The CALPHAD methodology

CALPHAD is originally an abbreviation for CALculation of PHAse Diagrams, but was later expanded to refer to Computer Coupling of Phase Diagrams and Thermochemistry.

In the CALPHAD method, one collects and assesses all available experimental and theoretical information available on phase equilibria and thermochemical properties in a system. The thermodynamic properties of each phase are then described through the Gibbs free energy, applying a mathematical model containing adjustable parameters. These parameters are evaluated by optimizing the fit of the model to all the assessed information, also involving coexisting phases. Following this it is possible to recalculate the phase diagram, as well as the thermodynamic properties of all the phases and the system as a whole. The philosophy of the CALPHAD method is to obtain a consistent description of the phase diagram and the thermodynamic properties so as to reliably predict the set of stable phases and their thermodynamic properties in regions without experimental information and for metastable states during simulations of phase transformations.

A core ingredient of the CALPHAD method is the development of models to represent thermodynamic properties for various phases which permit prediction of properties of multicomponent systems from those of binary and ternary subsystems. This is accomplished by considering physical and chemical properties of the system in the thermodynamic model, for example, account is taken for crystallography, type of bonding, order-disorder transitions and magnetic properties.

Additionally, the CALPHAD method can also be extended to model atomic mobilities in a similar way as the Gibbs free energy. It has proven a powerful method for a wide range of applications, where Gibbs free energies in combination with atomic mobilities are used as the basis for calculating properties such as inter-diffusion coefficients in order to perform simulations on phase transformations in real multicomponent materials. The ability to calculate quantities, such as chemical driving force and access to atomic mobilities, are crucial for simulation of kinetic processes such as the evolution of microstructure based on phase-field methods.

The history, principles, methodology, software/database developments and its application has been extensively described in the book “Computational Thermodynamics – The Calphad Method” by H.L. Lukas, S.G. Fries and B. Sundman (2007, Cambridge). However, the Calphad approach was first described in the book “Computer Calculations of Phase Diagrams” by L. Kaufman and H. Bernstein (1970), in which the important concept of lattice stability (that had been introduced earlier by L. Kaufman, 1959) for calculation of phase diagrams based on Gibbs free energies was developed. They explained clearly how thermodynamic model parameters describing Gibbs free energies in multicomponent systems could be derived both from experimental phase diagrams and from the rudimentary first-principles techniques available at that time, and how they could be used for calculations of phase diagrams. More details on the lattice stability concept can be read about in the paper “Hume-Rothery and Calphad Thermodynamics” by L. Kaufman (2002; in Calphad and Alloy Thermodynamics, Eds. P.E. Turchi, A. Gonis and R.D. Shull, Warrendale, PA: TMS, pp. 3-19). The lattice stability concept was essential for the development of multicomponent thermodynamic databases. The method of extrapolating solubility lines into the metastable range and to obtain a thermodynamic property (such as the melting temperature of metastable FCC Cr) shows one of the important advantages of combining phase diagrams and thermodynamics.

More information about CALPHAD can be found at: www.calphad.org and on Wikipedia.