PERFORMANCE OF THE COMPLETE TRAVEL-TIME EQUATION OF STATE AT SIMULTANEOUS HIGH-PRESSURE AND TEMPERATURE

The complete travel-time equation of state (CT-EOS) is presented by ut ilizing thermodynamics relations, such as; K(T) = K(S)(1 + alphagammaT )-1, gamma = alphaK(S)/rhoC(P), partial derivative C(P)/partial deriva tive P)T = -T/rho[alpha2 + partial derivative alpha/partial derivative T)P], etc. The CT-EOS enables us to analyze ultrasonic experimental d ata under simultaneous high pressure and high temperature without intr oducing 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 syn thesized travel-time data with random noise of 10(-5) and 10(-4) ampli tude 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 ther modynamic and elastic parameters, as well as their derivatives with un precedented accuracy, yielding second-order pressure derivatives (part ial derivative 2M/partial derivative P2) of the elastic moduli as well as the temperature derivatives of their first-order pressure derivati ves (partial derivative 2M/partial derivative P partial derivative T). The completeness of the CT-EOS provides an unambiguous criterion to e valuate the compatibility of empirical EOS with experimental data. Fur thermore because of this completeness, it offers the possibility of a new and absolute pressure calibration when X-ray (i.e., volume) measur ements are made simultaneously with the travel-time measurements.