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Mooraj et al. J Mater Inf 2023;3:4 https://dx.doi.org/10.20517/jmi.2022.41 Page 17 of 45

accurate data that can efficiently identify optimal compositions within a large composition space, thereby
overcoming the inherent weakness in each technique by leveraging the strengths of the other. Applying this
method to other combinations of computational techniques may offer researchers new opportunities to
expand the computational speed, size, and accuracy of future computational studies, which can accelerate
alloy discovery far beyond the current state-of-the-art results.

The use of combining MD simulations with ML techniques was also explored by Zhang et al. to explore the
non-equiatomic compositions within the Fe-Co-Cr-Ni-Mn alloy system . In this case, the deformation of
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100 compositions with a single-crystal structure was simulated in three different crystallographic directions,
[100], [110], and [111]. The simulated stress-strain responses of these compositions are shown in Figure 8A.
Three different ML techniques were then used to predict further the yield stress of non-equiatomic
compositions within the alloy system. Unlike other ML tasks, the authors of this work used ML techniques
to carry out binary classification of “Good” and “Weak” yield strength rather than quantitative prediction of
yield strength. The advantage of this method is that ML programs trained with simulations of single crystals
can be used to find optimized compositions that show promise as polycrystalline structures. Typically,
polycrystalline models are much larger than single-crystal ones, which can make them more
computationally expensive . By leveraging the ability of ML classification techniques and the
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computational efficiency of high-throughput MD simulations of single crystals, the authors can produce
highly efficient means to rapidly identify candidates for optimized compositions of HEA space. This
technique was used again by Zhang et al. to carry out similar classification predictions for the Cu-Fe-Cr-Co-
Ni alloy system . It was again shown to be highly accurate and efficient at pointing out candidates with
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optimal yield strength . This approach significantly refines the potential compositional space that
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experimentation needs to explore.

While MD simulations are useful in exploring the compositional space of a system, they can also be used to
study material performance within other design dimensions, such as application temperature. Jian et al.
used MD simulations to study the effect of aluminum concentration, temperature, and strain rate in
amorphous Al CoCrFeNi HEAs to study their potential as low-density structural materials . Figure 8B
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x
shows the stress-strain curves of two of the three simulated compositions ranging from 300 K to 1,200 K.
For all three compositions, the yield strength and Young’s modulus both strongly depended on the
temperature rather than the Al content. The temperature dependence of the yield strength originated from
the high migration ability of atoms at higher temperatures, especially at 1,200 K, which was above the
simulated glass transition temperature of about 1,100 K. The authors also varied the strain rate from
10 -10 /s and found that the yield strength and Young’s modulus increased with increasing the strain rate.
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The authors explained that a higher strain rate leads to a larger free volume but that at high strain rates, the
times required for free volume rearrangement and atomic diffusion increase greatly. This relationship
between free volume and atomic diffusion causes the effective free volume conducive to atomic migration to
decrease. Thus, the atomic motion is impeded, which leads to increased strength. This study highlights the
flexibility of MD simulations to explore compositional space and various ambient and application
conditions that can provide a more holistic understanding of material performance.

CALPHAD calculations
Phase diagrams are geometric representations of alloy systems under thermal equilibrium and typically
denote the boundaries of composition and temperature where phase transformations are expected to
occur . These diagrams form the basis for studying solidification, crystal growth, and solid-solid phase
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transformations. Since the 1970s, the calculation of phase diagrams has become an integral part of alloy
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design, specifically through CALPHAD technology . The technique relies on the minimization of the total
Gibbs free energy of the system using the temperature, pressure, overall composition, and Gibbs energy
function stored in databases .
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