A multiphase equation of state of three solid phases, liquid, and gas for titanium

A multiple-phase equation of state of the α phase, β phase, ω phase, liquid, and gas for titanium is presented. This equation of state is thermodynamically consistent, based on a three-term semiempirical model for the Helmholtz free energy. The parameters of the free energy are first evaluated from the experimental data and solid-state theoretical calculations. Then, the values of the parameters are adjusted using a numerical minimization scheme based on the simplex algorithm, to values that best reproduce measured phase diagrams and other experimental data. The predicted phase diagram shows a compression-induced β-ω transition, up to a β-ω-liquid triple point at ∼45GPa and ∼2200K. For pressures above this triple point, the melting occurs from the ω phase. Moreover, no β-ω transition is predicted along the Hugoniot curve starting at STP conditions.