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Mooraj et al. J Mater Inf 2023;3:4 https://dx.doi.org/10.20517/jmi.2022.41 Page 21 of 45

Figure 10. (A) Quaternary phase diagrams at fixed 10 at. % Co illustrating explored composition space. The red circle points out
the composition that is experimentally tested, and the red stars indicate the target compositions to maximize hardness (left) and
minimize stacking fault energy (right). This figure is quoted with permission from Conway et al. [135] ; (B) CSA predicted single-phase
solid solution compositional spaces for FCC and BCC at 1,400 K, 1,450 K, and 1,500 K. This figure is quoted with permission
from Abu-Odeh et al. [136] , copyright 2018, Elsevier. BCC: Body-centered cubic; CSA: constraint satisfaction algorithm; FCC: face-
centered cubic.

conditions that lead to the stabilization of desirable phases which produce high-performance materials. One
such example is to provide the coordinates composition and temperature space that result in SPSS for
HEAs. The approach Abu-Odeh et al. took to tackle this problem is described as a constraint satisfaction
algorithm (CSA) which involves the use of ML protocols executed in tandem with CALPHAD calculations
to satisfy specific material property criteria/constraints.

This method enables efficient exploration of a large composition region to identify regions of arbitrarily
complex phase constitution characteristics. This approach has the potential to design alloy compositions of
any phase fraction rather than just focusing on the discovery of SPSS, as previously shown in other works.
Abu-Odeh et al. applied their framework to the Cantor alloy (Co-Cr-Fe-Ni-Mn) system, where they
explored the regions of SPSS stability for both FCC and BCC phases. Figure 10B visually represents the
change in FCC and BCC stability with increasing temperature for a ternary sub-section of the compositions
explored. After confirming the outcomes of the SPSS regions in the quinary compositions of the system, the
approach was expanded to search for precipitation hardening compositions in the Al-CoCrFeNi system by
identifying composition regions that include minor secondary phases. It was expressed that the secondary
phase would only be considered if it did not form via spinodal decomposition, as this would not lead to any
significant precipitation hardening. With this technique, the authors could identify composition spaces
most likely to exhibit precipitation-hardening behavior. They highlighted that providing more detailed
constraints can further refine the predicted composition space to provide a target region that can be
practically explored via experimental methods.

Comparison of computational methods
The previous categories of computational methods all serve important functions in the process of predicting
and narrowing the huge compositional space of HEAs. To ensure efficient usage of computational resources