Three-dimensional crystal growth - II: Nonlinear simulation and control of the Mullins-Sekerka instability

Journal of Crystal Growth

Volumn 266, Issue 4, 2004, Pages 552-567

  Cristini, Vittorio ^a,b   Lowengrub, John ^b  

^a 200 Rockwell Engineering Center ^*  (United States)

^b UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

A1. 3D adaptive boundary integral methods; A1. Diffusion; A1. Shape control; A2. Growth from melt

Indexed keywords

COMPUTER SIMULATION; DIFFUSION; HEAT FLUX; MORPHOLOGY; PERTURBATION TECHNIQUES; SINGLE CRYSTALS; SURFACE TENSION;

3D ADAPTIVE BOUNDARY INTEGRAL METHODS; GROWTH FROM MELT; MULLINS-SKERKA INSTABILITY; SHAPE CONTROL;

CRYSTAL GROWTH;

EID: 2442446293     PISSN: 00220248     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jcrysgro.2004.02.115     Document Type: Article

References (30)

1. Cristini V., Lowengrub J. J. Crystal Growth. 240:2002;267.
2. Mullins W., Sekerka R. J. Appl. Phys. 34:1963;323.
3. Coriell S.R., Parker R.L. J. Appl. Phys. 36:1965;632.
4. Coriell S.R., Parker R.L. Peiser H.S. Crystal Growth. 1967;703 Pergamon Press, Oxford.
5. Brush L.N., Sekerka R.F. J. Crystal Growth. 96:1989;419.
6. Voorhees P.W. Ann. Rev. Mater. Sci. 22:1992;197.
7. Glicksman M.E., Smith R.N., Marsh S.P., Kuklinski R. Metter. Trans. A - Phys. Metter. Mat. Sci. 23:1992;659.
8. Glicksman M.E., Mizenko L.M., Rettenmayer M.E., Marsh S.P. Mater. Sci. Eng. A - Struct. Mater. Props. Microstruc. Process. 178:1994;137.
9. S. Marsh. Kinetics of diffusion-limited microstructural coarsening, Ph.D. Thesis, Rensselaer Polytechnic Institute, 1989; L. Meloro, Evolution of microstructures in tin-bismuth alloys, M.S. Thesis, Rensselaer Polytechnic Institute, 1988.
10. S. Marsh. Kinetics of diffusion-limited microstructural coarsening, Ph.D. Thesis, Rensselaer Polytechnic Institute, 1989; L. Meloro, Evolution of microstructures in tin-bismuth alloys, M.S. Thesis, Rensselaer Polytechnic Institute, 1988.
11. Li X., Lowengrub J.S., Nie Q., Cristini V., Leo P. Mett. Mater. Trans. A. 34A:2003;1421.
12. Thompson M., Voorhees P. Acta Mater. 47:1999;983.
13. Mueller R., Gross D. Comput. Mater. Sci. 11:1998;35.
14. Mueller R., Gross D. Comput. Mater. Sci. 16:1999;53.
15. Chen L.Q. Ann. Rev. Mater. Res. 32:2003;113.
16. Boettinger W.J., Warren J.A., Beckermann C., Karma A. Ann. Rev. Mater. Res. 32:2002;163.
17. Schmidt A. J. Comp. Phys. 125:1996;293.
18. Gibou F., Fedkiw R., Caflisch R., Osher S. SIAM J. Sci. Comput. 19:2003;183.
19. S. Li, J.S. Lowengrub, V. Cristini, P.H.Leo, J. Crystal Growth , in press.
20. Glicksman M.E., Schaefer R.J., Ayers J.D. Metal. Trans. A. 7A:1976;1749.
21. M.E. Glicksman, 2003, private communication; H. Singer, 2003, private communication.
22. M.E. Glicksman, 2003, private communication; H. Singer, 2003, private communication.
23. O.D. Kellogg, Foundations of Potential Theory, Springer, Berlin, 1929.
24. Zhu J., Chen X., Hou T.Y. J. Comp. Phys. 127:1996;246.
25. K.E. Atkinson, The Numerical Solution of Integral Equations of the Second Kind, Cambridge University Press, Cambridge, 1997.
26. Saad Y., Schultz M.R. SIAM J. Sci. Statist. Comput. 7:1986;856.
27. Zinchenko A.Z., Rother M.A., Davis R.H. Phys. Fluids. 9:1977;1493.
28. Cristini V., Blawzdziewcz J., Loewenberg M. Phys. Fluids. 10:1998;1781.
29. Cristini V., Blawzdziewcz J., Loewenberg M. J. Comp. Phys. 168:2001;445.
30. S. Li, Morphological control of crystal growth, Ph.D. Thesis, University of Minnesota, (degree expected 2005).