Rippling, buckling and melting of single- and multi-layer MoS$_2$

Large-scale atomistic simulations using the reactive empirical bond order force field approach is implemented to investigate thermal and mechanical properties of single-layer (SL) and multi-layer (ML) molybdenum disulfide (MoS$_2$). The amplitude of the intrinsic ripples of SL-MoS$_2$ are found to be smaller than those exhibited by graphene (GE). Furthermore, because of the van der Waals interaction between layers, the out-of-plane thermal fluctuations of ML-MoS$_2$ decreases rapidly with increasing number of layers. This trend is confirmed by the buckling transition due to uniaxial stress which occurs for a significantly larger applied tension as compared to graphene. For SL-MoS$_2$, the melting temperature is estimated to be 3700~K which occurs through dimerization followed by the formation of small molecules consisting of 2 to 5 atoms. When different types of vacancies are inserted in the SL-MoS$_2$ it results in a decrease of both the melting temperature as well as the stiffness.