Applying the first-principles density functional pseudopotential plane-wave calculations, the energetic, mechanical, and dynamic stabilities of boron-substituted M₂AlB (M=Sc, Ti, V, Cr, Mn, Y, Zr, Nb, Mo, Tc, Ru, Hf, Ta, W, Re, Os, Ir, Pt, Ag, and Au) compounds as the members of 211-MAX borides with Cr₂AlC-type crystal structure were investigated. After well-converged geometry optimizations, the cohesive energy, formation enthalpy, single-crystal elastic constants, and phonon dispersion curves were calculated to explain the stabilities of the compounds. Except for M=Y, Ag, and Au compounds, the others are thermodynamically stable due to the negative formation enthalpies. M=Sc, Y, Zr, Hf, Os, Ir, and Pt compounds are dynamically unstable because of the negative phonon frequencies, and M=Ag and Au compounds are mechanically unstable. Beyond the detailed stability analysis, the structural, elastic, and mechanical properties, anisotropy factors, exfoliation states, and specifically hardness nature of the stable compounds were examined. A new modified hardness method, which includes the metallicity, is proposed to characterize the softness nature of MAX-phases. The relevant quantities, such as bond electronegativity, ionicity, and metallicity, were debated. The presented data were compared with available theoretical and experimental literature.

应用第一原理密度泛函拟势平面波计算，硼取代的M ₂ AlB（M = Sc，Ti，V，Cr，Mn，Y，Zr，Nb，Mo，Tc的能量，机械和动态稳定性），Ru，Hf，Ta，W，Re，Os，Ir，Pt，Ag和Au）化合物作为含Cr ₂的211-MAX硼化物的成员研究了AlC型晶体结构。经过良好的几何优化收敛后，计算了内聚能，形成焓，单晶弹性常数和声子色散曲线，以解释化合物的稳定性。除M = Y，Ag和Au化合物外，其他化合物由于形成负焓而具有热力学稳定性。由于负声子频率，M = Sc，Y，Zr，Hf，Os，Ir和Pt化合物动态不稳定，而M = Ag和Au化合物机械上不稳定。除了详细的稳定性分析之外，还研究了稳定化合物的结构，弹性和机械性能，各向异性因素，剥离状态，特别是硬度性质。一种新的改良硬度方法，包括金属性，提出来表征MAX相的柔软性。有关的数量，如键电负性，离子性和金属性，已被讨论。提出的数据与现有的理论和实验文献进行了比较。