Exploration of MSi2-type high entropy silicides by machine learning and first-principles calculations

The structure of MSi₂-type high entropy silicides has been predicted using machine learning method. Using the random forest model, with three feature parameters, namely electronegativity difference$\Delta \chi$, atomic size difference ${\delta }_r$, and valence electron concentration VEC, as input features, the structure prediction accuracy for MSi₂-type high entropy silicides reaches 96.82 ± 1.80 %. First-principles calculations have also been employed to explore the structural, electronic, and mechanical properties of three high entropy silicides with C11_b structure, namely (MoNbWTaRe)Si₂, (MoVWTaRe)Si₂, and (MoCrWTaRe)Si₂. For these three MSi₂-type high entropy silicides, the formation enthalpies of C11_b structure are smaller than those of C40 structure, which reveals the good stability of the C11_b structure. The mechanical properties of these three MSi₂-type high entropy silicides have also been predicted using the calculated elastic constants. Combined with the calculated stress-strain curves, it can be concluded that (MoCrWTaRe)Si₂ should have a lower shear modulus compared with molybdenum disilicide. It is observed from the B/G and Poisson's ratio that (MoNbWTaRe)Si₂ has relatively high ductility, while (MoCrWTaRe)Si₂ exhibits more significant brittleness, which agrees well with the ideal shear strength calculations. As shown in the 3D models and 2D projections of the mechanical modulus, compared with pure MoSi₂, the anisotropy of (MoNbWTaRe)Si₂ and (MoVWTaRe)Si₂ is enhanced, while that of (MoCrWTaRe)Si₂ is not significant. The shear and Young's moduli of (MoNbWTaRe)Si₂ and (MoVWTaRe)Si₂ decrease along the [100] and [010] directions, while they change very little along the [001] and [110] directions, resulting in the enhanced elastic anisotropy. Moreover, the electronic properties of these three MSi₂-type high entropy silicides are also studied. A low DOS at the Fermi level of (MoCrWTaRe)Si₂ indicates that it should have weak metallic bonding and poor ductility, which corresponds to the aforementioned B/G and Poisson's ratio results.