Melting, thermal expansion, and the Lindemann rule for elemental substances

Abstract

An interpretation of a long-standing problem—the Lindemann melting rule—has been suggested within the framework of the interstitialcy theory. Melting is considered to be due to the rapid generation of thermodynamically equilibrium defects—dumbbell interstitials, which drastically decrease the shear modulus at the melting point. An analytical expression for the relationship between the thermal expansion coefficient and melting temperature coinciding with the Lindemann melting rule has been derived. The obtained results agree with available data on elemental substances. A correlation between the melting temperature and shear modulus has been discovered and explained within the framework of the same approach.