CalPhaD Coffee Lecture – SGTE - Scientific Group Thermodata Europe

The CALPHAD method has advanced considerably since the early development of Gibbs energy descriptions for stable and metastable elements and phases by Kaufman and Bernstein in 1970. While first-generation models of the Gibbs energy introduced relative lattice stabilities, second-generation descriptions such as the SGTE dataset standardised elemental reference functions for various solid modifications and the liquid. Despite their usefulness, these formulations usually are simple polynomial heat-capacity expressions, which restrict physical interpretability and lead to inaccurate extrapolations at 0 K and at very high temperatures.

Therefore, the current drive to develop “third-generation” Calphad descriptions should address these issues by describing the thermodynamic properties of elements and compounds using functions based on the Einstein model for the heat capacity with corrections for anharmonic contributions. For solid phases, single- or multi-Einstein approaches are used to model heat capacities and Gibbs energies, even those with complex vibrational spectra (e.g. C, CaO). The critical point remains the high temperature behavior of the Gibbs energy of solid phases far beyond their melting point. Hereby, strategies for high-temperature extrapolation, including different functional forms and the equal-entropy criterion, are also discussed.

For liquids, the two-state model is introduced, where a physically motivated functional form governs the behaviour of enthalpy and heat capacity. This representation establishes consistent links between thermodynamic properties and dynamic phenomena, such as the glass transition, as demonstrated for B₂O₃.

Extension to solutions is achieved through the interaction of end-member Einstein contributions, as illustrated for the binary Al-Zn and Fe-Mn-Ti ternary systems. Furthermore, an alternative way to generate more robust high-temperature extrapolations is presented: the explicit treatment of thermal vacancies in low- and high-melting metallic systems. Finally, the remaining challenges to the widespread adoption of these methods and possible solutions to these challenges are briefly discussed.