Abstract
The possibility of using the Cahn–Hilliard theory in the process of electrodeposition of nanostructures is studied. A correlation between the microscopic parameters included in the calculation formulas and the experimental kinetic coefficients is found. The theoretical results can explain the choice of the optimal parameters of electrochemical deposition.
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Weston, D.P., Gill, S.P.A., Fay, M., Harris, S.J., et al., Surf. Coat. Technol., 2013, vol. 236, pp. 75–83.
Weston, D.P., Harris, S.J., Shipway, P.H., Weston, N.J., et al., Electrochim. Acta, 2013, vol. 55, pp. 5695–5708.
Gamburg, Yu.D. and Zangari, G., Theory and Practice of Metal Electrodeposition, New York: Springer-Verlag, 2011.
Cahn, J.W. and Hilliard, D.J.E., J. Chem. Phys., 1958, vol. 28, no. 2, pp. 258–267.
Cahn, J.W. and Hilliard, D.J.E., J. Chem. Phys., 1959, vol. 30, no. 5, pp. 1121–1124.
Cahn, J.W. and Hilliard, D.J.E., J. Chem. Phys., 1959, vol. 30, no. 5, pp. 688–699.
Cahn, J.W., Trans. Metall. Soc., 1968, vol. 242, pp. 166–170.
Cahn, J.W. and Larché, F.C., Acta Metall., 1982, vol. 30, pp. 51–56.
Hillert, M., Metall Trans A. 1975, vol. 6, no. 1, pp. 5–19.
Khachaturyan, A.G., Theory of Structural Transformations in Solids, New York: Wiley, 1983.
Landau, L.D. and Lifshits, E.M., K teorii dispersii magnitnoi pronitsaemosti ferromagnitnykh tel. Sobranie trudov (The Theory of Dispersion of the Magnetic Permeability of the Ferromagnetic Bodies: Collection of Research Works), Moscow: Nauka, 1969, vol. 1, pp. 128–143.
Vonsovskii, S.V., Magnetizm (Magnetism), Moscow: Nauka, 1971.
Brown, W.F., Jr., Micromagnetics, New York: Wiley, 1963.
Gibbs, J.W., The Collected Works of J. Willard Gibbs, Vol. 1: Thermodynamics, New York: Longmans and Green, 1928.
Volmer, M. and Weber, A., Z. Phys. Chem., 1926, vol. 119, pp. 277–239.
Erdey-Gruz T. and Volmer, M. Z. Phys. Chem., 1931, vol. 157, pp. 165–170.
Vetter, K.J., Electrochemical Kinetics, Theoretical Aspects, New York: Academic, 1967.
Becker, R. and Döring, W., Ann. Phys., 1935, vol. 24, pp. 719–730.
Frenkel, Ja.I., J. Chem. Phys., 1939, vol. 7, pp. 200–201.
Landau, L.D., Phys. Z. Sowjetunion, 1937, vol. 11, pp. 26–36.
Landau, L.D., Phys. Z. Sowjetunion, 1937, vol. 11, pp. 545–553.
Kolmogoroff, A.N., Bull. Akad. Sci. URSS. Cl. Sci. Math. Nat., 1937, pp. 355–359.
Zeldovich, J.B., Acta Physicochim. URSS, 1943, vol. 18, pp. 1–17.
Lifshits, I.M. and Slezov, V.V., J. Phys. Chem. Solids, 1961, vol. 19, pp. 35–49.
Belavin, A.A. and Polyakov, A.M., JETP Lett., 1975, vol. 22, pp. 245–248.
Woo, G., J. Math. Phys., 1977, vol. 18, pp. 1264–1266.
Baranov, S.A., Surf. Eng. Appl. Electrochem., 2011, vol. 47, no. 4, pp. 316–330.
Baranov, S.A., Laroze, D., Vargas, P., and Vazquez, M., Phys. B, 2006, vol. 372, pp. 320–323.
Baranov, S.A., Gamburg, Yu.D., and Dikusar, A.I., Surf. Eng. Appl. Electrochem., 2007, vol. 43, no. 3, pp. 172–175.
Laroze, D., Baranov, S.A., Vargas, P., and Vazquez, M., Phys. Status Solidi C, 2007, vol. 4, no. 11, pp. 4170–4173.
Baranov, S.A., Dikusar, A.I., and Gamburg, Yu.D., Surf. Eng. Appl. Electrochem., 2008, vol. 44, no. 2, pp. 98–105.
Baranov, S.A., Mold. J. Phys. Sci., 2014, vol. 13, nos. 3–4, pp. 214–221.
Baranov, S.A., Handbook of Nanoelectrochemistry: Electrochemical Synthesis Methods, Properties and Characterization Techniques, Zurich: Springer-Verlag, 2015, pp. 1057–1069.
Abraham, F.F., Homogeneous Nucleation Theory, New York: Academic, 1974.
Martin, C.R., Science, 1994, vol. 266, pp. 1961–1966.
Puri, S. and Binder, K., J. Stat. Phys., 1994, vol. 77, no. 1, pp. 145–172.
Binder, K., Rep. Prog. Phys., 1987, vol. 50, pp. 783–859.
Gunton, J.D. and Droz, M., Introduction to the Theory of Metastable and Unstable States, Lect. Not. Phys., New York: Springer-Verlag, 1983.
Penrose, O., J. Stat. Phys., 1997, vol. 89, pp. 305–320.
Hill, T.L., Nano Lett., 2001, vol. 1, no. 3, pp. 111–112.
Kaishev, R., Izbrani trudove (Collected Works), Sofia: Bolg. Akad. Nauk, 1980.
Kashchiev, D., Nucleation: Basic Theory with Applications, Oxford: Butterworth, 2000.
Roldugin, V.I., Fizikokhimiya poverkhnosti (Physical Chemistry of a Surface), Dolgoprudnyi: Intellekt, 2008.
Rekhviashvili, S.Sh., Kishtikova, E.V., and Rozenberg, B.A., Russ. J. Phys. Chem. B, 2009, vol. 3, no. 6, pp. 1008–1014.
Rekhviashvili, S.Sh., Kishtikova, E.V., and Rozenberg B.A. Tech. Phys., 2009, vol. 54, no. 12, pp. 1731–1735.
Rekhviashvili, S.Sh. and Kishtikova, E.V., Tech. Phys., 2011, vol. 56, no. 1, pp. 143–146.
Ono, S. and Kondo, S., Molecular Theory of Surface Tension in Liquids, Berlin: Springer-Verlag, 1960.
Ma, S.-K., Modern Theory of Critical Phenomena, Benjamin, W.A., Ed., Massachusetts: Adv. Book Progr. Reading, 1976.
Fleury, P.A., Science, 1981, vol. 211, no. 4478, pp. 125–131.
Hubert, A., Theorie der Domänenwände in geordneten Medien (Theory of Domain Walls in Ordered Media), Berlin: Springer-Verlag, 1974.
Kittel, C., Introduction to Solid State Physics, New York: Wiley, 1963.
Katsnel’son, A.A. and Olemskoi, A.I., Mikroskopicheskaya teoriya neodnorodnykh struktur (Microscopic Theory of Heterogenic Structures), Moscow: Mosk. Gos. Univ., 1987.
Shirokobokov, M.Ya., Zh. Eksp. Teor. Fiz., 1945, vol. 15, pp. 57–68.
Landau, L.D. and Lifshits, E.M., Teoreticheskaya fizika. Tom 8. Elektrodinamika sploshnykh sred (Theoretical Physics, Vol. 8: Electrodynamics of Continuous Media), Moscow: Nauka, 1982.
Kosevich, A.M., Ivanov, B.A., and Kovalev, A.S., Nelineinye volny namagnichennosti. Dinamicheskie i topologicheskie solitony (Nonlinear Wave Magnetization. Dynamics and Topological Solitons), Kiev: Naukova Dumka, 1983.
Malozemoff, A.P. and Slonczewski, J.C., Magnetic Domain Walls in Bubble Materials, New York: Academic, 1979.
Ivanov, D.Yu., Critical phenomena in pure liquids, Vestn. Sib. Gos. Univ. Telekomm., 2009, vol. 3, pp. 94–104.
Anisimov, M.A., Critical Phenomena in Liquids and Crystals, Philadelphia: Gordon and Breach, 1991.
Feynman, R.P., Leighton, R.B., and Sands, M., The Feynman Lectures on Physics, Pasadena, CA: Calif. Inst. Technol., 1963, vol. 1.
Landau, L.D. and Lifshits, E.M., Teoreticheskaya fizika. Tom 3. Kvantovaya mekhanika, nerelyativistskaya teoriya (Theoretical Physics, Vol. 3: Quantum Mechanics and Nonrelativistic Theory), Moscow: Nauka, 1974.
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Original Russian Text © S.A. Baranov, 2017, published in Elektronnaya Obrabotka Materialov, 2017, No. 2, pp. 14–27.
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Baranov, S.A. On the possibility of using the Cahn–Hilliard model to describe electrodeposition of nanostructures. Surf. Engin. Appl.Electrochem. 53, 124–136 (2017). https://doi.org/10.3103/S1068375517020028
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DOI: https://doi.org/10.3103/S1068375517020028