Thermal equations of state for titanium obtained by high pressure—temperature diffraction studies

We have conducted in situ high-pressure diffraction experiments on titanium metal at pressures up to 8.2 GPa and temperatures up to 900 K. From the pressure $(P)$-volume $(V)$-temperature $(T)$ measurements, thermoelastic parameters were derived for α titanium based on a modified high-T Birch-Murnaghan equation of state and a thermal pressure approach. With the pressure derivative of the bulk modulus, K₀^', fixed at 4.0, we obtained: ambient bulk modulus K₀=114(3) GPa, temperature derivative of bulk modulus at constant pressure (∂K/∂T)P=-1.1(7)×10^-2 GPa K^-1 and at constant volume (∂K/∂T)V=-9.0×10^-4 GPa K^-1, volumetric thermal expansivity αT=a+bT with a=1.2(±0.6)×10^-5 K^-1 and b=2.5(±1.1)×10^-8 K^-2, and the pressure derivative of thermal expansion ${({∂}{α}/{∂}P)}T={-}8.5×{}{10}^{{-}7} {GPa}^{{-}1} {K}^{{-}1}$. The ambient bulk modulus and volumetric thermal expansion derived from this work are in good agreement with previous experimental results, whereas all other thermoelastic parameters represent the first determinations for the α phase of titanium. For the ω-phase Ti, we obtained K₀=107(3) GPa and volumetric thermal expansivity at 8.1 GPa αT=a+bT with a=6.5(±3.5)×10^-6 K^-1 and b=2.8(±0.6)×10^-8 K^-2. Within the experimental uncertainties, the $c/a$ ratios for α-Ti at both room and high temperatures remain constant over the experimental pressures up to 7.8 GPa, presenting a case against the isotropic force potential used in some theoretical modeling for hcp metals under high pressures.