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)].

Reinvestigation of high pressure polymorphism in hafnium metal

“…However, this transition was observed in compressed sample at elevated temperatures. This absence of high pressure phase transitions at ambient temperature is in disagreement with the results of Xia et al 4 Hrubiak et al 6 attributed this to the different pressure media (PTM) employed in the experiments. Xia et al did not use any PTM, while Hrubiak et al used essentially NaCl.…”

“…Our high pressure investigations re-establish the existence of α→ω→β transformation sequence in Hafnium under room temperature conditions and, hence, we do not support the recent result of Hrubiak et al 6 At room temperature, α↔ω transition exhibits large hysteresis encompassing a pressure range of over 30 GPa, similar to that observed by Xia et al …”

“…Therefore, disagreeing with earlier contradictory reports (references given in ref. 6), we feel and find that this increase in c/a ratio is not an artifact arising from the non-hydrostatic stresses in a DAC. The small difference between the transition pressures may also partly be due the use of neon and ethanol-methanol pressure media in two cases.…”

“…For example Vohra et al 10 reported that for Ti, change of oxygen content from 785 ppm to 3800 ppm shifted P α→ω from 3 GPa to above 8 GPa. In both the studies on Hf mentioned above 4,6 , high purity samples were reported to be used. However, no chemical composition has been provided by the authors, except for a statement in ref.…”

Pressure-induced crossing of the core levels in5dmetals

“…Hafnium (Hf) has attracted great scientific and technological interest due to the position of its d band in the middle of a broad sp band, which impacts its electronic and superconducting properties [6][7][8][9]. The instability of the hcp phase of Hf at high pressure was demonstrated both theoretically and experimentally [10,11]. Tantalum (Ta) is stable even at pressures of hundreds of GPa [12,13].…”