Elastic constants of single‐crystal corundum, α‐Al2O3, up to 1825 K (1.75 times the Debye temperature, θD) 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.
Measurements of the nine adiabatic elastic constants of single‐crystal forsterite are reported for the temperature range 300–1700 K at ambient pressure. The measured room temperature Cijs and their first temperature derivatives at ambient conditions are generally consistent with previous measurements, which were taken over a narrower temperature range. Slight nonlinear behavior is observed in the temperature dependence of the C11s, C22s, and C33s moduli. The resulting Hill‐averaged bulk and rigidity moduli Ks and G are lower at 1700 K than predicted by linear extrapolation of low‐temperature data. At 1700 K the new data give Ks = 103.8 ± 1.1 GPa and G = 61.3 ± 0.5 GPa. Isotropic elastic wave velocities have been calculated using the Hill averaging scheme over the range of temperatures measured. At T = 1700 K and ambient pressure we find vp = 7.79 ± 0.04 km s−1 and vs = 4.48 ± 0.03 km s−1. The parameter (∂ℓnvs/∂ℓnvp)P is near to 1.2 and independent of temperature. Calculations are presented for elastic properties and other parameters important for the equations of state and anharmonicity of forsterite. Recent high‐temperature thermal expansion measurements on a forsterite specimen from the same boule are used in this analysis. Effects of uncertainties in high‐temperature thermal expansion data on these parameters have been evaluated and are discussed.
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