Isothermal equation of state for gold with a He-pressure medium

Abstract

The isothermal equation of state (EOS) for gold has been determined by powder x-ray diffraction experiments up to 123 GPa at room temperature. We have performed experiments independently in two institutions to check the consistency of the results. A He-pressure medium was used to minimize the effect of uniaxial stress on the sample volume and ruby pressures. The stress state in the He-pressure medium gradually becomes nonhydrostatic above about 30 GPa, with the magnitude of the uniaxial stress largely depending on experiments. Since the measured lattice spacings deviate under different stress states, it is a likely cause of the disagreement of the EOS parameters found in the literature. The lattice spacing ${d}_{111}$ for the 111 reflection is least affected by the uniaxial stress in the case of gold. Hence we have calculated the sample volume from ${d}_{111}$ and fitted the obtained pressure-volume data to the Vinet form of EOS. The bulk modulus ${B}_{0}$ at atmospheric pressure was fixed to 167 GPa, a value well established by ultrasonic measurements. The fit gives the pressure derivative of the bulk modulus at atmospheric pressure as ${B}_{0}^{\ensuremath{'}}=5.5(1)$ for the current ruby pressure scale after Zha et al. [Proc. Natl. Acad. Sci. U.S.A. 97, 13494 (2000)]. Alternatively, if we use a different calibration of this standard [Phys. Rev. B 75, 024115 (2007)], we obtain ${B}_{0}^{\ensuremath{'}}=5.9(1)$, which is in excellent agreement with the ultrasonic measurements and first-principles calculations. Discussions are given to the use of gold as a pressure standard and the hydrostaticity of the He-pressure medium.