Rigorous Bounds for Thermodynamic Properties of Harmonic Solids

Abstract

A procedure for obtaining rigorous bounds to thermal properties of harmonic solids from moments of the frequency distribution is presented, and methods for improving these bounds when low-frequency expansion coefficients for the frequency distribution function are known are described. The technique is demonstrated by application to a face-centered-cubic crystal with nearest-neighbor interactions, and extremely precise bounds for the thermal properties are obtained.