Isothermal compressibility and thermal expansion of nitrogen doped hafnia

The isothermal compressibility of nitrogen doped hafnia ( β ′ hafnium oxonitride, Hf7O11N2) has been measured at room temperature up to 28 GPa in a hydrostatic pressure medium, using a diamond anvil cell and X-ray powder diffraction. From a least squares fit to the third-order Birch–Murnaghan Equation of State the values for the bulk modulus and its first pressure derivative were determined to B 0 = 269.4 GPa and B 0 ′ = 14.9 . The exceptionally high value for B 0 ′ arises as consequence of vacancy ordering and subsequently the almost one-dimensional compression of Hf7O11N2 up to pressures of about 12 GPa. The thermal expansion was investigated using temperature dependent X-ray powder diffraction. The coefficient of thermal expansion was calculated according to α v = 1 / V ∗ δ V / δ T = a 0 + a 1 ∗ T . The parameters were determined to a 0 = 10.389 ± 2.296 ∗ 1 0 − 6 K − 1 and a 1 = 7.34 ± 1.89 ∗ 1 0 − 9 K − 2 .