Application of density functional theory calculations to the statistical mechanics of normal and anomalous melting

Abstract

Density functional theory (DFT) calculations reliably aid in understanding the relative stability of different crystal phases as functions of pressure and temperature. Our purpose here is to employ DFT to analyze the character of the melting process, with an emphasis on comparing normal and anomalous melting. The normal-anomalous distinction is the absence or presence, respectively, of a significant electronic structure change between crystal and liquid. We study the normal melters Na and Cu, which are metallic in both phases, and the anomalous melter Ga, which has a partially covalent crystal and a nearly free-electron liquid. We calculate free energies from lattice dynamics for the crystal and from vibration-transit (V-T) theory for the liquid, where the liquid formulation is similar to that of the crystal but has an additional term representing the diffusive transits. Internal energies $U$ and entropies $S$ calculated for both phases of Na and Cu were previously shown to be in good agreement with experiment; here we find the same agreement for Ga. The dominant theoretical terms in the melting $\ensuremath{\Delta}U$ and $\ensuremath{\Delta}S$ are the structural potential energy, the vibrational entropy, and the purely liquid transit terms in both $U$ and $S$. The melting changes in structural energy and vibrational entropy are much larger in Ga than in Na and Cu. This behavior arises from the change in electronic structure in Ga, and is the identifying characteristic of anomalous melting. We interpret our DFT results in terms of the physical effects of the relatively few covalent bonds in the otherwise metallic Ga crystal.