Thermo-mechanical behavior of low-dimensional systems: The local bond average approach Chang Q. Sun * School of Electrical and Electronic Engineering, Nanyang Technological University, Singapore 639798, Singapore Key Laboratory of Low-Dimensional Materials and Application Technologies (Ministry of Education), Xiangtan University, Hunan 411105, China Tianjin Key Laboratory of Low-Dimensional Materials Physics and Preparing Technology, Tianjin University, Tianjin 300072, China article info Article history: Received 20 July 2008 Accepted 1 August 2008 abstract With the miniaturization of a solid, effects of surface strain and quantum trapping become increasingly important in determining its properties. As a result, low-dimensional materials manifest unu- sual features, especially in their energetic and mechanical behavior. The establishment of a consistent understanding on an atomic-level of the mechanism behind the fascinating behaviors of low-dimen- sional systems, which include monatomic chains, hollow tubes, liquid and solid surface skins, nanocavities, nanowires, and nano- grains, as well as interfaces, has long been a great challenge. In this report, a literature survey is presented, followed by a theoretical analysis culminating in the development of a local bond average (LBA) approach that may complement existing approximations in terms of continuum medium and quantum computations. The LBA approach correlates the measurable quantities of a specimen to the identities of its representative bonds, and the energetic responses of these bonds (bond nature, order, length and strength) to external stimuli, such as changes in temperatures and coordination environ- ments. It is shown that the shortened and strengthened bonds between under-coordinated atoms and the consequent local strain and quantum trapping dictate, intrinsically, the mechanical behav- ior of systems with a high proportion of such atoms. The thermally driven softening of a substance arises from bond expansion and lat- tice vibrations that weaken the bonds. The competition between the energy density gain and the residual atomic cohesive energy in the 0079-6425/$ - see front matter Ó 2008 Elsevier Ltd. All rights reserved. doi:10.1016/j.pmatsci.2008.08.001 * Address: School of Electrical and Electronic Engineering, Nanyang Technological University, Singapore 639798, Singapore. Associate affiliations at Xiangtan and Tianjin are with honorary/adjunct appointments. E-mail address: ecqsun@ntu.edu.sg URL: http://www3.ntu.edu.sg/home/ecqsun/ Progress in Materials Science 54 (2009) 179–307 Contents lists available at ScienceDirect Progress in Materials Science journal homepage: www.elsevier.com/locate/pmatsci