Paper No. 9

Presentation Time: 3:00 PM

# PRESSURE-VOLUME EQUATION OF STATE FOR SOLIDS

For thermodynamic calculations such as the effect of pressure on the thermochemical properties of solids, it is convenient to calculate volume as a function of pressure and obtain the various energies directly as a function of pressure and temperature. This is difficult with other commonly used equations of state (EoS). Previous formulations of this type work well only over a limited low-pressure range and are not useful for high pressures data. The following equation of Grover et al. (1973) is useful in this regard: alpha V/Vo=ln [ 1 + beta (P-Po)/Ko] (1) where alpha is a fitted constant and Ko bulk modulus at zero pressure. This is a proposal for adopting an empirical equation that is simple and can be used to express volume as a function of pressure. The available PV data on iron and several other solids may be used to establish an equation of state (EoS), which relates volume directly to pressure. We modify Eq. (1) of Grover et al (1973) in establishing an empirical relationship of the form: V (P)=Vo - B ln [(1 + C (P-1)] (2) where the parameters B and C are adjustable parameters and may be used to calculate the bulk modulus and its pressure derivative. The bulk modulus may be calculated from the inverse of compressibility beta as given by beta=(B*C/(1+C*(P-1)))/V (3) An advantage of the logarithmic equation is that we may also use it to calculate P as a function of V by recasting (2) as: P=1+ [Exp((Vo-V)/B) 1]/C (4) The success of any empirical EoS depends on its ability to predict the volume data over extreme range of P. The equation (2) is shown to be useful as an equation of state for many solids over a large pressure range. The solids (maximum pressure in bracket) examined are iron (305), gold (145), platinum (666), bismuth (222) and periclase (MgO) (65) with bulk modulus of 152, 167.267,34 and 189 GPa respectively.