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Calculations of Surface Stresses in Metals Under Mechanical Strains

기계적 변형하에서 금속재료의 표면응력 계산

  • 김성엽 (한국과학기술원 기계공학과) ;
  • 엄윤용 (한국과학기술원 기계공학과)
  • Published : 2008.03.01

Abstract

We calculate the variation of the surface stresses according to uniaxial and biaxial strains in face-centered cubic (FCC) metals. In our study, three mainly observed free surfaces of seven representative FCC metals are considered. Employed method is molecular mechanics, in which the interaction of atoms is described by empirical interatomic potentials. As uniaxial strain increases to tensile direction, the surface stresses on {100} and {110} free surfaces decrease monotonously, while those on {111} surface increase. These tendencies are the same regardless of the species of metals and interatomic potentials employed. However, when the system is under biaxial strain, surface stresses change different according to the surface directions, the species of metals, and even interatomic potentials. On {100} and {111} surfaces, heavy metals (Pt, Au) show the opposite variation to light metals (Ni, Cu). In the cases of Pd and Ag, the surface stresses reveal the opposite tendency, depending on interatomic potentials used.

Keywords

Surface Stress;FCC Metal;Strain Effect

References

  1. Ibach, H., 1997, 'The Role of Surface Stress in Reconstruction, Epixaxial Growth and Stabilization of Mesoscopic Structures,' Surf. Sci. Rep., Vol. 29, pp. 193-263 https://doi.org/10.1016/S0167-5729(97)00010-1
  2. Haiss, W., 2001, 'Surface Stress of Clean and Adsorbate-Covered Solids,' Rep. Prog. Phys., Vol. 64, pp.591-648 https://doi.org/10.1088/0034-4885/64/5/201
  3. Bimberg, D., Grundmann, M. and Ledentsov, N.N., 1999, Quantum dot Heterostructures, John wiley & Sons, England
  4. Alder, B. J., Vaisnys, J. R. and Jura, G., 1959, 'Penetration Depth of Surface Effects in Molecular Crystals,' J. Phys. Chem. Solids, Vol. 11, pp. 182-189 https://doi.org/10.1016/0022-3697(59)90212-4
  5. Price, C. W. and Hirth, J. P., 1976, 'Surface Energy and Surface Stress Tensor in an Atomistic Model,' Surf. Sci., Vol. 57, pp. 509-522 https://doi.org/10.1016/0039-6028(76)90344-7
  6. Miller, R. E. and Shenoy, V. B., 2000, 'Size-Dependent Elastic Properties of Nanosize Structural Elements,' Nanotechnology, Vol. 11, pp. 139-147 https://doi.org/10.1088/0957-4484/11/3/301
  7. Zhou, L. G. and Huang, H., 2004, 'Are Surfaces Elastically Softer or Stiffer?,' Appl. Phys. Lett., Vol. 84, pp. 1940-1942 https://doi.org/10.1063/1.1682698
  8. Pao, C.-W., Srolovitz, D. J. and Thompson, C. V., 2006, 'Effects of Surface Defects on Surface Stress of Cu(001) and Cu(111),' Phys. Rev. B, Vol. 74, p. 155437 https://doi.org/10.1103/PhysRevB.74.155437
  9. Shuttleworth, R., 1950, 'The Surface Tension of Solids,' Proc. Phys. Soc. A, Vol. 63, No. 5, pp. 444-456 https://doi.org/10.1088/0370-1298/63/5/302
  10. Cai, J. and Ye, Y. Y., 1996, 'Simple Analytical Embedded-Atom-Potential Model Including a Long-Range Force for FCC Metals and Their Alloys,' Phys. Rev. B, Vol. 54, pp. 8398-8412 https://doi.org/10.1103/PhysRevB.54.8398
  11. Cleri, F. and Rosato, V., 1993, 'Tight-Binding Potentials for Transition Metals and Alloys,' Phys. Rev. B, Vol. 54, pp.22-33 https://doi.org/10.1103/PhysRevB.48.22
  12. Streitz, F. H., Cammarata, R. C. and Sieradzki, K., 1994, 'Surface-Stress Effects on Elastic Properties. I. Thin Metal Films,' Phys. Rev. B, Vol. 49, pp. 10699-10706 https://doi.org/10.1103/PhysRevB.49.10699
  13. Gumbsch, P. and Daw, M. S., 1991, 'Interface Stresses and Their Effects on the Elastic Moduli of Metallic Multilayers,' Phys. Rev. B, Vol. 44, pp. 3934-3938 https://doi.org/10.1103/PhysRevB.44.3934
  14. Schmid, M., Hofer, W., Varga, P., Stoltze, P., Jacobsen, K. W. and Norskov, J. K., 1995, 'Surface Stress, Surface Elasticity, and the Size Effect in Surface Segregation,' Phys. Rev. B, Vol. 51, pp. 10937-10946 https://doi.org/10.1103/PhysRevB.51.10937
  15. Fiorentini, V., Methfessel, M. and Scheffler, M., 1993, 'Reconstruction Mechanism of FCC Transition Metal (001) Surfaces,' Phys. Rev. Lett., Vol. 71, pp. 1051-1054 https://doi.org/10.1103/PhysRevLett.71.1051
  16. Feibelman, P. J., 1995, 'Anisotropy of the Stress on FCC (110) Surfaces,' Phys. Rev. B, Vol. 51, pp. 17867-17875 https://doi.org/10.1103/PhysRevB.51.17867
  17. Wasserman, H. J. and Vermaak, J. S., 1970, 'On the Determination of a Lattice Contraction in very Small Silver Particles,' Surf. Sci., Vol. 22, pp. 164-172 https://doi.org/10.1016/0039-6028(70)90031-2
  18. Mays, C. W., Vermaak, J. S. and Kuhlmann-Wilsdorf, D., 1968, 'Determination of the Surface Stress of Gold,' Surf. Sci., Vol. 12, pp. 134-140 https://doi.org/10.1016/0039-6028(68)90119-2
  19. Tyson, W. R. and Miller, W. A., 1977, 'Surface Free Energies of Solid Metals: Estimation from Liquid Surface Tension Measurements,' Surf. Sci., Vol. 62, pp. 267-276 https://doi.org/10.1016/0039-6028(77)90442-3