\textit{Ab initio} calculations of MAX phases M$_{2}$TlC (M = Ti, Zr, Hf), and M$_{2}$GaN (M = Ti, V, Cr)

MAX phases have been a subject of interest recently [cf. M. W. Barsoum Prog. Solid St. Chem. 28, 201 (2000).] because of their useful mechanical, electrical and thermal properties. Here we have studied two groups of M$_{2}$AX : (i) M = Ti, V, Cr, A = Ga and X = N and (ii) M = Ti, Zr, Hf, A = Tl and X = C. We calculated the lattice parameters, bulk modulus B and local electronic density of states (LDOS) of these phases using first-principles total energy calculations. Our computed lattice structural parameters match the experimental values within 5{\%} for all six materials. Values for B were computed to be (i) 158, 170, and 180 GPa and (ii) 125, 120, and 131 GPa for the first and second group respectively. These values suggest that Ti$_{2}$TlC, Zr$_{2}$TlC and Hf$_{2}$TlC maybe the softest of all the MAX phases explored so far. The total density of states shows that all six materials are conducting. The major features in LDOS are i) the hybridization of the M d orbitals with X p orbitals and (ii) M d orbitals with A p orbitals.