Eur. Phys. J. Plus (2022) 137: 824
https://doi.org/10.1140/epjp/s13360-022-02982-3

Regular Article

Modeling the quantitative effects of size, dimensionality and temperature on Young’s modulus of nanocrystals

¹ State Key Laboratory of Coal Mine Disaster Dynamics and Control, Chongqing University, 400044, Chongqing, China
² College of Aerospace Engineering, Chongqing University, 400044, Chongqing, China
³ College of Materials Science and Engineering, Chongqing University, 400045, Chongqing, China
⁴ School of Physics and Electronic Information, Huaibei Normal University, 235000, Huaibei, China

^b wgli@cqu.edu.cn

Received: 15 April 2022
Accepted: 21 June 2022
Published online: 17 July 2022

Abstract

Young’s modulus is an essential property in determining the stiffness and durability of the devices in practical engineering applications, subjected to the size, dimensionality and temperature. Despite being the subject of many studies, the size, dimensionality and temperature effects on Young’s modulus of nanocrystals still lack a comprehensive understanding. To comprehensively understand the synergistic influences of the aforementioned parameters, based on the Lennard–Jones potential, a theoretical model for predicting the size and dimensionality effects on Young’s modulus of nanocrystals is established by considering the surface stress, size effect on surface energy, size and dimensionality effects on cohesive energy and atom distance. Then, we further consider the temperature effect on the cohesive energy, atom distance in equilibrium, thermal expansion coefficient, and specific heat at constant volume to establish the temperature effect on Young’s modulus of nanocrystals. The agreement between model predictions and experimental, simulation results confirmed the effectiveness and rationality of our model. This model not only reveals the quantitative relationship between the size and temperature effects on Young’s modulus and cohesive energy but also demonstrates theoretical support for reliability analysis and further provides the theoretical guide for the design and application of the nanoscale devices.