A Prototype First-Principles Only Phase Diagram: Al-Ni

Phase diagrams calculated entirely from first-principles have the potential to reduce time and expense in investigations for materials design by providing important thermodynamic information on new material systems at the prediction stage. However, it is still difficult to create a thermodynamic description of most systems using only calculated data and conventional methods. An approach is proposed that considers several theoretical techniques to inform a CALPHAD-based thermodynamic description derived only from first-principles data. 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]. Generally, other entropy contributions are indirectly contained within the excess energy terms that have optimized parameters fitted to experimental data. The Bragg-Williams entropy model with pure computational data does not give a proper description of the phase diagram, which is partially attributed to the lack of consideration of short range ordering. Other theoretical techniques, such as the Cluster Variation Method (CVM) [2], allow consideration of various order configurational entropy contributions, and can be shown to produce phase diagrams with topology consistent with the real physical case.

In this work, various techniques have been implemented to modify the Gibbs energy of the CALPHAD descriptions of the fcc and bcc phases, such as by using reciprocal interaction parameters in a structure based on the compound energy formalism (CEF) [3,4]. These Gibbs energy models are then populated directly with data calculated from first-principles, without any optimization.

The Al-Ni system has a variety of common topological features in its phase diagram, such as phases with significant solubility and line compounds, and ordered and disordered phases. As such, Al-Ni was chosen as a prototype system to compare the effectiveness of various thermodynamic models and to test the proposed new approach for calculating phase diagrams. Structures for the ordered phases were obtained via the Cluster Expansion Method (CEM) [5] and structures for the disordered phases were obtained from Special Quasirandom Structures (SQS) [6]. First-principles calculations for each phase consist of ground state electronic structure calculations, thermal electron contributions, and vibrational energy contributions up to 2500K from phonon calculations (quasiharmonic approximation) and the Debye-Grüneisen model. In addition to the known stable solid phases, various unstable phases were also considered.

We show that the effects of short range ordering are introduced with this framework, and further configurational entropy contributions can be directly included by comparison with other theoretical techniques such as the CVM. Using a CALPHAD platform and only first-principles data, a satisfactory solid phase diagram that reproduces all primary topological features of the experimental phase diagram is produced.

References
1) Shockley, W., J. Chem. Phys, Vol. 6 (1938): 130
2) Kikuchi, R., Physical Review, Vol. 81 Issue 6 (1951): 988
3) Kusoffsky, A., et al., Calphad, Vol. 25 No. 4 (2001): 549
4) Abe, T and Shimono, M., Calphad, Vol. 45 (2014): 40
5) Sanchez, J.M., et al., Physica A, Vol. 123 Issues 1-2 (1984): 334
6) Zunger, A., et al., Physical Review Letters, Vol. 65 No. 3 (1990): 353