Elastic constants of corundum up to 1825 K

Abstract

Elastic constants of single‐crystal corundum, α‐Al₂O₃, up to 1825 K (1.75 times the Debye temperature, θ_D) have been measured using a new device, the rectangular parallelepiped resonance method. This device uses a long, thin alumina buffer rod, which separates the transducer from the specimen and enables us to pick up the resonance vibration of the specimen at very high temperature. The elastic stiffness constants C₁₁ and C₃₃ show a large decrease, while C₁₂ and C₁₃ only slightly decrease with temperature. C₄₄ decreases linearly with temperature, and C₁₄ is almost constant in the measured range of temperature. The isotropic elastic parameters were calculated by means of Voigt, Reuss, and Hill averaging schemes, enabling us to analyze the high‐temperature elastic properties of corundum. The present elastic data also enable us to determine the thermodynamic parameters of corundum by combining them with the existing data on thermal expansivity and heat capacity. We find that (1) the evidence for anharmonicity in the thermal pressure is quite small, and the volume dependence of the thermal pressure diminishes above 1400 K; (2) the Grüneisen parameter decreases slightly with T at constant P above the Debye temperature; (3) the isothermal Anderson‐Grüneisen parameter approaches the value of the pressure derivative of the isothermal bulk modulus at high temperature; and (4) the parameter q = (∂ℓnγ/∂ℓnV)_T also approaches the value 1 at high temperature.