Precise calculation of melting curves by molecular dynamics

Abstract

The paper gives a brief review of methods to calculate melting curves by molecular dynamics and thoroughly investigates the so-called modified Z-method. The modified Z-method combines the ease of implementation inherent to the original Z-method with advantages the coexistence method offers, but, as it is shown, needs an improvement. In particular, the resulting liquid-solid states it gives are always not in hydrostatic equilibrium. To attain to hydrostatic equilibrium, it is necessary to equalize stress components in the calculation cell without changing its volume. In a series of simulations for aluminum, beryllium and iron we have demonstrated that the calculations by the modified Z-method with stress equalization are as accurate as those by the thermodynamic integration method but at much lower computational cost and do not depend on the system size. As a consequence calculated entropy changes across melting line allow us to evaluate solid-solid equilibrium lines between crystal phases involved. A system of 3×3×12 fcc unit cells (432 atoms) was the smallest for which we were able to obtain reliable results. Such a small system size means that, in principle, the method could be used for the calculation of melting curves by the quantum molecular dynamics.