Ab initio elastic stiffness of nano-laminate (MxM′2-x)AlC (M and M′ = Ti, V and Cr) solid solution

We have investigated the elastic stiffness and electronic band structure of nanolaminate (MxM2-x')AIC solid solutions, where M and M' = Ti, V and Cr by means of the ab initio pseudopotential total energy method. The second-order elastic constants, bulk moduli and anisotropic Young's moduli are computed for the solid solutions, in which x is changed from 0 to 2 in steps of 0.5. The bulk moduli of (MxM2-x')AIC is found to be approximately the average of the two end M(2)AIC and M-2'AIC phases as the substitution content x, as well as the valence electron concentration (VEC), varies in the compounds. On the other hand, the shear modulus c(44), which by itself represents a pure shear shape change and has a direct relationship with hardness, saturates to a maximum as VEC is in the range 8.4-8.6. It implies that solid solution hardening may be operative for alloys having VEC values in this range. Furthermore, trends in the elastic stiffness are interpreted in terms of the electronic band structure. We show that monotonically incrementing the bulk moduli is attributed to the occupying states involving transition-metal d-Al p covalent bonding and metal-to-metal dd bonding. The maximum in c44, on the other hand, originates from completely filling the shear resistive transition-metal d-Al p bonding states. Most importantly, we predict a method to optimize the desired elastic stiffness by properly tuning the valence electron concentration of (MxM2-x')AIC ceramics.