Pressure and Temperature Dependences of the Isotropic Elastic Moduli of Polycrystalline Alumina

The isotropic elastic moduli of polycrystalline alumina have been determined as a function of hydrostatic pressure up to 10 kbar and also as a function of temperature over the range 4.2° to about 1300°K. The pressure dependence of the elastic moduli is linear over this pressure range. The low‐temperature limit of the elastic Debye temperature, 1044 (±3) °K, compares very well with thermal Debye temperature. Values of various pressure derivatives evaluated at 298°K are as follows: $$\begin{array}{cccc}\mathrm{Pressure\hspace{0.17em}derivatives}& \mathrm{\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}dL/dp}& \mathrm{\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}dG/dp}& \mathrm{\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}dB/dp}\\ {\mathrm{(\partial M}}^s{\mathrm{/\partial p)}}_T& \text{6.57\hspace{0.17em}(6.58)}& \text{1.79\hspace{0.17em}(1.73)}& \text{4.19\hspace{0.17em}(4.27)}\\ {\mathrm{(\partial M}}^T{\mathrm{/\partial p)}}_T& \text{6.62}& \text{1.79}& \text{4.23}\\ {\mathrm{(\partial M}}^s{\mathrm{/\partial p)}}_s& \text{6.52}& \text{1.73}& \text{4.16}\end{array}$$ The quantities in the parentheses are averaged values calculated from the single‐crystal second‐order elastic constants and their first pressure derivatives. The experimental data are interpreted with respect to (a) the polycrystalline data calculated from the corresponding single‐crystal data, (b) the temperature dependence of the isotropic elastic moduli, (c) the acoustic Grüneisen parameters and their comparison with the corresponding quantities evaluated from thermodynamic properties, (d) the equation of state for alumina, and (e) the Debye temperature as a function of temperature and pressure.