On Linear Analysis of the Movement of the Interface under Directed Crystallization
Author(s)
Alex Guskov*
ABSTRACT
We present a detailed discussion of the boundary conditions of the directed crystallization problem, a formulation of the model considering temperature fields of external sources, the mechanism of attachment of particles to the growing solid surface, the influence of interphase component absorption on the phase distribution ratio of the components as well as the calculation of the period of the morphological interface instability which is made with due regard of all the aforementioned conditions.
Cite this paper
Guskov, A. (2014) On Linear Analysis of the Movement of the Interface under Directed Crystallization. Advances in Chemical Engineering and Science, 4, 103-119. doi: 10.4236/aces.2014.42014.
Guskov, A. (2014) On Linear Analysis of the Movement of the Interface under Directed Crystallization. Advances in Chemical Engineering and Science, 4, 103-119. doi: 10.4236/aces.2014.42014.
References
[1] Mullins, W.W. and Sekerka, R.F. (1964) Stability of a Planar Interface during Solidification of a Dilute Binary Alloy. Journal of Applied Physics, 35, 444.
http://dx.doi.org/10.1063/1.1713333 [2] Sekerka, R.F. and Wang, S.L. (2000) Lectures on the Theory of Phase Transformations. In: Aaronson, H.I., Ed., Moving Phase Boundary Problems, 2nd Edition, TMS, Warrendale, 231. [3] Muller, G., Jacques, J. and Rudolph, P. (1996) Crystal Growth—From Fundamentals to Technology, Elsevier, Amsterdam. [4] Saito, Y. (1996) Statistical Physics of Crystal Growth. World Scientific Publishing Co. Pte Ltd., Singapore City, New Jersey, London, Hong Kong. [5] Scheel, H.J. and Fukade, T. (2003) Crystal Growth Technology, John Wiley & Sons, Ltd., Hoboken.
http://dx.doi.org/10.1002/0470871687 [6] Byrappa, K. and Ohachi, T. (2003) Crystal Growth Technology. Springer, Berlin. [7] Taran, J.N. and Masur, V. (1978) Eutectics Allow Structure (Metallurgy (Russia). Moscow. [8] Gus’kov, A.P. (1999) A Model of Planar Crystallization of a Binary Melt. Physics-Doklady, 366, 468. [9] Gus’kov, A.P. (1999) Hierarchy of Interface Instabilities in Directional Solidification. Izvestija Akademii Nauk, Physics, 63, 1772. [10] Gus’kov, A.P. (2002) Dynamics of the Interface Displacement in the Case of Oriented Crystallization. Physics-Doklady, 387, 1. [11] Gus’kov, A.P. (2000) Model of Directed Crystallization of Binary Alloy. Computational Materials Science, 17, 555-559.
http://dx.doi.org/10.1016/S0927-0256(00)00087-2 [12] Gus’kov, A.P. and Orlov, A. (2002) Dependence of Period of Macrostructures on Kinetic Parameters under Directed Crystallization. Computational Materials Science, 24, 93-98.
http://dx.doi.org/10.1016/S0927-0256(02)00169-6 [13] Gus’kov, A.P. (2003) Dependence of the Structure Period on the Interface Velocity upon Eutectic Solidification. Technical Physics, 48, 569-575.
http://dx.doi.org/10.1134/1.1576469 [14] Minford, W.J., Bradt, R.C. and Stubican, V.S. (1979) Crystallography and Microstructure of Directionally Solidified Oxide Eutectics. Journal of the American Ceramic Society, 62, 154.
http://dx.doi.org/10.1111/j.1151-2916.1979.tb19043.x [15] Gus’kov, A. and Orlov, A. (2009) Influence of an Interphase Nonequilibrium Solution Layer on Formation Eutectic Pattern. Materials Science 2009, N 12, 2-6 (Russia). [16] Gus’kov, A.P. (2009) The Period of Decay of a Nonequilibrium Solution at the Directed Crystallization. Materials Science 2009, N 10, 9-13 (Russia). [17] Gus’kov, A.P. (1996) Striations in the Distribution of Impurity Concentration Due to Instability of the Phase Boundary. Physics-Doklady, 349, 468. [18] Gus’kov, A.P. (2001) Stability of the Interphase Boundary during the Crystallization of Eutectics. Technical Physics Letters, 27, 480-483.
http://dx.doi.org/10.1134/1.1383831 [19] Boettinger, W.J., Coriell, S.R., Greer, A.L., Karma, A., Kurz, W., Rappaz, M. and Trivedi, R. (2000) Solidification Microstructures: Recent Developments, Future Directions. Acta Materialia, 48, 43-70.
http://dx.doi.org/10.1016/S1359-6454(99)00287-6 [20] Pines, B.J. (1961) Sketches on Physics of Metal. Charkov, Russia. [21] Hall, R.N. (1953) Segregation of Impurities during the Growth of Germanium and Silicon. The Journal of Physical Chemistry, 57, 836-839.
http://dx.doi.org/10.1021/j150509a021 [22] Kreger, F.A. (1964) The Chemistry of Imperfect Crystals. North-Holland Publishing Company, Amsterdam. [23] Cahn, R.W. and Haasen, P. (1983) Physical Metallurgy. North-Holland physics Publishing, Amsterdam. [24] Guskov, A. (2008) Influence of Unequi-Librium Processes on Component Distribution under Directed Crystallization. Abstracts of 2008 China International Forum on Advanced Materials and Commercialization, Ningbo, 17-19 November 2008, 17-26. [25] Guskov, A. and Nekrasova, L. (2013) Decomposition of Solutions in Front of the Interface Induced by Directional Crystallization. Journal of Crystallization Process and Technology, 3, 170-174. [26] Beatty, K.M. and Jackson, K.A. (2004) Monte Carlo modeling of Dopant Segregation. Journal of Crystal Growth, 271, 495-512.
http://dx.doi.org/10.1016/j.jcrysgro.2004.07.074 [27] Wang, H., Liu, F., Yang, W., Chenand, Z., Yang, G. and Zhou, Y. (2008) Solute Trapping Model Incorporating Diffusive Interface. Acta Materialia, 56, 746-753. [28] Guskov, A. (2008) Influence of the Nonequilibrium Melt Layer on Stationary Regime of Directed Crystallization. Articles Collector of 18th Petersburg Lectures on Problem of Strength and Crystal Growth. Sanct-Petersburg, 21-24 October 2008, 111-113. [29] Bokshtain, B.S. (1978) Diffusion in Metal. Metallurgy, Russia.
[1] Mullins, W.W. and Sekerka, R.F. (1964) Stability of a Planar Interface during Solidification of a Dilute Binary Alloy. Journal of Applied Physics, 35, 444.
http://dx.doi.org/10.1063/1.1713333 [2] Sekerka, R.F. and Wang, S.L. (2000) Lectures on the Theory of Phase Transformations. In: Aaronson, H.I., Ed., Moving Phase Boundary Problems, 2nd Edition, TMS, Warrendale, 231. [3] Muller, G., Jacques, J. and Rudolph, P. (1996) Crystal Growth—From Fundamentals to Technology, Elsevier, Amsterdam. [4] Saito, Y. (1996) Statistical Physics of Crystal Growth. World Scientific Publishing Co. Pte Ltd., Singapore City, New Jersey, London, Hong Kong. [5] Scheel, H.J. and Fukade, T. (2003) Crystal Growth Technology, John Wiley & Sons, Ltd., Hoboken.
http://dx.doi.org/10.1002/0470871687 [6] Byrappa, K. and Ohachi, T. (2003) Crystal Growth Technology. Springer, Berlin. [7] Taran, J.N. and Masur, V. (1978) Eutectics Allow Structure (Metallurgy (Russia). Moscow. [8] Gus’kov, A.P. (1999) A Model of Planar Crystallization of a Binary Melt. Physics-Doklady, 366, 468. [9] Gus’kov, A.P. (1999) Hierarchy of Interface Instabilities in Directional Solidification. Izvestija Akademii Nauk, Physics, 63, 1772. [10] Gus’kov, A.P. (2002) Dynamics of the Interface Displacement in the Case of Oriented Crystallization. Physics-Doklady, 387, 1. [11] Gus’kov, A.P. (2000) Model of Directed Crystallization of Binary Alloy. Computational Materials Science, 17, 555-559.
http://dx.doi.org/10.1016/S0927-0256(00)00087-2 [12] Gus’kov, A.P. and Orlov, A. (2002) Dependence of Period of Macrostructures on Kinetic Parameters under Directed Crystallization. Computational Materials Science, 24, 93-98.
http://dx.doi.org/10.1016/S0927-0256(02)00169-6 [13] Gus’kov, A.P. (2003) Dependence of the Structure Period on the Interface Velocity upon Eutectic Solidification. Technical Physics, 48, 569-575.
http://dx.doi.org/10.1134/1.1576469 [14] Minford, W.J., Bradt, R.C. and Stubican, V.S. (1979) Crystallography and Microstructure of Directionally Solidified Oxide Eutectics. Journal of the American Ceramic Society, 62, 154.
http://dx.doi.org/10.1111/j.1151-2916.1979.tb19043.x [15] Gus’kov, A. and Orlov, A. (2009) Influence of an Interphase Nonequilibrium Solution Layer on Formation Eutectic Pattern. Materials Science 2009, N 12, 2-6 (Russia). [16] Gus’kov, A.P. (2009) The Period of Decay of a Nonequilibrium Solution at the Directed Crystallization. Materials Science 2009, N 10, 9-13 (Russia). [17] Gus’kov, A.P. (1996) Striations in the Distribution of Impurity Concentration Due to Instability of the Phase Boundary. Physics-Doklady, 349, 468. [18] Gus’kov, A.P. (2001) Stability of the Interphase Boundary during the Crystallization of Eutectics. Technical Physics Letters, 27, 480-483.
http://dx.doi.org/10.1134/1.1383831 [19] Boettinger, W.J., Coriell, S.R., Greer, A.L., Karma, A., Kurz, W., Rappaz, M. and Trivedi, R. (2000) Solidification Microstructures: Recent Developments, Future Directions. Acta Materialia, 48, 43-70.
http://dx.doi.org/10.1016/S1359-6454(99)00287-6 [20] Pines, B.J. (1961) Sketches on Physics of Metal. Charkov, Russia. [21] Hall, R.N. (1953) Segregation of Impurities during the Growth of Germanium and Silicon. The Journal of Physical Chemistry, 57, 836-839.
http://dx.doi.org/10.1021/j150509a021 [22] Kreger, F.A. (1964) The Chemistry of Imperfect Crystals. North-Holland Publishing Company, Amsterdam. [23] Cahn, R.W. and Haasen, P. (1983) Physical Metallurgy. North-Holland physics Publishing, Amsterdam. [24] Guskov, A. (2008) Influence of Unequi-Librium Processes on Component Distribution under Directed Crystallization. Abstracts of 2008 China International Forum on Advanced Materials and Commercialization, Ningbo, 17-19 November 2008, 17-26. [25] Guskov, A. and Nekrasova, L. (2013) Decomposition of Solutions in Front of the Interface Induced by Directional Crystallization. Journal of Crystallization Process and Technology, 3, 170-174. [26] Beatty, K.M. and Jackson, K.A. (2004) Monte Carlo modeling of Dopant Segregation. Journal of Crystal Growth, 271, 495-512.
http://dx.doi.org/10.1016/j.jcrysgro.2004.07.074 [27] Wang, H., Liu, F., Yang, W., Chenand, Z., Yang, G. and Zhou, Y. (2008) Solute Trapping Model Incorporating Diffusive Interface. Acta Materialia, 56, 746-753. [28] Guskov, A. (2008) Influence of the Nonequilibrium Melt Layer on Stationary Regime of Directed Crystallization. Articles Collector of 18th Petersburg Lectures on Problem of Strength and Crystal Growth. Sanct-Petersburg, 21-24 October 2008, 111-113. [29] Bokshtain, B.S. (1978) Diffusion in Metal. Metallurgy, Russia.