References on Stress-Induced Morphological Instabilities (for AMSC 698V) - B. Li

AMSC 698V: Advanced Topics in Applied Mathematics, Fall, 2003


Instructor: Bo Li

References on Stress-Induced Morphological Instabilities

  1. R. J. Asaro and W. A. Tiller, Surface morphology development during stress corrosion cracking: Part I: via surface diffusion, Metall. Trans., 3:1789-1796, 1972.
  2. J. Berr\'ehar, C. Caroli, C. Lapersonne-Meyer, and M. Schott, Surface patterns on single-crystal films under uniaxial stress: experimental evidence for the Grinfeld instability, Phys. Rev. B, 46(20):13487-13495, 1992.
  3. E. Bonnetier and A. Chambolle, Computing the equilibrium configuration of epitaxially strained crystalline films, SIAM J. Appl. Math., 2002.
  4. E. Bonnetier, R. S. Falk, and M. A. Grinfeld, Analysis of a one-dimensional variational model of the equilibrium shape of a deformable crystal, Math. Model. Anal. Numer., 33:573-591, 1999.
  5. C.-h. Chiu and H. Gao, Stresses singularities along a cycloid rough surface, Int. J. Solids Struct., 30:2983-3012, 1993.
  6. C.-h. Chiu and H. Gao, Numerical simulation of diffusion controlled surface evolution, Materials Research Symposium Proceedings, 317:369-374, 1994.
  7. C.-h. Chiu and H. Gao, A numerical study of stress controlled surface diffusion during epitaxial film growth, Materials Research Symposium Proceedings, 356:33-44, 1995.
  8. J. Colin, J. Grilh\'e, and N. Junqua, Morphological instabilities of a stressed pore channel, Acta mater., 45(9):3835-3841, 1996.
  9. J. Colin, J. Grilh\'e, and N. Junqua, Surface instabilities of a stressed cylindrical whisker, Phil. Mag. A, 76(4):793-805, 1997.
  10. J. Colin, J. Grilh\'e, and N. Junqua, Transformation of a cubic precipitate to a butterfly shape due to localized instabilities, Acta mater. 46(4):1249-1255, 1998.
  11. J. Colin, L. Thilly, F. Lecouturier, J. P. Peyrade, S. Ask\'enazy, and J. Grilh\'e", Axial and radial interface instabilities of Copper/Tantalum cylindrical conductors, Acta mater., 47(9):2761-2768, 1999.
  12. L. B. Freund and F. Jonsdottir, Instability of biaxially stressed thin film on a sbstrate due to material diffusion over its free surface, J. Mech. Phys. Solids, 41:1245-1255, 1993.
  13. H. Gao, Stress concentration at slightly undulating surfaces, J. Mech. Phys. Solids, 39:443-458, 1991.
  14. H. Gao, Morphological instabilities along surfaces of anisotropic solids, in Modern Theory of Anisotropic Elasticity and Applications, eds. J. J. Wu, T. C. T. Ting, and D. M. Barnett, SIAM, Philadelphia, pp. 139-150, 1991,
  15. H. Gao, A boundary perturbation analysis for elastic inclusion and interfaces, Int. J. Solids Struct., 28:703-726, 1991.
  16. H. Gao, Some general properties of stress-driven surface evolution in a heteroepitaxial thin film structure, J. Mech. Phys. Solids, 42:741-772, 1994.
  17. H. Gao and W. D. Nix, Surface roughening of heteroepitaxial thin films, Annu. Rev. Mater. Sci., 29:173-209, 1999.
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  20. M. A. Grinfeld, The stability of heterogeneous equilibrium in systems consisting of solid elastic phases, Doklady, Earth Sci. Sect. 265:21-24, 1982.
  21. M. A. Grinfeld, Instability of the separation boundry between a nonhydrostatically stressed elastic body and a melt, Sov. Phys. Doklady, 31:831-835, 1986.
  22. M. A. Grinfeld, Thermodynamic Methods in the Theory of Heterogeneous Systems, Longman, New York, 1991.
  23. M. A. Grinfeld, On the morphology of the stress-driven corrugations of the phase boundary between the solid and its melt., J. Phys. (Condens. Matter), 4L:647-652, 1992.
  24. M. A. Grinfeld, Interfacial diffusion relaxation of internal stresses in solids, Interface Sci., 1:237-241, 1993.
  25. M. A. Grinfeld, The stress driven rearrangement instability in ellastic crystals: mathematical models and physical manifestations, J. Nonlinear Sci., 3:35-83, 1993.
  26. M. A. Grinfeld, The stress driven ``rearrangement'' instability in crystal films, J. Intellig. Mater. Syst. Struct., 4:76-81, 1993.
  27. M. A. Grinfeld, Stress corrosion and stress induced surface morphology of epitaxial films, Scanning Microscopy, 8(4):869-882, 1994.
  28. C. Herring, Surface tension as a motivation for sintering, in The Physics of Powder Metallurgy, Editor: W. E. Kingston, McGraw-Hill, New York, pp. 143-179, 1951.
  29. F. Jonsdottir and L. B. Freund, Equilibrium surface roughness of a strained epitaxial film due to surface diffusion induced by interface misfit dislocations, Mech. Materials, 20:337-349, 1995.
  30. N. Junqua and J. Grilh\'e, Surface instability of epitaxial films on a surface, J. de Phys., III, 3:1589, 1993.
  31. F. Larche and J. W. Cahn, A linear theory of themochemical equilibrium of solids under stress, Acta Metall., 21:1051-1063, 1973.
  32. W. W. Mullins, Theory of thermal grooving, J. Appl. Phys., 28:333-339, 1957.
  33. P. H. Leo and R. F. Sekerka, The effect of surface stress on crysta-melt and crystal-crystal equilibrium, Acta Metall., 37:3119-3138, 1989.
  34. P. H. Leo and R. F. Sekerka, The effect of elastic fields on the morphological stability of a precipitate grown from solid solution, Acta Metall., 37:3139-3148, 1989.
  35. P. Nozi\`eres, Growth and shape of crystals, in Solids Far From Equilibrium, Editor: C. Godr\'eche, Cambridge Univ. Press, Cambridge, pp. 17-36, 1991.
  36. P. Nozi\`eres, Amplitude expansion for the Grinfeld instability due to uniaxial stress at a solid surface, J. Phys., 3:681-684, 1993.
  37. P. Politi, G. Grenet, A. Marty, A. Ponchet, and J. Villain, Instabilities in crystal growth by atomic or molecular beams, Phys. Reports, 324:271-404, 2000.
  38. B. J. Spencer, P. W. Voorhees, and S. H. Davis, Morphological instability in epitaxially-strained dislocation-free solid films, Phys. Rev. Lett., 67:3696-3699, 1991.
  39. B. J. Spencer, P. W. Voorhees, and S. H. Davis, Morphological instability in epitaxially-strained dislocation-free solid films: linear stability theory, J. Appl. Phys., 73:4955-4970, 1993.
  40. B. J. Spencer, S. H. Davis, and P. W. Voorhees, Morphological instability in epitaxially-strained dislocation-free solid films: nonlinear evolution, Phys. Rev. B, 47:9760-9777, 1993.
  41. B. J. Spencer and D. I. Meiron, Nonlinear evolution of the stress-driven morphological instability in a two-dimensional semi-infinite solid, Acta Metall. Mater., 42:3629-3641, 1994.
  42. B. J. Spencer, P. W. Voorhees, and J. Tersoff, Enhanced instability of strained alloy films due to compositional stresses, Phys. Rev. Lett., 84:2449-2452, 2000.
  43. D. J. Srolovitz, On the stability of surfaces of stressed solids, Acta metall., 37(2):621-625, 1989.
  44. B. Sun and Z. Suo, A finite element method for simulating interface motion: II. large shape change due to surface diffusion, Acta mater., 45:4953-4962, 1997.
  45. H. H. Yu and Z. Suo, A finite element method for simulating interface motion, in Computational and Mathematical Models of Microstructural Evolution, Editors: J. W. Bullard, L.-Q. Chen, R. K. Kalia, and A. M. Stoneham, Materials Research Society Symposium Proceedings, Vol. 529, pp. 113-124, 1998.
  46. W. H. Yang and D. J. Srolovitz, Crack-like surface instabilities in stressed solids, Phys. Rev. Lett., 71:1593-1596, 1993.