1ST TEMPERATURE DERIVATIVES OF THE FUNDAMENTAL ELASTIC-CONSTANTS OF QUARTZ

The existing temperature derivatives of the effective elastic constants of quartz are referred to the variable temperature-dependent intermediate position of material points rather than the fixed reference position, to which the fundamental elastic constants are referred. Since the existing temperature derivatives are not with respect to the fundamental elastic constants, they cannot conveniently be employed in calculations of thermally induced frequency changes in electroded quartz resonators. This is essentially a result of the fact that a knowledge of temperature-induced biasing strains and the third-order elastic constants cannot be used in the existing linearly based formalism, but requires a proper nonlinearly based formalism. In order to remedy the existing situation, the derivatives with respect to temperature of the fundamental elastic constants of quartz are determined from the original data from which the existing temperature derivatives of the effective elastic constants were obtained. As usual in such work, the electric field and piezoelectric effect are completely ignored in the analytical treatment.