## 3 Results and Discussion
### Assessment on the Phase Formation  
The evolution of phases in CrCoNiTa\({}_{\rm x}\), FCC or Laves in alloys, is easy to understand. The formation of single solid solutions in HEAs is accomplished by the reduction of the free energy and the high mixing entropy in alloy system. The Hume-Roseley's rule is a good predictor of solid solution formation and there are four or five alloying elements in HEA, so the limitations in the Hume-Roseley rule may not be applicable. We use the thermodynamic and electronegativity parameters to establish the evolution of phase selection for MEAs. The parameter \(\Omega\) is chosen to unveil that the systemic effect of the mixing entropy (\(\Delta S_{mix}\)), the mixing of the main components (\(\Delta S_{mix}\)), atomic size parameter and Valence Electron Concentration (VEC) on the phase formation is as follows [3; 22; 25]:  
\[\Delta S_{mix}=-R\sum_{i=0}^{n}c_{i}lnc_{i} \tag{1}\]  
\[\Delta H_{mix}=-\sum_{i=1,i\
eq j}^{n}4\Delta H_{mix}^{ij}c_{j}i \tag{2}\]  
\[\Omega=\frac{T_{m}\Delta S_{\rm mix}}{|\Delta H_{\rm mix}|} \tag{3}\]  
\[T_{m}=\sum_{i}^{n}c_{i}\left(T_{m}\right)_{i} \tag{4}\]  
\[\delta=\sqrt{\sum_{i=1}^{n}c_{i}(1-r_{i}/\overline{r})^{2}} \tag{5}\]  
\[VEC=\sum c_{i}VEC_{i} \tag{6}\]  
Here \(R\) is the gas constant, \(n\) is the number of the components in alloys, \(c_{i}\) is the atomic percentage of \(i\)th component. \(T_{m}\) is the average melting temperature of the \(n\) elements, \((T_{m})_{i}\) is the melting temperature of \(i\)th element, \(r_{i}\) is the atomic radius of the element, and \(\overline{r}=\sum_{i=1}^{n}c_{i}r_{i}\) is the average atomic radius. The value of enthalpy in the alloys is three orders of magnitude larger than that of entropy, therefore we consider \(T_{m}=T\), absolute temperature is assumed to be 1000 K for the linking between entropy and enthalpy for the CrCoNiTa\({}_{\rm x}\) alloy system. To further determine the component intervals of hyper-eutectic and hypo-eutectic, two additional components are introduced for discussion. As Ta solubility in CrCoNiTa\({}_{\rm x}\) which are taken from EDS results in Ta\({}_{0.1}\) alloy for FCC and Ta\({}_{0.7}\) alloy for Laves respectively. The FCC phase composition is Cr\({}_{32.6}\)Co\({}_{32.8}\)Ni\({}_{33.1}\)Ta\({}_{1.5}\) denoted by x = FCC, the Laves phase composition is Cr\({}_{23.8}\)Co\({}_{27.5}\)Ni\({}_{20.6}\)Ta\({}_{28.1}\) represented by x = Laves. The Ta in \"x = FCC\" is argued to be the maximum solubility, while Ta in  
Figure 3: (**a**) XRD patterns of as-cast CrCoNiTa\({}_{\rm x}\) alloys. (**b**) EBSD mapping of CrCoNiTa\({}_{0.4}\) alloy. The \(\gamma\) (FCC) and Laves (HCP) phases. The corresponding EBSD inverse pole figure of (**c**) Laves phase and (**d**) \(\gamma\) phase. The \(\Delta S_{mix}\) increased from 10.02 J mol\({}^{-1}\) K\({}^{-1}\) (Ta\({}_{0.1}\)) to 11.44 J mol\({}^{-1}\) K\({}^{-1}\) (Ta\({}_{0.7}\)) with addition of Ta in CrCoNiTa\({}_{\rm x}\) and reached the maximum value of 11.46 J mol\({}^{-1}\) K\({}^{-1}\) for x = Laves. Similarly, the value of \(\Delta H_{mix}\) became more negative and lay in the range of \(-\)7.06 kJ mol\({}^{-1}\) and \(-\)15.52 kJ mol\({}^{-1}\) for Ta\({}_{0.1}\) and Ta\({}_{0.7}\), respectively. However, when x increased from 0.1 to 0.7, the value of \(\Omega\) decreased from 1.42 to 0.74. This phenomenon indicated that \(\Delta S_{mix}\) played a negative role for solid solution formation in CrCoNiTa\({}_{\rm x}\) compared to \(\Delta H_{mix}\) and was the determination of the transformation of the two-phase eutectic structure. As a result, the volume of the Laves phase, yield strength and hardness increased when Ta was added. Therefore, \(\Delta H_{mix}\) seemed to determine the reaction of eutectic between the different constituent elements. The more negative \(\Delta H_{mix}\), the more chance of forming a two-phase structure [26]. Thus, \(\Delta H_{mix}\) reflected the driving force for forming the eutectic structure as the Ta possessed much negative \(\Delta H_{mix}\) alloying with other elements.