Abstract
A consistent description of the kinetics of the cellular decomposition of supersaturated solid solutions with the development of a spatially periodic structure of lamellar (platelike) type, which consists of alternating phases of precipitates on the basis of the impurity component and depleted initial solid solution, is given. One of the equations, which determines the relationship between the parameters that describe the process of decomposition, has been obtained from a comparison of two approaches in order to determine the rate of change in the free energy of the system. The other kinetic parameters can be described with the use of a variational method, namely, by the maximum velocity of motion of the decomposition boundary at a given temperature. It is shown that the mutual directions of growth of the lamellae of different phases are determined by the minimum value of the interphase surface energy. To determine the parameters of the decomposition, a simple thermodynamic model of states with a parabolic dependence of the free energy on the concentrations has been used. As a result, expressions that describe the decomposition rate, interlamellar distance, and the concentration of impurities in the phase that remain after the decomposition have been derived. This concentration proves to be equal to the half-sum of the initial concentration and the equilibrium concentration corresponding to the decomposition temperature.
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References
M. A. Ivanov and A. Yu. Naumuk, “Kinetics of eutectic crystallization,” Phys. Met. Metallogr. 115, 471–480 (2014).
H. C. H. Carpenter and J. M. Robertson, “The austenite-pearlite inversion,” J. Iron Steel Inst. London 125, 309 (1932).
D. Turnbull and H. N. Treaftis, “Kinetics of precipitation of tin from lead-tin solid solutions,” Acta Metall. 3, 43–54 (1955).
D. Turnbull, “Kinetics of precipitation in small leadtin spheres,” Acta Metall. 4, 495–509 (1956).
R. G. Rose, “The precipitation of copper from a silver-5.5% copper solid solution at 220 C,” Acta Metall. 5, 404–405 (1957).
N. N. Buinov and R. R. Zakharova, Decomposition of Supersaturated Solid Solutions (Metallurgiya, Moscow, 1964) [in Russian].
K. N. Tu and D. Turnbull, “Morphology of cellular precipitation of tin from lead-tin bicrystals,” Acta Metall. 15, 1317–1323 (1967).
R. O. Vatanabe, “On the phase precipitation as a result of reaction at grain boundaries,” Nihon Kinzoku Gakkai Kaik-ho 6, 435–450 (1967).
L. N. Larikov and O. A. Shmatko, “Mechanism and kinetics of supersaturated solid solution detachment of tungsten in cobalt,” Fiz. Met. Metalloved. 30, 1173–1181 (1970).
L. N. Larikov and O. A. Shmatko, Cellular Decomposition of Supersaturated Solid Solutions (Naukova Dumka, Kiev, 1976) [in Russian].
O. A. Shmatko, “On distinctive features of cellular decomposition of supersaturated solid solutions [Review],” Metallofizika 2(2), 97–105 (1980).
M. V. Itkin, V. S. Krasil’nikov, and O. A. Shmatko, “Cellular decomposition in Cu-5.7% at % Ti,” Metallofizika 7(6), 27–35 (1985).
W. H. Brandt, “Solution of the diffusion equation applicable to the edgewise growth of pearlite,” J. Appl. Phys. 16, 139–146 (1945).
C. Zener, “Kinetics of the decomposition of austenite,” Trans. AIME 167, 550–595 (1945).
D. Turnbull, “Theory of cellular precipitation,” Acta Metall. 3, 55–63 (1955).
M. Hillert, “Role of interfacial energy during solidstate phase transformations,” Jernkont. Ann. 141, 757–789 (1957).
J. W. Cahn, “The kinetics of cellular segregation reactions,” Acta Metall. 7, 18–28 (1959).
K. A. Jackson and J. D. Hunt, “Lamellar and rod eutectic growth,” Trans. AIME 236, 1129–1137 (1966).
J. M. Shapiro and J. S. Kirkaldy, “Theory of decomposition of eutectoids assuming local equilibrium and phase boundary diffusion,” Acta Metall. 16, 579–585 (1968).
B. E. Sundquist, “The edgewise growth of pearlite,” Acta Metall. 16, 1413–1427 (1968).
F. M. A. Carpay and J. Boomgard, “The relationship between interlamellar period and growth rate in the unidirectionally decomposed eutectoids Co3Si and β Ni-In,” Acta Metall. 19, 1279–1286 (1971).
M. A. Ivanov, V. I. Glushchenko, and A. Yu. Naumuk, “Shift of the transition temperature and the change in the free energy upon directional solidification of solutions at a given rate,” Phys. Met. Metallogr. 113, 1–8 (2012).
M. A. Ivanov, M. M. Churakov, and V. I. Glushchenko, “Motion of phase boundary in solid solutions,” Phys. Met. Metallogr. 83, 575–583 (1997).
G. V. Kurdyumov, L. M. Utevskii, and R. I. Entin, Transformations in Iron and Steel (Nauka, Moscow, 1977) [in Russian].
M. A. Ivanov, “Principle of maximum of entropy production rate for stationary nonequilibrium processes and self-organizing systems,” Proc. 5th Int. Workshop on Complex Systems in Natural and Social Sciences, Zakopane, Poland, 2000, p. 11.
J. S. Kirkaldy, “Entropy criteria applied to pattern selection in systems with free boundaries,” Metall. Trans. A 16, 1781–1797 (1968).
A. A. Bezpalii, V. F. Mazanko, M. I. Savchuk, I. O. Shmatko, and O. A. Shmatko, “Thermal effect of Pb-27.07 at % Sn alloy aging at heating,” Metallofiz. Noveish. Tekhnol. 34, 1265–1271 (2012).
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Original Russian Text © M.A. Ivanov, A.Yu. Naumuk, 2014, published in Fizika Metallov i Metallovedenie, 2014, Vol. 115, No. 9, pp. 941–950.
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Ivanov, M.A., Naumuk, A.Y. Kinetics of the cellular decomposition of supersaturated solid solutions. Phys. Metals Metallogr. 115, 884–893 (2014). https://doi.org/10.1134/S0031918X14090075
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DOI: https://doi.org/10.1134/S0031918X14090075