Principles of solidification: An introduction to modern casting and crystal growth concepts

Principles of Solidification: An Introduction to Modern Casting and Crystal Growth Concepts

Volumn , Issue , 2011, Pages 1-520

  Glicksman, Martin Eden ^a  

^a University of Florida   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 84892328893     PISSN: None     EISSN: None     Source Type: Book    
DOI: 10.1007/978-1-4419-7344-3     Document Type: Book

References (417)

1. E. Broda, Ludwig Boltzmann, Man ?Physicist ?Philosopher, Ox Bow Press, Woodbridge, CT, 1983, p. 102.
2. B. Chalmers, Principles of Solidification, Wiley, New York, NY, 1964.
3. M.E. Glicksman, Diffusion in Solids: Field Theory, Solid-State Principles and Applications, Wiley Interscience Publishers, New York, NY, 2000.
4. M. Che, W. Grellmann and S. Seidler, Appl. Polym. Sci., 64 (1997) 1079.
5. G.R. Luckhurst and E.T. Samulski, Liq. Cryst., 1 (1986) 1.
6. F.C. Frank, Proc. R. Soc. Lond., 215A (1952) 43.
7. D. Turnbull, J. Chem. Phys., 20 (1952) 411.
8. B.E. Warren, X-Ray Diffraction, Dover Publications, Inc., New York, NY, 1990.
9. F. Zernicke and J.A. Prins, Z. Physik, 41 (1927) 184.
10. L.P. Tarasov and B.E. Warren, J. Chem. Phys., 4 (1936) 236.
11. M. Ishitobi and J. Chihara, J. Phys. Condens. Matter, 4 (1992) 3679.
12. T. Morishita, Phys. Rev. Lett., 87 (2001) 105701-1.
13. H.S.M. Coxeter, Ill. J. Math., 2 (1958) 726.
14. J.D. Bernal, Nature, 185 (1960) 68.
15. J.D. Bernal, Proc. R. Soc. Lond., 280A (1964) 43.
16. G.D. Scott, Nature, 188 (1960) 908.
17. M.F. Ashby, F. Spaepen and S. Williams, Acta Metall., 78 (1978) 1647.
18. J.L. Finney, Proc. R. Soc. Lond., 319A (1970) 497.
19. R.D. Kamien and A.J. Liu, Phys. Rev. Lett. 99 155501.
20. G.S. Cargill III, Solid State Phys., F. Seitz and D. Turnbull, Eds., 30, Academic Press, New York, 1975, 227.
21. T. Ichikawa, Phys. Stat. Solidi, A19 (1973) 707.
22. C.H. Bennett, J. Appl. Phys. 43 (1972) 2727.
23. J.L. Finney, Mater Sci. Eng., 23 (1976) 199.
24. D.R. Nelson, Phys. Rev., B28 (1983) 5515.
25. D.R. Nelson and F. Spaepen, Solid State Phys., 42, Academic Press, New York, 1989, p. 1.
26. Y. Kajihara et al., J. Non-Cryst. Solids, 312-314 (2002) 489.
27. F.A. Lindemann, Physik. Z., 11 (1910) 609.
28. M. Rettenmayr, Int. Mater. Rev., 54 (2009) 1.
29. J.H. Hildebrand, J. Chem. Phys., 15 (1947) 225.
30. J. Huggins, J. Phys. Chem., 52 (1948) 248.
31. M.H. Cohen and D. Turnbull, J. Chem. Phys., 31 (1959) 1164.
32. P. Ramachandrarao, B. Cantor and R.W. Cahn, J. Mater. Sci., 12 (1977) 2488.
33. D. Tabor, Gases, Liquids, and Solids, and Other States of Matter, 3rd Ed., Cambridge University Press, Cambridge, UK, 1991.
34. J. Frenkel, Kinetic Theory of Liquids, Dover Publications, Inc., New York, NY, 1955, p. 176.
35. T. Altar, J. Chem. Phys., 5 (1941) 577.
36. R. Fürth, Proc. Camb. Phil. Soc., 37 (1941) 252.
37. F.C. Auluck and D.S. Kothari, Nature, 3895 (1944) 777.
38. S. Glasstone, K.J. Laidler and H. Eyring, Theory of Rate Processes, McGraw-Hill, New York, NY, 1941, 477.
39. N. Hirai and H. Eyring, J. Appl. Phys., 29 (1958) 810.
40. W.J. Moore, Physical Chemistry, 2nd Ed., Prentice-Hall, Inc., Englewood Cliffs, NJ, 1955.
41. H.B. Callen, Thermodynamics and an Introduction to Thermostatics, 2nd Ed., Wiley, New York, NY, 1985.
42. R.T. DeHoff, Thermodynamics in Materials Science, Chap. 3, McGraw-Hill, Inc. New York, NY, 1993.
43. M. Stier and M. Rettenmayr, J. Cryst. Growth, 311 (2008) 137.
44. P.W. Bridgman, Physics of High Pressure, Bell, London, 1949.
45. 'Undercooled metallic melts: properties, solidification and metastable phases', Proceedings of the NATO Advanced Research Workshop, D.M. Herlach, I. Egry, P. Baeri and F. Spaepen, Eds., II Ciocco, Italy, 1993.
46. J.T. Fourkas et al., Supercooled Liquids, ACS Symposium Series 676, American Chemical Society, Washington, DC, 1997.
47. Schmelze, Erstarrung und Grenzflächen, I. Egry, P.R. Sahm and T. Volkmann, Eds., Vieweg Verlag, Braunschweig, 1999.
48. L. Backerud, C. Guocai and J. Tamminen, Solidification Characteristics of Aluminium Alloys, 2, American Foundry Society, Des Plaines, IL, 1990.
49. Solidification Science and Processing, I. Ohnaka and D.M. Stefanescu Eds., TMS,Warrendale, PA, 1996.
50. Crystal Growth, C.H.L. Goodman, Ed., 1, Plenum Press, New York, NY, 1978.
51. Crystal Growth, C.H.L. Goodman, Ed., 2, Plenum Press, New York, NY, 1978.
52. Y. Yamada, J. Mater. Res., 10 (1995) 1601.
53. N.B. Singh et al., J. Cryst. Growth, 250 (2003) 107.
54. W. Kurz and D.J. Fisher, Fundamentals of Solidification, Chap. 1, 3rd Ed., Trans Tech Publications, Aedermannsdorf, 1989.
55. M. Rettenmayr, Int. Mater. Rev., 54 (2009) 1.
56. W. Kurz and D.J. Fisher, Fundamentals of Solidification, Hemisphere Press, Aedermannsdorf, 1980.
57. J. Fourier, Bull. des Sci., (1808) 112.
58. A. Bejan, Convection Heat Transfer, Wiley, New York, NY (1984).
59. D.P. DeWitt and G.D. Nutter, Theory and Practice of Radiation Thermometry, Wiley, New York, NY (1988).
60. D.R. Poirier and E.J. Poirier, Heat Transfer Fundamentals for Metal Casting, 2nd Ed., The Minerals Metals & Materials Society, Warrendale, PA, 1994, 9.
61. A.G. Ostrogorsky and B.B. Mikic, Heat Mass Transfer, DOI 10.1007/s00231-008-0438-9, Springer, New York, NY, 2008.
62. V. Alexiades and A.D. Solomon, Mathematical Modeling of Melting and Freezing Processes, Chap. 3, Hemisphere Publishing Corporation, Washington, DC, 1993.
63. Moving Boundary Problems, D.G. Wilson, A.D. Solomon and P.T. Boggs, Eds., Academic Press, New York, NY, 1978.
64. V.J. Lunardini, Heat Transfer with Freezing and Thawing, Elsevier, Amsterdam, 1991.
65. D. Poulikakos, Conduction Heat Transfer, Chaps. 9 and 10, Prentice Hall, Englewood Cliffs, NJ, 1994.
66. H.S. Carslaw and J.C. Jaeger, Conduction of Heat in Solids, 2nd Ed., Clarendon Press, Oxford, 1984.
67. J. Crank, Free and Moving Boundary Problems, Clarendon Press, Oxford, 1984.
68. M.E. Glicksman, Diffusion in Solids: Field Theory, Solid-State from an and Applications, Wiley Interscience Publishers, New York, NY, 2000.
69. G.H. Geiger and D.R. Poirier, Transport Phenomena in Metallurgy, Addison-Wesley, Reading, MA, 1973.
70. F.P. Incropera and D.P. DeWitt, Fundamentals of Heat and Mass Transfer, 3rd Ed., Wiley, New York, NY, 1990.
71. S. Kou, Transport Phenomena and Materials Processing, Wiley, New York, NY, 1996.
72. D.R. Poirier and E.J. Poirier, Heat Transfer Fundamentals for Metal Casting, 2nd Ed., The Minerals Metals & Materials Society, Warrendale, PA, 1994, 9.
73. H.W.B. Roozeboom, Z. Phys. Chem., 30 (1899) 385.
74. J.N. Lalena and D.A. Cleary, Phase Equilibria, Phase Diagrams, and Phase Modeling, Wiley, New York, NY (2005) 335.
75. R.T. DeHoff, Thermodynamics in Materials Science, Chap. 3, McGraw-Hill, Inc. New York, NY, 1993.
76. Diffusion in Materials: Part 1, H. Mehrer et al., Eds., Scitec Publications Ltd., Zürich-Ütikon, 1997, p. 185.
77. Diffusion in Materials: Part 2, H. Mehrer et al., Eds., Scitec Publications Ltd., Zürich-Ütikon, 1997, p. 1265.
78. E. Scheil, Z. Metall., 34 (1942) 70.
79. M.E. Glicksman and R.N. Hills, Philos. Mag. A, 81 (2001) 153.
80. G.H. Gulliver, J. Inst. Metals, 9 (1913) 120.
81. E. Scheuer, Z. Metall., 23 (1931) 237.
82. G.H. Gulliver, Metallic Alloys: Their Structure and Constitution, 4th Ed., Charles Griffin & Company Ltd., London, 1921, p. 397.
83. M.E. Glicksman, Diffusion in Solids: Field Theory, Solid-State from an and Applications, Wiley Interscience Publishers, New York, NY, 2000.
84. H.D. Brody and M.C. Flemings, Trans. Metall. Soc. AIME, 236 (1966) 615.
85. M.C. Flemings, Solidification Processing, McGraw-Hill, New York, NY, 1974.
86. T.W. Clyne and W. Kurz, Metall. Trans. A, 12A, (1981) 965.
87. I. Onaka, Trans. ISIJ, 26 (1986) 1045.
88. V.R. Voller, Modeling of Casting, Welding, and Advanced Solidification Processes VIII, B.G. Thomas and C. Beckermann, Eds., The Minerals Metals & Materials Society,Warrendale, PA, 1986, p. 265.
89. V.R. Voller and S. Sundarraj, Int. J. Heat Mass Transf., 38 (1995) 1009.
90. L.W. Davies, Trans. AIME, 215 (1959) 672.
91. W.G. Pfann, Trans. AIME, 194 (1952) 747-753.
92. I. Braun and S. Marshall, Br. J. Appl. Phys., 8 (1957), 157.
93. W.G. Pfann, Zone Refining, 2nd Ed.,Wiley Series on the Science and Technology of Materials, Wiley, New York, NY (1958, 1966) p. 38.
94. L. Burris, Jr., C.H. Stockman and I.G. Dillon, Trans. AIME, 203 (1955) 1017.
95. J.A. Spim, Jr., M.J.S. Bernadou and A. Garcia, J. Alloy Compd., 298 (2000) 299.
96. K. Ghosh, V.N. Mani and S. Dhar, J. Cryst. Growth, 312 (2009) 1521.
97. N. Cheung, R. Bertazzoli and A. Garcia, J. Cryst. Growth, 310 (2008) 1274.
98. W.G. Pfann, US Patents 2,739,088 and 2,739,045 (1956).
99. H.C. Theurer, US Patent 3,060,123 (1962).
100. N.W. Lord, Trans. AIME, 197 (1953) 1531.
101. M.E. Glicksman et al., J. Cryst. Growth, 89 (1988) 101.
102. M.E. Glicksman, Diffusion in Solids: Field Theory, Solid-State from an and Applications, Wiley Interscience Publishers, New York, NY, 2000.
103. B. Chalmers, Principles of Solidification, 133, Wiley, New York, NY, 1964.
104. W.A. Tiller, K.A. Jackson, J.W. Rutter and B. Chalmers, Acta Metall., 1 (1953) 428.
105. V.G. Smith, W.A. Tiller and J.W. Rutter, Can. J. Phys., 33 (1955) 723.
106. W. Tiller, Liquid Metals and Solidification, ASM, Cleveland, OH, 1958, p. 276.
107. J.D. Verhoeven,W.N. Gill, J.A. Puszynski and R.M. Gindé, J. Cryst. Growth, 89 (1988) 189.
108. A.N. Kolmogorov, Izv. Akad. Nauk SSSR Ser. Fiz., VI, No. 1-2, (1942) 56.
109. L. Prandtl, Uber ein neues Formelsystem für die ausgebildete Turbulenz, Nachrichten Akad. Wiss. Göttingen, 1945.
110. A. Bejan, Convection Heat Transfer, Wiley Interscience Publication, Wiley, New York, NY, 1984, p. 271.
111. S. Kou, Transport Phenomena and Materials Processing, Chap. 3, Wiley, New York, NY, 1996.
112. D.R. Poirier and G.H. Geiger, Transport Phenomena in Materials Processing, Chap. 8, TMS, Minerals, Metals Materials Society, Warrendale, PA, 1994.
113. M.E. Glicksman and S-C. Huang, Adv. Space Res., 1 (1981) 25.
114. M.E. Glicksman, S.R. Coriell and G.B. McFadden, Ann. Rev. Fluid Mech., 18 (1986) 307.
115. M.E. Glicksman, 'Solidification research in microgravity', ASM Handbook 15, Casting, ASM International, Metals Park, OH, 2009.
116. J.A. Burton, R.C. Prim and W.P. Slichter, J. Chem. Phys., 70 (1953) 1987.
117. R. Tönhardt, Convective Effects on Dendritic Solidification, Ph.D. dissertation, Royal Institution of Technology, Stockholm, 1998.
118. F.M. White, Fluid Mechanics, 2nd Ed., McGraw-Hill Book Company, New York, NY, 1986.
119. Journal of Crystal Growth, North-Holland Publishing, Elsevier, Amsterdam, 1967-2010.
120. Modern Casting, American Foundry Society, Schaumburg, IL, 1938-2010.
121. Journal of Crystal Growth Design, The American Chemical Society, Philadelphia, PA, 2001-2010.
122. J. Alkemper and P.W. Voorhees, J. Micros., 201 (2001) 388.
123. M.M. Lipschutz, Differential Geometry, McGrawHill Book Co., New York, NY, 1969.
124. D. Struik, Lectures on Classical Differential Geometry, Addison-Wesley, Reading, MA, 1950.
125. D.A. Drew, SIAM J. Appl. Math, 50 (1991) 649.
126. The Scientific Papers of J. Willard Gibbs, Thermodynamics, I, Dover Publications, Inc., New York, NY, 1961.
127. J.W. Gibbs, Trans. Conn. Acad., III (1875-1976) 108.
128. R. Mendoza, J. Alkemper and P.W. Voorhees, Metall. Mater. Trans., 34A (2003) 481.
129. J.W. Gibbs, Trans. Conn. Acad., III (1877-1978) 343.
130. R.T. DeHoff, Thermodynamics in Materials Science, Chap. 12, McGraw-Hill, Inc., New York, NY, 1993.
131. J. Alkemper, R. Mendoza and P.W. Voorhees, Adv. Eng. Mater., 4 (2002) 694.
132. J. Cahn and J. Hilliard, J. Chem. Phys., 28 (1958) 258.
133. H. Emmerich, Phase Field Methods, Springer, Berlin, 2003.
134. J.J. Hoyt, M. Asta and A. Karma, Phys. Rev. Lett., 86 (2001) 5530.
135. J.J. Hoyt, M. Asta and A. Karma, Mater. Sci. Eng. Rep., 41 (2003) 121.
136. N. Kulkarni and R.T. DeHoff, Acta Mater., 45 (1997) 4963.
137. S.P. Marsh and M.E. Glicksman, Mater. Sci. Eng., A238 (1997) 140.
138. M.E. Glicksman and S.P. Marsh, Geometric Statistical Mechanics for Non-Spherical Bubbles and Droplets, Drops and Bubbles, T.G. Wang, Ed., American Institute of Physics, Conference Proceeding 197, New York, NY, 1989, p. 216.
139. W.T. Thomson, Philos. Mag., 42 (1871) 448.
140. B. Chalmers, Trans. AIME, 200 (1956) 519.
141. J.W. Rutter and B. Chalmers, Can. J. Phys., 31 (1953).
142. W.A. Tiller, K.A. Jackson, J.W. Rutter and B. Chalmers, Acta. Metall., 1 (1953) 428.
143. W. Kurz andW. Fisher, Fundamentals of Solidification, Trans Tech Publications, Aedermannsdorf, 1989.
144. R.J. Schaefer and M.E. Glicksman, Metall. Trans. A, A1 (1970) 1973.
145. W.A. Tiller and J.W. Rutter, Can. J. Phys., 34, (1956) 96.
146. M. Rettenmayr and H.E. Exner, 'Directional Solidification of Crystals', in Encyclopedia of Materials: Science and Technology, Elsevier Science Ltd., Amsterdam, ISBN: 0-08-0431526, 2000.
147. W.W. Mullins and R.F. Sekerka, J. Appl. Phys., 34 (1963) 323.
148. W.W. Mullins and R.F. Sekerka, J. Appl. Phys., 35 (1964) 444.
149. W.W. Mullins and R.F. Sekerka, J. Appl. Phys., 34 (1963) 323.
150. W.W. Mullins and R.F. Sekerka, J. Appl. Phys., 35 (1964) 444.
151. V.V. Voronkov, Sov. Phys. Solid State, 6 (1964) 2278.
152. S.H. Davis, Theory of Solidification, Cambridge Monographs on Mechanics, Cambridge University Press, Cambridge, UK, 2001.
153. J.S. Langer, Rev. Mod. Phys., 52 (1980) 1.
154. G.J. Merchant, R.J. Braun, K. Brattkus and S.H. Davis, SIAM J. Appl. Math., 52 (1992) 1279.
155. P. Metzener, 'Long-wave and short-wave oscillatory patterns in rapid directional solidification', Interactive Dynamics of Convection and Solidification, P. Ehrhard, D.S. Riley and P.H. Steen, Eds., Kluwer Academic Publishers, Dordrecht, 2001, p. 13.
156. B. Chalmers, Principles of Solidification, Chap. 8, 253, Wiley, New York, NY, 1964.
157. D. Riley and S.H. Davis, IMAJ. Appl. Math., 45 (1990) 267.
158. S. de Cheveigné, C. Guthmann and M.-M Lebrun, J. Cryst. Growth, 73 (1985) 242.
159. W. Losert, B.Q. Shi and H.Z. Cummins, Proc. Natl. Acad. Sci. USA, 95 (1998) 431.
160. J.A. Warren and J.S. Langer, Phys. Rev. A, 42 (1990) 3518.
161. J.A. Warren and J.S. Langer, Phys. Rev. E, 47 (1993) 2702.
162. D.A. Huntley and S.H. Davis, Acta Metall. Mater., 41 (1993) 2025.
163. M. Gremaud, M. Carrard and W. Kurz, Acta Metall. Mater., 38 (1991) 2587.
164. J.A. Warren and J.S. Langer, Phys. Rev. A, 42 (1990) 3518.
165. J.A. Warren and J.S. Langer, Phys. Rev. E, 47 (1993) 2702.
166. D. Riley and S.H. Davis, IMAJ. Appl. Math., 45 (1990) 267 .
167. R.J. Schaefer and M.E. Glicksman, Metall. Trans. A, A1 (1970) 1973.
168. B. Chalmers, Trans. AIME, 200 (1956) 519.
169. J.W. Rutter and B. Chalmers, Can. J. Phys., 31 (1953).
170. G.B. McFadden, R.F. Boisvert and S.R. Coriell, J. Cryst. Growth, 84, (1987) 371.
171. G.B. McFadden and S.R. Coriell, Physica D, 12 (1984) 253.
172. V.K. LaMer, Ind. Eng. Chem., 44 (1952) 1270.
173. K.C. Russell, J. Chem. Phys., 50 (1969) 1809.
174. J.L. Katz, J. Stat. Phys., 2 (1970) 137.
175. M. Volmer, Z. Elektrochem., 35 (1929) 555.
176. M. Volmer and A. Weber, Z. Phys. Chem., 119, (1925) 277.
177. M. Volmer and H. Flood, Z. Phys. Chem., 170A (1934) 273.
178. L. Farkas, Z. Phys. Chem., 125, (1927) 239.
179. R. Becker and W. Döring, Ann. Phys., 24 (1935) 719.
180. J.B. Zeldovich, Acta Physicochim., 18 (1943) 1.
181. J. Frenkel, Kinetic Theory of Liquids, Dover Publications, Inc., New York, NY, 1955, p. 176.
182. D. Turnbull, J. Chem. Phys., 20 (1952) 411.
183. D. Turnbull, J. Phys. Chem. 18 (1950) 198.
184. D. Turnbull and J.C. Fisher, J. Phys. Chem. 17 (1949) 71.
185. K.F. Kelton and A.L. Greer, Nucleation in Condensed Matter, 15, Pergamon Materials Series, Elsevier BV, Holland, 2010.
186. G.S. Heffelfinger et al., Mol. Simul., 2 (1989) 393.
187. A. Schmidt and V. Smirnov, TopCatal., 32 (2005) 71.
188. M.K. Harbola, Proc. Natl. Acad. Sci. USA, 89 (1992) 1036.
189. D. Turnbull, J. Chem. Phys., 18 (1950) 198.
190. M.E. Glicksman and W.J. Childs, Acta Metall., 10 (1962) 925.
191. J.H. Perepezko and W.S. Tong, Phil. Trans. R. Soc. Lond. A, 361 (2003) 447.
192. W. Yourgrau, A. van der Merwe and G. Raw, Treatise on Irreversible and Statistical Thermophysics, Dover Publications, New York, NY, 1982.
193. E.H. Kennard, Kinetic Theory of Gases, McGraw-Hill Book Company, New York, NY, 1938.
194. M.C. Flemings et al., AFS Trans., 70 (1962) 1029.
195. C. Vivès, Metall. Trans. B, 27 (1996) 445.
196. M. Easton and D. St. John, Metall. Mater. Trans. A, 30 (2007) 1625.
197. J.P. Perepezko, 'Nucleation kinetics and grain refinement', ASM Handbook, 15, American Society for Materials, Int., Materials Park, OH, 2008, p. 276.
198. C. Limmaneevichitr and W. Eidhed, Mater. Sci. Eng. A, 349 (2003) 197.
199. E.B. Webb III, G.S. Grest, and D.R. Heine, Phys. Rev. Lett., 91 (2003) 236103.
200. N.H. Fletcher, J. Chem Phys., 29 (1958) 572.
201. N.H. Fletcher, J. Chem Phys., 31 (1958) 1136.
202. N.H. Fletcher, J. Chem Phys., 38 (1958) 237.
203. T.B. Blake and J.M. Haynes, J. Coll. Inter. Sci., 30 (1969) 421.
204. J.C. Fisher, J.H. Holloman and D. Turnbull, J. Appl. Phys., 19 (1948) 775.
205. G. Ghosh and G.B. Olsen, Acta Metall. Mater., 42 (1994) 3361.
206. P. Sajkiewicz, J. Polym. Sci. B, 41 (2003) 68.
207. W. Oldfield, Trans. ASM, 59 (1966) 945.
208. W.T. Kim, D.L. Zhang and B. Cantor, Metall. Trans. A, 22A (1991) 2487.
209. W.T. Kim and B. Cantor, J. Mater. Sci., 26 (1991) 2868.
210. W.T. Kim and B. Cantor, Acta Metall., 40 (1992) 3339.
211. W.T. Kim and B. Cantor, Acta Metall., 42 (1994) 3045.
212. T.E. Quested and A.L. Greer, Acta Mater., 53 (2005) 2683.
213. J. Szekely, Fluid Flow Phenomena in Metals Processing, Academic Press Ltd., New York, NY, 1979, 305.
214. M.E. Glicksman, C.J. Paradies, G.T. Kim and R.N. Smith, 'The effects of varying melt flow velocity on the grain fragmentation in a mushy zone', Light Metals 1993, S.K. Das, Ed., The Minerals, Metals & Materials Society, Warrendale, PA, 1993, p. 779.
215. M.E. Glicksman, R.N. Smith, C.J. Paradies and P. Rao, 'Grain refinement of castings via melt-flow interaction with the mushy zone', Near-Net Shape Casting in the Minimills, I.V. Samarasekera, Ed., The University of British Columbia, Vancouver, BC, 1995, p. 217.
216. C.J. Paradies, M.E. Glicksman and R.N. Smith, Metall. Mater. Trans. A, 28A (1997) 875.
217. U. Nakaya, Snow Crystals: Natural and Artificial, Harvard University Press, Cambridge, MA, 1954.
218. W.A. Bentley, Snowflakes in Photographs, Dover Publications,Mineola, NY, 2000.
219. Originally published as Snowcrystals, McGraw-Hill, New York, NY, 1931.
220. K.G. Libbrecht, The Snowflake: Winters Secret Beauty, Voyageur Press, Stillwater, MN, 2003, p. 112.
221. A. Janner, Acta Cryst., 53 (1997) 615.
222. G.A. Colligan and B.J. Bayles, Acta Metall., 8 (1962) 895.
223. Y. Wu et al., Metall. Mater. Trans. A, 18 (1987) 915.
224. THERMO-CALC R Software, a product of Thermo-Calc AB, Stockholm, Sweden. Applications brochure, TMS Annual Meeting, Seattle WA, 2010.
225. M.E. Glicksman and R.J. Schaefer, Acta Metall., 14 (1966) 1226.
226. M.E. Glicksman, R.J. Schaefer and J.D. Ayers, Metall. Trans. A, 7 (1976) 1747.
227. H. Esaka and W. Kurz, Z. Metall., 76 (1985) 127.
228. J.Blackford, http://www.cmse.ed.ac.uk/AdvMat45/superEng.pdf, Engineering of Superalloys, 2002.
229. M.E. Glicksman, A. Lupulescu and M.B. Koss, J. Thermophys. Heat Transf., 17 (2003) 69.
230. M.E. Glicksman and S.P. Marsh, 'The dendrite', Handbook of Crystal Growth. Hurle D.T.J. Ed., Elsevier Science Publishers, Amsterdam, 1993, p. 1075.
231. K.A. Jackson, Kinetic Processes: Crystal Growth, Diffusion, and Phase Transitions in Materials, Wiley-VCH, Weinheim, 2004.
232. G.P. Ivantsov, Dokl. Akad. Nauk. USSR, 558 (1947) 567.
233. A. Papapetrou, Z. Kristallographie, 92 (1935) 89.
234. P.M. Morse and H. Feshbach, Methods of Theoretical Physics, Part I, McGraw-Hill, New York, NY, 1953, p. 664.
235. P. Moon and D.E. Spencer, Field Theory Handbook, Including Coordinate Systems, Differential Equations, and Their Solutions, 2nd Ed., Springer, New York, NY and, Berlin, 1988, p. 47.
236. Y-Q Chen, X-X Tang, J-J Xu, Chinese Phys. B, 18 (2009) 671.
237. G. Horvay and J.C. Cahn, Acta Metall., 9 (1961) 695.
238. G.E. Nash and M.E. Glicksman, Acta Metall., 22 (1974) 1283.
239. G.E. Nash and M.E. Glicksman, Acta Metall., 22 (1974) 1291.
240. D. Kessler and H. Levine, Phys. Rev. A, 36, (1987) 4123.
241. D. Kessler and H. Levine, Phys. Rev. Lett., 57 (1986) 3069.
242. D. Kessler and H. Levine, Acta Metall., 36 (1987) 2693.
243. A. Barbieri and J.S. Langer, Phys. Rev. A., 39, (1989) 5314.
244. J.S. Langer and H. Müller-Krumbhaar, J. Cryst. Growth, 42 (1977) 11.
245. J.S. Langer and H. Muller-Krumbhaar, Acta Metall., 26 (1978) 1681.
246. J.S. Langer, Rev. Mod. Phys., 52 (1980) 1.
247. S.C. Huang and M.E. Glicksman, Acta Metall., 11 (1981) 701.
248. S.C. Huang and M.E. Glicksman, Acta Metall., 11 (1981) 717.
249. W. Oldfield, Mater. Sci. Eng., 11 (1973) 211.
250. M.E. Glicksman, M.B. Koss, L.T. Bushnell, J.C. LaCombe and E.A. Winsa, Adv. Space Res., 16 (1995) 181.
251. M.E. Glicksman, M.B. Koss, L.T. Bushnell, J.C. Lacombe and E.A. Winsa, Iron Steel Inst. Jpn Int., 35 (1995) 604.
252. T. Fujioka and R.F. Sekerka, J. Cryst. Growth, 24-25 (1974) 84.
253. M.E. Glicksman, M.B. Koss and E.A. Winsa, Phys. Rev. Lett., 73 (1994) 573.
254. D.A. Kessler and H. Levine, Phys. Rev. B, 33 (1986) 7867.
255. X.J. Chen, Y.Q. Chen, J.P. Xu and J.J. Xu, Front. Phys. China, 3 (2008) 1.
256. Y.Q. Chen, X.X. Tang and J.J. Xu, Chinese Phys. B 18 (2009) 686.
257. J.J. Xu, 'Dynamics of dendritic growth interacting with convective flow - global instabilities and limiting state selection', Advances in Mechanics and Mathematics 1, Springer, New York, NY, 2002, p. 113.
258. J.J. Xu, 'Dynamical heory of dendritic growth in convective flow', Advances in Mechanics and Mathematics Springer, New York, NY, 2004.
259. J.J. Xu, Introduction of Dynamical Theory of Solidification Interfacial Stability, Chinese Academy Press, Beijing, 2007.
260. M. Glicksman, J. Lowengrub and S. Li, Proceedings in Modelling of Casting, Welding and Advanced Solidification Processes XI, C.A. Gandin and M. Bellet, Eds., The Metallurgical Soc., Warrendale, OH, (2006) p. 521.
261. M.E. Glicksman, J. Lowengrub and S. Li, J. Metals, 59 (2007) 27.
262. R. Pieters and J. Langer, Phys. Rev. Lett., 56 (1986) 1948.
263. P. Pelce, Dynamics of Curved Fronts, Academic Press, New York, NY, 1988.
264. D.A. Kessler and H. Levine, Phys. Rev. A, 34 (1986) 4908.
265. Herring, C., Physics of Powder Metallurgy,W.E. Kingston, Ed., McGraw-Hill, New York, NY, 1951, 143.
266. N.B. Singh and M.E. Glicksman, Thermochim. Acta, 159 (1990) 93.
267. V.R. Voller and S. Sundarraj, Int. J. Heat Mass Transf., 38 (1995) 1009.
268. B. Prabhakar and F. Weinberg, Metall. Mater. Trans. B, 9 (1978) 150.
269. M.C. Flemings, Solidification Processing, McGraw-Hill, New York, NY, 1974.
270. H.D. Brody and M.C. Flemings, Trans. AIME, 236 (1966) 615.
271. T.W. Clyne and W. Kurz, Metall. Trans., 12A (1981) 965.
272. I. Ohnaka, Trans. Iron Steel Inst. Jpn, 26, (1986) 1045.
273. S. Kobayashi, Trans. Iron Steel Inst. Jpn, 28 (1988) 725.
274. T. Kraft, M. Rettenmayr and H.E. Exner, Mater. Sci. Eng., 4 (1996) 161.
275. L. Nastac, Modelling and Simulation of Microstructure Evolution in Solidifying Alloys, Kluwer Academic Publishers, New York, NY, 2004.
276. B. Chalmers, Principles of Solidication, Ch. 8, 253, John Wiley & Sons, Inc., New York, 1964.
277. M. Rappaz, EPFL Supercomput. Rev., 8, (1996). http://sawww.epfl.ch/SIC/ SA/publications/ SCR96/scr8-page11.html
278. J. Lipton, M.E. Glicksman and W. Kurz, Mater. Sci. Eng., 65 (1984) 57.
279. M. Rappaz, Ch.-A. Gandin, Acta Metall. Mater., 41 (1993) 345.
280. Ch.-A. Gandin, M. Rappaz and R. Tintillier, Metall. Trans. A, 25A (1994) 629.
281. M. Rappaz, Ch.-A. Gandin and J.-L. Desbiolles, Metall. Mater. Trans. A, 27A (1996) 695.
282. Ch.-A. Gandin, R.J. Schaefer and M. Rappaz, Acta Metall. Mater., 44 (1996) 3339.
283. B. Chalmers, Trans. AIME, 200 (1956) 519.
284. H.M. Cuppen, H. Meekes, W.J.P. van Enckevort and E. Vlieg, J. Cryst. Growth, 286 (2006)188.
285. K.A. Jackson, Acta. Metall., 7 (1959) 148.
286. R.T. DeHoff, Thermodynamics in Materials Science, Chap. 3, McGraw-Hill, Inc. New York, NY, 1993.
287. K.A. Jackson and B. Chalmers, Can. J. Phys., 34, (1956) 473.
288. K.A. Jackson, D.R. Uhlmann and J.D. Hunt, J. Cryst. Growth, 1 (1967) 1.
289. J.W. Cahn, W.B. Hillig and G.W. Sears, Acta Metall., 12 (1964) 1421.
290. M.E. Glicksman, Diffusion in Solids: Field Theory, Solid-State from an and Applications, Wiley Interscience Publishers, New York, NY, 2000.
291. H.A. Wilson, Philos. Mag., 50 (1900) 238.
292. J. Frenkel, Physik. Z. Sovjetunion, 1 (1932) 498.
293. M. Volmer and M. Marder, Z. Phys. Chem., 154 (1931) 97.
294. W.B. Hillig and D. Turnbull, J. Chem. Phys., 24 (1956) 914.
295. S. Kou, Transport Phenomena and Materials Processing, Wiley, New York, NY, 1996.
296. Robert H. Doremus, Glass Science, Chap. 5, Wiley, New York, NY, 1973.
297. J. Cahn and J. Hilliard, J. Chem. Phys., 28 (1958) 258.
298. J.W. Cahn, Acta Metall., 8 (1960) 554.
299. H. Emmerich, Phase Field Methods, Springer, Berlin, 2003.
300. H.R. Lillie, J. Am. Ceram. Soc., 22 (1939) 367.
301. J.P. Poole, J. Am. Ceram. Soc., 32 (1949) 230.
302. L. Shartsis, S. Spinner and W. Capps, J. Am. Ceram. Soc., 35 (1952) 155.
303. W. Kost, Z. Elektrochem. 57 (1953) 431.
304. J.O'M. Bockris, J.D. Mackenzie and J.A. Kitchener, Trans. Faradat Soc., 51 (1955) 1734.
305. W.D. Scott and J.A. Pask, J. Am. Ceram. Soc., 44 (1961) 181.
306. H. Pollatschek, Z. Phys. Chem., 142 (1929) 289.
307. L. Neumann and G. Micus, Z. Phys. Chem., 2 (1954) 245.
308. V.I. Malkin, Zh. Fiz. Khim., 28 (1954) 1966.
309. O. Jantsch, Z. Krist., 108 (1956) 185.
310. M.E. Glicksman and R.J. Schaefer, Acta Metall., 16 (1968) 1009.
311. S.D. Peteves and R. Abbaschian, Metall. Trans. A, 22A (1991) 1259.
312. S.D. Peteves and R. Abbaschian, Metall. Trans. A, 22A (1991) 1271.
313. M.E. Glicksman, 'Solidification Research in Microgravity', ASM Handbook, 15, Casting, ASM International, Materials Park, OH, 2008, p. 398.
314. R.W. Kraft and D.L. Allbright, Trans. Metall. Soc. AIME, 224 (1962) 1176.
315. G.A. Chadwick, Prog. Mater. Sci., 10 (1963) 97.
316. J.W. Hunt and K.A. Jackson, Trans. Metall. Soc. AIME, 236 (1966) 843.
317. Solidification Processing of Eutectic Alloys, Eds. D.M. Stefanescu, G.J. Abbaschian and R.J. Bayuzick, TMS, Warrendale, PA, 1988.
318. B. Sundquist and L.F. Mondolfo, Metall. Trans., 221 (1961) 157.
319. R. Vögel, Z. Anorg. Chem., 76, (1912) 425.
320. G. Tammann, Textbook of Metallography, Chemical Catalogue Co., New York, NY, 1925 p. 182.
321. W. Straumanis and N. Braaks, Z. Phys. Chem., 29 (1935) 30.
322. W. Tiller, Liquid Metals and Solidification, ASM, Cleveland, OH, 1958, p. 276.
323. H.B. Callen, Phys. Rev., 105 (1957) 360.
324. G.A. Chadwick, J. Inst. Metals, 91 (1963) 169.
325. G.A. Chadwick, J. Inst. Metals, 92 (1963) 18.
326. J.D. Hunt and J.P. Chilton, J. Inst. Metals, 92 (1964) 2214.
327. J.D. Hunt and K.A. Jackson, Trans. Metall. Soc., 236 (1966) 1129.
328. D.M. Stefanescu, Science and Engineering of Casting Solidification, 2nd Ed., Chap. 11, Springer, New York, NY, 2009.
329. S. Wang, T. Akatsu, Y. Tanabe and E. Yasuda, J. Mater. Sci., 35 (2000) 2757.
330. C. Herring, The Physics of Powder Metallurgy, R. Gomer and C.S. Smith, Eds., University of Chicago Press, Chicago, IL, 1953, p. 5.
331. W. Kurz and P.R. Sahm, Gerichtet erstarrte eutecktische Werkstoffe [Directionally Solidified Eutectic Materials], Springer, Berlin (1975).
332. H. Biloni and W.J. Boettinger, 'Solidification', Physical Metallurgy, 4th Ed., Chap. 8, North Holland, Amsterdam, 1996, p. 669.
333. Y. Nakamura and Y. Shiohara, J. Mater. Res., 11 (1996) 2450.
334. K.A. Jackson, 50 Years Progress in Crystal Growth, R.S. Feigelson, Ed., Elsevier, Amsterdam, 2004, p. 81.
335. M. Rettenmayr and H.E. Exner, 'Directional Solidification of Crystals', in Encyclopedia of Materials: Science and Technology, Elsevier Science Ltd., Amsterdam, ISBN: 0-08-0431526, 2000.
336. I. Minkoff, The Physical Metallurgy of Cast Iron, Wiley, New York, NY, 1983.
337. Pol Duwez, R.H. Willens and W. Klement, J. Appl. Phys., 31 Chap. 6 (1960) 1136.
338. D.O. Belanger, Enabling American Innovation, Purdue University Press, 1998, p. 165.
339. H.H. Liebermann, Ed., Rapidly Solidified Allos: Processes, Ptructures, Properties, CRC Press, Boca Raton, FL, 1993.
340. T.S. Srivatsan and T.S. Sudashan, Eds., Rapid Solidification Technology: An Engineering Guide, CRC Press, Boca Raton, FL, 1993.
341. H. Jones, J. Mater. Sci. Eng. A, 304 (2001) 11.
342. J.H. Perepezko et al., 'Rapid solidification of highly undercooled aluminum powders', Rapidly Solidified Powder Aluminum Alloys: A Symposium, M.E. Fine and E.A. Starke, Eds., ASTM International, W. Conshohocken, PA, 1986.
343. A.G. Leatham and A. Lawley, Int. J. Powder Metall., 29 (1993) 321.
344. G. Thursfield and H. Jones, J. Phys. E., 4 (1971) 675.
345. http://www.metglas.com/products/, Products and Solutions for the Electronics Industry, Allied Chemical Corp., undated.
346. A.A. Chernov, Growth of Crystals, 3, A.V. Shubnikov and N.N. Sheftal, Eds., Consultants Bureau, New York, NY, 1962, 65.
347. V.V. Voronkov and A.A. Chernov, Sov. Phys. Crystallog., 12 (1967) 186.
348. A.A. Chernov, Sov. Phys. Uspekhi, 13 (1970) 101.
349. M.J. Aziz and T. Kaplan, Acta Metall., 36 (1988) 2335.
350. M. Rettenmayr and M. Buchmann, Int. J. Mater. Res., 99 (2008) 961.
351. M.E. Glicksman and R.J. Schaefer, J. Cryst. Growth, 1 (1967) 297.
352. A. Ludwig, Scr. Mater., 34 (1996) 579.
353. M. Li and K. Kuribayashi, Acta Mater., 52 (2004) 3639.
354. J.H. Perepezko, Mater. Sci. Eng., 65 (1984) 125.
355. J.H. Perepezko and J.S. Palik, J. Non-Cryst. Solids, 61-62 (1984) 113.
356. R. Willnecker, D.M. Herlach, B. Feuerbacher and H.J. Fecht, J. Mater. Sci. Eng. A, 133 (1991) 443.
357. A.L. Greer, J. Less Common Metals, 145 (1988) 131.
358. K.F. Kelton and A.L. Greer, J. Non-Cryst. Solids, 79 (1986) 295.
359. M.B. Robinson, R.J. Bayuzick and W.H. Hofmeister, Adv. Space Res., 8 (1988) 321.
360. D.M. Herlach, R.F. Cochrane, I. Egry, H.J. Fecht and A.L. Greer, Int. Metals Rev., 38 (1994) 273.
361. D.M. Herlach, Mater. Sci. Eng. Rep., 11 (1994) 355.
362. M. Hillert and B. Sundman, Acta Metall., 25 (1977) 11.
363. J.C. Baker and J.W. Cahn, Acta Metall., 17 (1969) 575.
364. G.H. Gilmer, Mater. Res. Soc. Symp., 13 (1983) 249.
365. J.C. Baker and J.W. Cahn, Solidification, ASM, Metals Park, OH, 1970, p. 23.
366. R.F. Wood, Appl. Phys. Lett., 37 (1980) 302.
367. P. Baeri, et al., Appl. Phys. Lett., 37 (1980) 912.
368. C.W. White, et al., J. Appl. Phys., 51, (1980) 738.
369. J.W. Cahn, S.R. Coriell and W.J. Boettinger, Laser and Electron Beam Processing of Materials, C.W. White and P.S. Peercy, Eds., Academic Press, New York, NY, 1980, p. 8.
370. T.F. Ciszek, J. Cryst. Growth, 10 (1971) 263.
371. D.M. Zehner, C.W. White and G.W. Ownby, Surf. Sci., 92 (1980) 67.
372. A.A. Chernov, Sov. Phys. JETP, 26 (1968) 1182.
373. W.J. Boettinger and M.J. Aziz, Acta Metall., 37 (1989) 3379.
374. L.M. Goldman and M.J. Aziz, J. Mater. Res., 2 (1987) 524.
375. S.R. Coriell and D. Turnbull, Acta Metall., 30 (1982) 2135.
376. M.J. Aziz, et al., Mater. Res. Soc. Symp. Proc., 35 (1985) 153.
377. M.J. Aziz, Metall. Mater. Trans. A, 27A (1996) 671.
378. M.J. Aziz, J. Appl. Phys. 53 (1982) 1158.
379. N.A. Ahmad et al., Phys. Rev. E, 58 (1998) 3436.
380. G.F. Bolling and W.A. Tiller, J. Appl. Phys., 31 (1960) 1345.
381. R.J. Schaefer, M.E. Glicksman and J.D. Ayers, Phil. Mag., 32 (1975) 725.
382. M. Glicksman, J. Lowengrub and S. Li, Proceedings in Modelling of Casting, Welding and Advanced Solidification Processes XI, C.A. Gandin and M. Bellet, Eds., The Minerals,Metals and Material Society, Warrendale, PA, (2006) p. 521.
383. M.E. Glicksman, J. Lowengrub and S. Li, J. Metals, 59 (2007) 27.
384. W.W. Mullins and R.F. Sekerka, J. Appl. Phys., 34 (1963) 323.
385. J.S. Langer, Rev. Mod. Phys., 52 (1980) 1.
386. J.S. Langer and H. Müller-Krumbhaar, J. Cryst. Growth, 42 (1977) 11.
387. J.S. Langer and H. Muller-Krumbhaar, Acta Metall., 26 (1978) 1681.
388. R. Pieters and J. Langer, Phys. Rev. Lett., 56 (1986) 1948.
389. A. Dougherty, P. Kaplan and J. Gollub, Phys. Rev. Lett. 58 (1987) 1652.
390. A. Karma and W. Rappel, Phys. Rev. E, 60 (1999) 3614.
391. O. Martin and N. Goldenfeld, Phys. Rev. A, 35 (1987) 1382.
392. E. Ben Jacob and P. Garik, Nature, 343 (1990) 523.
393. R. Almgren, W. Dai and V. Hakim,Phys. Rev. Lett., 71 (1993) 3461.
394. Y. Couder, O. Cardoso, D. Dupuy, P. Tavernier andW. Thom, Euro. Phys. Lett., 2 (1986) 437.
395. Y. Couder, N. Gerard and M. Rabaud, Phys. Rev. A, 34 (1986) 5175.
396. T. Borzsonyi, T. Toth-Katona, A. Buka and L. Granasy, Phys. Rev. E, 62 (2000) 7817.
397. L. Kondic, P. Palffy-Muhoray and M. Shelley, Phys. Rev. E, 54 (1996) 4536.
398. L. Kondic, P. Palffy-Muhoray and M. Shelley, Phys. Rev. Lett., 80 (1997) 1433.
399. P. Fast, L. Kondic, P. Palffy-Muhoray and M. Shelley, Phys. fluid, 13 (2001) 1191.
400. P. Pelce, Europhysics Lett., 75 (2006) 220.
401. S. Li, J. Lowengrub, J.P. Leo and V. Cristini, J. Cryst. Growth, 267 (2004) 703.
402. S. Li, J.S. Lowengrub and P.H. Leo, J. Comput. Phys., 225 (2007) 554.
403. M.E. Glicksman and S.P. Marsh, 'The dendrite', Handbook of Crystal Growth, Ed. D. Hurle, Elsevier Science Publishers, Amsterdam, 1993, p. 1075.
404. S. Mikhlin, Integral Equations and Their Applications to Certain Problems in Mechanics, Mathematical Physics and Technology, Pergamon, New York, NY, 1957.
405. S. Li, J. Lowengrub, P. Leo and V. Cristini, J. Cryst. Growth 277 (2005) 578.
406. S. Li, J. Lowengrub and P. Leo, Physica D, 208 (2005) 209.
407. V. Cristini and J. Lowengrub, J. Crystal Growth, 266 (2004) 552.
408. X. Li, V. Cristini, Q. Nie and J. Lowengrub, Discrete Dynam. Syst. B, 7 (2007) 581.
409. Y. Saad and M. Schultz, SIAM J. Sci. Stat. Comput., 7 (1986) 856.
410. T. Hou, J. Lowengrub and M. Shelley, J. Comp. Phys., 114 (1994) 312.
411. H. Jou, P. Leo and J. Lowengrub, (1997) J. Comp. Phys., 131 109.
412. V. Cristini, J. Blawzdziewicz and M. Loewenberg, J. Comp. Phys., 168 (2001) 445.
413. A.Z. Zinchenko, M.A. Rother and R.H. Davis, Phys. Fluids, 9 (1997) 1493.
414. M. Rettenmayr and H.E. Exner, 'Directional Solidification of Crystals', in Encyclopedia of Materials: Science and Technology, Elsevier Science Ltd., Amsterdam, ISBN: 0-08-0431526, 2000.
415. J. Page, Smithsonian Mag., 30 (2000) 36-46.
416. J.D. Hunt and K.A. Jackson, Trans. Metall. Soc., 236 (1966) 1129.
417. R. Trivedi and W. Kurz, Solidification Processing of Eutectic Alloys, D.M. Stefanescu, G.J. Abbaschian and R.J. Bayuzick, Eds. The Metallurgical Society, Warrendale, OH, 1989, p. 4.