Research Article 2017, 2(2), 72-75 Advanced Materials Proceedings Copyright © 2017 VBRI Press 72 Modeling shape and size dependence of thermal expansion and Debye temperature of nanocrystals Madan Singh 1 *, Spirit Tlali 1 , Krishna Chandra 2 1 Department of Physics and Electronics, National University of Lesotho, P.O. Roma 180, Lesotho 2 Department of Physics, R.H. Govt. Post Graduate College, Kumaun University, Kashipur, Udham Singh Nagar (Uttarakhand), 244713, India * Corresponding author, E-mail: m.singh@nul.ls; Tel: (+266) 57044674 Received: 30 March 2016, Revised: 26 September 2016 and Accepted: 21 December 2016 DOI: 10.5185/amp.2017/202 www.vbripress.com/amp Abstract A simple theoretical model is developed to explore the size and shape dependence of thermal expansion and Debye temperature of nanomaterials. The model theory is based on cohesive energy and surface area change of the nanocrystals compared to the bulk crystals. It is found that the Debye temperature decreases with the decrease in particle size whereas, the thermal expansion increases as the particle size decreases. The present modelling results and predictions are very consistent with the available experiment results, implying that the model could be expected to be a general approach to understand the thermodynamic properties of nanomaterials. Copyright © 2017 VBRI Press. Keywords: Nanomaterials, Debye temperature, thermal expansion, thermodynamic properties, surface energy. Introduction Nanotechnology mainly consists of the processing of separation, consolidation and deformation of materials by one atom or by one molecule. Nanotechnology and nanoscience began in the early 1980’s with the advances in computing power and material modelling. A link between the depressions of the melting temperature and the Debye Temperature in metal nanowires was developed and check the validity of Lindeman relation on size reduction that connects these two physical quantities [1]. When the grain size of materials changes the nanometre scale, optic, electronic, magnetic, catalytic, biomedical and thermodynamic properties vary noticeably from those of an isolated atom and bulk materials [2-4]. It is recognized that the size dependence of thermal stability in nanomaterials is gradually becoming one of the major interests in upcoming technologies [5]. Cohesive energy, which is defined as the difference between the average energy of the atoms in a solid and the isolated atoms, is one of the most important physical parameters in quantifying the thermal stability of materials [6, 7]. Many experimental and theoretical efforts have been implemented to investigate the size-dependent cohesive energy of nanomaterials [8, 9]. At nanoscale Ag and Au have demonstrated many interesting chemical and physical properties that their bulk counterparts do not have. Liu et al. [10] have obtained such a model that is capable to reunite the observed size dependence of the lattice strain, core level shift, elastic modulus, and thermal stability of Au and Ag nanostructures from the perception of skin-depth bond order loss. For bulk materials, the surface effect can be neglected for most thermodynamic properties, however, surface effect cannot be ignored for nanomaterials. Surface effects results from the difference between the surface atom and inside atoms, the surface atoms are less stable than the inside atoms due to their less coordination number than that of inside atoms. The ratio of surface atoms to the total atoms is relatively large, which indicates to the size dependence of the thermodynamic properties of nanomaterials. In this paper, we register a theoretical model without adjustable parameters based on cohesive energy and surface effect for studying the particle size and shape dependent thermal expansion coefficient and Debye temperature of Sn, Pb, and Au nanosolids for spherical nanoparticles, nanowires, and nanofilms. It is found that the present model has good consistency with the available experimental data. The study established on cohesive energy and surface effect at decreased particle size, permits interpolation and extrapolation to the region for which adequate experimental data are not available. To the best of my knowledge this is the simple