## 4 Results and Discussion
### Experimental Datasets  
In this paper, the six datasets collected from Refs [2, 5, 8, 9, 14, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84  
As shown in Table 1, the first column is the index, the second column is the name of HEA samples, the third to seventh columns are the parameter values of HEAs, and the eighth column is the phases of HEAs.  
To understand the relationships between any two parameters in Table 1, the Pearson correlation coefficient \(H_{pq}\) is selected to evaluate the correlation between the parameters of HEAs. Calculating correlations on HEA datasets can quantitatively describe the degree of correlation between these parameters and is very helpful in helping readers understand the characteristics of different parameters and data. The Pearson correlation coefficient (\(H\)) between parameters p and q is shown in Equation (22) [5]:  
\[H_{pq}=\frac{\sum\limits_{i=1}^{n}(p_{i}-\overline{p})(q_{i}-\overline{q})}{ \sqrt{\sum\limits_{i=1}^{n}(p_{i}-\overline{p})^{2}}\sqrt{\sum\limits_{i=1}^{n }(q_{i}-\overline{q})^{2}}}, \tag{22}\]  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Index** & **High Entropy Alloys** & \(\Delta\)**Hmix** & \(\Delta\)**Smix** & \(\delta\) & \(\Delta\)**X** & \(\Omega\) & **Phase** \\ \hline
0 & Co1.4 CrFeMnNi & \(-\)4.115226 & 13.295461 & 1.100487 & 0.136445 & 5.792101 & SS \\
1 & CrCu0.5 FeMnNi & 0.098765 & 13.145213 & 1.185478 & 0.142370 & 233.301248 & SS \\
2 & CoCuFeNiSn0.07 & 5.066134 & 12.050142 & 2.849306 & 0.032278 & 3.909939 & SS + IM \\
3 & AlCoCrFeNiSi0.2 & \(-\)16.390533 & 14.221597 & 5.634042 & 0.120530 & 1.456954 & SS \\
4 & CoFeMoNiTiVZr & \(-\)21.800000 & 16.178297 & 8.800000 & 0.254045 & 1.529411 & AM \\
5 & CoCrFeMnNbNi & \(-\)12.000000 & 14.896688 & 5.900000 & 0.140643 & 2.424436 & IM \\ \hline \hline \end{tabular}
\end{table}
Table 1: A snapshot of the first six samples in HEAs dataset in Pandas DataFrame format.  
Figure 4: The occurrence numbers of each element in six datasets.  
where \(p_{i}\) and \(q_{i}\) are the sample values of parameters \(p\) and \(q\), respectively. \(\overline{p}\) and \(\overline{q}\) are the mean values of parameters \(p\) and \(q\), respectively. \(n\) is the number of samples. \(H_{pq}=1\) indicates that p and q are perfectly positively correlated. \(H_{pq}=-1\) indicates that p and q are perfectly negatively correlated. The correlation among the five parameters is shown in Figure 5.  
As shown in Figure 5, each cell represents the Pearson correlation coefficient value between the two parameters. Color intensity is proportional to the correlation coefficients. On the left side of the correlogram, the legend color shows the relationship between the correlation coefficients and the corresponding color. The darker the blue color, the higher the correlation; the darker the orange color, the lower the correlation. The range of the Pearson correlation coefficient value in the six datasets is between \(-0.81\) and \(0.78\). Among them, \(\Delta S_{mix}\) and \(\Omega\) in D\({}_{5}\) have the highest correlation.  
The phases of 986 HEA samples include SS, IM, AM, and SS + IM. The quantities of SS, IM, AM, and SS + IM of quinaries, senarios, and septenaries HEA samples in the six datasets are shown in Figure 6.  
As shown in Figure 6, (a) represents D\({}_{1}\), (b) represents D\({}_{2}\), (c) represents D\({}_{3}\), (d) represents D\({}_{4}\), (e) represents D\({}_{5}\), and (f) represents D\({}_{6}\). The numbers of SS, IM, AM, and SS + IM in quinaries, senarios, and septenaries samples in D\({}_{1}\), D\({}_{2}\), D\({}_{3}\), D\({}_{4}\), D\({}_{5}\), and D\({}_{6}\) are different. In the six datasets, the number of samples with the SS phase is the largest, whereas the number of samples with the AM phase is the smallest.  
Figure 5: The heatmap of Pearson correlation coefficient matrix among five parameters in D\({}_{1}\), D\({}_{2}\), D\({}_{3}\), D\({}_{4}\), D\({}_{5}\), and D\({}_{6}\).