Molecular dynamics study of vibrational entropy in bcc and hcp zirconium

Abstract

Molecular dynamics is employed to determine the vibrational entropy and the Gibbs free energy as a function of temperature in the homogeneous bcc and hcp zirconium. The bcc-hcp phase transition is identified at 1754 K, where the Gibbs free energy difference between the two phases is equal to zero. The corresponding vibrational entropy difference is ${0.29k}_{B}$ per atom. By rapidly reducing the temperature from 1800 to 1200 K in single molecular dynamics simulations with the homogeneous bcc as the initial configuration, the relation between the potential energy and the temperature is established. The potential energy curve also exhibits the phase transition. However, the transition temperature indicated by this method lies below 1350 K. It is because the bcc transforms into the so-called ``martensitic microstructure'' rather than the homogeneous hcp. The presence of the microstructure reduces the difference in the potential energy between the bcc and the martensitic phases. By reconsidering the Gibbs free energy, the transition temperature is then 1349 K and the vibrational entropy difference is ${0.22k}_{B}$ per atom.