CALPHAD

CALPHAD stands for CALculation of PHAse Diagrams. An equilibrium phase diagram is usually a diagram with axes for temperature and composition of a chemical system. It shows the regions where substances or solutions (i.e. phases) are stable and regions where two or more of them coexist. Phase diagrams are a very powerful tool for predicting the state of a system under different conditions and were initially a graphical method to rationalize experimental information on states of equilibrium. The CALPHAD approach is based on the fact that a phase diagram is a manifestation of the equilibrium thermodynamic properties of the system, which are the sum of the properties of the individual phases. It is thus possible to calculate a phase diagram by first assessing the thermodynamic properties of all the phases in a system.

With the CALPHAD method one collects all experimental information on phase equilibria in a system and all thermodynamic information obtained from thermochemical and thermophysical studies. The thermodynamic properties of each phase are then described with a mathematical model containing adjustable parameters. The parameters are evaluated by optimizing the fit of the model to all the information, also involving coexisting phases. It is then possible to recalculate the phase diagram as well as the thermodynamic properties of all the phases. The philosophy of the CALPHAD method is to obtain a consistent description of the phase diagram and the thermodynamic properties so 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.

There are two crucial factors for the success of the CALPHAD method. The first factor is to find realistic as well as convenient mathematical models for the Gibbs energy for each phase. The Gibbs energy is used because most experimental data have been determined at known temperature and pressure and any other thermodynamic quantities can be calculated from it. It is not possible to obtain an exact description of the behavior of the Gibbs energy of a multi-component system with analytical expressions. It is thus necessary to identify the main features and base the mathematical models on them. The discrepancy between model and reality is finally represented by a power series expansion in temperature, pressure and constitution of the phase. The adjustable parameters of these model descriptions are refined to reproduce the experimental data. The strength of the CALPHAD method is that the descriptions of the constituent sub-systems can be combined to describe a multi-component system.

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