Although significant progress has been made on understanding the structure–property relationship of MAX phases, a clear answer has not been given to the outstanding question whether MAX phases can be extended from carbides and nitrides (X = C and N) to borides (X = B). Herein, based on the systematically investigations on the general trend of lattice constants and elastic properties of the experimentally found MX and M₂AX (X = B, C, and N) with the valence electron concentration (VEC), a guideline for the discovery of new MAX borides is given. The MX and M₂AX (X = B, C, and N) compounds are situated in a small range of VEC, and their lattice constants generally decrease with VEC. Second-order elastic constants c₁₁, c₃₃, and bulk modulus B of M₂AX (X = B, C, and N) increase with VEC due to enhanced bonding, c₄₄ and G, however, increase up to some critical values and then decline with the further increase of VEC. Based on the electronic structure–elastic property relationship and the presence of rock salt–structured transition metal monoborides, nine possible MAX phase borides M₂AB (M = Zr, Hf, Nb, A = P, As, and Sb) are predicted. Thus, MAX phases can be extended from X = C and N to X = B, C, and N.

中文翻译：

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将 MAX 相从三元碳化物和氮化物（X = C 和 N）扩展到三元硼化物（X = B、C 和 N）：一般指南

尽管在理解 MAX 相的结构-性能关系方面取得了重大进展，但对于 MAX 相是否可以从碳化物和氮化物（X = C 和 N）扩展到硼化物（X = B). 在此，基于对实验发现的MX和M ₂ AX（X = B，C和N）的晶格常数和弹性性质的一般趋势与价电子浓度（VEC）的系统研究，指导发现给出了新的 MAX 硼化物。MX 和 M ₂ AX（X = B、C 和 N）化合物位于较小的 VEC 范围内，并且它们的晶格常数通常随 VEC 降低。二阶弹性常数c ₁₁ , c ₃₃和M _{2 AX（X = B、C 和 N）的体积模量}B由于增强的键合而随 VEC 增加，但是， c ₄₄和G增加到一些临界值，然后随着 VEC 的进一步增加而下降。基于电子结构-弹性特性关系和岩盐-结构过渡金属单硼化物的存在，预测了九种可能的 MAX 相硼化物 M _{2 AB（M = Zr、Hf、Nb，A = P、As 和 Sb）。}因此，MAX 阶段可以从 X = C 和 N 扩展到 X = B、C 和 N。