Structural evolution of (Ti0.5V0.5)+1GeC (n= 1–4) under pressure from first principles

The elastic properties and structural evolution of (Ti0.5V0.5)n+1GeCn (n = 1–4) are studied under pressure from first principles. Many general evolution trends are concluded for the six structures, including the lattice parameters (a, c), elastic constants (cij) and the degree of the isotropy (A, A1, A2), and the axial shrinkage tendency. The (Ti0.5V0.5)2GeC behaves the largest compressive anisotropy in (c/a)/(c0/a0) but (Ti0.5V0.5)5GeC4 behaves opposite compressive anisotropy which shows a value below 1 between 0 and 40 GPa, whereas (Ti0.5V0.5)4GeC3 exists a softening behavior between 20 and 40 GPa. The lowest volume contraction of (Ti0.5V0.5)4GeC3 is confirmed by the density of states, together with the observation of its minimum c12 and c13 among the same type of compounds. The density of states analysis observed the smaller contribution of Ti at Fermi level with respect to that of V. A common phenomenon is observed from the six structures, namely, for any considered heavy atoms including Ti or V, once the heavy atom is surrounded by one C layer and one Ge layer, its density of states contribution at Fermi level is larger than that of atom surrounded by two C layers originating mainly from the electronegativity difference of C and Ge. The bond length of C/GeTi is always slightly longer than that of C/GeV except for (Ti0.5V0.5)2GeC which shows totally equivalent length. A smaller shear modulus of (Ti0.5V0.5)2GeC is observed relative to its two end members. The electron density difference analysis reveals the diverse charge transfer directions and bonding features in these compounds.