Page 88 - Read Online

Mooraj et al. J Mater Inf 2023;3:4 https://dx.doi.org/10.20517/jmi.2022.41 Page 13 of 45

The computational efficiency of VCA makes it uniquely suited to explore HEA systems, as shown by Chen
[104]
et al., who used the VCA method to explore the effect of Ti within the Ti VNbMo system . VCA only
x
requires the construction and analysis of a primitive cell, while other DFT methods require the use of a
supercell as previously discussed, making them much more difficult to calculate. Since VCA has previously
achieved reliable results for studying RHEA systems, Chen et al. proposed that it is reasonable to implement
it to analyze the mechanical properties of this RHEA. Figure 5B illustrates the effect of Ti content on the
lattice elastic constants and elastic properties [Poisson ratio and ratio of the bulk modulus to the shear
modulus (B/G)]. Looking at the lattice elastic constants, it is clear that C > C for all compositions, and the
12 44
Cauchy pressure (C = C - C ) is positive for all the compositions. This suggests that the nature of the
12
p
44
bonding for all these compositions remains metallic. The Born-Huang mechanical stability criterion is also
met (C - C > 0, C + 2C > 0 and C > 0), which indicates that the BCC crystal structure remains stable for
12
11
11
12
44
these compositions. The Poisson ratio and B/G ratio seem to both increase with increasing Ti. Both of these
values have been suggested to correlate well with the ductility of a material, implying that higher Ti content
improves ductility. Chen et al. also indicated that Young’s modulus (and hence yield strength) decreases
with increasing Ti. To verify the accuracy of these results, the authors compared the properties of the
equiatomic composition TiVNbMo to experimental values from literature and found a reasonable
consistency.
New fist-principles methods such as Lederer-Toher-Vecchio-Curtarolo (LTVC) have been established over
the last five years to provide novel approaches towards calculating solid solution phase stability in HEAs in
[105]
order to guide future alloy discovery . This method incorporates energy calculations into a mean-field
statistical mechanics model, which uses order parameters to predict the transition temperature of a HEA
system into a solid solution phase. The authors lay out the development of their protocol in 3 stages: (i) The
[106]
automatic flow for material discovery (AFLOW) repositories are used to train cluster expansion (CE)
[107] [108]
models within the Alloy Theoretic Automated Toolkit (ATAT) and estimate zero temperature energy
configuration of atomic configurations, which are derivative structures from either FCC or BCC lattices, on
which HEAs show solid solution formability; (ii) Then, the estimated atomic configurations are entered into
[109]
a mean field statistical mechanical model called the generalized quasi-chemical approximation (GQCA) ;
(iii) Finally, an order parameter is proposed by calculating the evolution of the probability of finding certain
ordered configurations of atoms within the lattice.

To test this new method, the authors verified its accuracy by comparing its predictions to Monte Carlo
simulations and experimental data for binary alloys. They also compared CALPHAD predictions via
Thermo-calc for ternary alloys and experimental data from the literature. Once the method was considered
reliable and accurate, the authors used it to predict the solid solution formation in many different alloys.
They compared their predictions to the well-known empirical rules that usually inform the design of HEAs
to form solid solutions. Figure 6A and B show the plots of the electronegativity and atomic size differences,
as well as the VEC and atomic size differences. The large scatter of the green data points suggests that the
LTVC method can be used to predict the formation of solid solutions beyond what is typically expected by
the usual empirical rules. This study suggests that LTVC shows excellent potential to efficiently explore a
large compositional space and discover new alloys that would not be considered under previous knowledge.

As HEAs have been increasingly studied over the past decade, certain empirical rules have been established
[110]
that correlate well with the observed properties . In the past, it has been suggested that these empirical
rules can provide a guideline surrounding the design of HEAs with desirable properties, such as the
[111]
formation of single-phase solid solutions . However, certain empirical rules, such as the VEC threshold
for the stability of FCC and BCC solid solutions, have failed to maintain predictive accuracy over the