# Structural Particularities, Prediction, and Synthesis Methods in High-Entropy Alloys
## 2 Structural Particularities of HEAs, Prediction and Estimation Concepts
### Prediction and Estimation Concepts
#### 2.3.2. CALPHAD Method  
Currently, most commercial software uses thermodynamic calculations that are very popular in the fields of materials science and engineering. Thermodynamic databases, which are integral to all thermodynamic software packages, are developed using the CALPHAD method (CALculation of PHAse Diagrams) [52]. Phase diagrams are like a map that helps design materials and optimize processes. They provide essential information about a particular alloy composition and temperature and also offer details about the present phases, their compositions, and transformation temperatures [52]. Although most binary phase diagrams and a limited number of ternary phase diagrams have been determined experimentally, many multi-component systems remain largely unexplored. Experimentally defining phase diagrams for multi-component systems is highly challenging because of the considerable effort required. However, in recent years, the CALPHAD method, when integrated with key experimental data, has proven to be increasingly effective in elucidating complex phase diagrams for such systems [53; 54; 55; 56; 57]. The CALPHAD method primarily focuses on developing thermodynamic functions based on experimental data from binary and ternary phase diagrams. For quaternary and higher-order systems, these methods are less commonly employed because the interactions in higher-order systems are often too weak to significantly impact the results and can be considered negligible [58]. However, the use of complex alloys is possible by combining and exploring binary and ternary data [59]. Thermodynamic functions for a specific set of elements are compiled into a database. These databases are created to replicate known \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \multirow{2}{*}{**Material**} & \multicolumn{6}{c}{**Parameters**} & \multirow{2}{*}{**Phase Type**} & \multirow{2}{*}{**Experimental** [Reference]**} \\  & & & & & & & & \\ \cline{2-2} \cline{6-8}  & **J/molK** & & & & & & & \\ \hline CoCrFeMnNi & 13.38 & \(-\)4.16 & 3.27 & 5.79 & 4.465 & 8 & FCC & FCC [42] \\ \hline CoCrFeNi & 11.53 & \(-\)3.75 & 0.3 & 5.75 & 4.853 & 8.25 & FCC & FCC [43] \\ \hline CoCrFeNiAl\({}_{5}\)S & 12.71 & \(-\)6.75 & 3.47 & 3.42 & 5.315 & 7.94 & BCC + FCC & FCC [44] \\ \hline CrFeMnCoCo & 13.38 & 4.16 & 3.14 & 5.56 & 4.108 & 8.2 & FCC & FCC [42] \\ \hline WMnSbIr & 11.53 & \(-\)6.5 & 2.32 & 5.6 & 3.765 & 5.5 & BCC & BCC [45] \\ \hline WMoNbTaV & 13.38 & \(-\)4.64 & 3.15 & 8.54 & 4.488 & 5.4 & BCC & BCC [45] \\ \hline NbTaHfZrTh & 13.38 & 2.72 & 4.98 & 12.41 & 6.567 & 4.4 & BCC & BCC [46] \\ \hline CrMnFe\({}_{5}\)Ni\({}_{5}\)Al\({}_{5}\)S\({}_{4}\)S\({}_{5}\) & 12.66 & \(-\)7.26 & 5.15 & 3 & 4.822 & 7 & BCC + FCC & BCC + IM [47] \\ \hline CrMnFe\({}_{5}\)Ni\({}_{5}\)AlAl\({}_{5}\)S\({}_{4}\)S\({}_{5}\) & 12.94 & \(-\)11.29 & 6.02 & 1.85 & 5.244 & 6.46 & BCC & BCC [47] \\ \hline Cr\({}_{5}\)Ni\({}_{5}\)Fe\({}_{5}\)NiAlAl\({}_{5}\)S\({}_{5}\)MHV & 15.75 & \(-\)15.74 & 5.29 & 1.68 & 7.385 & 6.64 & BCC & BCC [47] \\ \hline CrNiCoMnV & 13.38 & \(-\)8.8 & 3.33 & 2.85 & 7.375 & 7.4 & BCC + FCC & FCC + IM [42] \\ \hline CrNiMnFeTi & 13.38 & \(-\)12.32 & 6.58 & 1.99 & 10.219 & 7 & BCC + FCC & BCC + FCC + IM [42] \\ \hline Al\({}_{5}\)Cu\({}_{5}\)Si\({}_{5}\)Zn\({}_{5}\)Nb\({}_{2}\)Nb\({}_{2}\)Nb\({}_{2}\) & 8.15 & \(-\)3.38 & 5.7 & 2.37 & 7.198 & 4.77 & BCC & FCC + HCP + IM [48] \\ \hline Al\({}_{5}\)Si\({}_{5}\)Si\({}_{5}\)Zn\({}_{5}\)Nb\({}_{2}\)Nb\({}_{2}\)Nb\({}_{2}\) & 9.75 & \(-\)13.79 & 9.03 & 0.75 & 10.774 & 3.72 & IM & FCC + IM [48] \\ \hline Al20 Re20 Re10815T135 & 12.69 & \(-\)40.42 & 11.15 & 0.51 & 11.987 & 3.8 & IM & IM [49] \\ \hline Al65 CFeCu6 Si15 Mn5T15 & 9.68 & \(-\)20.22 & 7.7 & 0.58 & 8.023 & 3.95 & IM & IM [50] \\ \hline Al\({}_{5}\)FeMnTe\({}_{5}\)S & 12.71 & \(-\)11.74 & 6.27 & 1.77 & 6.283 & 5.88 & BCC & BCC + La [51] \\ \hline \end{tabular}
\end{table} 
Table 1: Calculated parameters and experimental results for typical HEA compositions. data and predict phase equilibria for alloys where data is lacking.