Application of CALPHAD to high pressures

The current methods of performing CALPHAD (CALculation of PHAse Diagrams) calculations of high-pressure phase equilibria often lead to spurious predictions of negative thermal expansion or negative heat capacity at high pressures. It is shown that the origin of the problem lies in an incompatibility between the temperature dependence of the widely used SGTE (Scientific Group Thermodata Europe) database and that of typical equations of state of the Mie–Grüneisen type. This inconsistency is also linked to the general problem of describing mechanical instability in CALPHAD. In the present work, a new free energy formulation is developed specifically for inclusion of pressure effects in CALPHAD methodology. It is based on an interpolation between SGTE data at low pressures and the quasiharmonic lattice model at high pressures. The new formulation is constrained to physically credible predictions of the thermophysical properties, while preserving the simplicity of the CALPHAD method. Examples are given of calculations of thermophysical properties and high-pressure phase equilibria in Al, Si, MgO, Fe and the Al–Si binary alloy system.