Abstract
The influence of the phase transition temperature shift on the growth dynamics of a polydisperse ensemble of spherical crystals in metastable melts and solutions is studied. This shift is connected with the Gibbs–Thomson effect and the attachment kinetics of atoms at the phase transition interfaces of evolving crystals. The nonlinear model of kinetic and balance equations with allowance for the particle “diffusion” term is solved analytically. The obtained solution is compared with the case when this temperature shift is not taken into account. It is shown that the Gibbs–Thomson and attachment kinetics effects slightly accelerate the system desupercooling for a single-component titanium melt. This shifts the particle-size distribution function and changes the shape of its tail, which is responsible for the concluding stage of Ostwald ripening.
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References
D. Herlach, P. Galenko, D. Holland-Moritz,Metastable solids from undercooled melts (Elsevier, Amsterdam, 2007)
V.G. Dubrovskii,Nucleation theory and growth of nanostructures (Springer, Berlin, 2014)
P.K. Galenko, D.V. Alexandrov, Philos. Trans. R. Soc. A 376, 20170210 (2018)
D.V. Alexandrov, A.Yu. Zubarev, Philos. Trans. R. Soc. A 377, 20180353 (2019)
D.V. Alexandrov, A.Yu. Zubarev, Philos. Trans. R. Soc. A 378, 20200002 (2020)
W. Kurz, D.J. Fisher,Fundamentals of solidification (Trans. Tech. Publ., Aedermannsdorf, 1989)
A.H. Janse,Nucleation and crystal growth in batch crystallizers (Delft University of Technology, Delft, 1977)
A. Pot,Industrial sucrose crystallization (Delft University of Technology, Delft, 1980)
I.V. Alexandrova, D.V. Alexandrov, Philos. Trans. R. Soc. A 378, 20190245 (2020)
D.A. Barlow, J. Cryst. Growth 311, 2480 (2009)
D.V. Alexandrov, I.G. Nizovtseva, Philos. Trans. R. Soc. A 377, 20180214 (2019)
I.H. Leubner, J. Disp. Sci. Technol. 23, 577 (2002)
K.F. Kelton, A.L. Greer,Nucleation in condensed matter: applications in materials and biology (Elsevier, Amsterdam, 2008)
E.M. Lifshitz, L.P. Pitaevskii,Physical kinetics (Pergamon, Oxford, 1981)
D.V. Alexandrov, Philos. Mag. Lett. 94, 786 (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)
D.V. Alexandrov, Phys. Lett. A 378, 1501 (2014)
V.A. Shneidman, Phys. Rev. E 82, 031603 (2010)
V.A. Shneidman, Phys. Rev. E 84, 031602 (2011)
D.V. Alexandrov, P.K. Galenko, L.V. Toropova, Philos. Trans. R. Soc. A 376, 20170215 (2018)
P.K. Galenko, D.V. Alexandrov, E.A. Titova, Philos. Trans. R. Soc. A 376, 20170218 (2018)
V.P. Koverda, V.N. Skokov, V.P. Skripov, Phys. Status Solidi A 74, 343 (1982)
J. Gao, M. Han, A. Kao, K. Pericleous, D.V. Alexandrov, P.K. Galenko, Acta Mater. 103, 184 (2016)
P.K. Galenko, K. Reuther, O.V. Kazak, D.V. Alexandrov, M. Rettenmayr, Appl. Phys. Lett. 111, 031602 (2017)
D.V. Alexandrov, A.P. Malygin, J. Phys. A: Math. Theor. 46, 455101 (2013)
D.V. Alexandrov, I.V. Alexandrova, Philos. Trans. R. Soc. A 377, 20180209 (2019)
D.V. Alexandrov, I.V. Alexandrova, A.A. Ivanov, A.P. Malygin, I.O. Starodumov, L.V. Toropova, Russ. Metall. (Metally) 2019, 787 (2019)
V.A. Ditkin, A.P. Prudnikov,Integral transforms and operational calculus (Pergamon Press, Oxford, 1965)
V.V. Slezov, J. Phys. Chem. Solids 39, 367 (1978)
V.V. Slezov,Kinetics of first-order phase transitions (Wiley, VCH, Weinheim, 2009)
D.V. Alexandrov, J. Phys. A: Math. Theor. 48, 035103 (2015)
D.V. Alexandrov, I.V. Alexandrova, Philos. Trans. R. Soc. A 378, 20190247 (2020)
D.V. Alexandrov, J. Phys. Chem. Solids 91, 48 (2016)
R.N. Hills, D.E. Loper, P.H. Roberts, Q. J. Mech. Appl. Math. 36, 505 (1983)
A.C. Fowler, IMA J. Appl. Maths 35, 159 (1985)
V.T. Borisov,Theory of two-phase zone of a metal ingot (Metallurgiya Publishing House, Moscow, 1987)
A.A. Ivanov, I.V. Alexandrova, D.V. Alexandrov, Philos. Trans. R. Soc. A 377, 20180215 (2019)
D.V. Alexandrov, A.A. Ivanov, I.V. Alexandrova, Philos. Trans. R. Soc. A 376, 20170217 (2018)
R.C. Kerr, A.W. Woods, M.G. Worster, H.E. Huppert, J. Fluid Mech. 216, 323 (1990)
M.G. Worster, J. Fluid Mech. 167, 481 (1986)
D.V. Alexandrov, I.A. Bashkirtseva, L.B. Ryashko, Philos. Trans. R. Soc. A 376, 20170216 (2018)
D.V. Alexandrov, A.P. Malygin, Int. J. Heat Mass Trans. 54, 1144 (2011)
D.V. Alexandrov, Int. J. Heat Mass Trans. 47, 1383 (2004)
A.A. Ivanov, I.V. Alexandrova, D.V. Alexandrov, Eur. Phys. J. Special Topics 229, 365 (2020)
D.V. Alexandrov, Eur. Phys. J. Special Topics 229, 383 (2020)
I.G. Nizovtseva, D.V. Alexandrov, Philos. Trans. R. Soc. A 378, 20190248 (2020)
D.L. Aseev, D.V. Alexandrov, Acta Mater. 54, 2401 (2006)
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Makoveeva, E.V., Alexandrov, D.V. How the shift in the phase transition temperature influences the evolution of crystals during the intermediate stage of phase transformations. Eur. Phys. J. Spec. Top. 229, 2923–2935 (2020). https://doi.org/10.1140/epjst/e2020-000113-3
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DOI: https://doi.org/10.1140/epjst/e2020-000113-3