Theory of Crystal Growth Morphology

Crystal Growth - From Fundamentals to Technology

Volumn , Issue , 2004, Pages 55-93

  Sekerka, Robert F ^a  

^a CARNEGIE MELLON UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ANISOTROPY; CRYSTAL GROWTH; INTERFACE STATES; MORPHOLOGY; STABILITY;

CRYSTAL GROWTH MORPHOLOGY; CRYSTAL-MELT INTERFACE; CRYSTALLOGRAPHIC ANISOTROPY; FREE-BOUNDARY PROBLEMS; LINEAR STABILITY THEORY; MORPHOLOGICAL INSTABILITY; MORPHOLOGICAL STABILITY; THEORY OF CRYSTAL GROWTH;

GROWTH KINETICS;

EID: 84942316516     PISSN: None     EISSN: None     Source Type: Book    
DOI: 10.1016/B978-044451386-1/50005-2     Document Type: Chapter

References (100)

1. Jackson K.A., Uhlmann D.R., Hunt J.D. J. Crystal Growth 1967, 1:1.
2. Wulff G. Z. Krystallogr. 1901, 34:449.
3. Herring C. Surface Tension as a Motivation for Sintering. The physics of powder metallurgy 1951, 143. a symposium held at Bayside, L.I. New York, August 24-26, 1949, McGraw-Hill, New York. W.E. Kingston (Ed.).
4. Herring C. The Use of Classical Macroscopic Concepts in Surface-Energy Problems. Structure and properties of solid surfaces, a conference arranged by the National Research Council, Lake Geneva, WI, September 1952 1953, 5. U. Chicago Press, Chicago. R. Gomer, C.S. Smith (Eds.).
5. Hoffman D.W., Cahn J.W. Surface Science 1972, 31:368.
6. Cahn J.W., Hoffman D.W. Acta Met. 1974, 22:1205.
7. Mullins W.W. J. Math. Phys. 1962, 3:754.
8. Angenent S., Gurtin M.E. Archive for Rational Mechanics and Analysis 1989, 108:323.
9. Yokoyama E., Sekerka R.F. J. Crystal Growth 1992, 125:389.
10. Chernov A.A. Soviet Physics Crystallography 1964, 8:401.
11. Frank F.C. On the Kinematic Theory of Crystal Growth and Dissolution Processes. Growth and Perfection in Crystals 1958, 411. John Wiley & Sons Inc., New York. R.H. Doremus, B.W. Roberts, D. Turnbull (Eds.).
12. Sekerka R.F., Wang S-L Moving Phase Boundary Problems. Lectures on the Theory of Phase Transformations 2000, 231. TMS, Warrendale. second edition. H.I. Aaronson (Ed.).
13. R.F. Sekerka, Morphology: From Sharp Interface to Phase Field Models, in: Fifty Years of Progress in Crystal Growth, R. Feigelson (ed.), to be published by Elsevier.
14. Tiller W.A., Rutter J.W., Jackson K.A., Chalmers B. Acta Met. 1953, 1:428.
15. Mullins W.W., Sekerka R.F. J. Applied Physics 1963, 34:323.
16. Mullins W.W., Sekerka R.F. J. Applied Physics 1964, 35:444.
17. Sekerka R.F. Phase Interfaces: Morphological Stability. Encyclopedia of Materials Science & Engineering 1986, 3486. Pergamon, Oxford. M.B. Bever (Ed.).
18. Sekerka R.F. J. of Applied Physics 1965, 36:264.
19. Cahn J.W. Crystal Growth 1967, 681. Pergamon, Oxford. H.S. Peiser (Ed.).
20. Coriell S.R., Parker R.L. J. Applied Physics 1965, 36:632.
21. Coriell S.R., Hardy S.C. J. Research National Bureau of Standards 1969, 73A:65.
22. Sekerka R.F., Growth Melt Proceedings International School of Crystallography, 7th Course: Interfacial Aspects of Phase Transformation, Erice-Traponi, Sicily 1982, 489. D. Reidel Publishing Co., Dordrecht. B. Mutafschiev (Ed.).
23. Langer J.S., Müller-Krumbhaar H. J. Crystal Growth 1977, 42:11.
24. Langer J.S., Sekerka R.F., Fujioka T. J. Crystal Growth 1978, 44:414.
25. Barbieri A., Langer J.S. Phys. Rev. A 1989, 39:5314.
26. Ben Amar M., Pelcé P. Phys. Rev. A 1989, 39:4263.
27. Pomeau Y., Ben Amar M. Dendritic Growth and Related Topics. Solids Far From Equilibrium 1992, 365. Cambridge University Press, Cambridge. C. Godrèche (Ed.).
28. Coriell S.R., McFadden G.B. Morphological Stability. Handbook of Crystal Growth 1B, Transport and Stability 1993, 785. North-Holland, Amsterdam. D.T.J. Hurle (Ed.).
29. Wollkind D.J., Segel L.A. Proc. Roy. Soc. 1970, 268:351.
30. McFadden G.B., Coriell S.R. Physica 1984, 12D:253.
31. Ungar L.H., Brown R.A. Phys. Rev. 1985, B31:5931.
32. J.S. Langer, unpublished notes, August 1978.
33. Collins J.B., Levine H. Phys. Rev. 1985, B31:6119.
34. Langer J.S. Models of Pattern Formation in First-Order Phase Transitions. Directions in Condensed Matter Physics 1986, 165. World Scientific, Singapore. G. Grinstein, G. Mazenko (Eds.).
35. Cahn J.W., Hilliard J.E. J. Chem. Phys. 1958, 28:258.
36. Wang S-L., Sekerka R.F., Wheeler A.A., Murray B.T., Coriell S.R., Braun R.J., McFadden G.B. Physica 1993, D69:189.
37. McFadden G.B., Wheeler A.A., Anderson D.M. Physica 2000, D144:154.
38. Karma A., Rappel W.-J. Phys. Rev. 1996, E53:3017.
39. McFadden G.B., Wheeler A.A., Braun R.J., Coriell S.R., Sekerka R.F. Phys. Rev. 1993, E48:2016.
40. Wheeler A.A., McFadden G.B. Eur. J. Appl. Math. 1996, 7:367.
41. Wheeler A.A., McFadden G.B. Proc. Roy. Soc. London A 1997, 453:1611.
42. Sekerka R.F. Fundamentals of phase field theory. Advances in Crystal Growth Research 2001, 21. Elsevier, Amsterdam. K. Sato, Y. Furukawa, K. Nakajima (Eds.).
43. Wheeler A., Murray B., Glicksman M.E. J. Crystal Growth 1995, 154:386.
44. Coriell S.R., Sekerka R.F. J. Physico-Chem. Hydrodyn. 1981, 2:281.
45. Delves R.T. Theory of Interface Stability. Crystal Growth 1974, 40. Pergamon, Oxford. B. Pamplin (Ed.).
46. Coriell S.R., McFadden G.B., Boisvert R.F., Sekerka R.F. J. Crystal Growth 1984, 69:15.
47. Davis S.H. Effects of Flow on Morphological Stability. Handbook of Crystal Growth 1B, Transport and Stability 1993, 859. North-Holland, Amsterdam. D.T.J. Hurle (Ed.).
48. Coriell S.R., McFadden G.B., Sekerka R.F. J. Crystal Growth 1990, 100:459.
49. Coriell S.R., Sekerka R.F. J. Crystal Growth 1976, 34:157.
50. McFadden G.B., Coriell S.R., Sekerka R.F. J. Crystal Growth 1988, 91:180.
51. Uehara T., Sekerka R.F. J. Crystal Growth 2003, 254:251.
52. Debierre J-M., Karma A., Celestini F., Guérin R. Phys. Rev. 2003, E68:041604.
53. Coriell S.R., Sekerka R.F. Interface Stability During Rapid Solidification. Rapid Solidification Processing: Principles and Technologies 2 1980, 35. Claitor's, Baton Rouge. R. Mehrabian, B.H. Kear, M. Cohen (Eds.).
54. Coriell S.R., Sekerka R.F. J. Crystal Growth 1983, 61:499.
55. Wheeler A.A., Boettinger W.J., McFadden G.B. Phys. Rev. A 1992, 45:7424.
56. Wheeler A.A., Boettinger W.J. Towards a Phase Field Model for Phase Transitions in Binary Alloys. The IMA Volumes in Mathematics and Its Applications 1992, 43:127. Springer-Verlag, Berlin. M.E. Gurtin, G.B. McFadden (Eds.).
57. Wheeler A.A., Boettinger W.J., McFadden G.B. Phys. Rev. 1993, E47:1893.
58. Boettinger W.J., Wheeler A.A., Murray B.T., McFadden G.B., Kobayashi R. A phase-field, diffuse interface solidification model for pure metals and binary alloys. Modeling of Coarsening and Grain Growth 1993, 45. TMS, Warrendale. S.P. Marsh, C.S. Pande (Eds.).
59. Bi Z., Sekerka R.F. Physica 1998, A261:95.
60. Charach Ch., Fife P.C. SIAM J. Appl. Math. 1998, 58:1826.
61. Charach Ch., Fife P.C. Open Systems, Information Dynamics 1998, 5:99.
62. Warren J.A., Boettinger W.J. Acta Metall. Mater. 1995, 43:689.
63. Conti M. Phys. Rev. E 1997, 56:3197.
64. Warren J.A., Boettinger W.J. Prediction of dendritic microstructure patterns using a diffuse interface phase field model. Welding and Advanced Solidification Processes 1995, VII:601. TMS, Warrendale. M. Cross, J. Campbell (Eds.).
65. Warren J.A., Boettinger W.J. Numerical Simulation of Dendritic Alloy Solidification using a phase field model. Solidification Processing 1997 1997, 422. Department of Engineering Materials, University of Sheffeld, UK. J. Beach, H. Jones (Eds.).
66. Bi Z., Sekerka R.F. J. Crystal Growth 2002, 237:138.
67. Bi Z. Directional Solidification of a Binary Alloy Using the Phase Field Model. Doctoral Thesis 2001, Carnegie Mellon University, Pittsburgh.
68. George W., Warren J.A. Parallel 3D Dendritic Growth Simulator using the Phase-Field Method. J. Comp. Phys. 2002, 177:264.
69. Gurtin M.E., Polignone D., Viñals J. Math. Models Methods Appl. Sci. 1996, 6:815.
70. Anderson D.M., McFadden G.B. Phys. Fluids 1997, 9:1870.
71. Anderson D.M., McFadden G.B., Wheeler A.A. Ann. Rev. Fluid Mech. 1998, 30:139.
72. Anderson D.M., McFadden G.B., Wheeler A.A. Physica 2000, D135:175.
73. Sekerka R.F., Bi Z. Phase Field Model of Multicomponent Alloy with Hydrodynamics. Interfaces for the Twenty-First Century 2001, 147. Imperial College Press, London. M.K. Smith, M.J. Mixis, G.B. McFadden, G.P. Neitzel, D.R. Canright (Eds.).
74. Anderson D.M., McFadden G.B., Wheeler A.A. Physica 2001, D2711:1.
75. Anderson D.M., McFadden G.B., Wheeler A.A. A Phase-Field Model of Solidification with Convection: Numerical Simulations. Interfaces for the Twenty-First Century 2001, 131. Imperial College Press, London. M.K. Smith, M.J. Mixis, G.B. McFadden, G.P. Neitzel, D.R. Canright (Eds.).
76. Tönhardt R., Amberg G. J. Crystal Growth 1998, 194:406.
77. Tönhardt R., Amberg G. J. Crystal Growth 2000, 213:161.
78. Tönhardt R., Amberg G. Phys. Rev. 2000, E62:828.
79. Beckermann C., Diepers H.J., Steinbach I., Karma A., Tong X. J. Comp. Phys. 1999, 154:468.
80. Boettinger W.J., Warren J.A., Beckermann C., Karma A. Ann. Rev. Mater. Res. 2002, 32:163.
81. Braun R.A., Murray B.T. J. Crystal Growth 1997, 174:41.
82. Provatas N., Goldenfeld N., Dantzig J. J. Comput. Phys. 1999, 148:265.
83. Schmidt A. J. Comput. Phys. 1996, 125:293.
84. Provatas N., Goldenfeld N., Dantzig J. Phys. Rev. Letters 1998, 80:3308.
85. Jeong J-H, Goldenfeld N., Dantzig J.A. Phys. Rev. 2001, E64:41602.
86. Karma A., Plapp M. Phys. Rev. Letters 2000, 84:1740.
87. Karma A., Lee Y.H., Plapp M. Phys. Rev. 2000, E61:3996.
88. Boettinger W.J., Wheeler A.A., Murray B.T., McFadden G.B. Material Science and Engineering 1994, A178:217.
89. Conti M. Phys. Rev. 1997, E55:701.
90. Conti M. Phys. Rev. 1997, E55:765.
91. Ahmad N.A., Wheeler A.A., Boettinger W.J., McFadden G.B. Phys. Rev. 1998, E58:3436.
92. Charach Ch., Chen C.K., Fife P.C. J. Stat. Phys. 1999, 95:1141.
93. Charach Ch., Fife P.C. J. Crystal Growth 1999, 198/199:1267.
94. McFadden G.B., Wheeler A.A., Anderson D.M. Physica 2000, D144:154.
95. Karma A. Phys. Rev. Letters 2001, 87:115701.
96. B. Echebarria, R. Folch, A. Karma and M. Plapp, submitted to Phys. Rev. E.
97. Kobayashi R., Warren J.A., Carter W.C. Physics 2000, D140:141.
98. Kassner K., Misbah C., Müller J., Kappey J., Kohlert P. J. Crystal Growth 2001, 225:289.
99. Gránásy L., Börzsönyi T., Pusztai T. J. Crystal Growth 2002, 237-239:1813.
100. G. Amberg, A semi-sharp phase field method for quantitative phase change simulations, to appear in Phys. Rev. Letters.