## 2 Computational Details  
To study mechanical properties, it is necessary to evaluate structural stability. A solid-solution model was used to study the phase structure based on empirical parameters. The valence electron concentration (VEC) was used to determine the phase structure (BCC or FCC) [40; 41]. For HEAs, the VEC is expressed as [40]:  
\[\text{VEC}=\sum_{i}^{n}c_{i}(\text{VEC})_{i} \tag{1}\]where \(c_{i}\) represents the atomic percentage of the \(i\)th element, and \(\left(\text{VEC}\right)_{i}\) is the VEC of the current element. For \(3d\) transition elements, VEC includes all electrons together with \(d\) orbitals. The valence electrons of elements are Cr3d\({}^{5}\)4s\({}^{1}\), Fe3d\({}^{6}\)4s\({}^{2}\), Co3d\({}^{7}\)4s\({}^{2}\), and Ni3d\({}^{8}\)4s\({}^{2}\). The atomic size difference (\(\delta\)) is an important parameter related to the solid-solution phase. A larger \(\delta\) corresponds to severe lattice distortion and sluggish diffusion effects, resulting in a decrease in the stability and transformation rate of the solid-solution phase and precipitate formation in the HEAs [42]. The hardness changes monotonously with \(\delta\), which means that the lattice distortion hinders the dislocation motion of plastic deformation, resulting in solid-solution strengthening [40]. Accordingly, \(\delta\) is defined as [42]:  
\[\delta=\sqrt{\sum\limits_{i=1}^{n}c_{i}\Big{(}1-\frac{r_{i}}{\bar{r}}\Big{)}^{ 2}},\bar{r}=\sum\limits_{i=1}^{n}c_{i}r_{i} \tag{2}\]  
where \(r_{i}\) represents the atomic radius of the \(i\)th element. We use the atomic radius measured by X-ray diffraction in the elemental state [43]. The enthalpy of mixing (\(\Delta H_{mix}\)) affects the solid-solution phase or compound formation in HEAs [44]. A negative \(\Delta H_{mix}\) means that different elements form intermetallic compounds, while positive a \(\Delta H_{mix}\) leads to phase separation in alloys. Only when the absolute value of \(\Delta H_{mix}\) is close to zero is the solid-solution phase stable in the solid phase. \(\Delta H_{mix}\) is defined as [45]:  
\[\Delta H_{mix}=\sum\limits_{i=1,\
eq j}^{n}4\Delta H_{AB}^{mix}c_{i}c_{j} \tag{3}\]  
where \(\Delta H_{AB}^{mix}\) is the enthalpy of mixing of the binary liquid alloy. The value of \(\Delta H_{AB}^{mix}\) can be found from Ref. [46], which is calculated by the Miedema macroscopic model [47]. High-entropy alloys mean higher entropy of mixing (\(\Delta S_{mix}\)) and the value of \(\Delta S_{mix}\) is positive in the alloy. A higher \(\Delta S_{mix}\) corresponds to an increase in the degree of confusion in the multicomponent alloy system, and a decrease in the ordering and separation of different elements in the alloy, resulting in easier and more stable random solid-solution formation. \(\Delta S_{mix}\) is expressed as [42]:  
\[\Delta S_{mix}=-R\sum\limits_{i=1}^{n}(c_{i}\text{ln}c_{i}) \tag{4}\]  
where \(R\) is the gas constant. HEAs of equal molar ratios have the largest entropy of mixing. According to thermodynamics, the energy \(T\Delta S_{mix}\) increases with increasing temperature, and \(T\Delta S_{mix}\) is related to the formation of the solid-solution phase. The phase formation of the alloy usually occurs near the melting point (\(T_{m}\)) if the solid-state phase transformation is not considered. In terms of the Gibbs free energy of multicomponent alloy systems, [PERSON] and [PERSON] [42] defined a parameter \(\Omega\) for predicting the solid-solution formation for HEAs as:  
\[\Omega=\frac{T_{m}\Delta S_{mix}}{\left|\Delta H_{mix}\right|} \tag{5}\]  
where \(T_{m}=\sum\limits_{i=1}^{n}c_{i}\left(T_{m}\right)_{i}\) is the melting point of HEAs following the mixing rules of multicomponent HEAs [42]. The \(T_{m}\) of the atom can be found from Ref. [48]. Equations (1)-(5) or their combination can be used to evaluate the phase stability of HEAs, thereby laying a theoretical foundation for the study of mechanical properties.