Theoretical investigation of the solubility in (M_xM_2−x′)AlC (M and M′ = Ti, V, Cr)

We have performed theoretical studies of the solubility within (M_xM_2−x′)AlC, where M and M′ = Ti, V, and Cr by means of ab initio total energy calculations. The theoretical values of equilibrium volume and the optimized c/a ratios are in good agreement with those of experiments (within ∼ ± 4% and ∼ ± 1.3%, respectively). Furthermore we show that if x is increased from 0 to 2 the bulk modulus can be increased by as much as 36%. Based on the total density of states analysis as well as the energy of formation, we suggest that the investigated systems show solubility except for the (Cr, Ti)₂AlC system. This conclusion is consistent with the published work where solubility within the system (V, M)₂AlC, (M = Ti and Cr) as well as a miscibility gap in the system (Cr, Ti)₂AlC were experimentally observed [Schuster et al., J. Solid State Chem. 32, 213 (1980)].