Phase diagrams calculated entirely from first principles have the potential to reduce both time and expense in investigations for materials design by providing important thermodynamic information on new material systems at the prediction stage. Currently, it is difficult to create a thermodynamic description of most systems using only calculated data. An approach is considered by which several theoretical techniques are used together to inform a CALculation of PHase Diagrams (CALPHAD)-based thermodynamic description derived from first principles without optimization.
Commonly, thermodynamic descriptions made using the CALPHAD approach use the Bragg-Williams approximation to describe the configurational entropy of a solid, which is a point correlation model ignoring the pair and higher order interactions . Generally, other entropy contributions are indirectly contained within the excess energy terms that are optimized to fit experimental and theoretical data. The Bragg-Williams entropy model does not give a description of the fcc (metastable) phase diagram that is consistent with other first principles methods or as derived using the Cluster Variation Method (CVM) . The incorrect features are attributed to the lack of consideration of short range ordering, and various techniques have been implemented to modify the Gibbs energy of the CALPHAD descriptions of ordered fcc phases, such as by using reciprocal interaction parameters .
Using aluminium-nickel as a test system, several compatible thermodynamic models were created using various first principles calculations from Density Functional Theory (DFT) and Cluster Expansion Method (CEM). Through comparison of these methods, the interaction parameters required to correctly describe the topology of the fcc phase diagram using a modified CALPHAD model are determined. By following this approach, a fcc phase diagram with topology as expected can be obtained directly without optimization. In doing this, higher order contributions to the configurational entropy are included.
 Shockley, W. J. Chem. Phys., Vol. 6 (1938): 130-144
 Kikuchi, R. Prog. Theo. Phys. Supp., No. 87 (1986): 69-76
 Kusoffsky, A., et al. Calphad, Vol. 25 No. 4 (2001): 549-565