High P-T phase transitions and P-V-T equation of state of hafnium

Abstract

We measured the volume of hafnium at several pressures up to 67 GPa and at temperatures between 300 to 780 K using a resistively heated diamond anvil cell with synchrotron x-ray diffraction at the Advanced Photon Source. The measured data allows us to determine the P-V-T equation of state of hafnium. The previously described [Xia et al., Phys. Rev. B 42, 6736–6738 (1990)] phase transition from hcp (α) to simple hexagonal (ω) phase at 38 GPa at room temperature was not observed even up to 51 GPa. The ω phase was only observed at elevated temperatures. Our measurements have also improved the experimental constraint on the high P-T phase boundary between the ω phase and high pressure bcc (β) phase of hafnium. Isothermal room temperature bulk modulus and its pressure derivative for the α-phase of hafnium were measured to be B0 = 112.9 ± 0.5 GPa and B0′ = 3.29 ± 0.05, respectively. P-V-T data for the α-phase of hafnium was used to obtain a fit to a thermodynamic P-V-T equation of state based on model by Brosh et al. [CALPHAD 31, 173–185 (2007)].