## 3 Results and Discussion
### Mechanical Properties
\begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \(x\) & \(C_{\textbf{11}}\) & \(C_{\textbf{22}}\) & \(C_{\textbf{33}}\) & \(C_{\textbf{44}}\) & \(C_{\textbf{55}}\) & \(C_{\textbf{66}}\) & \(C_{\textbf{12}}\) & \(C_{\textbf{13}}\) & \(C_{\textbf{23}}\) \\ \hline Co-0.2 & 364.3 & 397.3 & 386.4 & 186.2 & 193.4 & 188.7 & 220.9 & 207.4 & 163.0 \\ Co-0.56 & 358.0 & 399.9 & 412.2 & 189.4 & 186.9 & 188.0 & 211.6 & 200.1 & 175.0 \\ Co-1 & 379.5 & 400.6 & 400.3 & 193.5 & 188.6 & 184.4 & 192.6 & 216.2 & 179.3 \\ Co-1.57 & 382.0 & 401.0 & 395.1 & 193.3 & 186.4 & 188.0 & 194.0 & 206.8 & 181.0 \\ Co-2 & 380.6 & 402.8 & 384.9 & 199.4 & 188.1 & 187.8 & 183.2 & 209.4 & 182.9 \\ \hline Cr-0.2 & 379.7 & 371.3 & 384.5 & 184.7 & 184.5 & 194.3 & 198.3 & 188.5 & 196.4 \\ Cr-0.56 & 386.8 & 372.1 & 386.4 & 185.7 & 186.3 & 194.0 & 196.4 & 186.6 & 205.0 \\ Cr-1 & 379.5 & 400.6 & 400.3 & 193.5 & 188.6 & 184.4 & 192.6 & 216.2 & 179.3 \\ Cr-1.57 & 347.4 & 387.9 & 365.0 & 178.8 & 189.6 & 175.7 & 201.4 & 228.1 & 184.6 \\ Cr-2 & 346.0 & 372.2 & 362.5 & 190.6 & 200.6 & 192.8 & 210.7 & 222.8 & 194.2 \\ \hline Fe-0.2 & 347.8 & 358.8 & 374.7 & 171.3 & 161.7 & 182.1 & 210.5 & 190.5 & 177.4 \\ Fe-0.56 & 366.0 & 375.0 & 389.4 & 181.7 & 171.6 & 183.7 & 213.2 & 191.8 & 174.6 \\ Fe-1 & 379.5 & 400.6 & 400.3 & 193.5 & 188.6 & 184.4 & 192.6 & 216.2 & 179.3 \\ Fe-1.57 & 391.5 & 418.0 & 406.8 & 203.1 & 194.4 & 196.5 & 194.5 & 213.8 & 179.3 \\ Fe-2 & 388.9 & 412.7 & 392.9 & 209.8 & 205.8 & 205.5 & 200.4 & 222.9 & 192.2 \\ \hline Ni-0.2 & 386.4 & 402.3 & 401.6 & 204.6 & 212.9 & 215.7 & 217.0 & 213.8 & 201.1 \\ Ni-0.56 & 391.9 & 412.7 & 393.6 & 193.1 & 201.0 & 203.2 & 188.0 & 220.7 & 193.3 \\ Ni-1 & 379.5 & 400.6 & 400.3 & 193.5 & 188.6 & 184.4 & 192.6 & 216.2 & 179.3 \\ Ni-1.57 & 365.5 & 382.2 & 374.7 & 182.6 & 177.7 & 177.9 & 191.8 & 202.8 & 180.4 \\ Ni-2 & 344.4 & 370.1 & 358.3 & 175.9 & 166.6 & 161.7 & 174.5 & 199.8 & 175.9 \\ \hline \end{tabular}
\end{table} 
Table 2: Elastic constant \(C_{ij}\) of Co-Cr-Fe-Ni HEAs. The unit is GPa. \begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \(x\) & \(C_{\textbf{11}}\) & \(C_{\textbf{12}}\) & \(C_{\textbf{44}}\) & \(B\) & \(G\) & \(E\) & \(\
u\) & \(B/G\) & **Ref.** & **Model** & **Package** & **Magnetism** \\ \hline  & 379.48 & 192.62 & 193.47 & 261.31 & 144.75 & 366.56 & 0.266 & 1.81 & & SQS & CASTEP & FM \\ CoCrFeNi & 376.63 & 197.04 & 184.71 & 245.3 & 146.73 & 367.01 & 0.251 & 1.67 [58] & Single & VASP & NM \\  & 271 & 175 & 189 & 207 & 110 & 280 & 0.275 & 1.88 [37] & EMTO-CPA & PM \\  & & & & & 204 & 118.6 & 298 & 0.256 & 1.71 [50] & USPEX & VASP & NM \\ \hline \end{tabular}
\end{table} 
Table 3: Elastic constants (\(C_{ij}\)) and polycrystal elastic moduli (\(B\), \(G\), \(E\), \(\
u\), and \(B/G\)) for CoCrFeNi alloy. The unit is GPa, except for the dimensionless \(\
u\) and \(B/G\). The brittle-ductile behavior is an important mechanical performance indicator of the energy absorption and plastic deformation ability of materials under external forces. The Pugh ratio is usually used to describe the brittle-ductile behavior of HEAs [61]. Ductile materials typically show \(B/G>1.75\), while brittle materials show \(B/G<1.75\). [PERSON]'s ratio can also reflect the brittle-ductile behavior of HEAs. For isotropic materials, \(B/G>1.75\) implies \(\
u>0.26\)[37], which has been confirmed by [PERSON] et al. [62]. As shown in Figure 4a,b, according to \(B/G\) and \(\
u\), we find that all Co-Cr-Fe-Ni HEAs are predicted to be ductile, except for Fe-1.57. For CoCrFeNi alloy, this is in line with experiments [15; 18]. Unfortunately, no available experimental information on the brittle-ductile behavior was reported for the other HEAs that can be compared with our results. \(\
u\) has the same changing trend as \(B/G\). Alloys have high values of \(\
u\) and \(B/G\) as the contents of Cr and Ni increase and the contents of Co and Fe decrease, indicating that the ductility of the alloys enhances.