Acoustic mode vibrational anharmonicity of hexahelometallate crystals

Abstract

The vibrational anharmonicity and Grüneisen parameters of hexahelometallate A₂MX₆ single crystals have been determined theoretically by making use of phonon lattice theory. The potential model employed to calculate these properties consists of long range coulomb, three body interactions, short range overlap repulsion effective upto the nearest neighbour ions and phonon-lattice interactions. These antifluorite structure compounds contain large MX²⁻₆- ions and as the interionic spacings are much greater than those of the alkaline-earth fluorite structure halides, their elastic constants are correspondingly smaller. The hydrostatic pressure derivatives of the second order elastic constants (SOEC) calculated for K₂SnCl₆, K₂ReCl₆, (NH₄)₂SnCl₆, (NH₄)₂TeCl₆, (NH₄)₂SnBr₆, and (NH₄)₂TeBr₆, are found to be positive and close to the experimental values. The vibrational anharmonicities of the long-wavelength modes are explained in terms of the acoustic mode Grüneisen parameters.