RAPID SOLIDIFICATION: FUNDAMENTALS AND MODELING

Annual Review of Heat Transfer

Volumn 11, Issue , 2000, Pages 207-305

  Wang, G X ^a   Prasad, V ^a  

^a NONE

Author keywords

[No Author keywords available]

Indexed keywords

GROWTH KINETICS; KINETICS; LASER HEATING; MELT SPINNING; MELTING; MICROSTRUCTURE; PULSED LASERS; THERMODYNAMICS;

ADVANCED MATERIALS PROCESSING; HIGH-ENERGY BEAMS; LASER MELTING; MELT ATOMIZATION; MICROSTRUCTURE FORMATION; PHASE SELECTION; PHYSICAL AND MECHANICAL PROPERTIES; PROCESSING TECHNIQUE; RESOLIDIFICATION; THERMAL SPRAY COATINGS;

RAPID SOLIDIFICATION;

EID: 85162890543     PISSN: 10490787     EISSN: 23750294     Source Type: Book Series    
DOI: 10.1615/AnnualRevHeatTransfer.v11.60     Document Type: Chapter

References (186)

1. W. Kurz and D. J. Fisher, Fundamentals ofSolidification, 3rd ed., Trans Tech, 1989.
2. P. Duwez, Metastable Phases Obtained by Rapid Quenching from the Liquid State, Prog. Solid State Chem., Vol. 3, pp. 377-406, 1966.
3. T. R. Anantharaman and C. Suryanarayana, Rapidly Solidified Metals, Trans Tech, 1987.
4. C. Suryanarayana, F. H. Froes, and R. G. Rowe, Rapid Solidification Processing of Titanium Alloys, Int. Mat. Rev., Vol. 36, pp. 85-123, 1991.
5. H. Jones, Splat Cooling and Metastable Phases, Rep. Prog. Phys., Vol. 36, pp. 1425-1497, 1973.
6. H. Jones, Rapid Solidification ofMetals and Alloys, Institute of Metallurgists, London, 1982.
7. T S. Srivatsan and T S. Sudarshan, Rapid Solidification Technology: An Engineering Guide, Technomic, Lancaster, PA, 1993.
8. L. A. Jacobson and J. McKittrick, Rapid Solidification Processing, Mat. Sei. Eng. R, Vol. R l l, pp. 355-408, 1994.
9. J. H. Perepezko and W. J. Boettinger, Kinetics of Resolidification, in L. E. Rehn, S. T. Picraux, and H. Wiedersich (eds.), Surface Alloying by Ion, Electron and Laser Beams, ASM, Metals Park, OH, pp. 51-90, 1987.
10. J. H. Perepezko and M. J. Uttormark, Nucleation-Controlled Solidification Kinetics, Metall. Mat. Trans. A, Vol. 27A, pp. 533-547, 1996.
11. M. J. Aziz, Interface Attachment Kinetics in Alloy Solidification, Metall. Mat. Trans. A, Vol. 27A, pp. 671-686, 1996.
12. J. H. Perepezko, Kinetic Processes in Undercooled Melts, Mat. Sci. Eng. A, Vol. A226-227, pp. 374-382, 1997.
13. R. Trivedi and W. Kurz, Dendritic Growth, Int. Mat. Rev., Vol. 39, pp. 49-74, 1994.
14. P. Gilgien, A. Zryd, and W. Kurz, Microstructure Selection Maps for Al-Fe Alloys, Acta. Metall. Mat., Vol. 43, pp. 3477-3487, 1995.
15. G.-X. Wang and E. F. Matthys, On the Heat Transfer at the Interface between a Solidifying Metal and a Solid Substrate, in E. F. Matthys and W. G. Truckncr (eds.), Melt-Spinning, Strip Casting, and Slab Casting, pp. 205-236, TMS, Warrendale, PA, 1996.
16. J. Fukai, Z. Zhao, D. Poulikakos, C. M. Megaridis, and O. Miyatake, Modeling of the Deformation of a Liquid Droplet Impinging on a Flat Surface, Phys. Fluids, Vol. 5, pp. 2588-2599, 1993.
17. H. Liu, E. J. Lavernia, and R. H. Rangel, Numerical Simulation of Substrate Impact and Freezing of Droplets in Plasma Spray Processes, J. Phys. D: Appi. Phys., Vol. 26, pp. 1900-1908, 1993.
18. G. Trapaga, E. F. Matthys, J. J. Valencia, and J. Szekely, Fluid Flow, Heat Transfer, and Solidification of Molten Metal Droplets Impinging on Substrates: Comparsion of Numerical and Experimental Results, Melali. Trans. B, Vol. 23B, pp. 701 -718, 1992.
19. G.-X. Wang and E. F. Matthys, An Improved Boundary-Layer Model for the Planar Flow Melt-Spinning Process, in E. F. Matthys and B. Kushner (eds.), Advanced Sensing, Modeling, and Control of Materials Processing, pp. 231-252, TMS, Warrendale, PA, 1992.
20. G.-X. Wang and E. F. Matthys, Modeling of Planar Flow Melt-Spinning with Undercooling, in E. F. Matthys (ed.), Melt-Spinning and Strip Casting: Research and Implementation, pp. 263-282, TMS, Warrendale, PA, 1992.
21. P. H. Steen and C. Karcher, Fluid Mechanics of Spin Casting of Metals, An. Rev. Fluid Mech., Vol. 29, pp. 373-397, 1997.
22. R. C. Ruhl, Cooling Rate in Splat Cooling, Mat. Sci. Eng., Vol. 1, pp. 313-320, 1967.
23. P. Shingu and R. Ozaki, Solidification Rate in Rapid Conduction Cooling, Metal. Trans. A, Vol. 6A, pp. 33-37, 1975.
24. C. G. Levi and R. Mehrabian, Heat Flow during Rapid Solidification of Undercooled Metal Droplets, Metall. Trans. A, Vol. 13A, pp. 221-234, 1982.
25. R. Mehrabian, Rapid Solidification, Int. Metals Rev., Vol. 27, pp. 185-208, 1982.
26. E. Gutierrez-Miravete, Mathematical Modeling of Rapid Solidification, in T. S. Srivatsan and T. S. Sudarshan (eds.), Rapid Solidification Technology: An Engineering Guide, pp. 3-70, 1993.
27. G.-X. Wang and V. Prasad, Non-equilibrium Phenomena in Rapid Solidification: Theoretical Treatment for Process Modeling, Microscale Thermophys. Eng., Vol. 1, pp. 143-157, 1997.
28. B. Feuerbacher, Phase Formation in Metastable Solidification of Metals, Mat. Sci. Rep. Vol. 4, pp. 1-40, 1989.
29. D. M. Herlach, Non-equilibrium Solidification of Undercooled Metallic Melts, Mat. Sci. Eng. R, Vol. R I 2, pp. ill-212, 1994.
30. Ludwig and W. Kurz, 1996, Direct Observation of Solidification Microstructures around Absolute Stability, Acta Mat., Vol. 44, pp. 3643-3654, 1996.
31. W. J. Boettinger, L. Bendersky, and J. G. Early, An Analysis of the Microstructure of Rapidly Solidified A l - 8 Wt Pet Fe Powder, Metall. Trans. A, Vol. 17 A, pp. 781-790, 1986.
32. C. G. Levi, V Jayaram, J. J. Valencia, and R. Mehrabian, Phase Selection in Electrohydrodynamic Atomization of Alumina, J. Mat. Res., Vol. .3, pp. 969-983, 1988.
33. R. F. Wood, Model for Nonequilibri urn Segregation during Pulsed Laser Annealing, Appi. Phys. Lett., Vol. 37, pp. 302-304, 1980.
34. P. S. Peercy, Measurement of Melt and Solidification Dynamics during Pulsed Laser Irradiation, in C. W. Draper and P. Mazzoldi (eds.), Laser Surface Treatment of Metals, Martimus Nijhoff, Dordrecht, pp. 611-637, 1986.
35. W. M. Steen, Laser Material Processing, 2nd ed., Springer, London, 1998.
36. M. von Allmen, Laser Quenching, in H. Beck and H.-J. (eds.) Glassy Metals 11, pp. 261-281, Guntherodt, Springer, Berlin, 1983.
37. C. W. Draper and J. M. Poatc, Laser Surface Alloying, Int. Metal Rev., Vol. 30, pp. 85-108, 1985.
38. M. D. Shirk and P. Molían, A Review of Ultrashort Pulsed Laser Ablation of Materials, J. Laser Appi., Vol. 10, pp. 18-28, 1998.
39. D. Kochan, Solid Freeform Manufacturing, Elsevier, Amsterdam, pp. 93-107, 1993.
40. S. Sampath and H. Herman, Rapid Solidification and Microstructure Development during Plasma Spraying, J. Thermal Spray Tech., Vol. 5, pp. 445-456, 1996.
41. H. H. Libermann, Rapidly Solidified Alloys by Chill Block Melt-Spinning Processes, J. Crystal Growth, Vol. 70, pp. 497-506, 1984.
42. S. N. Tewari and T. K. Glasgow, Cellular Microstructure of Chill Block Melt-Spun Ni-Mo Alloys, Metall. Trans. A, Vol. I8A, pp. 1663-1678, 1987.
43. M. G. Chu and D. A. Granger, Solidification and Microstructure Analysis of Rapidly Solidified Melt-Spun Al-Fe Alloys, Metall. Trans. A, Vol. 21A, pp. 205-212, 1990.
44. S. M. Lee, K. A. Q. O'Reilly, C. P. Hong, and B. Cantor, Effect of Process Parameters on Planar Flow Cast A l - C u Ribbons, Int. J. Cast Metals Res., Vol. 10, pp. 181 — 190, 1998.
45. R. Viskanta, Heat Transfer during Melting and Solidification of Metals, J. Heat Transfer, Vol. 110, pp. 1205-1219, 1988.
46. M. Rappaz, Modelling of Microstructure Formation in Solidification Processes, Int. Mat. Rev., Vol. 34, pp. 93-123, 1989.
47. V. R. Voller, C. R. Swaminathan, and B. G. Thomas, Fixed Grid Techniques for Phase Change Problems: A Review, Int. J. Num. Methods Eng., Vol. 30, pp. 875-898, 1990.
48. O. Adetutu and V. Prasad, Melting in a Cylindrical Cavity: Combined Effects of Curvature, Aspect Ratio, Buoyancy and Surface Tension Forces, Proc. 1st Int. Conf. Transport Phenomena in Processing, pp. 362-373, Technomac 1992.
49. O. Adetutu and V. Prasad, Melting in Rectangular and Cylindrical Cavities: Effect of Curvature, Aspect Ratio and Buoyancy Forces, Adv. Comput. Mat. Proc, HTD-Vol. 241, pp. 45-56, ASME, 1993.
50. C. Beckermann and C. Y. Wang, Multiphase/-Scale Modeling of Alloy Solidification, An. Rev. Heat Transfer, Vol. 6, pp. 115-198, 1995.
51. P. J. Prescott and F. P. Incropera, Convection Heat and Mass Transfer in Alloy Solidification, Heat Transfer, Vol. 28, pp. 231-337, 1996.
52. B. G. Thomas and C. Beckermann (eds.), Modeling of Casting, Welding and Advanced Solidification Processes—VIII, TMS, Warrendale, PA, 1998.
53. S. R. Coriell and R. F. Sekerka, Oscillation Morphological Instability to Non-equilibrium Segregation, J. Crystal Growth, Vol. 61, pp. 499-508, 1983.
54. J. Crank, Free and Moving Boundary Problems, Clarendon Press, Oxford, 1984.
55. T. W. Clyne, Numerical Treatment of Rapid Solidification, Metall. Trans. B, Vol. 15B, pp. 369-381, 1984.
56. R. F. Wood and G. A. Geist, Modeling of Non-equilibrium Melting and Solidification in Laser-Irradiated Materials, Phys. Rev. B, Vol. 34, pp. 2606-2620, 1986.
57. J. Madejski, Solidification of Droplets on a Cold Surface, Int. J. Heat Mass Transfer, Vol. 19, pp. 1009-1013, 1976.
58. H. Zhang, Theoretical Analysis of Spreading and Solidification of Molten Droplet during Thermal Spray Deposition, Int. J. Heat Mass Transfer, Vol. 42, pp. 2499-2508, 1999.
59. Y. P. Wan, H. Zhang, X. Y Jiang, S. Sampath, and V. Prasad, Role of Solidification, Substrate Temperature and Reynolds Number on Droplet Spreading in Thermal Spray Deposition: Measurements and Modeling, National Heat Transfer Conf, A l - buquerque, New Mexico, N H T C 99-121, 1999.
60. G.-X. Wang and E. F. Matthys, Numerical Modeling of Phase Change and Heat Transfer during Rapid Solidification Processes: Use of Control Volume Integral with Element Subdivision, Int. J. Heat Mass Transfer, Vol. 35, pp. 141-153, 1992.
61. S.-P. Wang, G.-X. Wang, and E. F. Matthys, Deposition of a Molten layer of High Melting Point Material: Substrate Melting and Resolidification, Mat. Sci. Eng., Vol. A262, pp. 25-32, 1999.
62. G.-X. Wang and E. F. Matthys, Interfacial Thermal Contact during Rapid Solidification on a Substrate, in Heat Transfer 1994, Proc. 10th Int. Heat Transfer Conf, Vol. 4, IChem Pub., UK, pp. 169-174, 1994.
63. G.-X. Wang and E. F. Matthys, Experimental Investigation of Interfacial Thermal Resistance for Molten Metal Solidification on a Substrate, J. Hetit Transfer, Vol. 118, pp. 157-163, 1996.
64. J. C. Baker and J. W. Cahn, Thermodynamics of Solidification, in Solidification, American Society for Metals, Metals Park, OH, pp. 23-58, 1971.
65. T. W. Clyne, Numerical Modeling of Directional Solidification of Metallic Alloys, Metal Science, Vol. 16, pp. 441-450, 1982.
66. L. Granasy and A. Ludwig, Impact of Casting Conditions on the Dendritic Solidification in Single Roller Quenching Methods (Simulation), in E. F. Matthys (ed.), Melt-Spinning ana Strip Casting: Research and Implementation, TMS, Warrendale, PA, pp. 53-68, 1992.
67. C. Y. Wang and C. Beckermann, A Unified Solute Diffusion Model for Columnar and Equiaxed Dendritic Alloy Solidification, Mat. Sci. Eng. A, Vol. A171, pp. 199-211, 1993.
68. S. G. Kim, S. H. Shin, T. Suzuki, and T. Umeda, Numerical Analysis of the Rapid Solidification of Gas-Atomized AI-8 wt pet Fe Droplets, Metall. Mat. Trans. A, Vol. 25A, pp. 2815-2826, 1994.
69. G.-X. Wang, S. Sampath, V. Prasad, and H. Herman, Modeling of Rapid Solidification during Splat Quenching, in S. P. Marsh et al. (eds.), Solidification 1998, pp. 485-496, TMS, Warrendale, PA 1998.
70. G.-X. Wang, V. Prasad, and E. F. Matthys, An Interface-Tracking Numerical Method for Rapid Planar Solidification of Binary Alloys with Application to Microsegregation, Mat. Sci. Eng. A, Vol. A225, pp. 47-58, 1997.
71. H. Zhang and V. Prasad, An Advanced Numerical Scheme for Materials Process Modeling, Computer Modeling and Simulation, Vol. 3, pp. 322-343, 1997.
72. D. A. Porter and K. E. Easterling, Phase Transformation in Metals and Alloys, Chapman and Hall, London, pp. 186-262, 1981.
73. M. Volmer and A. Weber, Z. Phys. Chem., Vol. 119, pp. 227-, 1926.
74. C. Becker and W. Döring, An. Phys., Vol. 24, pp. 719-, 1935.
75. D. Turnbull and J. C. Fisher, Rate of Nucleation in Condensed Systems, J. Chem. Phys., Vol. 17, pp. 71-73, 1949.
76. D. Turnbull, Under What Conditions Can a Glass Be Formed? Contemp. Phys., Vol. 10, pp. 473-488, 1969.
77. C. G. Levi, The Evolution of Microcrystalline Structures in Supercooled Metal Powders, Metall. Trans. A, Vol. I9A, pp. 699-708, 1988.
78. C. V. Thompson and F. Spaepen, Homogeneous Crystal Nucleation in Binary Metallic Melts, Acta Metall, Vol. 31, pp. 2021-2027, 1983.
79. F. Spaepen, A Structural Model for the Solid-Liquid Interface in Monalomie Systems, Acta Metall, Vol. 23, pp. 729-743, 1975.
80. F. Spaepen and R. B. Meyer, The Surface Tension in a Structural Model for the Solid-Liquid Interface, Script. Metall, Vol. 10, pp. 257-263, 1976.
81. X. Zhang, A General Model for the Calculation of Crystal Nucleation Kinetics in Binary Melts, Acta Mat., Vol. 46, pp. 1135-1141, 1998.
82. H. Fujino, T. Suzuki, and 1. Jimbo, A Numerical Model for Cooling Rate Dependence of the Degree of Undercooling during Rapid Solidification of 18Cr-8Ni Stainless Steel, ISU Int., Vol. 37, pp. 1107-1111, 1997.
83. K. F. Kelton, Crystal Nucleation in Liquids and Glasses, Solid State Phys., Vol. 45, pp. 75-177, 1991.
84. D. Kashchiev, Solution of the Non-Steady State Problem in Nucleation Kinetics, Surface Science, Vol. 14, pp. 209-220, 1969.
85. H. Reiss and J. L. Katz, Nucleation in Rapid Solidification, in R. Mehrabian, B. H. Kear, and M. Cohen (eds.), Rapid Solidification Processing, Principles and Technologies, pp. 64-77, Clator's Baton Rouge, L A, 1978.
86. H.-M. Lin, Y.-W. Kim, and T. F. Kelly, Solidification Structures in Submicron Spheres of Iron-Nickel: An Analytical Evaluation, Acta Metall., Vol. 36, pp. 2537-2550, 1988.
87. F. Spaepen, Homogeneous Nucleation and Temperature Dependence of the Crystal-Mell Interfacial Tension, Solid Stale Phys., Vol. 47, pp. 1-32, 1994.
88. L. Granasy, Diffuse Interface Theory of Nucleation, J. Non-crystalline Solids, Vol. 162, pp. 301-303, 1993.
89. L. Granasy, Nucleation Theory for Diffuse Interfaces, Mat. Sci. Eng. A, Vol. A178, pp. 121-124, 1994.
90. S. A. Moir and D. M. Herlach, Observation of Phase Selection from Dendrite Growth in Undercooled Fe-Ni-Cr Melts, Acta Mat., Vol. 45, pp. 2827-2837, 1997.
91. K. A. Jackson, Theory of Melt Growth, in R. Ueda and J. B. Mullin (eds.), Crystal Growth and Characterization, pp. 21-32, North-Holland, Amsterdam, 1975.
92. C. A. MacDonald, A. M. Malvezzi, and F. Spaepen, Picosecond Time-Resolved Measurements of Crystallization in Noble Metals, J. Appi. Phys., Vol. 65, pp. 129—136, 1989.
93. Turnbull, Metastable Structures in Metallurgy, Metall. Trans. H, Vol. I2B, pp. 217-230, 1981.
94. M. J. Aziz and W. J. Boettinger, On the Transition from Short-Range Diffusion-Limited to Collision-Limited Growth in Alloy Solidification, Acta Metall. Mat., Vol. 42, pp. 527-537, 1994.
95. M. D. Kluge and J. R. Ray, Velocity Versus Temperature Relation for Solidification and Melting of Silicon: A Molecular-dynamic Study, Phys. Rev. B, Vol. 39, pp. 1738-1746, 1989.
96. G.-X. Wang and E. F. Matthys, Modeling of Surface Melting and Resolidification for Pure Metals and Binary Alloys: Effect of Non-equilibrium Kinetics, J. Heat Transfer, Vol. 118, pp. 944-951, 1996.
97. M. J. Aziz and T. Kaplan, Continuous Growth Model for Interface Motion during Alloy Solidification, Acta Metall., Vol. 36, pp. 2335-2347, 1988.
98. W. J. Boettinger and S. R. Coriell, Microstructure Formation in Rapidly Solidified Alloys, in P. R. Sahm, H. Jones, and C. M. Adam (eds.), Science and Technology of the Undercooled Melt, pp. 81-109, Martinus Nijhoff, Dordrecht, 1986.
99. M. J. Aziz, Model for Solute Redistribution during Rapid Solidification, J. Appi. Phys., Vol. 53, pp. 1158-1168, 1982.
100. M. Carrard, M. Gremaud, M. Zimmermann and W. Kurz, About the Banded Structure in Rapidly Solidified Dendritic and Eutectic Alloys, Acta Metall. Mat., Vol. 40, pp. 983-996, 1992.
101. R. Trivedi and W. Kurz, Modeling of Solidification Microstructures in Concentrated Solutions and Intermetallic Systems, Metall. Trans. A, Vol. 21A, pp. 1311-1318, 1990.
102. V. Prasad, H. Zhang, and A. Anselmo, Transport Phenomena in Czochralski Crystal Growth Processes, Adv. Heal Transfer, Vol. 30, pp. 313-435, Academic Press, New York, 1997.
103. W. W. Mullins and R. F. Sekerka, Stability of a Planar Interface during Solidification of a Dilute Binary Alloy, J. Appi. Phys., Vol. 35, pp. 444 - 4 5 1, 1964.
104. R. Trivedi and W. Kurz, Morphological Stability of a Planar Interface under Rapid Solidification Conditions, Acta Metall., Vol. 34, pp. 1663-1670, 1986.
105. A. Ludwig, Limit of Absolute Stability for Crystal Growth into Undercooled Alloy Melts, Acta Metall. Mat., Vol. 39, pp. 2795-2798, 1991.
106. G.-X. Wang, S. Sampath, V. Prasad, and H. Herman, On the Stability of Rapid Solidification during Melt-Substrate Quenching, Mat. Sci. Eng. A, Vol. A226-228, pp. 1035-1038, 1997.
107. R. Billia and R. Trivedi, Pattern Formation in Crystal Growth, in Handbook of Crystal Growth, Vol. lb, pp. 900-1073, 1993.
108. M. E. Glicksman and S. P. Marsh, The Dendrite, in Handbook ofCrystal Growth, Vol. lb, pp. 1075-1122, 1993.
109. J. S. Langer, Instabilities and Pattern Formation in Crystal Growth, Rev. Modern Phys., Vol. 52, pp. 1-28, 1980.
110. J. Lipton, W. Kurz, and R. Trivedi, Rapid Dendritic Growth in Undercooled Alloys, Acta Metall., Vol. 35, pp. 957-964, 1987.
111. W. Kurz, B. Giovanola, and R. Trivedi, Theory of Microstructural Development during Rapid Solidification, Acta Metall., Vol. 34, pp. 823-830, 1986.
112. D. J. Thoma et al., Effects of Process Parameters on Melt-Spun Ag-Cu, Mat. Sci. Eng., Vol. 98, pp. 89-93, 1988.
113. S. C. Gill and W. Kurz, Rapidly Solidified Al-Cu Alloys—II. Calculation of the Microstructure Selection Map, Acta. Metall. Mat., Vol. 43, pp. 139-151, 1995.
114. W. Kurz and R. Trivedi, Banded Solidification Microstructure, Metall. Mat. Trans. A, Vol. 27A, pp. 625-634, 1996.
115. G. V. S. Sastry and C. Suryanarayana, Metastable Effects in Melt-Quenched Al-Pd Alloys, Mat. Sci. Eng., Vol. 47, pp. 193-208, 1981.
116. W. J. Boettinger, D. Shechtman, R. J. Schaefer, and F. S. Biancaiello, The Effect of Rapid Solidification Velocity on the Microstructure of Ag-Cu Alloys, Metall. Trans. A, Vol. 15A, pp. 55-66, 1984.
117. B. Caroli, C. Caroli, and B. Roulet, Interface Kinetics and Solidification of Alloys: A Discussion of Some Phenomenological Models, Acta Metall., Vol. 34, pp. 1867-1877, 1986.
118. G. J. Merchant and S. H. Davis, Morphological Instability in Rapid Directional Solidification, Acta Metall. Mat., Vol. 38, pp. 2683-2693, 1990.
119. A. Karma and A. Sarkissian, Interface Dynamics and Banding in Rapid Solidification, Phys. Rev. E, Vol. 47, pp. 513-533, 1993.
120. B. Jónsson, Modeling of Crystal Growth during Rapid Solidification, Metall. Trans. A, Vol. 22A, 2475-2485, 1991.
121. R. Trivedi, Interdendritic Spacing: Part I I. A Comparison of Theory and Experiment, Metall. Trans. A, Vol. 15A, pp. 977-982, 1984.
122. J. D. Hunt, Solidification and Casting ofMetals, Metals Society, Book 192, London, pp. 3-9, 1979.
123. D. Ma and P. R. Sahm, Primary Spacing in Directional Solidification, Metall. Mat. Trans. A, Vol. 29A, pp. 1113-1119, 1998.
124. J. D. Hunt and S. Z. Lu, Numerical Modeling of Cellular/Dendritic Array Growth: Spacing and Structure Predictions, Metall. Mat. Trans. A, Vol. 27A, pp. 611-623, 1996.
125. S. Z. L u, J. D. Hunt, P. Gilgien, and W. Kurz, Cellular and Dendritic Growth in Rapidly Solidified A l - F e and A l - C u Alloys, Acta Metall. Mat., Vol. 42, pp. 1653-1660, 1994.
126. S. Z. Lu and J. D. Hunt, Numerical Analysis of Dendritic and Cellular Array Growth: The Spacing Adjustment Mechanisms, J. Crystal Growth, Vol. 123, pp. 17-34, 1992.
127. T. P. Battle, Mathematical Modeling of Solute Segregation in Solidifying Materials, Int. Mat. Rev., Vol. 37, pp. 249-270, 1992.
128. E. Scheil, Bemerkunge Zur Schichtkristallbildung, Z. Metallkd., Vol. 34, pp. 70-, 1942.
129. T. Z. Kattamis, Redistribution of Solute in Highly Undercooled Iron-Nickel Alloy, Z. Metallkd., Vol. 61, pp. 856-860, 1970.
130. T. Z. Kattamis and R. Mehrabian, Undercooling during Atomization of VM300 Maraging Steel, J. Mat. Sci., Vol. 9, pp. 1040-1043, 1974.
131. S. D. Peteves, D. D. McDevitt, and G. J. Abbaschian, Solute Redistribution during Solidification of Supercooled Alloys, in R. Mehrabian (ed.), Rapid Solidification Processing: Principle and Technology III, NBS, pp. 129-134, 1983.
132. Munitz and G. J. Abbaschian, Effects of Supercooling on Solute Distribution and Microstructures, in E. W. Collings and C. C. Kock (eds.), UndercooledAlloy Phases, pp. 23-49, AIME, Metallurgical Society, 1986.
133. J. A. Sarreal and G. J. Abbaschian, The Effect of Solidification Rate on Microsegregation, Metall. Trans. A, Vol. I7A, pp. 2063-2073, 1986.
134. M. Solari and H. Buoni, Microsegregati on in Cellular and Cellular Dendritic Growth, J. Crystal Growth, Vol. 49, pp. 451-457, 1980.
135. Giovanola and W. Kurz, Modeling of Microsegregation under Rapid Solidification Conditions, Metall. Trans. A, Vol. 21 A, pp. 260-263, 1990.
136. M. H. Burden and J. D. Hunt, Cellular and Dendritic Growth I, J. Crystal Growth, Vol. 22, pp. 99-108, 1974.
137. L. A. Bendersky, and W. J. Boettinger, Cellular Microsegregation in Rapidly Solidified Ag-15 Wt% Cu Alloys, in Rapidly Quenched Metals, pp. 887-890, Würzburg, Germany, 1985.
138. J. F. McCarthy and N. W. Blake, A Front Tracking Model for the Rapid Solidification of Dendritic Alloys, Acta Mat., Vol. 44, pp. 2093-2100, 1996.
139. Wang et al. (unpublished work).
140. V. R. Voller and S. Sundarraj, Modeling of Microsegregation, Mat. Sci. Techn., Vol. 9, pp. 474-481, 1993.
141. T. Kraft, M. Rettenmayr, and H. E. Exner, An Extended Numerical Procedure for Predicting Microstructure and Microsegregation of Multicomonent Alloys, Modelling Simul. Mat. Sci. Eng., Vol. 4, pp. 161-177, 1996.
142. T. Kraft, A. Roosz, and M. Rettenmayr, Undercooling Effects in Microsegregation Modeling, Script. Mat., Vol. 35, pp. 77-82, 1996.
143. G.-X. Wang, V. Prasad, and E. F. Matthys, Solute Distribution during Rapid Solidification into an Undercooled Melt, J. Crystal Growth, Vol. 174, pp. 35-40, 1997.
144. G.-X. Wang, S. Sampath, V. Prasad, and H. Herman, A Mathematical Model for Microsegregation in Rapidly Solidified Alloys, in B. G. Thomas and C. Beckermann (eds.), Modeling Casting, Welding Advanced Solidification Processes—VIII, pp. 219-226, Warrendale, PA, TMS, 1998.
145. L. J. Masur and M. C. Flemings, 1982, Solute Redistribution in Rapidly Solidified A l - C u Alloys: Theory and Experiment, Proc. 4th Int. Conf. on Rapid Quenched Metals, pp. 1557-1560, Sendai, 1981.
146. H. D. Brody and M. C. Flemings, Solute Redistribution in Dendritic Solidification, Trans. AIME, Vol. 236, pp. 615-623, 1966.
147. D. E. Temkin, Kinetics of Growth of a Crystal Needle in a Supercooled Binary Melt, Soviet Phys.—Crystallography, Vol. 7, pp. 354-357, 1962.
148. C. G Levi and R. Mehrabian, Phase Selection and Solute Redistribution During Rapid Solidification Processing, in Rapid Solidification Processing: Principles and Technologies IV, R. Mehrabian and P. A. Parrish, pp. 26-64, Claitor's Publishing Division, 1986.
149. R. McPherson, Formation of Metastable Phases in Flame- and Plasma-Prepared Alumina, J. Mat. Sci., Vol. 8, pp. 851-858, 1973.
150. R. McPherson, The Relationship between the Mechanism of Formation, Microstructure and Properties of Plasma-Sprayed Coatings, Thin Solid Films, Vol. 83, pp. 297-310, 1981.
151. T. Volkmann, W. Löser, and D. M. Herlach, Nucleation and Phase Selection in Undercooled Fe-Cr-Ni Melts: Part I. Theoretical Analysis of Nucleation Behavior, Metall. Mat. Trans. A, Vol. 28A, pp. 453-460, 1997.
152. J. W. Cahn, W. B. Hillig, and G. W. Scars, The Molecular Mechanism of Solidification, Acto Metall, Vol. 12, pp. 1421-1439, 1964.
153. C. G. Levi, Thermal Considerations on the Recalescence of Alloy Powders, Metall. Trans. A, Vol. 19A, pp. 687-697, 1988.
154. O. Salas and C. G. Levi, Solute Redistribution and Interfacial Stability in Ultrafine Al-Fe-Ce Powders, Int. J. Rapid Solidification, Vol. 4, pp. 1-21, 1988.
155. C P. Grigoropoulos, Heat Transfer in Laser Processing of Thin Films, An. Rev. Heat Transfer, Vol. 5, pp. 77-130, 1994.
156. C. P. Grigoropoulos, T. D. Bennett, J.-R. Ho, X. Xu, and X. Zhang, Heat and Mass Transfer in Pulsed-Laser-lnduced Phase Transformations, Adv. Heat Transfer, Vol. 28, pp. 75-144, 1996.
157. A. Majumdar, 1997, Microscale Energy Tranmsport in Solids, in C. L. Tien, A. Majumdar, and F. M. Gemer (eds.), Microscale Energy Transport, pp. 3-94, Taylor and Francis, Washington, 1997.
158. C. L. Tien and G. Chen, Challenges in Microscale Conductive and Radiative Heat Transfer, J. Heat Transfer, Vol. 116, pp. 799-807, 1994.
159. S. C. Hsu, S. Chakravorty, and R. Mehrabian, Rapid Melting and Solidification of a Surface Layer, Metall. Trans. B, Vol. 9B, pp. 221-229, 1978.
160. S. C. Hsu, S. Kou, and R. Mehrabian, Rapid Melting and Solidification of a Surface due to a Stationary Heat Flux, Metall. Trans. B, Vol. I I B, pp. 29-38, 1980.
161. A. Sekhar, S. Kou, and R. Mehrabian, Heat Flow Model for Surface Melting and Solidification of an Alloy, Metall. Trans. A, Vol. 14A, pp. 1169-1177, 1983.
162. P. Baeri, S. U. Campisano, G. Foti, and E. Rimini, A Melting Mode! for Pulsed-Laser Annealing of Implanted Semiconductors, J. Appi. Phys., Vol. 50, p. 788, 1979.
163. X. Xu, C. P. Grigoropoulous, and R. E. Russo, Transient Temperature during Pulsed Excimer Laser Heating of Thin Polysilicon Films Obtained by Optical Reflectivity Measurement, J. Heat Transfer, Vol. 117, pp. 17-24, 1995.
164. X. Xu, C. P. Grigoropoulos, and R. E. Russo, Heat Transfer in Excimer Laser Melting of Thin Polysilicon Layers, J. Heat Transfer, Vol. 117, pp. 708-715, 1995.
165. +-Junction Formation in Silicon by Excimer Laser Doping: A Heat and Mass Transfer Perspective, Int. J. Heat Mass Transfer, Vol. 39, pp. 3835-3844, 1996.
166. A. Kar and J. Mazumder, One-dimensional Diffusion Model for Extended Solid Solution in Laser Cladding, J. Appi. Phys., Vol. 61, pp. 2645-2655, 1987.
167. A. Vardelle, C. Robert, G.-X. Wang, and S. Sampath, Analysis of Nucleation, Phase Selection and Rapid Solidification of an Alumina Splat, in C. C. Brendt (ed.), Thermal Spray: A United Forum for Scientific and Technological Advances, pp. 635-643, ASM Int., Materials Park, OH, 1997.
168. st Century, Prot: 15th Int. Thermal Spray Confi, Nice, France, pp. 407-412, 1998.
169. G.-X. Wang and E. F. Matthys, Modeling of Heat Transfer and Solidification during Splat Cooling: Effect of Splat Thickness and Splat/Substrate Thermal Contact, Int. J. Rapid Solidification, Vol. 6, pp. 141-174, 1991.
170. G.-X. Wang and E. F. Matthys, Heat Transfer Modeling of Rapid Solidification on a Substrate: A Parametric Investigation for Large Undercooling, int. J. Rapid Solidification, Vol. 6, pp. 297-324, 1991.
171. X. Zhang and A. Atrens, A Thermokinetic Model for Rapid Solidification, Int. J. Rapid Solidification, Vol. 7, pp. 83-107, 1992.
172. N. H. Pryds and J. H. Hattel, Numerical Modeling of Rapid Solidification, Model. Simula. Mat. Sci. Eng., Vol. 5, pp. 451-472, 1997.
173. C. Yao, G. - X. Wang, and B. T. F. Chung, A Non-equilibrium Solidification Model for Semitransparent Materials, A I A A J. Thcrmophysics Heat Transfer, 2000 (in press).
174. P. V. Evans and A. L. Greer, Modelling of Crystal Growth and Solute Redistribution during Rapid Solidification, Mat. Sci. Eng., Vol. 98, pp. 357-361, 1988.
175. G.-X. Wang and E. F. Matthys, Modeling of Rapid Planar Solidification of a Binary Alloy, in Heat Mass Transfer Mat. Proc. Manufi, Vol. 261, ASME, pp. 35-44, 1993.
176. S. C. Flood and J. D. Hunt, Columnar and Equiaxed Growth I. A Model of a Columnar Front with a Temperature Dependent Velocity, /. Crystal Growth, Vol. 82, pp. 543-551, 1987.
177. W. Kurz and R. Trivedi, Eutectic Growth under Rapid Solidification Conditions, Metall. Trans. A, Vol. 22A, pp. 3051-3057, 1991.
178. 2Cu Eutectic: The Coupled Zone, Acta Metall. Mat., Vol. 40, pp. 2895-2906, 1992.
179. S. C. Flood and J. D. Hunt, Columnar and Equiaxed Growth I I. Equiaxed Growth ahead of a Columnar Front, J. Crystal Growth, Vol. 82, pp. 552-560, 1987.
180. M. Gaumann, R. Trivedi, and W. Kurz, Nucleation Ahead of the Advancing Interface in Directional Solidification, Mat. Sci. Eng. A, Vol. A226-228, pp. 763-769, 1997.
181. H. W. Kerr and W. Kurz, Solidification of Peritectic Alloys, Int. Mat. Rev., Vol. 41, pp. 129-164, 1996.
182. M. C. Schneider, J. P. Gu, C. Beckermann, W. J. Boettinger, and U. R. Kattner, Modeling of Micro- and Macrosegregation and Freckle Formation in Single-Crystal Nickel-Base Superalloy Directional Solidification, Metall. Mat. Trans. A, Vol. 28A, pp. 1517-1531, 1997.
183. S. G. R. Brown and J. A. Spittle, Computer Simulation of Grain Growth and Macrostructure Development during Solidification, Mat. Sei. Technol., Vol. 5, pp. 362-368, 1989.
184. Ch.-A. Gandin and M. Rappaz, 1994, A Coupled Finite Element-Cellular Automation Model for the Prediction of Dendritic Grain Structures in Solidification Processes, Acta Metall. Mat., Vol. 42, pp. 2233-2246, 1994.
185. Y. H. Chang, S. M. Lee, K. Y. Lee, and C. P. Hong, Three-Dimensional Simulation of Dendritic Grain Structures of Gas-Atomized Al-Cu Alloy Droplets, ISIJ Int., Vol. 38, pp. 63-70.
186. K. Y. Lee and C. P. Hong, Stochastic Modeling of Solidification Grain Structures of Al-Cu Crystalline Ribbons in Planar Flow Casting, ISIJ Int., Vol. 37, pp. 38-46, 1997.