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To build a model using the CALPHAD approach, i.e. Gibbs free energy as a function of composition and temperature, typically taking the form of a Redlich-Kister polynomial, what kind of thermodynamic data needs to be collected from experiment (or from first principles calculations)?

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I concur with the answer by Alone programmer, but his answer only gives half the story. The coefficients or the model parameters come into the picture later and are actually obtained by optimization of both the experimentally obtained and theoretically calculated data. Here I will discuss the experimental data since the DFT part has already been discussed. The experimental data can be basically classified into three categories:

  1. Structural (Crystallographic): this helps in selecting the Gibbs energy models

  2. Constitutional: for example, tie-line, invariant points, special points, phase boundaries, phase amounts, etcetera. These can be obtained through suitable experiments.

  3. Thermochemical: for example, enthalpy, activity, heat capacity, etcetera. This data actually serves as constraints during the optimization of the model parameters since using only the constitutional data will make the calculation of model parameters difficult as many solutions are possible without using constraints.

Hope this helps.

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Basically you need to find $L_{ij}^{m}$ coefficients in the Redlich-Kister polynomials from DFT calculations, related to temperature as:

$$L_{ij}^{m} = a_{ij}^{m} + b_{ij}^{m} T + c_{ij}^{m} T \ln(T) + d_{ij}^{m} T^{2} + e_{ij}^{m} T^{3} + \frac{f_{ij}^{m}}{T}$$

Typically you need just the values for $m \leq 2$. I think this is a good reference for the data infrastructure that is needed for CALPHAD simulations: https://link.springer.com/content/pdf/10.1186/2193-9772-3-12.pdf

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As a retired professor in Computational Thermodynamics I am happy that young students try to use the Calphad methods to understand materials. However, to model a phase using Calphad there are some background needed. A Calphad database is built from a set of data for the pure elements in different phases describing how the Gibbs energy of the element vary with T from 300 K up to some higher T. Such data are obtained from experimental data for the stable state or estimated for metastable phases for the elements. It also include the heat capacity of the element. For solution phases one can introduce excess parameters which depend on the fraction of the elements and is normally constant or linearly T dependent. One does not use higher T terms (such as Tln(T)) unless one has experimental heat capacity for the solution. There are several models to select from which can describe LRO or SRO transitions in the phase which require more model parameters. Some of these can be determined by DFT calculations unless there are experimental data. In short, try to find some reference paper or book to read about Calphad, it is not just and an equation or a black box.

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