Anisotropic edge energy and phonon-governed failure mechanism of 2D MoSi₂N₄ family

Two-dimensional (2D) materials with unique mechanical properties hold significant promise for applications in nano electronics, optics, and electromechanics. Herein, we investigate the nonlinear mechanical response and anisotropic failure mechanisms of the 2D MoSi2N4 family using density functional theory and a continuum constitutive model. MoSi2N4 and WSi2N4 exhibit excellent stability and mechanical properties, with maximum strains up to 17% and tensile strengths exceeding 40 GPa. The edge energy anisotropy, with an energy range of 2.31-3.40 eV/Å, reaches a ratio of 1.4. Failure mechanisms of the 2D MoSi2N4 family are explored from a phonon perspective. Under biaxial strains, the out-of-plane vibrations of M atoms lead to the softening of optical phonon modes, while under uniaxial stress/strain, the collective vibrations cause the softening of acoustic phonon modes. Our findings provide theoretical guidance for the potential applications of the 2D MoSi2N4 family in micro-nano flexible devices involving mechanical properties.