Electronic origin of shearing in M₂AC (M = Ti,V,Cr,A = Al,Ga)

We have studied shearing in M₂AC (space group P6₃/mmc, prototype Cr₂AlC), where M is Ti, V and Cr, and A is Al and Ga, using ab initio calculations. These compounds can be described as interleaved layers of MC and A. As Ti in Ti₂AlC is substituted by V, c₄₄ increases by 24.3%. Increasing the transition metal valence electron concentration further, through a substitution of V by Cr, results in 2.2% decrease of c₄₄. The electronic origin of this c₄₄ versus valence electron concentration dependence may be understood by analysing the decomposed band structure: in the vicinity of the Fermi level, we find two types of dd bonding. One contributes to shearing (t_2g+e_g symmetry or MC–MC coupling) and the other does not (e_g symmetry). We provide evidence that filling of the transition metal dd bonding states with the t_2g+e_g symmetry may be responsible for the behaviour of c₄₄. The results presented enable tailoring of the shear properties of M₂AC phases.