Melting of elements

Abstract

The aim is to identify and evaluate the most important factors that determine the melting temperature T$_{\text{m}}$ of the elements. Experimental data are analysed in terms of statistical mechanical theories of the energy and entropy of crystal and liquid phases. The elements are divided into two groups, according to their value of the entropy of fusion at constant density, $\Delta $S: the normal elements have $\Delta $S close to 0.79k per atom, and the anomalous elements have $\Delta $S much larger. For the normal elements, a melting rule is constructed in terms of two factors, the lattice dynamics characteristic temperature for entropy, and the liquid correlation entropy. For the anomalous elements, the large $\Delta $S is attributed to a change in electronic groundstate upon melting, and the melting rule depends also on the corresponding electronic energy change. The melting rules give T$_{\text{m}}$ to an accuracy of around 20%, and at this level, anharmonicity and crystal symmetry effects are negligible. Two conclusions regarding the relative motion of ions in crystal and liquid phases are: (a) liquid higher order correlations lower T$_{\text{m}}$ because they lead to a more ordered liquid, and (b) the loss of long-range order in melting corresponds to $\Delta $S $\approx $ 0.79k per atom for normal and anomalous elements alike.