Interplay between nanolaminated structure and electron-phonon coupling in Ti-based MAX phases

Abstract

A linear-response method to the density functional theory is used to derive lattice dynamics, the transport spectral function, and the electron-phonon coupling (EPC) constant of $\mathrm{T}{\mathrm{i}}_{2}\mathrm{AlC}$, a member of the very large class of nanolaminated conducting ceramics named MAX phases (where $M$ is a transition metal, $A$ is an element from groups IIIA to VIA, and $X$ is carbon and/or nitrogen). By coupling ab initio calculations with the semiclassical Boltzmann transport theory for electron-phonon scattering, the experimentally observed anisotropic electrical transport properties of $\mathrm{T}{\mathrm{i}}_{2}\mathrm{AlC}$ are rationalized. Our results indicate that in $\mathrm{T}{\mathrm{i}}_{2}\mathrm{AlC}$, because of the weak dependence of the EPC constant $\phantom{\rule{4pt}{0ex}}{\ensuremath{\lambda}}_{\mathrm{tr},\ensuremath{\alpha}}$ $(\ensuremath{\alpha}=xx$ and $zz)$ on the crystallographic direction, the anisotropy of $\ensuremath{\rho}(T)$ results from the anisotropy of the Fermi surface. These conclusions, in contrast with those obtained on $\mathrm{T}{\mathrm{i}}_{3}\mathrm{Si}{\mathrm{C}}_{2}$ (another member of the MAX phases family) using a similar approach, establish a correlation between the nanolaminated structure of the MAX phases and the origin of the anisotropy of their transport properties.