Third-Order Elastic Constants of Calcite

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). 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, C₁₁₄ and C₁₃₄ are definitely positive, and all the others are negative, with ambiguities for C₁₂₄ and C₄₄₄. The approximate magnitude is equally large for C₁₁₁, C₂₂₂, and C₃₃₃, intermediate for C₁₁₂, C₁₁₃, C₁₁₄, C₁₃₃, C₁₅₅, C₃₄₄, and very small for C₁₂₃, C₁₂₄, C₁₃₄, C₁₄₄, C₄₄₄. 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 CᵢⱼₖR 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.