Correlation between AO ₆ Polyhedral Distortion and Negative Thermal Expansion in Orthorhombic Y ₂ Mo ₃ O ₁₂ and Related Materials

The Pbcn orthorhombic phase of Y 2 Mo 3 O 12 has been examined through high-resolution X-ray powder diffraction (10−450 K), heat capacity determination (2−390 K), and differential scanning calorimetry (103−673 K). No phase transition was found over this temperature range. The overall thermal expansion is negative, and the average linear thermal expansion coefficient, α l, is −9.02 × 10 −6 K −1 averaged over T = 20−450 K. From a thorough analysis of the structure of Y 2 Mo 3 O 12, we find that the YO 6 octahedra and MoO 4 tetrahedra are increasingly distorted with increasing temperature. The inherent volume distortion parameter (υ) of A O 6 has been introduced to quantitatively evaluate polyhedral distortion and it is observed that this parameter is strongly correlated with the linear coefficient thermal expansion (α l ) of different members of the A 2 M 3 O 12 family. We attribute the negative thermal expansion to the reduction of the mean Y−Mo nonbonded distances and Y−O−Mo bond angles with increasing temperature, the joint action of high-energy optical and low-energy translational and librational modes.