Level-set method for the evolution of faceted crystals

SIAM Journal on Scientific Computing

Volumn 21, Issue 6, 2000, Pages 2073-2095

  Russo, Giovanni ^a   Smereka, Peter ^b  

^a UNIVERSITY OF L'AQUILA   (Italy)

^b UNIVERSITY OF MICHIGAN   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

FACET EVOLUTION; LEGENDRE TRANSFORMATION; LEVEL SET METHOD;

BOUNDARY CONDITIONS; CRYSTAL ORIENTATION; INTERFACES (MATERIALS); MATHEMATICAL TRANSFORMATIONS; PARAMETER ESTIMATION; PARTIAL DIFFERENTIAL EQUATIONS; POLYCRYSTALS; SINGLE CRYSTALS;

SET THEORY;

EID: 0034497398     PISSN: 10648275     EISSN: None     Source Type: Journal    
DOI: 10.1137/S1064827599351921     Document Type: Article

References (26)

1. A. VAN DER DRIFT, Evolutionary selection, a principle governing growth orientation in vapourdeposited layers, Philips Research Reports, 22 (1967), p. 267.
2. D. J. PARITOSH, D. J. SROLOVITZ, C. C. BATTAILE, X. LI, AND J.E. BUTLER, Simulation of faceted film growth in 2D: Microstructure, morphology and texture, Acta Materialia, 47 (1999), pp. 2269-2281.
3. A. J. DAMMERS AND S. RADELAAR, 2-dimensional computer modeling of polycrystalline film growth, Texture Microstruct., 14 (1991), pp. 757-762.
4. J. E. TAYLOR, Constructions and conjectures in crystalline nondifferential geometry, in Differential Geometry, A Symposium in Honor of Manfredo do Carmo, B. Lawson and K. Tenenblat, eds., Longman, Essex, 1991, pp. 321-336.
5. J. E. TAYLOR Motion of curves by crystalline curvature, including triple junctions and boundary points, Proc. Sympos. Pure Math., 54 (1993), pp. 417-439.
6. J. E. TAYLOR, J. CAHN, AND C. A. HANDWERKER, Geometrical models of crystal growth, Acta Metallurgy Materialia, 40 (1992), pp. 1443-1474.
7. J. CAHN, J. E. TAYLOR, AND C. A. HANDWERKER, Evolving crystal forms: Frank's characteristics, revisited, in Sir Charles Prank OBC, FRS: An Eightieth Birthday Tribute, R. G. Chambers et al., eds., Adam Hilger, Bristol, UK, 1991, pp. 88-118.
8. A. HARTEN, The artificial compression method for computation of shocks and contact discontinuities. I. Single conservation laws, Comm. Pure Appl. Math., 30 (1977), pp. 611-638.
9. G. B. MCFADDEN, A. A. WHEELER, R. BRAUN, S. R. CORIEL, AND R. F. SEKERKA, Phase-field models for anisotropic interfaces, Phys. Rev. E, 48 (1993), pp. 2016-2024.
10. F. C. FRANK, On the kinematic theory of crystal growth and dissolution processes. Growth and perfection of crystals, in Growth and Perfection of Crystals, R.H. Doremus, B.W. Roberts, and D. Turnbull, eds., John Wiley, New York, 1958.
11. R. GOGLIONE AND M. PAOLINI, Numerical Simulation of Crystalline Motion by Mean Curvature with Allen-Cahn Relaxation, work in progress.
12. A. N. KOLMOGOROV, To the "geometrical selection" of crystals, Dokl. Acad. Nauk. USSR, 65 (1940), pp. 681-684.
13. S. OSHER AND B. MERRIMAN, The Wulff shape as the asymptotic limit of a growing crystalline interface, Asian J. Math., 1 (1997), pp. 560-571.
14. D. PENG, S. OSHER, B. MERRIMAN, AND H. ZHAO, The Geometry of Wulff Crystal Shapes and its Relations with Riemann Problems, UCLA CAM Report 98-51, 1998.
15. B. MERRIMAN, J. BENCE, AND S. OSHER, Motion of multiple junctions: A level set approach, J. Comput. Phys., 112 (1994), pp. 334-363.
16. S. OSHER AND J. SETHIAN, Fronts propagating with curvature-dependent speed: Algorithms based on Hamilton-Jacobi formulation, J. Comput. Phys., 79 (1988), pp. 12-49.
17. E. ROUY AND A. TOURIN, A viscosity solutions approach to shape-from-shading, SIAM J. Numer. Anal., 29 (1992), pp. 867-884.
18. J. A. SETHIAN, A review of the theory, algorithms, and applications of level set methods for propagating interfaces, in Acta Numerica, Cambridge University Press, Cambridge, UK, 1996.
19. R. KOBAYASHI, J. A. WARREN, AND W. C. CARTER, Vector-valued phase field model for crystallization and grain boundary formation, Phys. D, 119 (1998), pp. 415-423.
20. L. Q. CHEN AND W. YANG, Computer simulation of the domain dynamics of a quenched system with large number of nonconserved order parameters: The grain growth kinetics, Phys. Rev. B, 50 (1994), pp. 15752-15756.
21. P. SORAVIA, Generalized motion of a front propagating along its normal direction: A differential games approach, Nonlinear Anal., 22 (1994), pp. 1247-1262.
22. J. E. TAYLOR AND J. W. CAHN, Diffuse interfaces with sharp corners and facets: Phase field models with strongly anisotropic surfaces, Phys. D, 112 (1998), pp. 381-411.
23. J. E. TAYLOR, AND J.W. CAHN, Linking anisotropic sharp and diffuse surface motion laws via gradient flows, J. Statist. Phys., 77 (1994), pp. 183-197.
24. J. M. THIJSSEN, H. J. F. KNOPS, AND A. DAMMERS, Dynamic scaling in polycrystalline growth, Phys. Rev. B, 45 (1992), pp. 8650-8656.
25. J. S. WETTLAUFER, M. JACKSON, AND M. ELBAUM, A geometric model for anisotropic crystal growth, J. Phys. A, 27 (1994), pp. 5957-5967.
26. G. WULFF, Frage der Geshwindigkeit des Wachstums und der Anflosung der Kristallflachen, Z. Krystall. Min, 34 (1901), pp. 449-530.