A first-principles study of the relationship between modulus and ideal strength of single-layer, transition metal dichalcogenides

Abstract

Electronic properties of single-layer transition metal dichalcogenides (TMDs), such as bond gap, can be tuned by elastic strain. The regulating range of such strain engineering is determined by ideal strengths, which, according to Griffth's strength limit, is usually estimated as E/10, where E is the elastic modulus. Despite being extensively used, this relationship between ideal strength and moduli has yet to be thoroughly investigated for TMDs. Our extensive density functional theory calculations on six representative, single-layer TMDs (MoS₂, MoSe₂, NbS₂, NbSe₂, ReS₂, ReSe₂) showed that the moduli of TMDs increase as their transition metal elements change from the V to VII group. However, despite having higher moduli, ReS₂ and ReSe₂ exhibit lower strengths and failure strains than MoS₂, MoSe₂, and NbSe₂. Such strength degeneration is attributed to the multiple bond directions in ReS₂ and ReSe₂. As strain softening renders stretched bonds easier to deform, deformation gradually concentrates on the bonds most close to the loading direction. Since only a small portion of covalent bonds are stretched, the ideal strength of the whole structure is diminished. Overall, our findings suggest that reducing the variety of bond orientations could increase the apparent ductility of TMDs without decreasing the strength.