Synthesis of Hf$_8$O$_7$, a new binary hafnium oxide, at high pressures and high temperatures

Two binary phases in the system Hf–O have been synthesized at pressures between 12 and 34 GPa and at temperatures up to 3000 K by reacting Hf with HfO$_2$ using a laser-heated diamond anvil cell. In situ X-ray diffraction in conjunction with density functional theory calculations has been employed to characterize a previously unreported tetragonal Hf$_8$O$_7$ phase. This phase has a structure which is based on an fcc Hf packing with oxygen atoms occupying octahedral interstitial positions. Its predicted bulk modulus is 223(1) GPa. The second phase has a composition close to Hf$_6$O, where oxygen atoms occupy octahedral interstitial sites in an hcp Hf packing. Its experimentally determined bulk modulus is 128(30) GPa. The phase diagram of Hf metal was further constrained at high pressures and temperatures, where we show that α-Hf transforms to β-Hf around 2160(150) K and 18.2 GPa and β-Hf remains stable up to at least 2800 K at this pressure