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We delineated the role of thermally excited ripples on thermal expansionproperties of 2D honeycomb materials (free-standing graphene, 2D h-BN, andML-MoS2), by explicitly carrying out three-dimensional (3D) and two-dimensional(2D) molecular dynamics simulations. In 3D simulations, the in-plane latticeparameter (a-lattice) of graphene and 2D h-BN shows thermal contraction over awide range of temperatures and exhibits a strong system size dependence. The 2Dsimulations of the very same system show a reverse trend, where the a-latticeis expanding in the whole computed temperature range. Contrary to graphene and2D h-BN, the a-lattice of ML-MoS2 shows thermal expansion in both 2D and 3Dsimulations and their system size dependence is marginal. By analyzing thephonon dispersion at 300 K, we found that the discrepancy between 2D and 3Dsimulations of graphene and 2D h-BN is due to the absence of out-of-planebending mode (ZA) in 2D simulations, which is responsible for thermalcontraction of a-lattice at low temperature. Meanwhile, all the phonon modesare present in 2D phonon dispersion of ML-MoS2, which indicates that the originof ZA mode is not purely due to out-of-plane movement of atoms and also itseffect on thermal expansion is not significant as found in graphene and 2D h-BN

Delineating the role of ripples on thermal expansion of honeycomb materials:graphene, 2D-h-BN and monolayer(ML)-MoS2