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Research Article Open Access

Modeling shape and size dependence of thermal expansion and Debye temperature of nanocrystals

Madan Singh1*, Spirit Tlali1, Krishna Chandra2

1Department of Physics and Electronics, National University of Lesotho, P.O. Roma 180, Lesotho

2Department of Physics, R.H. Govt. Post Graduate College, Kumaun University, Kashipur,

Udham Singh Nagar (Uttarakhand), 244713, India

Adv. Mater. Proc., 2017, 2 (2), 72-75

DOI: 10.5185/amp.2017/202

Publication Date (Web):05 February 2017

Copyright © IAAM-VBRI Press



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


Nanomaterials, Debye temperature, thermal expansion, thermodynamic properties, surface energy.