Size- and temperature-dependent Young’s modulus and size-dependent thermal expansion coefficient of nanowires

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Abstract

Nanowires (NWs) exhibit size-dependent mechanical properties due to the high surface/volume ratio, in which temperature also plays an important role. The surface eigenstress model is further developed here to quantitatively predict the size-dependent mechanical properties of NWs and results in analytic formulas. Molecular dynamics (MD) simulations are conducted to study the size-dependent mechanical of [100], [110] and [111] Ni and Si nanowires within the temperature range of 100–400 K and the MD results verify perfectly the newly developed surface eigenstress model.

Keywords

surface eigenstress model Size- and temperature-dependent Young’s modulus Size-dependent thermal expansion coefficient Nanowires Molecular dynamics simulations 

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References

  1. 1.
    Gurtin M E, Markenscoff X, Thurston R N. Effect of surface stress on the natural frequency of thin crystals. Appl Phys Lett, 1976, 29: 529–530CrossRefGoogle Scholar
  2. 2.
    Cammarata R C. Surface and interface stress effects in thin films. Prog Surf Sci, 1994, 46: 1–38CrossRefGoogle Scholar
  3. 3.
    Ibach H. The role of surface stress in reconstruction, epitaxial growth and stabilization of mesoscopic structures. Surf Sci Rep, 1997, 29: 195–263CrossRefGoogle Scholar
  4. 4.
    Wang S, Shan Z, Huang H. The mechanical properties of nanowires. Adv Sci, 2017, 4: 1600332CrossRefGoogle Scholar
  5. 5.
    Kim W W. A studies of mechanical properties of Si nanowire through molecular dynamics simulation. J Adv Inform Tech Conv, 2015, 5: 29Google Scholar
  6. 6.
    Volokitin Y, Sinzig J, de Jongh L J, et al. Quantum-size effects in the thermodynamic properties of metallic nanoparticles. Nature, 1996, 384: 621–623CrossRefGoogle Scholar
  7. 7.
    Weber W M, Mikolajick T. Silicon and germanium nanowire electronics: Physics of conventional and unconventional transistors. Rep Prog Phys, 2017, 80: 066502CrossRefGoogle Scholar
  8. 8.
    Baldauf T, Heinzig A, Trommer J, et al. Tuning the tunneling probability by mechanical stress in Schottky barrier based reconfigurable nanowire transistors. Solid-State Electron, 2017, 128: 148–154CrossRefGoogle Scholar
  9. 9.
    Baldauf T, Heinzig A, Trommer J, et al. Stress-dependent performance optimization of reconfigurable silicon nanowire transistors. IEEE Electron Device Lett, 2015, 36: 991–993CrossRefGoogle Scholar
  10. 10.
    Wu B, Heidelberg A, Boland J J. Mechanical properties of ultrahighstrength gold nanowires. Nat Mater, 2005, 4: 525–529CrossRefGoogle Scholar
  11. 11.
    Wen B, Sader J E, Boland J J. Mechanical properties of ZnO nanowires. Phys Rev Lett, 2008, 101: 175502CrossRefGoogle Scholar
  12. 12.
    Chen H, Kou X, Yang Z, et al. Shape-and size-dependent refractive index sensitivity of gold nanoparticles. Langmuir, 2008, 24: 5233–5237CrossRefGoogle Scholar
  13. 13.
    Zhang B, Jung Y, Chung H S, et al. Nanowire transformation by sizedependent cation exchange reactions. Nano Lett, 2010, 10: 149–155CrossRefGoogle Scholar
  14. 14.
    Lee B, Rudd R E. First-principles calculation of mechanical properties of Si 〈001〉 nanowires and comparison to nanomechanical theory. Phys Rev B, 2007, 75: 195328CrossRefGoogle Scholar
  15. 15.
    Tang Z, Aluru N R. Calculation of thermodynamic and mechanical properties of silicon nanostructures using the local phonon density of states. Phys Rev B, 2006, 74: 235441CrossRefGoogle Scholar
  16. 16.
    Makeev M A, Srivastava D, Menon M. Silicon carbide nanowires under external loads: An atomistic simulation study. Phys Rev B, 2006, 74: 165303CrossRefGoogle Scholar
  17. 17.
    Branício P S, Rino J P. Large deformation and amorphization of Ni nanowires under uniaxial strain: A molecular dynamics study. Phys Rev B, 2000, 62: 16950–16955CrossRefGoogle Scholar
  18. 18.
    Villain P, Beauchamp P, Badawi K F, et al. Atomistic calculation of size effects on elastic coefficients in nanometre-sized tungsten layers and wires. Scripta Mater, 2004, 50: 1247–1251CrossRefGoogle Scholar
  19. 19.
    Liang H, Upmanyu M, Huang H. Size-dependent elasticity of nanowires: Nonlinear effects. Phys Rev B, 2005, 71: 1403CrossRefGoogle Scholar
  20. 20.
    Chen C Q, Shi Y, Zhang Y S, et al. Size dependence of Young’s modulus in ZnO nanowires. Phys Rev Lett, 2006, 96: 075505CrossRefGoogle Scholar
  21. 21.
    Diao J, Gall K, L. Dunn M. Atomistic simulation of the structure and elastic properties of gold nanowires. J Mech Phys Solids, 2004, 52: 1935–1962Google Scholar
  22. 22.
    Gibbs J W. The Scientific Papers of J. Willard Gibbs. Longmans: Green and Company, 1906MATHGoogle Scholar
  23. 23.
    Wang J, Huang Z, Duan H, et al. Surface stress effect in mechanics of nanostructured materials. Acta Mech Solid Sin, 2011, 24: 52–82CrossRefGoogle Scholar
  24. 24.
    Duan H L, Wang J, Karihaloo B L. Theory of elasticity at the nanoscale. Adv Appl Mech, 2009, 42: 1–68CrossRefGoogle Scholar
  25. 25.
    Gurtin M E, Ian Murdoch A. A continuum theory of elastic material surfaces. Arch Rational Mech Anal, 1975, 57: 291–323MathSciNetCrossRefMATHGoogle Scholar
  26. 26.
    Gurtin M E, Ian Murdoch A. Surface stress in solids. Int J Solids Struct, 1978, 14: 431–440CrossRefMATHGoogle Scholar
  27. 27.
    Miller R E, Shenoy V B. Size-dependent elastic properties of nanosized structural elements. Nanotechnology, 2000, 11: 139–147CrossRefGoogle Scholar
  28. 28.
    Park H S, Klein P A, Wagner G J. A surface Cauchy-Born model for nanoscale materials. Int J Numer Meth Engng, 2006, 68: 1072–1095MathSciNetCrossRefMATHGoogle Scholar
  29. 29.
    Park H S, Klein P A. Surface stress effects on the resonant properties of metal nanowires: The importance of finite deformation kinematics and the impact of the residual surface stress. J Mech Phys Solids, 2008, 56: 3144–3166CrossRefMATHGoogle Scholar
  30. 30.
    Dingreville R, Kulkarni A J, Zhou M, et al. A semi-analytical method for quantifying the size-dependent elasticity of nanostructures. Model Simul Mater Sci Eng, 2008, 16: 025002CrossRefGoogle Scholar
  31. 31.
    Dingreville R, Qu J. Interfacial excess energy, excess stress and excess strain in elastic solids: Planar interfaces. J Mech Phys Solids, 2008, 56: 1944–1954MathSciNetCrossRefMATHGoogle Scholar
  32. 32.
    Zhang T Y, Luo M, Chan W K. Size-dependent surface stress, surface stiffness, and Young’s modulus of hexagonal prism [111] β-SiC nanowires. J Appl Phys, 2008, 103: 104308–104308CrossRefGoogle Scholar
  33. 33.
    Zhang T Y, Wang Z J, Chan W K. Eigenstress model for surface stress of solids. Phys Rev B, 2010, 81: 195427CrossRefGoogle Scholar
  34. 34.
    Zhang T Y, Ren H, Wang Z J, et al. Surface eigen-displacement and surface Poisson’s ratios of solids. Acta Mater, 2011, 59: 4437–4447CrossRefGoogle Scholar
  35. 35.
    Zhou X Y, Ren H, Huang B L, et al. Size-dependent elastic properties of thin films: Surface anisotropy and surface bonding. Sci China Tech Sci, 2014, 57: 680–691CrossRefGoogle Scholar
  36. 36.
    Wang Z J, Liu C, Li Z, et al. Size-dependent elastic properties of Au nanowires under bending and tension—Surfaces versus core nonlinearity. J Appl Phys, 2010, 108: 083506–083506CrossRefGoogle Scholar
  37. 37.
    Zhou X Y, Huang B L, Zhang T Y. Size-and temperature-dependent Young’s modulus and size-dependent thermal expansion coefficient of thin films. Phys Chem Chem Phys, 2016, 18: 21508–21517CrossRefGoogle Scholar
  38. 38.
    Steneteg P, Hellman O, Vekilova O Y, et al. Temperature dependence of TiN elastic constants from ab initio molecular dynamics simulations. Phys Rev B, 2013, 87: 94114CrossRefGoogle Scholar
  39. 39.
    Karimi M, Stapay G, Kaplan T, et al. Temperature dependence of the elastic constants of Ni: Reliability of EAM in predicting thermal properties. Model Simul Mater Sci Eng, 1997, 5: 337–346CrossRefGoogle Scholar
  40. 40.
    Wachtman J B, Tefft W E, Lam D G, et al. Exponential temperature dependence of Young’s modulus for several oxides. Phys Rev, 1961, 122: 1754–1759CrossRefGoogle Scholar
  41. 41.
    Varshni Y P. Temperature dependence of the elastic constants. Phys Rev B, 1970, 2: 3952–3958CrossRefGoogle Scholar
  42. 42.
    Araujo L L, Giulian R, Sprouster D J, et al. Size-dependent characterization of embedded Ge nanocrystals: Structural and thermal properties. Phys Rev B, 2008, 78: 094112CrossRefGoogle Scholar
  43. 43.
    Kumar R, Sharma G, Kumar M. Size and temperature effect on thermal expansion coefficient and lattice parameter of nanomaterials. Mod Phys Lett B, 2013, 27: 1350180CrossRefGoogle Scholar
  44. 44.
    Yang C C, Xiao M X, Li W, et al. Size effects on Debye temperature, Einstein temperature, and volume thermal expansion coefficient of nanocrystals. Solid State Commun, 2006, 139: 148–152CrossRefGoogle Scholar
  45. 45.
    Plimpton S. Fast parallel algorithms for short-range molecular dynamics. J Comput Phys, 1995, 117: 1–19CrossRefMATHGoogle Scholar
  46. 46.
    Foiles S M, Baskes M I, Daw M S. Embedded-atom-method functions for the fcc metals Cu, Ag, Au, Ni, Pd, Pt, and their alloys. Phys Rev B, 1986, 33: 7983–7991CrossRefGoogle Scholar
  47. 47.
    Stillinger F H, Weber T A. Computer simulation of local order in condensed phases of silicon. Phys Rev B, 1985, 31: 5262–5271CrossRefGoogle Scholar
  48. 48.
    Nosé S. A molecular dynamics method for simulations in the canonical ensemble. Mol Phys, 1984, 52: 255–268CrossRefGoogle Scholar
  49. 49.
    Martyna G J, Tobias D J, Klein M L. Constant pressure molecular dynamics algorithms. J Chem Phys, 1994, 101: 4177–4189CrossRefGoogle Scholar
  50. 50.
    Parrinello M, Rahman A. Polymorphic transitions in single crystals: A new molecular dynamics method. J Appl Phys, 1981, 52: 7182–7190CrossRefGoogle Scholar
  51. 51.
    Shinoda W, Shiga M, Mikami M. Rapid estimation of elastic constants by molecular dynamics simulation under constant stress. Phys Rev B, 2004, 69: 134103CrossRefGoogle Scholar

Copyright information

© Science China Press and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Materials Genome InstituteShanghai University, and Shanghai Materials Genome InstituteShanghaiChina

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