Melting curve and fluid equation of state of carbon dioxide at high pressure and high temperature

Accepted by Journal of Chemical Physics; in pressThe melting curve and fluid equation of state of carbon dioxide have been determined under high pressure in a resistively-heated diamond anvil cell. The melting line was determined from room temperature up to $11.1\pm0.1$~GPa and $800\pm5$~K by visual observation of the solid-fluid equilibrium and in-situ measurements of pressure and temperature. Raman spectroscopy was used to identify the solid phase in equilibrium with the melt, showing that solid I is the stable phase along the melting curve in the probed range. Interferometric and Brillouin scattering experiments were conducted to determine the refractive index and sound velocity of the fluid phase. A dispersion of the sound velocity between ultrasonic and Brillouin frequencies is evidenced and could be reproduced by postulating the presence of a thermal relaxation process. The Brillouin sound velocities were then transformed to thermodynamic values in order to calculate the equation of state of fluid CO$_2$. An analytic formulation of the density with respect to pressure and temperature is proposed, suitable in the $P-T$ range 0.1-8~GPa and 300-700~K and accurate within 2\%. Our results show that the fluid above 500 K is less compressible than predicted from various phenomenological models