Thermal equation of state of rhenium diboride by high pressure-temperature synchrotron x-ray studies

Abstract

The unit-cell volume of rhenium diboride $({\text{ReB}}_{2})$ has been measured by synchrotron x-ray diffraction at pressures and temperatures of up to 7.5 GPa and 1100 K with a cubic anvil apparatus. From the pressure $(P)$-volume $(V)$-temperature $(T)$ measurements, thermoelastic parameters were derived for ${\text{ReB}}_{2}$ based on a modified high-$T$ Birch-Murnaghan equation of state and a thermal-pressure approach. With the pressure derivative of the bulk modulus, ${K}_{0}^{\ensuremath{'}}$, fixed at 4.0, we obtain: the ambient bulk modulus ${K}_{0}=334(23)\text{ }\text{GPa}$, temperature derivative of bulk modulus at constant pressure ${(\ensuremath{\partial}K/\ensuremath{\partial}T)}_{P}=\ensuremath{-}0.064(6)\text{ }\text{GPa}\text{ }{\text{K}}^{\ensuremath{-}1}$, volumetric thermal expansivity ${\ensuremath{\alpha}}_{T}({\text{K}}^{\ensuremath{-}1})=a+bT$ with $a=1.33(25)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}5}\text{ }{\text{K}}^{\ensuremath{-}1}$ and $b=1.48(64)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}8}\text{ }{\text{K}}^{\ensuremath{-}2}$, pressure derivative of thermal expansion ${(\ensuremath{\partial}\ensuremath{\alpha}/\ensuremath{\partial}P)}_{T}=\ensuremath{-}5.76(95)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}7}\text{ }{\text{GPa}}^{\ensuremath{-}1}\text{ }{\text{K}}^{\ensuremath{-}1}$, and temperature derivative of bulk modulus at constant volume ${(\ensuremath{\partial}K/\ensuremath{\partial}T)}_{V}=\ensuremath{-}0.049(11)\text{ }\text{GPa}\text{ }{\text{K}}^{\ensuremath{-}1}$. The ambient bulk modulus derived from this work is comparable to previous experimental and theoretical results. These results, including the ambient bulk modulus and other thermoelastic parameters determined in present study, extend our knowledge of the fundamental thermophysical properties on ${\text{ReB}}_{2}$ and are important to the development of theoretical and computational modelings of hard materials.