▎ 摘　　要

The mechanical stability of graphene as temperature rises is analyzed based on three different self-consistent phonon (SCP) models. Compared with three-dimensional (3-D) materials, the critical temperature T-i at which instability occurs for graphene is much closer to its melting temperature T-m obtained from Monte Carlo simulation (T-i similar or equal to 2T(m), K. V. Zakharchenko, A. Fasolino, J. H. Los, and M. I. Katsnelson, J. Phys. Condens. Matter 23, 202202). This suggests that thermal vibration plays a significant role in melting of graphene while melting for 3-D materials is often dominated by topologic defects. This peculiar property of graphene derives from its high structural anisotropy, which is characterized by the vibrational anisotropic coefficient (VAC), defined upon its Lindermann ratios in different directions. For any carbon based material with a graphene-like structure, the VAC value must be smaller than 5.4 to maintain its stability. It is also found that the high VAC value of graphene is responsible for its negative thermal expansion coefficient at low temperature range. We believe that the VAC can be regarded as a new criterion concerning the vibrational stability of any low-dimensional (low-D) materials. (C) 2013 Author(s). All article content, except where otherwise noted, is licensed under a Creative Commons Attribution 3.0 Unported License.