Interface evolution in three dimensions with curvature-dependent energy and surface diffusion: Interface-controlled evolution, phase transitions, epitaxial growth of elastic films

Archive for Rational Mechanics and Analysis

Volumn 163, Issue 3, 2002, Pages 171-208

  Gurtin, Morton E ^a   Jabbour, Michel E ^b  

^a CARNEGIE MELLON UNIVERSITY   (United States)

^b UNIVERSITY OF KENTUCKY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0036627609     PISSN: 00039527     EISSN: None     Source Type: Journal    
DOI: 10.1007/s002050200193     Document Type: Article

References (51)

1. [1951] C. HERRING, Some theorems on the free energies of crystal surfaces, Phys. Rev. 82, 87-93.
2. [1952] J. E. BURKE & D. TURNBULL, Recrystallization and grain growth, Progress in Metal Physics 3, 220-292.
3. [1956] W. W. MULLINS, Two-dimensional motion of idealized grain boundaries, J. Appl. Phys. 27, 900-904.
4. [1958] F. C. FRANK, On the kinematic theory of crystal growth and dissolution processes, in Growth and perfection of crystals (eds. R. H. Doremus, B. W. Roberts and D. Turnbull), John Wiley.
5. [1963] N. A. GJOSTEIN, Adsorption and surface energy (II): Thermal faceting from minimization of surface energy, Acta Metall. 11, 969-977.
6. [1974] J. W. CAHN & D. W. HOFFMAN, A vector thermodynamics for anisotropic surfaces-II. Curved and faceted surfaces, Acta Metall. 22, 1205-1214.
7. [1978] K. A. BRAKKE, The motion of a surface by its mean curvature, Princeton University Press.
8. [1985] W. HEUDUG & F. K. LEANER, Thermodynamics of coherent phase transformations in nonhydrostatically stessed solids, Pure Appl. Geophys. 12, 91-98.
9. [1985] J. A. SETHIAN, Curvature and evolution of fronts, Commun. Math. Phys. 101, 487-499.
10. [1986] U. ABRESCH & J. LANGER, The normalized curve shortening flow and homothetic solutions, J. Diff. Geom. 23, 175-196.
11. [1986] M. GAGE & R. S. HAMILTON, The heat equation shrinking convex plane curves, J. Diff. Geom. 23, 69-96.
12. [1987] M. A. GRAYSON, The heat equation shrinks embedded plane curves to round points, J. Diff. Geom. 26, 285-314.
13. [1987] L. TRUSKINOVSKY, Dynamics of nonequilibrium phase boundaries in a heat conducting nonlinear elastic medium, J. Appl. Math. Mech. (PMM) 51, 777-784.
14. [1987] M. UWAHA, Asymptotic growth shape developed in two-dimensional nuclei, J. Crystal Growth 80, 84-90.
15. [1988] M. E. GURTIN, Multiphase thermomechanics with interracial structure. 1. Heat conduction and the capillary balance law, Arch. Rational Mech. Anal. 104, 185-221.
16. [1988] S. OSHER & J. A. SETHIAN, Fronts propagating with curvature dependent speed, J. Comp. Phys. 79, 12-49.
17. [1989] S. ANGENENT & M. E. GURTIN, Multiphase thermomechanics with interfacial structure. 2. Evolution of an isothermal interface, Arch. Rational Mech. Anal. 108, 323-391.
18. [1989] M. E. GURTIN, A. STRUTHERS, & W. O. WILLIAMS, A transport theorem for moving interfaces, Quart. Appl. Math. 47, 773-777.
19. [1990] R. ABEYARATNE & J. K. KNOWLES, On the driving traction acting on a surface of strain discontinuity in a continuum, J. Mech. Phys. Solids, 38, 345-360.
20. [1990] S. B. ANGENENT, Parabolic equations for curves on surfaces. I. Curves with p-integrable curvature, Ann. Math. (2), 132, 171-215.
21. [1990] M. E. GURTIN & A. STRUTHERS, Multiphase thermomechanics with interfacial structure. 3. Evolving phase boundaries in the presence of bulk deformation, Arch. Rational Mech. Anal. 112, 97-160.
22. [1991] S. B. ANGENENT, Parabolic equations for curves on surfaces. II. Intersections, blow-up and generalized solutions, Ann. Math. (2) 133, 451-483.
23. [1991] Y.-G. CHEN, Y. GIGA & S. GOTO, Uniqueness and existence of viscosity solutions of generalized mean curvature flow equations, J. Diff. Geom. 33, 749-786.
24. [1991] L. C. EVANS & J. SPRUCK, Motion of level sets by mean curvature I, J. Diff. Geom. 33, 635-681.
25. [1991] Y. GIGA & M. H. SATO, Generalized interface condition with the Neumann boundary condition, Proc. Japan Acad., Ser. A Math., 67, 263-266.
26. [1991] B. J. SPENCER, P. W. VOORHEES & S. H. DAVIS, Morphological instability in epitaxially strained dislocation-free solid films, Phys. Rev. Letters 67, 3696-3699.
27. [1992] A. DICARLO, M. E. GURTIN & P. PODIO-GUIDUGLI, A regularized equation for anisotropic motion-by-curvature, SIAM J. Appl. Math. 52, 1111-1119.
28. [1992] L. C. EVANS & J. SPRUCK, Motion of level sets by mean curvature II, Trans. AMS 330 321-332; III, J. Geom. Anal., 2, 121-150.
29. [1992] L. C. EVANS & J. SPRUCK, Motion of level sets by mean curvature II, Trans. AMS 330 321-332; III, J. Geom. Anal., 2, 121-150.
30. [1992] J. STEWART & N. GOLDENFELD, Spinodal decomposition of a crystal surface, Phys. Rev. A 46, 6505-6512.
31. [1992] J. E. TAYLOR, Mean curvature and weighted mean curvature, Acta Metall. 40, 1475-1485.
32. [1992] J. E. TAYLOR, J. W. CAHN & C. A. HANDWERKER, Geometric models of crystal growth I, Acta Metall. bf 40, 1443-1474.
33. [1993] F. ALMGREN, J. E. TAYLOR & L. WANG, Curvature driven flows: a variational approach, SIAM J. Control Opt. 31, 439-469.
34. [1993] G. BARLES, H. M. SONER & P. E. SOUGANIDIS, Front propagation and phase field theory, SIAM J. Control Optim. 31, 439-469.
35. [1993] M. E. GURTIN, Thermomechanics of evolving phase boundaries in the plane, Oxford University Press.
36. [1993] M. E. GURTIN & P. W. VOORHEES, The continuum mechanics of coherent two-phase elastic bodies with mass transport, Proc. R. Soc. Lond. A 440, 323-343.
37. [1993] H. M. SONER, Motion of a set by the curvature of its boundary, J. Diff. Eqts. 101, 313-3372.
38. [1993] B. J. SPENCER, P. W. VOORHEES & S. H. DAVIS, Morphological instability in epitaxially strained dislocation-free solid films: linear stability theory J. Appl. Phys., 73, 4955-4970.
39. [1994] S. B. ANGENENT & M. E. GURTIN, Anisotropic motion of a phase interface. Well-posedness of the initial value problem and qualitative properties of the interface, J. Reine Angew. Math. 446, 1-47.
40. [1995] M. E. GURTIN, The nature of configurational forces, Arch. Rational Mech. Anal. 131, 67-100.
41. [1996] M. E. GURTIN & P. W. VOORHEES, The thermodynamics of evolving interfaces far from equilibrium, Acta Mater 44, 235-247.
42. [1996] J. E. GUYER & P. W. VOORHEES, Morphological stability of alloy thin films, Phys. Rev. B 54, 11710-11724.
43. [1998] A. A. GOLOVIN, S. H. DAVIS & A. A. NEPOMNYASHCHY, A convective Cahn-Hilliard model for the formation of facets and corners in crystal growth, Physica D 122, 202-230.
44. [1998] M. E. GURTIN & P. W. VOORHEES, On the effects of elastic stress on the motion of fully faceted interfaces, Acta Mater. 46, 2103-2112.
45. [1998] J. E. GUYER & P. W. VOORHEES, Morphological stability and compositional uniformity of alloy thin films, J. Crystal Growth 187, 150-165.
46. [1999] E. FRIED & M. E. GURTIN, Coherent solid-state phase transitions with atomic diffusion: a thermo-mechanical treatment, J. Statist. Phys. 95, 1361-1427.
47. [1999] A. A. GOLOVIN, S. H. DAVIS & A. A. NEPOMNYASHCHY, Model for faceting in a kinetically controlled crystal growth, Phys. Rev. E 59, 803-825.
48. [1999] Y. W. ZHANG & A. P. BOWER, Numerical simulations of island formation in a coherent strained epitaxial thin film system, J. Mech. Phys. Solids 47, 2273-2297.
49. [2000] M. E. GURTIN, Configurational forces as basic concepts of continuum physics, Applied mathematical sciences, 137, Springer-Verlag.
50. [2000] B. J. SPENCER, P. W. VOORHEES & J. TERSOFF, Enhanced instability of strained alloy films due to compositional stresses, Phys. Rev. Letters 84, 2449-2452.
51. [2001] Y. W. ZHANG & A. F. BOWER, Three-dimensional analysis of shape transitions in strained heteroepitaxial islands, Appl. Phys. Letters 78, 2706-2708.