Paper 8.6

Equations of state for modelling of high-pressure equilibria

Brosh Eli ¹, Makov Guy ², Shneck Roni Z. ¹

¹ Department of Materials Engineering, Ben-Gurion University of the Negev,

P.O.Box 653, Beer Sheva, Israel

²  NRCN , P.O.Box 9001 Beer-Sheva, Israel

A key component in the CALPHAD (Calculation of Alloy PHase Diagrams) analysis of high-pressure equilibria is the equation of state (EOS) that is used to describe the pressure-volume-temperature dependence for a given substance.

We present a new semi-empirical EOS, which may be integrated to yield an explicit, analytic expression of G(T,P) and thus implemented in existing thermodynamic software. The volume is expressed as a sum of two parts: a “cold” part which depends only on the pressure and a “warm” part which depends on both the temperature and the pressure. This warm term is designed so that all the isotherms approach the cold P-V curve at (moderately) high pressures.

For the description of cold (T=0 K) compression, the input parameters in the new EOS are: V₀, B₀ and , the molar volume, the bulk modulus and its pressure derivatve, all taken at zero pressure and temperature. The chemical identity of the substance, enters the EOS only  through the atomic numbers Z of the constituent elements. The porposed cold curve is an intrapolation between the low pressure behaviour, which is characterized by the adjustable parameters and the Thomas-Fermi-Kirzhnits model at very high pressures.

For the “warm” part, at least one more adjustable parameter is required: a₀ which is equivalent to the thermal expansion coefficient at ambient conditions. More adjustable parameters may be used, when required by the complexity of the available data.  For example, the Anderson-Gruneisen parameter d  may be also adjusted.

The new EOS agrees well with experimental data and ab-initio calculations. The utilization of the new EOS in CALPHAD is illustrated  by an analysis of the available experimental data on uranium.