First-principles-only phase diagram for the Al-Ni system

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 higher 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.

Al-Ni was taken as a prototype system to compare various thermodynamic models and test the proposed new approach for calculating phase diagrams. First principles calculations for ordered phases include Density Functional Theory (DFT) ground state calculations, electronic energy 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.

A satisfactory solid phase diagram that reproduces all primary topological features of the experimental phase diagram is produced, using a CALPHAD platform and only first principles data. Comparing the descriptions produced from each type of theoretical data, the computational accuracy required for a thermodynamic description without experimental insight is considered.

References
[1] Shockley, W. “Theory of Order for the Copper Gold Alloy System,” J. Chem. Phys, Vol. 6 (1938): 130
[2] Kikuchi, R. “A theory of cooperative phenomena,” Physical Review, Vol. 81 Issue 6 (1951): 988
[3] Kusoffsky, A., et al. “On the Compound Energy Formalism Applied of fcc Ordering,” Calphad, Vol. 25 No. 4 (2001): 549
[4] Abe, T and Shimono, M. “A description of the effect of short-range ordering in BCC phases with four sublattices,” Calphad, Vol. 45 (2014): 40