MATERIALS
Towards the theory of evolution of spherical and ellipsoidal particles in metastable melts and solutions
- 1 Ural Federal University, Russian Federation
Abstract
This study is concerned with the dynamical laws for particle velocities in supercooled and supersaturated liquids. The cases of spherical and ellipsoidal particle shapes are considered. Also, we consider various growth conditions such as stationary and non-stationary approximations, the shift of crystallization temperature caused by the phase interface curvature, and the kinetics of atoms sticking to the solid-liquid boundary. The dynamical laws under consideration are in good agreement with experiments.
Keywords
References
- A.C. Zettlemoyer, Nucleation (Dekker, New York, 1969)
- J.W. Mullin, Crystallization (Butterworth, London, 1972)
- S. Martin, P. Kauffman, J. Fluid Mech. 64, 507 (1974)
- Y.A. Buyevich, D.V. Alexandrov, IOP Conf. Ser.: Mater. Sci. Eng. 192, 012001 (2017)
- D.V. Alexandrov, A.P. Malygin, J. Phys. A: Math. Theor. 46, 455101 (2013)
- D.V. Alexandrov, P.K. Galenko, Philos. Trans. R. Soc. A 378, 20190243 (2020)
- D.V. Alexandrov, I.G. Nizovtseva, Proc. R. Soc. A 470, 20130647 (2014)
- Yu.A. Buyevich, V.V. Mansurov, J. Cryst. Growth 104, 861 (1990)
- D.V. Alexandrov, A.P. Malygin, Modelling Simul. Mater. Sci. Eng. 22, 015003 (2014)
- D.V. Alexandrov, Phys. Lett. A 378, 1501 (2014)
- D.A. Barlow, J. Cryst. Growth 470, 8 (2017)
- I.M. Lifshitz, V.V. Slyozov, J. Phys. Chem. Solids 19, 35 (1961)
- E.M. Lifshitz, L.P. Pitaevskii, Physical kinetics (Pergamon, Oxford, 1981)
- J.R. Hunt, J. Fluid Mech. 122, 169 (1982)
- D.V. Alexandrov, Commun. Theor. Phys. 68, 269 (2017)
- Y. Enomoto, A. Okada, J. Phys.: Condens. Matter. 2, 4531 (1990)
- A.V. Alyab’eva, Yu.A. Buyevich, V.V. Mansurov, J. Phys. II (France) 4, 951 (1994)
- S. Simons, J. Phys. A: Math. Gen. 29, 1139 (1996)
- D.V. Alexandrov, J. Phys. Chem. Solids 91, 48 (2016)
- D.V. Alexandrov, I.V. Alexandrova, Philos. Trans. R. Soc. A 378, 20190247 (2020)
- D.V. Alexandrov, Phil. Mag. Lett. 96, 355 (2016)
- D.V. Alexandrov, J. Phys.: Condens. Matter 28, 035102 (2016)
- D.V. Alexandrov, J. Mater. Science 52, 6987 (2017)
- D.V. Alexandrov, J. Cryst. Growth 457, 11 (2017)
- Yu.A. Buyevich, V.V. Mansurov, I.A. Natalukha, Chem. Eng. Sci. 46, 2573 (1991)
- D.V. Alexandrov, Chem. Eng. Sci. 117, 156 (2014)
- E.V. Makoveeva, D.V. Alexandrov, Philos. Trans. R. Soc. A 376, 20170327 (2018)
- E.V. Makoveeva, D.V. Alexandrov, Philos. Trans. R. Soc. A 377, 20180210 (2019)
- Yu.A. Buyevich, I.A. Natalukha, Chem. Eng. Sci. 49, 3241 (1994)
- A.A. Ivanov, I.V. Alexandrova, D.V. Alexandrov, Philos. Trans. R. Soc. A 377, 20180215 (2019)
- D.V. Alexandrov, Phil. Mag. Lett. 96, 132 (2016)
- A.O. Ivanov, A.Yu. Zubarev, Physica A 251, 348 (1998)
- R.F. Strickland-Constable, Kinetics and mechanisms of crystallization (Academic Press, London, 1968)
- P. Bennema, Theory and experiment for crystal growth from solutions: Implications for industrial crystallization, in Industrial Crystallization, edited by J.W. Mullin (Springer, Boston, MA, 1976)
- M. Ocaña, M.P. Morales, C.J. Serna, J. Colloid Int. Sci. 171, 85 (1995)
- T. Sugimoto, A. Muramatsu, J. Colloid Int. Sci. 184, 626 (1996)
- W. Kurz, D.J. Fisher, Fundamentals of solidification (Trans. Tech. Publ., Aedermannsdorf, 1989)
- D. Herlach, P. Galenko, D. Holland-Moritz, Metastable solids from undercooled melts (Elsevier, Amsterdam, 2007)
- E.V. Makoveeva, D.V. Alexandrov, Phys. Lett. A 384, 126259 (2020)
- E.V. Makoveeva, D.V. Alexandrov, Eur. Phys. J. Special Topics 229, 2923 (2020)
- D.V. Alexandrov, J. Phys. A: Math. Theor. 51, 075102 (2018)
- D.V. Alexandrov, I.G. Nizovtseva, I.V. Alexandrova, Int. J. Heat Mass Trans. 128, 46 (2019)
- D.V. Alexandrov, I.V. Alexandrova, Philos. Trans. R. Soc. A 377, 20180209 (2019)
- K. Toyokura, K. Yamazoe, J. Mogi, N. Yago, Y. Aoyama, Secondary nucleation of potash alum, in Industrial Crystallization, edited by J.W. Mullin (Springer, Boston, MA, 1976)
- P.K. Galenko, K. Reuther, O.V. Kazak, D.V. Alexandrov, M. Rettenmayr, Appl. Phys. Lett. 111, 031602 (2017)
- I.V. Alexandrova, D.V. Alexandrov, Philos. Trans. R. Soc. A 378, 20190245 (2020)
- G.A. Korn, T.M. Korn, Mathematical handbook for scientists and engineers: definitions, theorems, and formulas for reference and review (McGraw-Hill Book Company, New York, 1968)
- M.A. Nikishina, D.V. Alexandrov, Eur. Phys. J. Special Topics 229, 2937 (2020)
- M.A. Nikishina, D.V. Alexandrov, Math. Meth. Appl. Sci. 44, 12252 (2021)
- M.A. Nikishina, D.V. Alexandrov, Eur. Phys. J. Special Topics 231, 1107 (2022)
- J. Garside, C. Gaska, J.W. Mullin, J. Cryst. Growth 13/14, 510 (1972)
- C. Laguerie, H. Angelino, Growth rate of citric acid monohydrate crystals in a liquid fluidized bed, in Industrial Crystallization, edited by J.W. Mullin (Springer, Boston, MA, 1976)
- D.V. Alexandrov, J. Phys. A: Math. Theor. 48, 245101 (2015)
- D.V. Alexandrov, A.A. Ivanov, I.V. Alexandrova, Philos. Trans. R. Soc. A 376, 20170217 (2018)
- D.V. Alexandrov, A.Y. Zubarev, Philos. Trans. R. Soc. A 377, 20180353 (2019)
- D.V. Alexandrov, A.A. Ivanov, I.V. Alexandrova, J. Phys. A: Math. Theor. 52, 015101 (2019)
- D.V. Alexandrov, A.Y. Zubarev, Philos. Trans. R. Soc. A 378, 20200002 (2020)
- D.V. Alexandrov, Eur. Phys. J. Special Topics 229, 383 (2020)
- D.V. Alexandrov, Acta Mater. 49, 759 (2001)
- D.V. Alexandrov, A.P. Malygin, I.V. Alexandrova, Ann. Glaciol. 44, 118 (2006)
- D.L. Aseev, D.V. Alexandrov, Int. J. Heat Mass Trans. 49, 4903 (2006)
- D.V. Alexandrov, I.G. Nizovtseva, Int. J. Heat Mass Trans. 51, 5204 (2008)
- P.K. Galenko, D.V. Alexandrov, Philos. Trans. R. Soc. A 376, 20170210 (2018)
- P.K. Galenko, D.V. Alexandrov, E.A. Titova, Philos. Trans. R. Soc. A 376, 20170218 (2018)
- D.V. Alexandrov, I.A. Bashkirtseva, L.B. Ryashko, Philos. Trans. R. Soc. A 376, 20170216 (2018)
- I.G. Nizovtseva, D.V. Alexandrov, Philos. Trans. R. Soc. A 378, 20190248 (2020)
- G.P. Yasnikov, J. Eng. Phys. 42, 163 (1982)
- Yu.A. Buyevich, Yu.M. Goldobin, G.P. Yasnikov, Int. J. Heat Mass Trans. 37, 3003 (1994)
- Yu.A. Buyevich, N.A. Korolyova, I.A. Natalukha, Int. J. Heat Mass Trans. 36, 2223 (1993)
- Yu.A. Buyevich, N.A. Korolyova, I.A. Natalukha, Int. J. Heat Mass Trans. 36, 2233 (1993)
- K. Masters, Spray drying in practice (Spray Dry Consult, Charlottenlund, Denmark, 2002)
- A.A. Ivanov, D.V. Alexandrov, I.V. Alexandrova, Philos. Trans. R. Soc. A 378, 20190246 (2020)
- J. Schlichtkrull, Acta Chem. Scand. 11, 439 (1957)
- J. Schlichtkrull, Acta Chem. Scand. 11, 1248 (1957)
- D.V. Alexandrov, A.A. Ivanov, I.G. Nizovtseva, S. Lippmann, I.V. Alexandrova, E.V. Makoveeva, Crystals 12, 949 (2022)