Instability in Crystals and Thermal Expansion Coefficients

Abstract

An analysis is made of the Grüneisen parameter ${\gamma }_i=\frac{-d\ln {\nu }_i}{d\ln V}$, where ${\nu }_i$ is a normal mode frequency and $V$ is the volume for certain ideal and real crystals. It is shown that negative thermal expansion or anomalous positive expansion in a solid is a possible result of an approach to instability of the modes of vibration.