References |
Kurz, W., Fisher, D.J., (1992) Fundamentals of Solidification, , Aedermannsdorf: Trans. Tech; Herlach, D.M., Galenko, P., Holland-Moritz, D., (2007) Metastable Solids from Undercooled Melts, , Amsterdam: Elsevier; Asta, M., Beckermann, C., Karma, A., Kurz, W., Napolitano, R., Plapp, M., Purdy, G., Trivedi, R., Solidification microstructures and solid-state parallels: recent developments, future directions (2009) Acta Mater., 57, pp. 941-971; Galenko, P.K., Funke, O., Wang, J., Herlach, D.M., Kinetics of dendritic growth under the influence of convective flow in solidification of undercooled droplets (2004) Mater. Sci. Eng. A, 488, pp. 375-377; Funke, O., Phanikumar, G., Galenko, P.K., Chernova, L., Reutzel, S., Kolbe, M., Herlach, D.M., Dendrite growth velocity in levitated undercooled nickel melts (2006) J. Cryst. Growth, 297, pp. 211-222; Ivantsov, G.P., Temperature field around a spherical, cylindrical, or needlelike dendrite growing in a super-cooled melt (1947) Dokl. Akad. Nauk SSSR, 58, pp. 567-570; Ivantsov, G.P., On the growth of a spherical or a needlelike crystal of a binary alloy (1952) Dokl. Akad. Nauk SSSR, 83, pp. 573-576; Temkin, D.E., On the growth of a crystalline needle in a supercooled melt (1960) Dokl. Akad. Nauk SSSR, 132, pp. 1307-1310; Temkin, D.E., Growth kinetics of a crystalline needle in a supercooled binary melt (1962) Kristallografiya, 7, pp. 446-450; Horvay, G., Cahn, J.W., Dendritic and spheroidal growth (1961) Acta Metall., 9, pp. 695-705; Mullins, W.W., Sekerka, R.F., Stability of a planar interface during solidification of a dilute binary alloy (1964) J. Appl. Phys., 35, pp. 444-451; Nash, G.E., Glicksman, M.E., Capillarity-limited steady-state dendritic growth: I. Theoretical development (1974) Acta Metall., 22, pp. 1283-1290; Langer, J.S., Müller-Krunbhaar, H., Theory of dendritic growth: I. Elements of a stability analysis (1978) Acta Metall., 26, pp. 1681-1687; Willnecker, R., Herlach, D., Feuerbacher, B., Evidence of nonequilibrium processes in rapid solidification of undercooled metals (1989) Phys. Rev. Lett., 62, pp. 2707-2710; Kessler, D.A., Koplik, J., Levine, H., Pattern selection in fingered growth phenomena (1988) Adv. Phys., 37, pp. 255-339; Brener, E., Melnikov, V.I., Pattern selection in two-dimensional dendritic growth (1991) Adv. Phys., 40, pp. 53-97; Dash, S.K., Gill, W.N., Forced convection heat and momentum transfer to dendritic structures (parabolic cylinders and paraboloids of revolution) (1984) Int. J. Heat Mass Transf., 27, pp. 1345-1356; Ben-Amar, M., Bouisou, P., Pelce, P., An exact solution for the shape of a crystal growing in a forced flow (1988) J. Cryst. Growth, 92, pp. 97-100; Bouissou, P., Pelce, P., Effect of a forced flow on dendritic growth (1989) Phys. Rev. A, 40, pp. 6673-6680; Ben Amar, M., Pelce, P., Impurity effect on dendritic growth (1989) Phys. Rev. A, 39, pp. 4263-4269; Alexandrov, D.V., Galenko, P.K., Malygin, A.P., Kherlakh, D.M., Selection of the steady-state growth mode of the tip of a parabolic dendrite during the forced convection flow and solidification of a binary liquid (2010) Vestn. Udmurt, Univ., 1, pp. 3-16; Alexandrov, D.V., Galenko, P.K., Herlach, D.M., Selection criterion for the growing dendritic tip in a non-isothermal binary system under forced convective flow (2010) J. Crystal Growth, 312, pp. 2122-2127; Bokshtein, B.S., (1978) Diffusion in Metals, , Moscow: Metallurgiya; Praizey, J.P., Benefits of microgravity for measuring thermotransport coefficients in liquid metallic alloys (1989) Int. J. Heat Mass Trans., 32, pp. 2385-2401; van Vaerenbergh, S., Garandet, J.P., Praizey, J.P., Legros, J.C., Reference Soret coefficients of natural isotopes and diluted alloys of tin (1998) Phys. Rev. E, 58, pp. 1866-1873; van Vaerenbergh, S., Coriell, S.R., McFadden, G.B., Murray, B.T., Legros, J.C., Modification of morphological stability by Soret diffusion (1995) J. Crystal Growth, 147, pp. 207-214; van Vaerenbergh, S., Coriell, S.R., McFadden, G.B., Morphological stability of a binary alloy: thermodiffusion and temperature-dependent diffusivity (2001) J. Crystal Growth, 223, pp. 565-572; Hollinger, S., Lücke, M., Influence of the Dufour effect on convection in binary gas mixtures (1995) Phys. Rev. E, 52, pp. 642-657; Bruson, A., Gerl, M., Diffusion coefficient of Sn, Sb, Ag and Au in liquid Sn (1980) Phys. Rev. B, 21, pp. 5447-5454; Huppert, H.E., The fluid mechanics of solidification (1990) J. Fluid Mech., 212, pp. 209-240; Warren, J.A., Langer, J.S., Prediction of dendritic spacings in a directional-solidification experiment (1993) Phys. Rev. E, 47, pp. 2702-2712; Buyevich, Y.A., Alexandrov, D.V., Mansurov, V.V., (2001) Macrokinetics of Crystallization, , New York: Begell House; Borisov, V.T., Vinogradov, V.V., Tyazhel'nikova, I.L., Quasiequilibrium theory of the mushy zone and its application to the solidification of alloys (1977) Izv. Vyssh. Uchebn. Zaved., Chern. Metall., (5), pp. 127-134; Hills, R.N., Loper, D.E., Roberts, P.H., A thermodynamically consistent model of a mushy zone (1983) Q. J. Mech. Appl. Math., 36, pp. 505-539; Borisov, V.T., (1987) Theory of the Mushy Zone of a Metallic Ingot, , Moscow: Metallurgiya; Alexandrov, D.V., On the theory of solidification with a quasiu-equilibrium mushy zone (2000) Dokl. Ross. Akad. Nauk, 375 (2), pp. 172-176; Alexandrov, D.V., Solidification with a quasiequilibrium mushy zone: exact analytical solution (2000) Int. J. Fluid Mech. Research, 27 (2-4), pp. 213-222; Alexandrov, D.V., Solidification with a quasiequilibrium mushy region: analytical solution of nonlinear model (2001) J. Crystal Growth, 222, pp. 816-821; Alexandrov, D.V., Solidification with a quasiequilibrium two-phase zone (2001) Acta Materialia, 49, pp. 759-764; Aseev, D.L., Alexandrov, D.V., Unidirectional solidification with a mushy layer. The influence of weak convection (2006) Acta Materialia, 54, pp. 2401-2406; Alexandrov, D.V., Rakhmatullina, I.V., Malygin, A.P., On the theory of solidification with a two-phase concentration supercooling zone (2010) Rasplavy, 4, pp. 88-96; Malygin, A.P., Alexandrov, D.V., Analytical description of the quasi-stationary solidification of ternary systems (2011) Rasplavy, 6, pp. 11-24; Alexandrov, D.V., Malygin, A.P., Aleksandrova, I.V., Quasi-stationary solidification of ternary systems in the presence of mobile phase transition regions (2011) Vestn. Udmurt. Univ., 2, pp. 12-23; Alexandrov, D.V., Malygin, A.P., Self-similar solidification of an alloy from a cooled boundary (2006) Int. J. Heat and Mass Transfer, 49, pp. 763-769; Alexandrov, D.V., Nonlinear dynamics of solidification of three-component systems (2008) Dokl. Ross. Akad. Nauk, 422 (3), pp. 322-326; Alexandrov, D.V., Ivanov, A.A., Malygin, A.P., On the theory of nonstationary solidification in the presence of a mushy zone (2008) Rasplavy, 5, pp. 69-76; Alexandrov, D.V., Ivanov, A.A., Malygin, A.P., Self-similar solidification with a mushy zone from a cooled wall (2008) Vestn. Udmurt. Univ., 1, pp. 14-25; Alexandrov, D.V., Ivanov, A.A., Malygin, A.P., Self-similar solidification of binary alloys (2009) Acta Physica Polonica A, 115, pp. 795-799; Alexandrov, D.V., Ivanov, A.A., The Stefan problem of solidification of ternary systems in the presence of moving phase transition regions (2009) J. Exp. Theor. Phys., 135, pp. 858-964; Alexandrov, D.V., Ivanov, A.A., Analytical solution for a problem of directional solidification in a ternary system (2009) Acta Physica Polonica A, 115, pp. 786-790; Alexandrov, D.V., Ivanov, A.A., Nonlinear dynamics of directional solidification of ternary solutions with mushy layers (2009) Heat Mass Transfer, 45, pp. 1467-1472; Alexandrov, D.V., Ivanov, A.A., Solidification of a ternary melt from a cooled boundary or nonlinear dynamics of mushy layers (2009) Int. J. Heat Mass Transfer, 52, pp. 4807-4811; Alexandrov, D.V., Churbanov, A.G., Vabishchevich, P.N., Emergence of a mushy region in processes of binary melt solidification (1999) Int. J. Fluid Mech. Research, 26 (2), pp. 248-264; Alexandrov, D.V., Incipience of a mushy zone in binary melt solidification processes (2000) Int. J. Fluid Mech. Research, 27 (2-4), pp. 223-238; Alexandrov, D.V., On the theory of the nucleation of a concentration supercooling mushy zone (2003) Dokl. Ross. Akad. Nauk, 392, pp. 322-327; Alexandrov, D.V., Malygin, A.P., Analytical description of the crystallography of sea water in ice cracks and their effect on the ocean-atmosphere heat exchange (2006) Dokl. Ross. Akad. Nauk, 411 (3), pp. 390-394; Alexandrov, D.V., Aseev, D.L., Nizovtseva, I.G., Huang, H.-N., Lee, D., Nonlinear dynamics of directional solidification with a mushy layer. Analytic solutions of the problem (2007) Int. J. Heat Mass Transfer, 50, pp. 3616-3623; Alexandrov, D.V., Nizovtseva, I.G., Malygin, A.P., Huang, H.-N., Lee, D., Unidirectional solidification of binary melts from a cooled boundary: analytical solutions of a nonlinear diffusion-limited problem (2008) J. Phys.: Cond. Matt., 20. , 114105-01-11410506; Alexandrov, D.V., Nizovtseva, I.G., Lee, D., Huang, H.-N., Solidification from a cooled boundary with a mushy layer under conditions of nonturbulent and turbulent heat and mass transfer in the ocean (2010) Int. J. Fluid Mech. Research, 37 (1), pp. 1-14; Alexandrov, D.V., Nizovtseva, I.G., Nonlinear dynamics of the false bottom during the solidification of sea water (2008) Dokl. Ross. Akad. Nauk, 419, pp. 262-265; Alexandrov, D.V., Nizovtseva, I.G., To the theory of underwater ice evolution, or nonlinear dynamics of "false bottoms (2008) Int. J. Heat Mass Transfer, 51, pp. 5204-5208; Alexandrova, I.V., Alexandrov, D.V., Aseev, D.L., Bulitcheva, S.V., Mushy layer formation during solidification of binary alloys from a cooled wall: the role of boundary conditions (2009) Acta Physica Polonica A, 115, pp. 791-794; Alexandrov, D.V., Malygin, A.P., Alexandrova, I.V., Solidification of leads: approximate solutions of nonlinear problem (2006) Annals of Glaciology, 44, pp. 118-122; Alexandrov, D.V., Netreba, A.V., Malygin, A.P., On the theory of directional solidification with a phase transition zone under convection and kinetics in a melt (2011) Rasplavy, 4, pp. 62-76; Alexandrov, D.V., Malygin, A.P., Effect of convection, anisotropy, and heterogeneity of a medium in the structure-phase transitions during solidification (2010) Dokl. Ross. Akad. Nauk, 434, pp. 327-331; Alexandrov, D.V., Aseev, D.L., One-dimensional solidification of an alloy with a mushy zone: thermodiffusion and temperature-dependent diffusivity (2005) J. Fluid Mechanics, 527, pp. 57-66; Alexandrov, D.V., Aseev, D.L., Directional solidification with a two-phase zone: thermodiffusion and temperature-dependent diffusivity (2006) Computational Materials Science, 37, pp. 1-6; Lamb, G., (1947) Hydrodynamics, , Moscow: OGIZ; Kochin, N.E., Kibel', I.A., Roze, N.V., (1947) Theoretical Hydromechanics, , Moscow: OGIZ; Alexandrov, D.V., Mansurov, V.V., Methodical notes on the strong solution of some well-known problems of hydrodynamics (1999) Int. J. Fluid Mech. Research, 26, pp. 232-247; Aseev, D.L., Aleksandrov, D.V., Nonlinear solidification dynamics of binary melts with a nonequilibrium mushy zone (2006) Dokl. Ross. Akad. Nauk, 408, pp. 609-613; Aseev, D.L., Alexandrov, D.V., Directional solidification of binary melts with a non-equilibrium mushy layer (2006) International J. Heat and Mass Transfer, 49, pp. 4903-4909; Alexandrov, D.V., Aseev, D.L., Malygin, A.P., On the theory of the solidification processes with a nonequilibrium mushy zone (2011) Rasplavy, 1, pp. 16-30; Alexandrov, D.V., Mansurov, V.V., Galenko, P.K., Morphological stability of the plane interface of the phases in a binary melt during high-rate solidification (1996) Dokl. Ross. Akad. Nauk, 351, pp. 37-39; Alexandrov, D.V., Mansurov, V.V., Dynamic instability of the quasi-stationary solidification of a binary melt in the presence of a narrow quasi-equilibrium mushy zone (1996) Kristallografiya, 41 (2), pp. 376-378; Alexandrov, D.V., Mansurov, V.V., Dynamic stability of a solidification process of a binary melt in the presence of a broad quasiequilibrium mushy region (1996) Scripta Materialia, 35 (7), pp. 787-790; Alexandrov, D.V., Mansurov, V.V., Dynamic instability of the quasi-stationary solidification of a binary melt in the presence of a broad quasi-equilibrium mushy zone (1997) Kristallografiya, 42 (3), pp. 402-404; Alexandrov, D.V., Linear analysis of dynamic instability of solidification with a quasiequilibrium mushy zone (2000) Int. J. Fluid Mech. Research, 27 (2-4), pp. 239-247; Alexandrov, D.V., The effect of concentrational supercooling on the morphological stability of self-similar solidification with a planar front (2001) Doklady Physics, 46, pp. 453-458; Alexandrov, D.V., Ivanov, A.O., Dynamic stability analysis of the solidification of binary melts in the presence of a mushy region: changeover of instability (2000) J. Crystal Growth, 210, pp. 797-810; Alexandrov, D.V., A nonlinear instability analysis of crystallization processes with a two-phase zone (2004) J. Metast. Nanocryst. Mater., 20-21, pp. 468-475; Alexandrov, D.V., Malygin, A.P., Convective instability of directional crystallization in a forced flow: The role of brine channels in a mushy layer on nonlinear dynamics of binary systems (2011) Int. J. Heat Mass Transfer, 54, pp. 1144-1149; Alexandrov, D.V., Malygin, A.P., Convective instability of solidification with a phase transition zone (2011) Zh. Eksp. Teor. Fiz., 139, pp. 688-694; Alexandrov, D.V., Malygin, A.P., Coupled convective and morphological instability of the inner core boundary of the Earth (2011) Physics of the Earth and Planetary Interiors, 189, pp. 134-141 |