Table 1 Mathematical equations and symbols of chosen alloy descriptors.
From: Designing of high entropy alloys with high hardness: a metaheuristic approach
S.no. | Descriptor | Formula |
|---|---|---|
1 | Average values of elemental descriptors | \(p= \sum_{i=1}^{n}XiPi\) Xi = elemental composition of ith element, Pi = elemental properties of ith element |
2 | Standard deviation | \(\updelta = \sqrt{\sum Xi{(1-\frac{Pi}{P})}^{2}}\) |
3 | Atomic volume24 | \(Vm= \sum_{i=1}^{n}Xi(\frac{4}{3}{\pi r}^{3})\) |
4 | Mixing entropy17 | \(Smix= -R\sum_{i=1}^{n}Xi{\text{ln}}Xi\) R = 8.31* 10–3 kJ/Mol |
5 | Mixing enthalpy25 | \(Hmix=4\sum_{i=1 ,j\ne 1}^{n}\Delta Hij Xi Xj\) |
6 | Gibbs free energy | \(Gmix=Hmix-TavgSmix\) |
7 | Average temperature21 | \(Tavg= \sum_{i=1}^{n}XiTmi\) |
8 | Combination effect-121 | \(\Omega = \frac{TavgSmix}{\left|Hmix\right|}\) |
9 | Combination effect-2 (\(\Lambda\))23 | \(\Lambda = \frac{Smix}{({\delta }_{r}{)}^{2}}\) |
10 | Ď’22 | \(\Upsilon =(1-\frac{\sqrt{\frac{\left({\text{min}}\left\{ri\right\}+{r}^{2}\right)-{r}^{2}}{({\text{min}}\left\{ri\right\}+r{)}^{2}}}}{\sqrt{\frac{\left({\text{max}}\left\{ri\right\}+{r}^{2}\right)-{r}^{2}}{({\text{max}}\left\{ri\right\}+r{)}^{2}}}})\) |
11 | Valency electron difference20 | \(\mathrm{\Delta VEC}= \sqrt{\sum_{i=1}^{n}Xi(VEC-VECi{)}^{2}}\) |
