Elastic Constants Of Calcite Research Articles

Higher Order Elastic Constants, Gruneisen Parameters and Lattice Thermal Expansion of Trigonal Calcite

The second‐ and third‐order elastic constants of trigonal calcite have been obtained using the deformation theory. The strain energy density derived using the deformation theory is compared with the strain dependent lattice energy obtained from the elastic continuum model approximation to get the expressions for the second‐ and third‐order elastic constants. Higher order elastic constants are a measure of the anharmonicity of a crystal lattice. The seven second‐order elastic constants and the fourteen non‐vanishing third‐order elastic constants of trigonal calcite are obtained. The second‐order elastic constants C11, which corresponds to the elastic stiffness along the basal plane of the crystal is greater than C33, which corresponds to the elastic stiffness tensor component along the c‐axis of the crystal. First order pressure derivatives of the second‐order elastic constants of calcite are evaluated. The higher order elastic constants are used to find the generalized Gruneisen parameters of the elastic waves propagating in different directions in calcite. The Brugger gammas are evaluated and the low temperature limit of the Gruneisen gamma is obtained. The results are compared with available reported values.

Optically-active Vibrations and Elastic Constants of Calcite and Aragonite

Abstract Treatments of the normal coordinate and the elastic constant were undertaken for two calcium carbonate crystals. By the use of the least-squares technique, we obtained sets of the force constants which reproduce satisfactorily both the observed vibrational frequencies and the macroscopic elastic constants. The intermolecular interactions, the elastic strains of the internal coordinates, and the nature of the splitting of the normal frequencies in these crystals were briefly discussed.

Variation in the Elastic Constants of Calcite with Temperature

The temperature dependence of the elastic constants of calcite have been investigated by the ultrasonic phase-comparison method from 25° to 375°C. The variation in the elastic constants and the elastic moduli of calcite is smooth and linear over the temperature range, and does not show the break in the variation of the elastic moduli with temperature reported by Reddy and Subrahmanyam at 200°C. The results of the present investigation are in agreement with the other related high-temperature studies of calcite. The reported discontinuity in the variation of elastic moduli with temperature thus seems to be inconsistent with the high-temperature behavior of calcite. This conviction is strengthened by the impossible behavior of compressibility of calcite with temperature as obtained from the calcite data of Reddy and Subrahmanyam. The elastic constants of calcite at T°C within the temperature range of the present work are adequately represented by the following equations: C11=14.7994−57.82×10−4×(T−25)C33=8.5694−14.06×10−4×(T−25)C44=3.2790−14.36×10−4×(T−25)C66=4.6316−14.03×10−4×(T−25)C13=5.4540−25.76×10−4×(T−25) C14=−2.0966+8.32×10−4×(T−25).

Elastic Constants of Calcite

Elastic Constants of Calcite

Elastic Constants of Calcite

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Elastic constants of calcite and sodium nitrate

Elastic constants of calcite and sodium nitrate