Mechanical properties of monolayer sulphides: a comparative study between MoS2, HfS2 and TiS3

Abstract

The in-plane stiffness (C), Poisson's ratio (ν), Young's modulus and ultimate strength (σ) along two different crystallographic orientations are calculated for the single layer crystals: MoS₂, HfS₂ and TiS₃ in 1H, 1T and monoclinic phases. We find that MoS₂ and HfS₂ have isotropic in-plane stiffnesses of 124.24 N m⁻¹ and 79.86 N m⁻¹, respectively. While for TiS₃ the in-plane stiffness is highly anisotropic due to its monoclinic structure, with C_x = 83.33 N m⁻¹ and C_y = 133.56 N m⁻¹ (x and y are parallel to its longer and shorter in-plane lattice vectors.). HfS₂ which is in the 1T phase has the smallest anisotropy in its ultimate strength, whereas TiS₃ in the monoclinic phase has the largest. Along the armchair direction MoS₂ has the largest σ of 23.48 GPa, whereas along y TiS₃ has the largest σ of 18.32 GPa. We have further analyzed the band gap response of these materials under uniaxial tensile strain, and find that they exhibit different behavior. Along both armchair and zigzag directions, the band gap of MoS₂ (HfS₂) decreases (increases) as strain increases, and the response is almost isotropic. For TiS₃, the band gap decreases when strain is along x, while if strain is along y, the band gap increases first and then decreases beyond a threshold strain value. The different characteristics observed in these sulphides with different structures shed light on the relationship between the structure and properties, which is useful for applications in nanotechnology.