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 [ ] 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 (≃ 0.08 Å). The results prove the constraint strategy to be a reasonable approach based on the ratcheting mechanism.

The solid solution in the system Zr-Mo-W-O with composition ZrW 1.75 Mo 0.25 O 8 (zirconium tungsten molybdenum octaoxide) 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 octahedra (.

Experimental
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.  . 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 structureproperty 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 -x Mo x O 8 , we were able to extend the thermal stability range of cubic ZrW 2 O 8 type compounds. Recently, we have reported the high-temperature synthesis of the solid solution ZrW 2 -x Mo x O 8 series (Zhao et al., 2007), and found that the order-disorder phase transition temperature (T tr ) and the order degree of the ZrW 2 -x Mo x O 8 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-ZrW 2 O 8 structure at room temperature. However, the detailed average crystal structures are not reported.
In this paper, we describe the synthesis of cubic ZrW 1.75 Mo 0.25 O 8 and the average crystal structure as determined from neutron powder diffraction data using the Rietveld method. The crystal structure is presented in Fig.1  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 M2O 4 tetrahedron is proved by larger distortions in terms of bond angles and distances of M1O 4 tetrahedra than that of M2O 4 tetrahedra. The values of the bond length distortion index D (Baur, 1974), 0.02028, and of the bond angle variance σ 2 (Robinson et al., 1971), 58.12 °2, of M1O 4 tetrahedra are both larger than that of M2O 4 tetrahedra in which D is 0.01355 and σ 2 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-ZrW 2 O 8 (Evans et al., , 1999, some special conditions were constrained to match the 'ratcheting mechanism' described by Hampson et al. (2004Hampson et al. ( , 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 supplementary materials sup-2 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 M 2 O 8 units was determined. The fraction of unflipped M 2 O 8 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.

Experimental
Cubic ZrW 1.75 Mo 0.25 O 8 was prepared using a similar procedure described previously (Zhao et al., 2007) 4H 2 O 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 1.7 Mo 0.3 O 8 . During the sintering process, the weight loss of this sample, which is attributed to the volatility of MoO 3 , is 1.4 wt %, so the exact formula is ZrW 1.75 Mo 0.25 O 8 . The trace of ZrO 2 as an impurity in the powder is undetectable by neutron diffraction.

Refinement
The starting structure model for refinement is based on the crystal structure of α-ZrW 2 O 8 (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(Hampson et al., , 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 M 2 O 8 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 ZrW 1.75 Mo 0.25 O 8 . ZrO 6 octahedra and MO 4 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.