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

Thresiamma Phlip,C S Menon,K Indulekha

doi:10.1155/2005/913794

Abstract

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.

Highlights

Knowledge of higher order elastic constants is essential for the study of the anharmonic properties of solids
In the calcite there are six different ion-pair types, but the carbon atoms are deeply buried inside oxygen triads so the carbon atoms will not be considered explicitly and the number of different ion-pairs is reduced to three: metalion-metal-ion (M-M), metal-ion-oxygen-ion (M-O) and oxygen-ion-oxygen-ion (O-O).[1]
In the present study we make an attempt to calculate the complete set of second and third-order elastic constants, pressure derivatives of the second-order elastic constants, generalized Gruneisen parameters of elastic waves and low temperature thermal expansion of trigonal calcite and are compared with those obtained by other workers.[2,4,5,6,10,11,12]

Summary

Introduction

Knowledge of higher order elastic constants is essential for the study of the anharmonic properties of solids. In the present study we make an attempt to calculate the complete set of second and third-order elastic constants, pressure derivatives of the second-order elastic constants, generalized Gruneisen parameters of elastic waves and low temperature thermal expansion of trigonal calcite and are compared with those obtained by other workers.[2,4,5,6,10,11,12] These values are used in equation (8) to obtain the second-order elastic constants of calcite.

Results

Conclusion