Transient nucleation kinetics of crystal growth at the intermediate stage of bulk phase transitions / Alexandrov D.V., Malygin A.P. // Journal of Physics A: Mathematical and Theoretical. - 2013. - V. 46, l. 45.

ISSN:
17518113
Type:
Article
Abstract:
A complete analytical solution of an integro-differential model describing the transient nucleation of solid particles and their subsequent growth at the intermediate stage of phase transitions in metastable systems is constructed. A Fokker-Plank type equation for the density distribution function is solved exactly for arbitrary nucleation kinetics. A non-linear integral equation with memory kernel connecting the density distribution function and the system supercooling/supersaturation is analytically solved on the basis of the saddle-point method for the Laplace integral. The analytical solution obtained shows that the process at the intermediate stage is divided into three phases: initially the high rate nucleation stage occurs, then this process is accompanied by the particle growth reducing the level of metastability, and finally the mechanism of particle coarsening becomes predominant. © 2013 IOP Publishing Ltd.
Author keywords:
Index keywords:
нет данных
DOI:
10.1088/1751-8113/46/45/455101
Смотреть в Scopus:
https://www.scopus.com/inward/record.uri?eid=2-s2.0-84887269184&doi=10.1088%2f1751-8113%2f46%2f45%2f455101&partnerID=40&md5=614928abedd2b8aaa1c1e4fa829275a4
Соавторы в МНС:
Другие поля
Поле Значение
Art. No. 455101
Link https://www.scopus.com/inward/record.uri?eid=2-s2.0-84887269184&doi=10.1088%2f1751-8113%2f46%2f45%2f455101&partnerID=40&md5=614928abedd2b8aaa1c1e4fa829275a4
Affiliations Department of Mathematical Physics, Ural Federal University, Lenin ave. 51, Ekaterinburg, 620000, Russian Federation
References Madras, G., McCoy, B.J., Transition from nucleation and growth to Ostwald ripening (2002) Chemical Engineering Science, 57 (18), pp. 3809-3818. , DOI 10.1016/S0009-2509(02)00313-5, PII S0009250902003135; Zhang, T.H., Liu, X.Y., Nucleation: What happens at the initial stage? (2009) Angew. Chem. Int. Edn, 48, pp. 1308-1312. , 10.1002/anie.200804743 1433-7851; Uwaha, M., Koyama, K., Transition from nucleation to ripening in the classical nucleation model (2010) J. Cryst. Growth, 312, pp. 1046-1054. , 10.1016/j.jcrysgro.2010.01.017 0022-0248; Chernov, A.A., (1984) Modern Crystallography III, , 10.1007/978-3-642-81835-6; Chalmers, B., (1959) Physical Metallurgy; Todes, O.M., Seballo, V.A., Gol'Tsiker, L.D., (1984) Bath Crystallization from Solutions; Poon, J.M.-H., Immanuel, C.D., Doyle III, F.J., Litser, J.D., A three-dimensional population balance model of granulation with a mechanistic representation of the nucleation and aggregation phenomena (2008) Chem. Eng. Sci., 63, pp. 1315-1329. , 10.1016/j.ces.2007.07.048 0009-2509; Poon, J.M.-H., Ramachandran, R., Sanders, C.F.W., Glaser, T., Immanuel, C.D., Doyle III, F.J., Litser, J.D., Cameron, I.T., Experimental validation studies on a multi-scale and multi-dimensional population balance model of batch granulation (2009) Chem. Eng. Sci., 64, pp. 775-786. , 10.1016/j.ces.2008.08.037 0009-2509; Aseev, D.L., Alexandrov, D.V., Nonlinear dynamics for the solidification of binary melt with a nonequilibrium two-phase zone (2006) Doklady Physics, 51 (6), pp. 291-295. , DOI 10.1134/S1028335806060024; Aseev, D.L., Alexandrov, D.V., Directional solidification of binary melts with a non-equilibrium mushy layer (2006) International Journal of Heat and Mass Transfer, 49 (25-26), pp. 4903-4909. , DOI 10.1016/j.ijheatmasstransfer.2006.05.046, PII S001793100600411X; Alexandrov, D.V., Malygin, A.P., Coupled convective and morphological instability of the inner core boundary of the Earth (2011) Phys. Earth Planet. Inter., 189, pp. 134-141. , 10.1016/j.pepi.2011.08.004 0031-9201; Thompson, C.V., Spaepen, F., Homogeneous crystal nucleation in binary metallic melts (1983) Acta Metallurgica, 31 (12), pp. 2021-2027. , DOI 10.1016/0001-6160(83)90019-6; Kelton, K.F., Greer, A.L., (2010) Nucleation in Condensed Matter: Applications in Materials and Biology; Zettlemoyer, A.C., (1969) Nucleation; Volmer, M., (1939) Kinetik der Phasenbildung; Frenkel, J., (1955) Kinetic Theory of Liquids; Velmurugan, J., Noël, J.-M., Nogala, W., Mirkin, M.V., Nucleation and growth of metal on nanoelectrodes (2012) Chem. Sci., 3, pp. 3307-3314. , 10.1039/c2sc21005c; Lifshitz, I.M., Slyozov, V.V., The kinetics of precipitation from supersaturated solid solutions (1961) J. Phys. Chem. Solids, 19, pp. 35-50. , 10.1016/0022-3697(61)90054-3 0022-3697; Tokuyama, M., Kawasaki, M., Enomoto, V., Kinetic equations for Ostwald ripening (1986) Physica, 134, pp. 323-338. , 10.1016/0378-4371(86)90053-1 0378-4371 A; Akaiwa, N., Meiron, D.I., Numerical simulation of two-dimensional late-stage coarsening for nucleation and growth (1995) Phys. Rev., 51, pp. 5408-5421. , 10.1103/PhysRevE.51.5408 1063-651X E; Farjoun, Y., Neu, J.C., Aggregation according to classical kinetics: From nucleation to coarsening (2011) Phys. Rev., 83. , 10.1103/PhysRevE.83.051607 1063-651X E 051607; Avrami, M., Granulation, phase change, and microstructure kinetics of phase change: III (1941) J. Chem. Phys., 9, pp. 177-184. , 10.1063/1.1750872; Aastuen, D.J.W., Clark, N.A., Swindal, J.C., Muzny, C.D., Determination of the colloidal crystal nucleation rate density (1990) Phase Transit., 21, pp. 139-155. , 10.1080/01411599008206887 0141-1594; Binder, K., Stauffer, D., Statistical theory of nucleation, condensation and coagulation (1976) Adv. Phys., 25, pp. 343-396. , 10.1080/00018737600101402 0001-8732; Langer, J.S., Schwartz, A.J., Kinetics of nucleation in near-critical fluids (1980) Phys. Rev., 21, pp. 948-958. , 10.1103/PhysRevA.21.948 0556-2791 A; Shneidman, V.A., Transient nucleation with a monotonically changing barrier (2010) Phys. Rev., 82. , 10.1103/PhysRevE.82.031603 1063-651X E 031603; Shneidman, V.A., Time-dependent distributions in self-quenching nucleation (2011) Phys. Rev., 84. , 10.1103/PhysRevE.84.031602 1063-651X E 031602; Buyevich Yu, A., Mansurov, V.V., Kinetics of the intermediate stage of phase transition in batch crystallization (1990) J. Cryst. Growth, 104, pp. 861-867. , 10.1016/0022-0248(90)90112-X 0022-0248; Solomatov, V.S., Stevenson, D.J., Kinetics of crystal growth in a terrestrial magma ocean (1993) Journal of Geophysical Research, 98 (E3), pp. 5407-5418; Buyevich Yu, A., Ivanov, A.O., Kinetics of phase separation in colloids: II. Non-linear evolution of a metastable colloid (1993) Physica, 193, pp. 221-240. , 10.1016/0378-4371(93)90027-2 0378-4371 A; Ivanov, A.O., Zubarev, A.Yu., Non-linear evolution of a system of elongated droplike aggregates in a metastable magnetic fluid (1998) Physica A: Statistical Mechanics and its Applications, 251 (3-4), pp. 348-367. , PII S037843719700561X; Barlow, D.A., Theory of the intermediate stage of crystal growth with applications to protein crystallization (2009) J. Cryst. Growth, 311, pp. 2480-2483. , 10.1016/j.jcrysgro.2009.02.035 0022-0248; Barlow, D.A., Baird, J.K., Su, C.-H., Theory of the von Weimarn rules governing the average size of crystals precipitated from a supersaturated solution (2004) J. Cryst. Growth, 264, pp. 417-423. , 10.1016/j.jcrysgro.2003.12.047 0022-0248; Buyevich Yu, A., Alexandrov, D.V., (2005) Heat Transfer in Dispersions; Volmer, M., Weber, A., Keimbildung in übersättigten Gebilden (1926) Z. Phys. Chem., 119, pp. 277-301; Zel'Dovich, J.B., On the theory of formation of new phases: Cavitation (1942) J. Exp. Theor. Phys., 12, pp. 525-538; Lifshitz, E.M., Pitaevskii, L.P., (1981) Physical Kinetics; Landau, L.D., Lifshitz, E.M., (1980) Statistical Physics; Mullin, J.W., (1972) Crystallization; Gherras, N., Fevotte, G., Comparison between approaches for the experimental determination of metastable zone width: A case study of the batch cooling crystallization of ammonium oxalate in water (2012) J. Cryst. Growth, 342, pp. 88-98. , 10.1016/j.jcrysgro.2011.06.058 0022-0248; Avdonin, N.A., (1980) Mathematical Description of Crystallization Processes; Kidyarov, B.I., (1979) Kinetics of Crystal Formation from the Liquid Phase; Nguyen, T.N.P., Kim, K.-J., Kinetic study on hemipenta hydrate risedronate monosodium in batch crystallization by cooling mode (2008) Int. J. Pharm., 364, pp. 1-8. , 10.1016/j.ijpharm.2008.05.037 0378-5173; Randolph, A., Larson, M., (1988) Theory of Particulate Processes; Nývlt, J., Söhnel, O., Matuchova, M., Broul, M., (1985) The Kinetics of Industrial Crystallization; Fedoruk, M.V., (1977) Saddle-Point Method; Skripov, V.P., (1974) Metastable Liquids; Porter, D.A., Easterling, K.E., (1981) Phase Transformations in Metals and Alloys; Hamza, M.A., Berge, B., Mikosch, W., Rühl, E., Homogeneous nucleation of supersaturated KCl-solutions from single levitated microdroplets (2004) Phys. Chem. Chem. Phys., 6, pp. 3484-3489. , 10.1039/b401807a 1463-9076; Alexandrov, D.V., Malygin, A.P., Flow-induced morphological instability and solidification with the slurry and mushy layers in the presence of convection (2012) Int. J. Heat Mass Transfer, 55, pp. 3196-3204. , 10.1016/j.ijheatmasstransfer.2012.02.048 0017-9310; Janse, A.H., (1977) Nucleation and Crystal Growth in Batch Crystallizers; Pot, A., (1980) Industrial Sucrose Crystallization; Leubner, I.H., Balanced nucleation and growth model for controlled crystal size distribution (2002) Journal of Dispersion Science and Technology, 23 (4), pp. 577-590. , DOI 10.1081/DIS-120014026; Hanhoun, M., Montastruc, L., Azzaro-Pantel, C., Biscans, B., Frèche, M., Pibouleau, L., Simultaneous determination of nucleation and crystal growth kinetics of struvite using a thermodynamic modeling approach (2013) Chem. Eng. J., 215-216, pp. 903-912. , 10.1016/j.cej.2012.10.038 1385-8947; Perez, M., Gibbs-Thomson effects in phase transformations (2005) Scripta Materialia, 52 (8), pp. 709-712. , DOI 10.1016/j.scriptamat.2004.12.026, PII S1359646204007195
Correspondence Address Department of Mathematical Physics, Ural Federal University, Lenin ave. 51, Ekaterinburg, 620000, Russian Federation
Language of Original Document English
Abbreviated Source Title J. Phys. Math. Theor.
Source Scopus