Electronic structure and optical conductivities of 20 MAX-phase compounds

Yuxiang Mo, Paul Rulis, and W. Y. Ching

Phys. Rev. B 86, 165122 – Published 16 October 2012

Abstract

The electronic structure and optical conductivities of 20 so-called MAX phases Ti $_{3}$ AC $_{2}$ (A $=$ Al, Si, Ge), Ti $_{2}$ AC (A $=$ Al, Ga, In, Si, Ge, Sn, P, As, S), Ti $_{2}$ AlN, M $_{2}$ AlC (M $=$ V, Nb, Cr), and Ta $_{n}$ $_{+ 1}$ AlC $_{n}$ ( $n$ $=$ 1 to 4) are studied using the first-principles orthogonalized linear combination of atomic orbitals (OLCAO) method. The calculated results include total and partial density of states, effective charge on each atom, and quantitative bond order values. Also calculated are directionally resolved interband optical conductivities. By analyzing such results regarding these phases (that have different atomic compositions and layered structures) several important features on structural stability and electrical conductivities are identified and compared with experimental data. We confirm the trend of increasing $N$ ( $E_{f}$ ) (total density of states at the Fermi level $E_{f}$ ) as the number of valence electrons of the composing elements increases. The local feature of total density of states (TDOS) near $E_{f}$ is used to predict structural stability. The calculated effective charge on each atom shows that the M (transition-metal) atoms always lose charge to the X (C or N) atoms, whereas the A-group atoms mostly gain charge but some lose charge. Bond order values are obtained and critically analyzed for all types of interatomic bonds in all the 20 MAX phases.