# Exploring first principles-based phase diagrams using a modified CALPHAD approach

Theresa Davey^{1}, Nguyen-Dung Tran ^{1}, Ying Chen^{1}

1. School of Engineering, Tohoku University, Japan

CALPHAD XLVII, Queretaro, Mexico

Contributed poster presentation

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 to new material systems at the prediction stage. Currently, it is difficult to create a thermodynamic description of most systems entirely from calculated data. An approach is considered by which several theoretical techniques are used together to inform a CALPHAD-based thermodynamic description derived from first principles without optimization.

In this work, the aluminium-nickel system was chosen as a test case as it contains many features commonly found in phase diagrams, including ordered and disordered phases of various structures including bcc and fcc. 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 [1]. Other entropy contributions are indirectly contained within the fitted excess energy terms of optimized descriptions.

It has been seen in past investigations that the Bragg- Williams entropy model implemented within the Compound Energy Formalism (CEF) does not give a description of the fcc (metastable) phase diagram for certain systems that is consistent with other first principles methods or as derived using the Cluster Variation Method (CVM) [2].

The fcc phase diagram for the aluminium-nickel system from ground state first principles calculations without optimization using a pure CEF description is shown in Figure 1. Key features of these diagrams are the single maxima for the order-disorder transition, and unreasonably high transition temperatures, while experimental, CVM, and Monte Carlo (MC) phase diagrams for the same system show separated maxima for each ordered phase. These incorrect features are attributed to the lack of consideration of short range ordering in the CEF model without excess terms, and various techniques have been implemented to modify the topology of the CEF fcc phase diagram, such as by using reciprocal interaction parameters [3].

Using Density Functional Theory (DFT) calculations of the formation enthalpies and various effective cluster interaction energies from the Cluster Expansion Method (CEM), compatible CEF and CVM models are created. Through comparison of these methods, the interaction parameters required to correctly describe the topology of the fcc phase diagram using a modified CEF are determined. By following this approach, a fcc phase diagram with topology as expected can be obtained directly without optimization. In doing this, contributions to the configurational entropy beyond the point contributions (as in the Bragg-Williams approximation) are introduced.

The progress in this work of developing a first principles-based fcc phase diagram directly from calculation is presented and the shortcomings and challenges of the models discussed.

References

[1] Shockley, W. “Theory of Order for the Copper Gold Alloy System,”, J. Chem. Phys., Vol. 6 (1938): 130-144

[2] Kikuchi, R. “Solution of the Controversy in the fcc- Based Phase Diagram,”, Prog. Theo. Phys. Supp., No. 87 (1986): 69-76

[3] Kusoffsky, A., et al. “On the Compound Energy Formalism Applied of fcc Ordering,”, Calphad, Vol. 25 No. 4 (2001): 549-565