An Equation of State for Titanium

Abstract

In hydrocode simulations the equations that govern fluid motion are solved. The variation of density of a material with pressure and temperature is needed. This is called the equation of state (EoS). In this work the development of an EoS for titanium is discussed, and comparisons with the theoretical model and experimental data are shown. The EoS produced is a thermodynamically consistent multiphase EoS where solid-solid, as well as, solid-liquid phase transitions are modelled. The Helmholtz free energy as a function of density and temperature is calculated for each phase. The stable phase is the phase with the lowest Gibbs free energy, and phase boundaries are where the Gibbs free energy is the same for two phases. For the solid phase the Helmholtz free energy is decomposed into three terms, the cold curve contribution, the thermal electron contribution, and the thermal contribution from lattice vibrations, and for the liquid phase just the thermal electron and ion contribution is needed. In most cases a classical approach is used to model these contributions, but for one of the solid phases density functional theory is used to calculate the cold curve contribution. The final model covers a large range of phase space and accurately reproduces regions of shock instability, caused by one of the solid-solid phase transitions.