Relationships between elastic anisotropy and thermal expansion in A₂Mo₃O₁₂ materials

We report calculated elastic tensors, axial Grüneisen parameters, and thermal stress distributions in Al₂Mo₃O₁₂, ZrMgMo₃O₁₂, Sc₂Mo₃O₁₂, and Y₂Mo₃O₁₂, a series of isomorphic materials for which the coefficients of thermal expansion range from low-positive to negative. Thermal stress in polycrystalline materials arises from interactions between thermal expansion and mechanical properties, and both can be highly anisotropic. Thermal expansion anisotropy was found to be correlated with elastic anisotropy: axes with negative thermal expansion were less compliant. Calculations of axial Grüneisen parameters revealed that the thermal expansion anisotropy in these materials is in part due to the Poisson effect. Models of thermal stress due to thermal expansion anisotropy in polycrystals following cooling showed thermal stresses of sufficient magnitude to cause microcracking in all cases. The thermal expansion anisotropy was found to couple to elastic anisotropy, decreasing the bulk coefficient of thermal expansion and leading to lognormal extremes of the thermal stress distributions.