An ab initio study on the investigation of structural, electronic, mechanical and lattice dynamical properties of the M ₂ AX type MAX phases Sc₂AlB_0.5C_0.5, Sc₂AlB_0.5N_0.5 and Sc₂AlC_0.5N_0.5 compounds

The hypothetical Sc₂AlB_0.5C_0.5, Sc₂AlB_0.5N_0.5 and Sc₂AlC_0.5N_0.5 compounds are M ₂ AX type MAX phases referred to as #211 and have hexagonal crystal structure which conforms to P6₃/mmc space group. These compounds have been investigated by using generalized gradient approximation in the Density Functional Theory and plane-wave pseudopotential method. After the optimization process of the compounds, their structural, electronic, mechanical, and lattice dynamical properties have been examined in detail. The calculated electronic band structure and the total electronic density of states indicated that all of our compounds have metallic behavior. The estimated elastic constants show that they are stable and have anisotropic character mechanically. Moreover, Sc₂AlB_0.5C_0.5 and Sc₂AlB_0.5N_0.5 are ductile, while Sc₂AlC_0.5N_0.5 is brittle. Also, the obtained phonon dispersion curves indicate that Sc₂AlC_0.5N_0.5 is stable, whereas Sc₂AlB_0.5C_0.5 and Sc₂AlB_0.5N_0.5 compounds are dynamically unstable with imaginary vibrational modes. (paper)