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 alpha titanium based on a modified high-T Birch-Mumaghan equation of state and a thermal pressure approach. With the pressure derivative of the bulk modulus, K(0)('), fixed at 4.0, we obtained: ambient bulk modulus K(0) = 114(3) GPa, temperature derivative of bulk modulus at constant pressure (partial derivative K/partial derivative T)(P) = -1.1(7) X 10(-2) GPa K(-1) and at constant volume (partial derivative K/partial derivative T)(V) = -9.0 X 10(-4) GPa K(-1), volumetric thermal expansivity alpha(T) = alpha+bT with a = 1.2(+/- 0.6) X 10(-5) K(-1) and b = 2.5(+/- 1.1) X 10(-8) K(-2), and the pressure derivative of thermal expansion (partial derivative alpha/partial derivative P)(T) = -8-5 X 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 alpha phase of titanium. For the omega-phase Ti, we obtained K(0) = 107(3) GPa and volumetric thermal expansivity at 8.1 GPa alpha(T) = a+bT with a = 6.5 (+/- 3.5) X 10(-6) K(-1) and b = 2.8(+/- 0.6) X 10(-8) K(-2), Within the experimental uncertainties, the c/a ratios for alpha-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.