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Mooraj et al. J Mater Inf 2023;3:4 https://dx.doi.org/10.20517/jmi.2022.41 Page 19 of 45

[130]
calculate every equiatomic alloy containing 3-6 elements out of 26 elements . This calculation resulted in
screening 130,000 different alloy compositions to predict the phases at both their melting temperatures and
600 °C. Interestingly, Senkov et al. found that the proportion of alloys with solid solution (SS)
[130]
microstructures decreased as the number of components increased, as seen in Figure 9A . This
contradicts the general notion that increasing the number of elements would increase the configurational
entropy and thus promote SS formation. In order to investigate the cause of this discrepancy, Senkov et al.
calculated the entropy of mixing (ΔS ) and enthalpy of mixing (ΔH ) for each composition which
mix
mix
describes the Gibbs free energy for SS phases. They also calculated the entropy of formation (ΔS) and
f
enthalpy of formation (ΔH) for the intermetallic (IM) phases in each composition using CALPHAD. Then
f
they used the entropy and enthalpy change of the different predicted phases to calculate the minimized
Gibbs free energy to obtain quantitative predictions of the phase formation within each composition and
compare them to reported phases in the experimental literature.

Through the previous analysis, they explained that the configurational entropy increases with ln(N), where
N is the number of elements, while the possible binary interactions increase with (N/2)∙(N-1). Thus, the
number of binary interactions increases much faster than the configurational entropy, which increases the
likelihood that an IM phase with a highly negative enthalpy of formation exists within a HEA system. Thus,
the Gibbs free energy of possible IM phases decreases more rapidly than that of solid solution solutions as
the number of elements increases. This work highlights the ability of large computational datasets to allow
us to re-evaluate our fundamental assumptions of alloy design by providing large statistical datasets that
reveal trends that may not be obvious from experimental testing.

Although many HEAs have been reported to form SS phases at lower temperatures, these are often
metastable due to the inherent sluggish diffusion in HEAs. The fast computational speed of CALPHAD
methods allows researchers to rapidly screen the composition phase for compositions that maintain a SS as
the stable equilibrium phase even at low temperatures. Such methods have been utilized to predict the stable
phases of 3 million compositions in 4 different alloy systems of AlCrMnNbTiV, AlCrMoNbTiV, AlCrFeTiV
and AlCrMnMoTi . This process was enabled by running approximately 100 calculations in parallel on
[131]
single CPU cores in a computing cluster. This study aimed to identify various compositions that form
single-phase solid solutions (SPSS) at low temperatures and then design compositions that are likely to
exhibit good oxidation resistance. By incrementally adjusting the contents of various elements, the authors
were able to investigate the effect of each element on the stability of SPSS. The alloy systems shown to have
the most significant number of SPSS compositions were the AlCrMnNbTiV and AlCrMoNbTiV systems.
Figure 9B shows the 2D projection of the compositional space explored in the AlCrMoNbTiV, where each
red dot represents a composition with a predicted single-phase BCC microstructure. It was found that
placing constraints to limit the Al and Cr contents can improve SPSS formation, as seen in the top 2 rows of
Figure 9B but lowers the oxidation resistance. Thus, the optimal compositions found near the center of the
high SPSS formation region and still maintaining a high oxidation resistance were Al Cr Mn Nb Ti V or
25
7
1
41
25
1
Al Cr Mn Nb Ti V . This study highlights the ability of high throughput CALPHAD methods to reduce a
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1
21
7
41
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massive design space of over 3 million compositions down to a handful of promising candidates that can
feasibly be explored even using conventional manufacturing methods.
The equiatomic Cantor alloy (CoCrFeMnNi) has been studied extensively in the past, including its
deformation mechanism, phase formation, and mechanical properties at varying temperatures [132-134] .
However, the non-equiatomic compositions have not been explored as deeply . Assuming that a 1 at. %
[135]
increment in any element’s atomic fraction constitutes a new alloy then the compositional space for a
6
generic 5-element alloy system covers an excess of 10 unique compositions. Thus, CALPHAD or ML