Acta Mechanica Sinica

, Volume 33, Issue 1, pp 77–82 | Cite as

A universal method to calculate the surface energy density of spherical surfaces in crystals

  • Jian Wang
  • Jianjun Bian
  • Xinrui NiuEmail author
  • Gangfeng WangEmail author
Research Paper


Surface energy plays an important role in the mechanical performance of nanomaterials; however, determining the surface energy density of curved surfaces remains a challenge. In this paper, we conduct atomic simulations to calculate the surface energy density of spherical surfaces in various crystalline metals. It is found that the average surface energy density of spherical surfaces remains almost constant once its radius exceeds 5 nm. Then, using a geometrical analysis and the scaling law, we develop an analytical approach to estimate the surface energy density of spherical surfaces through that of planar surfaces. The theoretical prediction agrees well with the direct atomic simulations, and thus provides a simple and general method to calculate the surface energy density in crystals.


Surface energy density Nanoparticle Nanocavity 



This project was supported by the National Natural Science Foundation of China (Grants 11272249 and 11525209).


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Copyright information

© The Chinese Society of Theoretical and Applied Mechanics; Institute of Mechanics, Chinese Academy of Sciences and Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  1. 1.Department of Engineering Mechanics, SVLXi’an Jiaotong UniversityXi’anChina
  2. 2.CASM and Department of Mechanical and Biomedical EngineeringCity University of Hong KongHong KongChina

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