**3. Basics of HEAs**

HEAs are multicomponent systems containing five or more elements in significant proportions unlike conventional alloys [6]. This leads to increase in the overall configurational entropy of system, which was first reported by Yeh et. al. for CuCoNiCrAlFe system [4]. It was believed that due to high configurational entropy of mixture, the alloys tend to crystallize as SS instead of intermetallic compounds (IM). These compositions exhibit superior mechanical, oxidation and corrosion resistance properties under conditions ranging from high temperatures to cryogenic temperatures [5, 6]. Due to the prominence of high entropy effect in multi-principal element alloys, such alloys are commonly referred as high entropy alloys. There are four core effects and one postulate, as follows:

### **3.1 The high entropy effect**

The name perhaps has gathered enormous attention of researchers in this system. It states that high configurational entropy of mixing (Δ*Sconf* ) supports the

formation of SS instead of IM [4]. This also limits the number of phases predicted by the Gibbs Phase Rule. Δ*Sconf* is given by Eq. (1),

$$
\Delta S\_{conf} = -R\sum\_{i=1}^{n} X\_i \ln X\_i \tag{1}
$$

On dealing with this phenomenon on the grounds of probability, the possible explanation of absence of IM is in the basic nature of these compounds. Intermetallics are strictly ordered in nature but in case of HEAs, there is interaction with various elements with significantly higher compositions. As a result, even if thermodynamic and kinetic factors favor compound formation, the probability of tendency to form a two elements compound being in vicinity, is reduced. Intermetallics (IMs) are established by a high value of negative enthalpy of mixing (Δ*Hmix*) and so entropy maximization plays an important role in lowering the Gibbs free energy of mixing and promoting SS formation. Here, Δ*Hmix* Denotes enthalpy of mixing of all elements and is given by Eq. (2). In cases, where Δ*Hmix* of an intermetallic is higher compared to the solid solution phases, there is formation of IM and SS together. The Ω factor introduced by Yang and Zhang [7], should ideally be greater than 1.1 to stabilize the SS.

$$
\Delta H\_{\text{mix}} = \sum\_{i=1, j>1}^{n} 4 \Delta H\_{AB}^{\text{mix}} c\_i c\_j \tag{2}
$$

$$\mathcal{Q} = \frac{T\_m \Delta S\_{conf}}{|\Delta H\_{mix}|} \tag{3}$$

$$T\_m = \sum^n T\_i c\_i$$

$$\text{The first-order coupling between the two-dimensional } \mathcal{N} \text{-matrices is the only possible } \mathcal{N} \text{-matrices with } \mathcal{N} = \{0, 1, 2, \dots, N\} \text{ and } \mathcal{N} = \{0, 1, 2, \dots, N\}.$$
