Materials for Design Open Repository. High Entropy Alloys

The current dataset is composed of a collection of High Entropy Alloys (HEAs). It contains the alloy composition, the number of chemical elements (No), the phase in a simple form (S_Phase), where 4 classes of phases were considered, namely amorphous (AM), intermetallic (IM), solid solution (SS), and solid solution + intermetallic (SS+IM). It contains also a second phase column (Phase), where we added the type of phase present in alloys with SS and repeated the S_Phase entry for the other cases. We have calculated 13 design parameters (see their definition below) used to design HEAs, known as the parametric approach. Finally, a set of columns containing the chemical elements and their corresponding fraction in the alloy is included. This dataset was developed in the framework of the European project ACHIEF for the discovery of novel materials to be used in industrial processes.

1. Mean atomic radius a (Å)
   • \(a = \displaystyle\sum_{i=1}^{n} c_i r_i\)
2. Atomic size difference δ
   • \(\delta = \sqrt{\displaystyle\sum_{i=1}^{n} c_i \bigg(1 - \dfrac{r_i}{a} \bigg)^2}\)
3. Average melting temperature T_m (K)
   • \(T_m = \displaystyle\sum_{i=1}^{n} c_i T_{mi}\)
4. Average melting temperature standard deviation (K)
   • \(\sigma_{T_m} = \sqrt{\displaystyle\sum_{i=1}^{n} c_i \bigg(1 - \dfrac{T_{mi}}{T_m} \bigg)^2}\)
5. Mixing enthalpy ΔH_mix (kJ/mol)
   • \(\Delta H_{mix} = 4 \displaystyle\sum_{i \neq j} c_i c_j H_{ij}\)
6. Mixing enthalpy standard deviation (kJ/mol)
   • \(\sigma_{\Delta H_{mix}} = \sqrt{\displaystyle\sum_{i \neq j} c_i c_j (H_{ij} - \Delta H_{mix})^2}\)
7. Ideal mixing entropy S_id (R)*
   • \(S_{id} = \Delta S_{mix} = -R \displaystyle\sum_{i=1}^{n} c_i \ln c_i\)
8. Electronegativity χ
   • \(\chi = \displaystyle\sum_{i=1}^{n} c_i \chi_i\)
9. Electronegativity difference in a multi-component alloy system
   • \(\Delta\chi = \displaystyle\sqrt{\sum_{i=1}^{n} c_i(\chi_i - \chi)^2}\)
10. Valence electron concentration VEC
    • \(VEC = \displaystyle\sum_{i=1}^{n} c_i \cdot VEC_i\)
11. Valence electron concentration standard deviation
    • \(\sigma_{VEC} = \sqrt{\displaystyle\sum_{i=1}^{n} c_i (VEC_i - VEC)^2}\)
12. Mean bulk modulus K (GPa)
    • \(K = \displaystyle\sum_{i=1}^{n} c_i K_i\)
13. Bulk modulus standard deviation (GPa)
    • \(\sigma_{K} = \sqrt{\displaystyle\sum_{i=1}^{n} c_i (K_i - K)^2}\)
14. Young's modulus E (GPa)
    • \(E = \displaystyle\sum_{i=1}^{n} c_i E_i\)
15. Shear modulus G (GPa)
    • \(G = \displaystyle\sum_{i=1}^{n} c_i G_i\)

where n is the number of components in the alloy system, c_i is the stoichiometric ratio, r_i is the atomic radius, T_mi is the melting temperature, χ_i is the Pauli electronegativity, VEC_i is the valence electron concentration, and K_i is the bulk modulus, E_i is the Young's modulus, and G_i is shear modulus for the i-th component of the alloy. H_ij is the binary mixing enthalpy in the liquid phase, and R is the gas constant.

*Note: the ideal mixing entropy S_id units in the first version of the dataset appear as kJ/mol, but they should be written in terms of the gas constant R, e.g., the compound Ag₂Al has S_id = 0.636 R, where R = 8.314 J · K⁻¹ · mol⁻¹. The second version the S_id units are corrected and two new features are included.