Third-Order Elastic Constants of Calcite

Abstract

The third-order elastic constants of calcite at 0°C have been determined by measuring the stress and temperature dependence of sound velocities in it by means of an improved pulse-superposition method (average sensitivity of 2×${10}^{-7\mathrm{}}$). Within the small temperature range considered (about 2°C), a nonlinear temperature dependence which varies with pressure has been clearly observed. Out of 14 independent third-order moduli, $C_{114}$ and $C_{134}$ are definitely positive, and all the others are negative, with ambiguities for $C_{124}$ and $C_{444}$. The approximate magnitude is equally large for $C_{111}$, $C_{222}$, and $C_{333}$, intermediate for $C_{112}$, $C_{113}$, $C_{114}$, $C_{133}$, $C_{155}$, $C_{344}$, and very small for $C_{123}$, $C_{124}$, $C_{134}$, $C_{144}$, $C_{444}$. The pressure derivative of the bulk modulus calculated using these constants is in reasonable agreement with Bridgman's data for the change in compressibility with pressure. The contribution of the ion-core, short-range repulsive interaction ${C_{\mathrm{ijk}}}^R$ to the third-order elastic constants has been evaluated for the carbonate and nitrate crystals of the calcite type using an inverse-power potential. The repulsive contributions were found to be predominant over the other contributions to almost all the third-order constants. Under the assumption that the remaining contribution is the electrostatic interaction alone, and using the experimental data for calcite, complete sets of the third-order constants have been estimated for other carbonate crystals.