Performance of the Complete Travel-time Equation of State at Simultaneous High Pressure and Temperature

Abstract

The complete travel-time equation of state (CT-EOS) is presented by utilizing thermodynamics relations, such as;

$${\begin{array}{*{20}{c}} {{K_T} = {K_S}(1 + x\gamma T){^1},}&{\gamma = \frac{{x{K_S}}}{{\rho {C_P}}},\frac{{\partial {C_P}}}{{\partial P}})} \end{array}_T} = \frac{T}{\rho }{[{x^2} + \frac{{\partial x}}{{\partial T}})_P}],etc.$$

The CT-EOS enables us to analyze ultrasonic experimental data under simultaneous high pressure and high temperature without introducing any assumption, as long as the density, or thermal expansivity, and heat capacity are also available as functions of temperature at zero pressure. The performance of the CT-EOS was examined by using synthesized travel-time data with random noise of 10⁻⁵ and 10⁻⁴ amplitude up to 4 GPa and 1500 K. Those test conditions are to be met with the newly developed GHz interferometry in a gas medium piston cylinder apparatus. The results suggest that the combination of the CT-EOS and accurate experimental data (10⁻⁴ in travel time) can determine thermodynamic and elastic parameters, as well as their derivatives with unprecedented accuracy, yielding second-order pressure derivatives (∂² M/∂P ²) of the elastic moduli as well as the temperature derivatives of their first-order pressure derivatives (∂² M/∂P ∂T). The completeness of the CT-EOS provides an unambiguous criterion to evaluate the compatibility of empirical EOS with experimental data. Furthermore because of this completeness, it offers the possibility of a new and absolute pressure calibration when X-ray (i. e., volume) measurements are made simultaneously with the travel-time measurements.