A geometric model for coarsening during spiral-mode growth of thin films

Physica D: Nonlinear Phenomena

Volumn 132, Issue 4, 1999, Pages 520-542

  Schulze, T P ^a   Kohn, R V ^a  

^a NEW YORK UNIVERSITY   (United States)

Author keywords

Coarsening; Spiral growth; Thin films; YBCO

Indexed keywords

EID: 0039765174     PISSN: 01672789     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0167-2789(99)00108-6     Document Type: Article

References (33)

1. Chernov A.A. Formation of crystals in solutions. Cont. Phys. 30:1989;251-276.
2. Burton W.K., Cabrera N., Frank F.C. The growth of crystals and the equilibrium structure of their surfaces. Phil. Trans. R. Soc. London. 243A:1951;299-358.
3. Cabrera N., Levine M.M. On the dislocation theory of evaporation of crystals. Phil. Mag. 1:1956;450-458.
4. Müller-Krumbhaar H., Burkhardt T.W., Kroll D.M. Generalized kinetic equation for crystal growth. J. Cryst. Growth. 38:1977;13-22.
5. Swendsen R.H., Kortman P.J., Landau D.P., Müller-Krumbhaar H. Spiral growth of crystals: simulations on a stochastic model. J. Cryst. Growth. 35:1976;73-78.
6. Xiao R., Alexander J.I.D., Rosenberger F. Growth morphologies of crystal surfaces. Phys. Rev. A. 43:1991;2976-2992.
7. Aranson I.S., Bishop A.R., Daruka I., Vinokur V.M. Ginzburg-Landau theory of spiral surface growth. Phys. Rev. Lett. 80:1998;1770-1773.
8. Karma A., Plapp M. Spiral surface growth without desorption. Phys Rev. Lett. 81:1998;4444-4447.
9. c Superconducting Systems, Springer, New York, 1994, pp. 28-70.
10. 7-δ thin films J. Cryst. Growth. 172:1997;145-155.
11. Blank D.H.A., Bijlsma M.E., Moerman R., Rogalla H., Stork F.J.B., Roshko A. Surface roughness and height-height correlations dependence on thickness of YBaCuO thin films. J. Alloys Compounds. 251:1997;31-33.
12. M. Ortiz, E. Repetto, H. Si, A continuum model of kinetic roughening and coarsening in thin films, J. Mech. Phys. Solids (1998), submitted for publication.
13. Tang C., Alexander S., Bruinsma R. Scaling theory for the growth of amorphous films. Phys. Rev. Let. 64:1990;772-775.
14. Thijssen J.M., Knops H.J.F., Dammers A.J. Dynamic scaling in polycrystalline growth. Phys. Rev. B. 45:1992;8650-8656.
15. d Ann. Appl. Prob. 7:1997;200-228.
16. 7-x films Physica C. 202:1992;1-11.
17. Schlom D.G., Anselmetti D., Bednorz J.G., Gerber Ch., Mannhart J. Epitaxial growth of cuprate superconductors from the gas phase. J. Cryst. Growth. 137:1994;259-267.
18. Osher S., Sethian J.A. Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulation. J. Comp. Phys. 79:1988;12-49.
19. J.A. Sethian, Level Set Methods, Cambridge University Press, Cambridge, 1996.
20. F.C. Frank, On the kinematic theory of crystal growth and dissolution processes, in: R.H. Doremus (Ed.), Growth and Perfection of Crystals, Chapman & Hall, London, 1958, pp. 411-419.
21. J.W. Cahn, J.E. Taylor, C. Handwerker, Evolving crystal forms: Frank's characteristics revisited, in: R.G. Chambers, J.E. Enderby, A. Keller, A.R. Lang, J.W. Steeds (Eds.), Sir Charles Frank, OBE, FRS, An Eightieth Birthday Tribute, Hilger, New York, 1991, pp. 88-118.
22. L.C. Evans, Partial Differential Equations, American Mathematical Society, Providence, RI, 1998.
23. Fonseca I. The Wulff theorem revisited. Proc. R. Soc. London, Ser. A. 432:1991;125-145.
24. Soravia P. Generalized motion of a front propagating along its normal direction: a differential games approach. Nonlinear Anal., Theory, Methods & Applns. 22:1994;1247-1262.
25. Taylor J.E., Cahn J.W., Handwerker C.A. Geometric models of crystal growth. Acta Metall. Mater. 40:1992;1443-1474.
26. Zhao H.-K., Chan T., Merriman B., Osher S. A variational level set approach to multiphase motion. J. Comp. Phys. 127:1996;179-195.
27. Taylor J.E. The motion of multiple-phase junctions under prescribed phase-boundary velocities. J. Diff. Eqns. 119:1995;109-136.
28. J.E. Taylor, A variational approach to crystalline triple junction motion, J. Stat. Phys. (1999), in press.
29. Reitich F., Soner H.M. Three-phase boundary motions under constant velocities I: The vanishing viscosity method. Proc. R. Soc. Edinburgh. 126A:1996;837-865.
30. J. Moller, Lectures on random Voronoi tessellations, in: Lecture Notes in Statistics, vol. 87, Springer, New York, 1994.
31. J.F.C. Kingman, Poisson Processes, Oxford University Press, Oxford, 1993.
32. C.M. Bender, S.A. Orszag, Advanced Mathematical Methods for Scientists and Engineers, McGraw-Hill, New York, 1978.
33. Rodgers S.T., Jensen K.F. Multiscale modeling of chemical vapor deposition. J. Appl. Phys. 83:1998;524-530.