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2007 | Vol. 59, nr 3 | 259-281
Tytuł artykułu

Eshelby formalism for multi-shell nano-inhomogeneities

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Języki publikacji
Nano-particles consisting of a core surrounded by multiple outer shells (multi-shell particles) are used as novel functional materials as well as stiffeners/toughners in conventional composites and nanocomposites. In these heterogeneous particles, the mismatch of thermal expansion coefficients and lattice constants between neighboring shells induces stress/strain fields in the core and shells, which in turn affect the physical/mechanical properties of the particles themselves and/or of the composites containing them. In this paper, we solve the elastostatic inhomogeneous indusion problem of an infinite medium containing a multi-shell spherical particle when the eigenstrains are prescribed in the particle and in the multi-shells, and the inhomogeneity problem when an arbitrary remote stress field is applied to the infinite medium. The corresponding Eshelby and stress concentration tensors of the two problems are obtained and specialised to inhomogeneous inclusions in finite spherical domains with fixed displacement or traction-free boundary conditions. Finally, the Eshelby tensor of a spherical inhomogeneity with non-uniform eigenstrain is obtained and applied to quantum dots of uniform and non-uniform compositions.

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Bibliogr. 52 poz.
  • LTCS and Department of Mechanics and Engineering Science Peking University Beijing, 100871, P. R. China
  • 1. J. WIGGINS, E. E. CARPENTER, C. J. O'CONNOR, Phenomenological magnetic modeling oj Au : Fe : Au nano-onions, J. Appl. Phys., 87, 5651-5653, 2000.
  • 2. M. ABE, T. SUWA, Surface plasma resonance and magneto-optical enhancement in com-posites containing multicore-shell structured nanoparticles, Phys. Rev. B, 70, 235103-1-5, 2004.
  • 3. J. PEREZ-CONDE, A. K. BHATTACHARJEE, CdS/HgS/CdS guantum dot ąuantum wells: A tight-binding study, Physica Status Solidi B, 229, 485-488, 2002.
  • 4. H. BORCHERT, D. DORFS, C. McGlNLEY, S. ADAM, T. MÓLLER, H. WELLER, A. EYCHMULLER, Photoemission study of onion-like quantum dot quantum well and double quantum well nanocrystals of CdS and HgS, J. Phys. Chem. B, 107, 7486-7491, 2003.
  • 5. M. ABE, J. KURODA, M. MATSUMOTO, Granular composites containing "micro-onions", permeability, and permittivity calculated for application to microwave absorbers, J. Appl. Phys., 91, 7373-7375, 2002.
  • 6. J. CHOI, A. F. YEE, R. M. LAINE, Toughening of cubic silsesquioxane epoxy nanocom-posites using core-shell rubber particles: A three-component hybrid system, Macromolecules, 37, 3267-3276, 2004.
  • 7. H. S. ZHOU, I. HONMA, J. W. HAUS, H. SASABE, H. KOMIYAMA, Synthesis and optical properties of coated nanoparticles composites, J. Luminescence, 70, 21-34, 1996.
  • 8. J. ROCKENBERGER, L. TROGER, A. L. ROGACH, M. TlSCHER, M. GRUNDMANN, A. EYCHMULLER, H. WELLER, The contribution of partide core and surface to strain, disorder and vibrations in thiolcapped CdTe nanocrystals, J. Chem. Phys., 108, 7807-7815, 1998.
  • 9. E. PRODAN, P. NORDLANDER, N. J. HAŁAS, Electronic structures and optical properties of gold nanoshells, Nano Lett., 3, 1411-1415, 2003.
  • 10. M. L. BRONGERSMA, Nanoshells: gifts in a gold wrapper, Nature Mater., 2, 296-297, 2003.
  • 11. H. KIM, M. ACHERMANN, L. P. BALET, J. A. HOLLINGSWORTH, V. I. KLIMOY, Synthesis and characterization of Co/CdSe core-shell nanocomposites: Bifunctional magnetic-optical nanocrystals, J. Am. Chem. Soc., 127, 544-546, 2005.
  • 12. A. J. WILLIAMSON, A. ZUNGER, In As quantum dots: Predicted electronic structure of free-standing versus GaAs-embedded structures, Phys. Rev. B, 59, 15819-15824, 1999.
  • 13. K. RAJESHWAR, N. R. TACCONI, C. R. CHENTHAMARAKSHAN, Semiconductor-based composite materials: Preparation, properties, and performance, Chem. Mater., 13, 2765-2782, 2001.
  • 14. L. J. LAUHON, M. S. GUDIKSEN, C. L. WANG, C. M. LIEBER, Epitaxial core-shell and core-multishell nanowire heterostructures, Naturę, 420, 57-61, 2002.
  • 15. M. GRUNDMANN, O. STIER, D. BIMBERG, InAs/GaAs pyramidal quantum dots: strain distribution, optical phonons and electronic structure, Phys. Rev. B, 52, 11969-11981, 1995.
  • 16. H. J. Chu, J. Wang, Strain distribution in arbitrarily shaped quantum dots with nonuniform composition, J. Appl. Phys., 98, 034315-1-7, 2005.
  • 17. R. B. LITTLE, M. A. EL-SAYED, G. W. BRYANT, S. BURKĘ, Formation of quantum-dot quantum-well heteronanostructures with large lattice mismatch: ZnS/CdS/ZnS, J. Chem. Phys., 114, 1813-1822, 2001.
  • 18. X. B. CHEN, Y. B. Lou, A. C. SAMIA, C. BURDA, Coherency strain effects on the optical response of core/shell heteronanostructures, Nano Lett., 3, 799-803, 2003.
  • 19. J. PEREZ-CONDE, A. K. BHATTACHARJEE, Electronic structure and optical properties of ZnS/CdS nanoheterostructures, Phys. Rev. B, 67, 235303-1-4, 2003.
  • 20. I. E. ITSKEYICH, S. G. LYAPIN, I. A. TROYAN, P. C. KLIPSTEIN, L. EAYES, P. C. MAIN, M. HENINI, Energy levels in self-assembled InAs/GaAs quantum dots above the pressure-induced Gamma-X crossover, Phys. Rev. B, 58, 4250-4253, 1998.
  • 21. M. E. GURTIN, A. I. MURDOCH, A continuum theory of elastic material surfaces, Arch. Rat. Mech. Anal., 57, 291-323, 1975.
  • 22. R. E. MILLER, V. B. SHENOY, Size-dependent elastic properties of nanosized structural elements, Nanotech., 11, 139-147, 2000.
  • 23. D. J. BOTTOMLEY, T. OGINO, Alternative to the Shuttleworth formulation of solid surface stress, Phys. Rev. B, 63, 165412-1-5, 2001.
  • 24. P. SHARMA, S. GANTI, N. BHATE, Effect of surfaces on the size-dependent elastic stale of nano-inhomogeneities, Appl. Phys. Lett., 82, 535-537, 2003.
  • 25. V. B. SHENOY, Atomistic calculations of elastic properties of metallic for crystal surfaces, Phys. Rev. B, 71, 094104-1-11 , 2005.
  • 26. H. L. DUAN, J. WANG, Z. P. HUANG, B. L. KARIHALOO, Eshelby formalism for nano-inhomogeneities, Proc. Roy. Soc. Lond. A, 461, 3335-3353, 2005.
  • 27. H. L. DUAN, J. WANG, Z. P. HUANG, B. L. KARIHALOO, Size-dependent effectwe elastic constants of solids containing nano-inhomogeneities with interface stress, J. Mech. Phys. Solids, 53, 1574-1596, 2005.
  • 28. J. WANG, H. L. DUAN, Z. P. HUANG, B. L. KARIHALOO, A scaling law for properties of nano-structured materials, Proc. Roy. Soc. Lond. A, 462, 1355-1363, 2006.
  • 29. B. I. YAKOBSON, R. E. SMALLEY, Fullerene nanotubes: C-1000000 and beyond, American Scientist, 85, 324-337, 1997.
  • 30. P. S. THEOCARIS, The Mesophase Concept in Composites, Springer-Verlag, Berlin 1987.
  • 31. P. A. TZIKA, M. C. BOYCE, D. M. PARKS, Micromechanics of deformation in particle-toughened polyamide, J. Mech. Phys. Solids, 48, 1893-1929, 2000.
  • 32. K. JAYARAMAN, K. L. REIFSNIDER, Residual stresses in a composite with continuously varying Young's modulus in the fiber/matrix interphase, J. Compos. Mater., 26, 770-791, 1992.
  • 33. E. HERYE, A. ZAOUI, N-layered inclusion-based micromechanical modelling. Int. J. Eng. Sci., 31, 1-10, 1993.
  • 34. M. HORI, S. NEMAT-NASSER, Double-inclusion model and oyerall moduli of multi-phase composites, Mech. Mater., 14, 189-206, 1993.
  • 35. M. BORNERT, E. HERYE, C. STOLZ, A. ZAOUI, Self-Consistent approaches and strain heterogeneities in two-phase elastoplastic materials, Appl. Mech. Rev., 47, 66-76, 1994.
  • 36. C. Q. Ru, A new method for an inhomogeneity with stepwise graded interphase under thermomechanical loadings, J. Elasticity, 56, 107-127, 1999.
  • 37. J. Y. Li, Thermoelastic behavior of composites with functionally graded interphase: a multi-indusion model, Int. J. Solids and Struct., 37, 5579-5597, 2000.
  • 38. Z. HASHIN, Thin interphase/imperfect interface in elasticity with application to coated fiber composites, J. Mech. Phys. Solids, 50, 2509-2537, 2002.
  • 39. H. L. DUAN, Y. JIAO, X. Yi, J. WANG, Z. P. HUANG, Solution of inhomogeneity problems with graded shells and application to core-shell nanoparticles and composites, J. Mech. Phys. Solids, 54, 1401-1425, 2006.
  • 40. J. D. ESHELBY, The determination of the elastic field of an ellipsoidal inclusion and related problems, Proc. R. Soc. Lond. A, 241, 376-396, 1957.
  • 41. J. D. ESHELBY, The elastic field outside an ellipsoidal inclusion, Proc. R. Soc. Lond. A, 252, 561-569, 1959.
  • 42. H. L. DUAN, B. L. KARIHALOO, J. WANG, X. Yi, Strain distributions in nano-onions with uniform and non-uniform compositions, Nanotech., 17, 3380-3387, 2006.
  • 43. H. L. DUAN, B. L. KARIHALOO, J. WANG, X. Yi, Compatible composition profiles and critical sizes of alloyed quantum dots, Phys. Rev. B, 74, 195328-1-4, 2006.
  • 44. F. H. STREITZ, R. C. CAMMARATA, K. SIERADZKI, Surface-stress effects on elastic properties. L Thin metal films, Phys. Rev. B, 49, 10 699-10 706, 1994.
  • 45. P. MULLER, A. SAUL, Elastic effects on surface physics, Surf. Sci. Reports, 54, 157-258, 2004.
  • 46. A. I. LUR'E, Three-dimensional Problems of Theory of Elasticity, Interscience, New York, 1964.
  • 47. L. J. WALPOLE, Elastic behaviour of composite materials: theoretical foundations, [in:j YIH CHIA-SHUN [Ed.], Advances in Applied Mechanics, Academic Press, New York 21, 169-242, 1981.
  • 48. L. YEGARD, The constitution of the mixed crystals and the filling of space of the atoms, Z. Physik, 5, 17-26, 1921.
  • 49. R. DINGREYILLE, J. M. Qu, M. CHERKAOUI, Surface free energy and its effect on the elastic behavior of nano-sized particles, wires and films, J. Mech. Phys. Solids, 53, 1827-1854, 2005.
  • 50. G. Y. JING, H. L. DUAN, X. M. SUN, Z. S. ZHANG, J. Xu, Y. D. Li, J. WANG, AND D. P. Yu, Surface effects on elastic properties of siCver nanowires: contact atomie-force microscopy, Phys. Rev. B, 73, 235409=1-6, 2006.
  • 51. G. F. WANG, T. J. WANG, Deformation around a nanosized elliptical hole luith surface effect, Appl. Phys. Lett., 89, 161901-1-3, 2006.
  • 52. P. LIPINSKI, E. H. BARHDADI, M. CHERKAOUI, Micromechanical modelling of an arbi-trary ellipsoidal multi-coated inclusion, Phil. Mag., 86, 1305-1326, 2006.
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