72 (10)O2—M1-1—O4-1101.27 (10)
O2vi—Zr1—O2-1i88.52 (6)O2—M1-1—O1-1vii115.68 (10)
O2vi—Zr1—O2-1ii88.53 (6)O2—M1-1—O1-1viii116.42 (11)
O2vi—Zr1—O2-1iii179.5122 (9)O2vii—M1-1—O2viii116.27 (6)
O1-1iv—Zr1—O1-1v91.52 (10)O2vii—M1-1—O4-1101.27 (10)
O1-1iv—Zr1—O1-1vi91.52 (10)O2vii—M1-1—O1-1116.42 (11)
O1-1iv—Zr1—O2-1i178.51 (10)O2vii—M1-1—O1-1viii115.68 (10)
O1-1iv—Zr1—O2-1ii87.63 (8)O2viii—M1-1—O4-1101.27 (10)
O1-1iv—Zr1—O2-1iii89.73 (9)O2viii—M1-1—O1-1115.68 (10)
O1-1v—Zr1—O1-1vi91.52 (10)O2viii—M1-1—O1-1vii116.42 (11)
O1-1v—Zr1—O2-1i89.73 (9)O4-1—M1-1—O1-1101.96 (9)
O1-1v—Zr1—O2-1ii178.51 (10)O4-1—M1-1—O1-1vii101.96 (9)
O1-1v—Zr1—O2-1iii87.63 (8)O4-1—M1-1—O1-1viii101.96 (9)
O1-1vi—Zr1—O2-1i87.63 (8)O1-1—M1-1—O1-1vii115.82 (6)
O1-1vi—Zr1—O2-1ii89.73 (9)O1-1—M1-1—O1-1viii115.82 (6)
O1-1vi—Zr1—O2-1iii178.51 (10)O1-1vii—M1-1—O1-1viii115.82 (6)
O2-1i—Zr1—O2-1ii91.13 (9)M1—M2-1—O172.57 (8)
O2-1i—Zr1—O2-1iii91.13 (9)M1—M2-1—O1vii72.57 (8)
O2-1ii—Zr1—O2-1iii91.13 (9)M1—M2-1—O1viii72.57 (8)
O1—M1—O1vii115.82 (6)M1—M2-1—O3179.9802
O1—M1—O1viii115.82 (6)M1—M2-1—O3-1179.972
O1—M1—O4101.96 (9)M1—M2-1—O2-170.72 (9)
O1—M1—M2-178.04 (9)M1—M2-1—O2-1vii70.72 (9)
O1—M1—O2-1vii116.42 (11)M1—M2-1—O2-1viii70.72 (9)
O1—M1—O2-1viii115.68 (10)O1—M2-1—O1vii111.43 (8)
O1vii—M1—O1viii115.82 (6)O1—M2-1—O1viii111.43 (8)
O1vii—M1—O4101.96 (9)O1—M2-1—O3107.43 (8)
O1vii—M1—M2-178.04 (9)O1—M2-1—O3-1107.43 (8)
O1vii—M1—O2-1115.68 (10)O1—M2-1—O2-1vii110.90 (10)
O1vii—M1—O2-1viii116.42 (11)O1—M2-1—O2-1viii110.24 (11)
O1viii—M1—O4101.96 (9)O1vii—M2-1—O1viii111.43 (8)
O1viii—M1—M2-178.04 (9)O1vii—M2-1—O3107.43 (8)
O1viii—M1—O2-1116.42 (11)O1vii—M2-1—O3-1107.43 (8)
O1viii—M1—O2-1vii115.68 (10)O1vii—M2-1—O2-1110.24 (11)
O4—M1—M2-1179.9802O1vii—M2-1—O2-1viii110.90 (10)
O4—M1—O2-1101.27 (10)O1viii—M2-1—O3107.43 (8)
O4—M1—O2-1vii101.27 (10)O1viii—M2-1—O3-1107.43 (8)
O4—M1—O2-1viii101.27 (10)O1viii—M2-1—O2-1110.90 (10)
M2-1—M1—O2-178.73 (10)O1viii—M2-1—O2-1vii110.24 (11)
M2-1—M1—O2-1vii78.73 (10)O3—M2-1—O2-1109.28 (9)
M2-1—M1—O2-1viii78.73 (10)O3—M2-1—O2-1vii109.28 (9)
O2-1—M1—O2-1vii116.28 (6)O3—M2-1—O2-1viii109.28 (9)
O2-1—M1—O2-1viii116.28 (6)O3-1—M2-1—O2-1109.28 (9)
O2-1vii—M1—O2-1viii116.28 (6)O3-1—M2-1—O2-1vii109.28 (9)
O2—M2—O2vii109.66 (9)O3-1—M2-1—O2-1viii109.28 (9)
O2—M2—O2viii109.66 (9)O2-1—M2-1—O2-1vii109.66 (9)
O2—M2—O3109.28 (9)O2-1—M2-1—O2-1viii109.66 (9)
O2—M2—M1-170.72 (9)O2-1vii—M2-1—O2-1viii109.66 (9)
O2—M2—O3-1109.28 (9)M2—O3-1—O3179.972
O2—M2—O1-1vii110.24 (11)M2—O3-1—M2-1179.972
O2—M2—O1-1viii110.90 (10)Zr1x—O1-1—M2174.64 (11)
O2vii—M2—O2viii109.66 (9)Zr1x—O1-1—O2140.0 (22)
O2vii—M2—O3109.28 (9)Zr1x—O1-1—M1-1153.95 (13)
O2vii—M2—M1-170.72 (9)Zr1ix—O2-1—M1155.76 (13)
O2vii—M2—O3-1109.28 (9)Zr1ix—O2-1—M2-1171.56 (13)
O2vii—M2—O1-1110.90 (10)M1—O2-1—O1162.9 (23)
O2vii—M2—O1-1viii110.24 (11)O1—O2-1—M2-1133.9 (22)

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.


Supplementary data and figures for this paper are available from the IUCr electronic archives (Reference: WM2222).


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