Encyclopedia of Continuum Mechanics

Living Edition
| Editors: Holm Altenbach, Andreas Öchsner

Surface Energy and Its Effects on Nanomaterials

Living reference work entry
DOI: https://doi.org/10.1007/978-3-662-53605-6_166-1



Atoms at a free surface experience a different local environment than do atoms in the bulk of a material. As a result, the energy associated with these atoms will, in general, be different from that of the atoms in the bulk. The excess energy associated with surface atoms is called surface free energy. In traditional continuum mechanics, such surface free energy is typically neglected because it is associated with only a few layers of atoms near the surface and the ratio of the volume occupied by the surface atoms and the total volume of material of interest is extremely small. However, for nano-sized particles, wires, and films, the surface-to-volume ratio becomes significant and so does the effect of surface free energy. Consequently, the effective modulus of nano-sized structural elements should be considered, which by definition becomes size dependent.


The elastic behavior of a material is...


Surface Free Energy Density Effective Modulus Tensor Third-order Elastic Constants Surface Stress Self-equilibrium State 
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  1. Baker SP, Small MK, Vlassak JJ, Daniels BJ, Nix WD (1993) The search for the supermodulus effect. In: Mechanical properties and deformation behavior of materials having ultra-fine microstructures. Springer Netherlands.  https://doi.org/10.1007/978-94-011-1765-4_9 CrossRefGoogle Scholar
  2. Capolungo L, Cherkaoui M, Qu J (2006) Homogenization method for strength and inelastic behavior of nanocrystalline materials. In: IUTAM symposium on size effects on material and structural behavior at micron- and nano-scales. Springer Netherlands.  https://doi.org/10.1007/978-1-4020-4946-0_22
  3. Diao J, Gall K, Dunn ML (2003) Surface-stress-induced phase transformation in metal nanowires. Nat Mater 2(10):656–660.  https://doi.org/10.1038/nmat977 CrossRefGoogle Scholar
  4. Diao J, Gall K, Dunn ML (2004) Atomistic simulation of the structure and elastic properties of gold nanowires. J Mech Phys Solids 52(9):1935–1962.  https://doi.org/10.1016/j.jmps.2004.03.009 CrossRefzbMATHGoogle Scholar
  5. Dingreville R, Kulkarni AJ, Zhou M, Qu J (2008) A semi-analytical method for quantifying the size-dependent elasticity of nanostructures. Model Simul Mater Sci Eng 16(2):025002.  https://doi.org/10.1088/0965-0393/16/2/025002 CrossRefGoogle Scholar
  6. Dingreville R, Qu J (2007) A semi-analytical method to compute surface elastic properties. Acta Mater 55(1):141–147.  https://doi.org/10.1016/j.actamat.2006.08.007 CrossRefGoogle Scholar
  7. Dingreville R, Qu J (2009) A semi-analytical method to estimate interface elastic properties. Comput Mater Sci 46(1):83–91.  https://doi.org/10.1016/j.commatsci.2009.02.011 CrossRefGoogle Scholar
  8. Dingreville R, Qu J, Cherkaoui M (2005) Surface free energy and its effect on the elastic behavior of nano-sized particles, wires and films. J Mech Phys Solids 53(8):1827–1854.  https://doi.org/10.1016/j.jmps.2005.02.012 MathSciNetCrossRefzbMATHGoogle Scholar
  9. Nix WD, Gao H (1998) An atomistic interpretation of interface stress. Scr Mater 39(12):1653–1661.  https://doi.org/10.1016/s1359-6462(98)00352-2 CrossRefGoogle Scholar
  10. Sanfeld A, Steinchen A (2000) Surface energy, stress, capillary-elastic pressure and chemical equilibrium constant in nanoparticles. Surf Sci 463(3):157–173.  https://doi.org/10.1016/s0039-6028(00)00644-0 CrossRefGoogle Scholar
  11. Shuttleworth R (1950) The surface tension of solids. Proc Phys Soc Sect A 63(5):444–457.  https://doi.org/10.1088/0370-1298/63/5/302 CrossRefGoogle Scholar
  12. Streitz FH, Cammarata RC, Sieradzki K (1994a) Surface-stress effects on elastic properties. I. Thin metal films. Phys Rev B 49(15):10699–10706.  https://doi.org/10.1103/physrevb.49.10699 CrossRefGoogle Scholar
  13. Streitz FH, Cammarata RC, Sieradzki K (1994b) Surface-stress effects on elastic properties. II. Metallic multilayers. Phys Rev B 49(15):10707–10716.  https://doi.org/10.1103/physrevb.49.10707 CrossRefGoogle Scholar

Authors and Affiliations

  1. 1.School of EngineeringTufts UniversityMedfordUSA
  2. 2.Sandia National LaboratoriesAlbuquerqueUSA

Section editors and affiliations

  • Victor A. Eremeyev
    • 1
  1. 1.Gdańsk University of TechnologyGdańskPoland