FREE VIBRATION OF A RECTANGULAR PARALLELEPIPED CRYSTAL AND ITS APPLICATION TO DETERMINATION OF ELASTIC CONSTANTS OF ORTHORHOMBIC CRYSTALS

Abstract

A theory was developed on the free vibration of a crystal of rectangular parallelepiped and of general symmetry by extending Demarest's theory of cube resonance. All vibrational modes were classified and described in detail for the case of orthorhombic symmetry. The theory is applied to determine elastic constants of crystals from the resonance frequencies of its free vibrations. The method of numerical analysis of resonance frequency data was studied to derive a practical way of elastic constant determination. As an example, the elastic constants of two specimens of single crystal olivine (Mg_1.8Fe_0.2SiO₄) were determined. The applicability of the resonance method is largely extended by the present theory to the precise determination of elastic constants of single crystals.