Development and verification of the relationship between atomic vibrational amplitude and thermal expansion of crystalline solids

Abstract

The relationship between the mean square vibrational amplitude of the atoms of a crystalline solid and the thermal expansion of that solid is derived from basic principles, assuming a simple potential energy function between atoms. The functional accuracy of this relationship is proven for several cubic lattice elements and compounds by experimental data reported in the literature. The constants of the relationship are calculated for the materials investigated.