supplementary materials

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 - x}Mo_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 - x}Mo_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 - x}Mo_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-ZrW₂O₈ structure 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.