Effect of Axial Ratio Changes on the Elastic Moduli and Grüneisen γ for Lower Symmetry Crystals

Gerlich has shown that Sheard's model for calculating mode γ's from hydrostatic pressure derivatives of the elastic moduli of hcp Mg and Cd yields Gruneisen γ's at both high and low temperatures that are in good agreement with the γ's derived from thermal-expansion measurements. For hcp Ti and Zr, however, large differences arise, primarily from very small values for dC44/dP. It is proposed that these small values are caused by the changes in c/a ratio with hydrostatic pressure because of a large dependence of C44 on the c/a ratio. The disagreement with thermal-expansion data can be removed by taking into account the difference in d(c/a)/dV between hydrostatic-pressure and thermal-expansion conditions. The effect of Δ(c/a) is not found in tetragonal TiO2, rutile, where γ̄H is in excellent agreement with the thermal expansion γ∞.