Density Functional Theory Study of Mn+1AXn Phases: A Review

M(n+1)AX(n) phases (MAX phases for short with M: transition metal, A: A group elements, X: C or N, and n = 1-3) have attracted considerable attention due to the unique combination of the ceramic- and metal-like properties. The density functional theory (DFT) has emerged as a powerful theoretical approach that complements experimental testing and serves as a predictive tool in the identification and characterization of MAX phases. After the beginning with a brief introduction of the MAX phase and DFT, we review the DFT study on this class of materials, including crystal structure, electronic structure, point defects, lattice dynamics, and related properties, phase stability, compressibility, and elastic properties. Comparison between the theoretical values and available experimental ones shows that they are in decent agreement for most part, especially in the lattice constants, elastic properties, and compressibility. This article is concluded with an outlook of future research on DFT study of MAX phases, major challenges to be met and possible solutions in some cases.