A robust three-parameter reference curve for condensed phase materials

Many isothermal equations of state lead to numerical problems under tension conditions due to negative bulk modulus. We summarize the properties of four existing models and devise a continuous non-piecewise reference curve to address this issue. The final functional form contains three fitting parameters that are directly related to the bulk modulus and its pressure derivative at the reference state and at infinite pressures. We also include bounds that guarantee the monotonicity of its pressure derivative in all volume space. To demonstrate the qualitative features of each isotherm, we conduct calibrations against experimental data for cyclotetramethylene tetranitramine, magnesium oxide, gold, and platinum. Pressure residuals and root mean square deviations show that the proposed functional form is capable of adequately fitting the data compared to other three-parameter models.