Comparison of Various Lattice Dynamical Models for the Calculation of Thermal Expansion of Solids

Abstract

A critical comparison of the Debye continuum, the modified rigid ion, the simple shell and the breathing shell models in the calculation of lattice dynamics of ionic solids is made. With the help of the Mie‐Grűneisen equation of state under the quasi‐harmonic approximation, the coefficient of thermal expansion can be calculated if the pressure dependence of lattice dynamics is available. All the above models may be adapted for this purpose. More elaborate lattice dynamical theories of thermal expansion involving anharmonicity are shown to be equivalent to this simple approach. The relative significance of different normal mode phonons in connection with anomalous thermal expansion, pressure induced phase transition and melting is pointed out.