M_n+1AX_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.

中文翻译：

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M _{n +1} AX _n相的密度泛函理论研究：综述

M _{n +1} AX _n个相（以下简称MAX相：M：过渡金属，A：A族元素，X：C或N，n= 1-3）由于类陶瓷和金属特性的独特结合而引起了极大的关注。密度泛函理论（DFT）已经成为一种功能强大的理论方法，可作为实验测试的补充，并在MAX相的鉴定和表征中充当预测工具。在简要介绍MAX相和DFT之后，我们回顾了有关此类材料的DFT研究，包括晶体结构，电子结构，点缺陷，晶格动力学以及相关特性，相稳定性，可压缩性和弹性特性。 。理论值和可用的实验值之间的比较表明，它们在大多数情况下是相当一致的，尤其是在晶格常数，弹性性质和可压缩性方面。