Review
Thermal convection and related instabilities in models of crystal growth from the melt on earth and in microgravity: Past history and current status
Marcello Lappa,
Marcello Lappa
MARS (Microgravity Advanced Research and Support Center), Via Gianturco 31, 80146, Napoli, Italy
Search for more papers by this authorMarcello Lappa,
Marcello Lappa
MARS (Microgravity Advanced Research and Support Center), Via Gianturco 31, 80146, Napoli, Italy
Search for more papers by this authorAbstract
The paper presents a comparative study of a number of theoretical/experimental/numerical results concerning the dynamics of natural (gravitational), Marangoni and related mixed convection in various geometrical models of widely-used technologies for the production of single-crystalline materials (Horizontal and vertical Bridgman growth, Czochralski method, Floating Zone Technique). Emphasis is given to fundamental knowledge provided over the years by landmark analyses as well as to very recent contributions. Such a knowledge is of paramount importance since it is validating new, more complex models, accelerating the current trend towards predictable and reproducible phenomena and finally providing an adequate scientific foundation to industrial processes which are still conducted on a largely empirical basis. A deductive approach is followed with fluid-dynamic systems of growing complexity being treated as the discussion progresses. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)
References
- [1] A. Schlüter, D. Lortz, and F. H. Busse, J. Fluid Mech. 23, 129 (1965).
- [2] F. H. Busse, Rep. Prog. Phys. 41, 1929 (1978).
- [3] A. Yu. Gelfgat, J. Comput. Phys. 156, 300 (1999).
- [4] I. Catton, Int. J. Heat Mass Transfer 15, 665 (1972).
- [5] J. M. Luijkx and J. K. Platten, J. Non-EquilibriumThermodynam. 6, 141 (1981).
- [6] P. G. Daniels, J. Fluid Mech. 143, 125 (1984).
- [7] J. Pallares, F. X. Grau, and F. Girlt, Int. J. Heat Mass Transf. 43, 753 (1999).
- [8] D. Puigjaner, J. Herrero, F. Giralt, and C. Simó, Phys Fluids 16(10), 3639 (2004).
- [9] G. S. Charlson and R. Sani, Int. J. Heat Mass. Transf. 13 (1970).
- [10] G. S. Charlson and R. Sani, Int. J. Heat Mass. Transf. 14, 2157 (1971).
- [11] R. Touihri, H. Ben Hadid, and D. Henry, Phys. Fluids 11(8), 2078 (1999).
- [12] G. Müller, G. Neumann, and W. Weber, J. Cryst. Growth 70, 78 (1984).
- [13] G. Neumann, J. Fluid Mech. 214, 559 (1990).
- [14] C. Wagner, R. Friedrich, and R. Narayanan, Phys. Fluids 6, 1425 (1994).
- [15] M. Wanschura, H. C. Kuhlmann, and H. J. Rath, J. Fluid Mech. 326, 399 (1996).
- [16] J. R. Carruthers, in “Preparation and Properties of Solid State Materials” (Edited by W. R. Wilcox and R. A. Lefever), Vol. 3, Marcel Dekker, New York, 1977.
- [17] D. T. J. Hurle, Phil. Mag. 13, 305 (1966).
- [18] F. Dupret and N. Van der Bogaert, in “Handbook of Crystal Growth” (ed. D. T. J. Hurle) 2, 877 (1994), North-Holland, Amsterdam.
- [19] E. Monberg, in “Handbook of Crystal Growth” (ed. D. T. J. Hurle), 2, 53 (1994), North-Holland, Amsterdam.
- [20] G. Z. Gershuni, P. Laure, V. M. Myznikov, B. Roux, and E. M. Zhukhovitsky, Microgravity Q. 2(3), 141 (1992).
- [21] H. P. Kuo and S. A. Korpela, Phys. Fluids 31, 33 (1988).
- [22] J. E. Hart, J. Atmospheric Sciences 29, 687 (1972).
- [23] J. E. Hart, J. Fluid Mech. 132, 271 (1983).
- [24] A. E. Gill, J. Fluid Mech. 64(3), 577 (1974).
- [25] P. Laure, J. Mèc. Thèor. Appl. 6, 351 (1987).
- [26] G. K. Batchelor, Q. Appl. Math. 12, 209 (1954).
- [27] D. E. Cormack, L. G. Leal, and J. Imberger, J. Fluid Mech. 65, 209 (1974).
- [28] P. Bontoux, B. Roux, G. H. Schiroky, B. L. Markham, and F. Rosenberger, Int. J. Heat Mass Transfer 29(2), 227 (1986).
- [29] A.Yu. Gelfgat, P. Z. Bar-Yoseph, and A. L. Yarin, J. Fluid Mech. 388, 315 (1999).
- [30] A.Yu. Gelfgat, P. Z. Bar-Yoseph, and A. L. Yarin, Int. J. Comput. Fluid Dynamics 11, 261 (1999).
- [31] A. Bejan and C. L. Tien, Int. J. Heat Mass Transfer 21, 701 (1978).
- [32] J. P. Pulicani, S. Krukowski, J. I. D. Alexander, J. Quazzani, and F. Rosenberger, Int. J. Heat Mass Transfer 35(9), 2119 (1992).
- [33] A. Yu. Gelfgat, P. Z. Bar-Yoseph, and A. Solan, J. Cryst. Growth 220, 316 (2000).
- [34] M. J. Crochet, F. Dupret, Y. Ryckmans, F. T. Geyling, and E. M. Monberg, J. Cryst. Growth 97, 173 (1989).
- [35] J. J. Favier, J. Cryst. Growth 99, 18 (1990).
- [36] C. R. Lopez, J. R. Mileham, and R. Abbaschian, J. Cryst. Growth 200, 1 (1999).
- [37] K. Eckert, M. Bestehorn, and A. Thess, J. Fluid Mech. 356, 155 (1998).
- [38] P. Colinet, J. C. Legros, and M. G. Velarde, “Nonlinear Dynamics of Surface-Tension-Driven Instabilities”, Wiley-VCH, Berlin, pp. 1–527, 2001.
- [39] D. T. J. Hurle (Ed.), “Handbook of crystal growth”, North-Holland, Amsterdam, 1994.
- [40] S. Nakamura, M. Eguchi, T. Azami, and T. Hibiya, J. Cryst. Growth 207, 55 (1999).
- [41] M. K. Smith and S. H. Davis, J. Fluid Mech. 132, 119 (1983).
- [42] M. K. Smith, Phys. Fluids 29(10), 3182 (1986).
- [43] L. Peltier and S. Biringen, Phys. Fluids 257, 339 (1993).
- [44] J. Xu and A. Zebib, J. Fluid Mech. 364, 187 (1998).
- [45] H. Ben Hadid and B. Roux, J. Fluid Mech. 221, 77 (1990).
- [46] M. Mundrane and A. Zebib, Phys. Fluids 10, 3294 (1994).
- [47] D. Villers and J. Platten, J. Fluid Mech. 234, 487 (1992).
- [48] C. De Saedeleer, A. Garcimartin, G. Chavepeyer, J. K. Platten, and G. Lebon, Phys. Fluids 8(3), 670 (1996).
- [49] R. J. Riley and G. P. Neitzel, J. Fluid Mech. 359, 143 (1998).
- [50] J. Burguete, N. Mukolobwiez, N. Daviaud, N. Garnier, and A. Chiffaudel, Phys. Fluids 13(10), 2773 (2001).
- [51] E. Bucchignani, Phys. Fluids 16(11), 3839 (2004).
- [52] P. Parmentier, V. Regnier, and G. Lebon, Int. J. Heat Mass Transf. 36, 2417 (1993).
- [53] J. F. Mercier and C. Normand, Phys. Fluids 8(6), 1433 (1996).
- [54] M. Kassemi and N. Rashidnia, Phys. Fluids 12(12), 3133 (1999).
- [55] D. Schwabe, J. Cryst. Growth 237-239, 1849 (2002).
- [56] Y. R. Li, N. Imaishi, T. Azami, and T. Hibiya, J. Cryst. Growth 260, 28 (2004).
- [57] C. H. Chun and W. Wuest, Acta Astronautica 6, 1073 (1979).
- [58] F. Preisser, D. Schwabe, and A. Scharmann, J. Fluid Mech. 126, 545 (1983).
- [59] R. Velten, D. Schwabe, and A. Scharmann, Phys. Fluids A 3, 267 (1991).
- [60] S. Frank and D. Schwabe, Exp. in Fluids 23, 234 (1998).
- [61] H. C. Kuhlmann and H. J. Rath, J. Fluid Mech. 247, 247 (1993).
- [62] M. Wanschura, V. Shevtsova, H. C. Kuhlmann, and H. J. Rath, Phys. Fluids 5, 912 (1995).
- [63] M. Lappa, R. Savino, and R. Monti, Int. J. Num. Meth. Fluids 36(1), 53 (2001).
- [64] W. R. Hu and Z. M. Tang, Cryst. Res. Technol. 38, 627 (2003).
- [65] R. Rupp, G. Müller, and G. Neumann, J. Cryst. Growth 97, 34 (1989).
- [66] M. Levenstam and G. Amberg, J. Fluid Mech. 297, 357 (1995).
- [67] M. Lappa and R. Savino, J. Comput. Phys. 180(2), 751 (2002).
- [68] N. Imaishi, S. Yasuhiro, Y. Akiyama, and S. Yoda, J. Cryst. Growth 230, 164 (2001).
- [69] M. Lappa, R. Savino, and R. Monti, Int. J. Heat Mass Transf. 44(10), 1983 (2001).
- [70] Q. S. Chen, W. R. Hu, and V. Prasad, J. Cryst. Growth 203, 261 (1999).
- [71] M. Lappa, S. Yasushiro, and N. Imaishi, Int. J. Num. Meth. Heat Fluid Flow 13(3), 309 (2003).
- [72] J. Baumgartl, M. Gewald, R. Rupp, J. Stierlen, and G. Müller, Proceedings VIIth European Symposium on Materials and Fluid Sciences in Microgravity Oxford (United Kingdom), 10/15 September (1990), ESA SP 295.
- [73] A. Cröll, Th. Kaiser, M. Schweizer, A. N. Danilewsky, S. Lauer, A. Tegetmeier, and K. W. Benz, J. Cryst. Growth 191, 365 (1998).
- [74] C. W. Lan and C. H. Chian, J. Cryst. Growth 230, 172 (2001).
- [75] M. Lappa, Phys. Fluids 15(3), 776 (2003).
- [76] M. Lappa, Computers & Fluids 34(6), 743 (2005).
- [77] M. Lappa, Phys. Fluids 16(2), 331 (2004).
- [78] M. Lappa, “Fluids, Materials and Microgravity: Numerical Techniques and Insights into the Physics”, Elsevier Science (Oxford, 2004), pp. 1-520 - ISBN 00-804-4508-X.
