An improved Lindemann melting rule

Abstract

The Lindemann melting rule associates the value of the melting point with that of the temperature-dependent thermal vibration amplitude at the melting point. We test the rule over a wide range of metallic elements. It works fairly well over the entire periodic system, from Li to Pu, provided that the temperature dependence of the elastic properties and the variation in the critical vibrational amplitude with mass are taken into account. The accuracy of various modifications of the Lindemann rule is evaluated. We propose a new physical interpretation of the Lindemann rule, based on the phonon mean free path.