Abstract
A consistent thermodynamic description of the process of stationary eutectic solidification at low supercoolings is presented. To find the relation between the parameters that characterize this process, a new approach has been used that is based on obtaining an expression for the rate of the free-energy change by two different methods. This has made it possible to obtain a new relationship between the parameters of the arising structure. The first method is based on the consideration of the free-energy change that is due to the dissipative process of separative diffusion, which occurs in the bulk of the liquid phase. The second method involves the consideration of the balance of changes in the free energy far from the solidification front. Based on various extremum principles, analytical expressions for the rate of solidification and for the parameters of the arising eutectic structure have been derived. Rodlike and lamellar structures, which are observed most often in experiments, have been considered. It has been shown that conditions for the appearance of a particular structure are governed by the minimum values of the surface energy of the interfaces between the solid phases and by the “decomposition structure factor,” which is introduced in this work.
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References
M. McLean, Directionally Solidifed Materials for High Temperature Service (Metals Society, London, 1983).
H. Weiss, “Physical properties on in situ composites,” Proc. Conf. on in situ composites II, Ed. by M. R. Jackson et al., Xerox Individualized Publishing Program, pp. 377–384 (1976).
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).
M. Hillert, “Role of interfacial energy during solidstate phase transformations,” Jern-kont. Ann. 141, 757–789 (1957).
W. A. Tiller, “Polyphase solidification,” in Liquid Metals and Solidification (ASM, Cleveland, 1958), pp. 276–318.
K. A. Jackson and J. D. Hunt, “Lamellar and rod eutectic growth,” Trans. AIME 236, 1129–1137 (1966).
J. W. Cahn, “The kinetics of cellular segregation reactions,” Acta Metall. 7, 18–28 (1959).
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).
M. A. Ivanov, M. M. Churakov, and V. I. Glushchenko, “Description of the growth of a two-component layer with allowance for the diffusion-controlled and interface-controlled transport of atoms,” Phys. Met. Metallogr. 88, 111–121 (1999).
M. A. Ivanov and V. I. Glushchenko, “Propagation of an interphase interface in a two-component system at a given composition of one phase,” Phys. Met. Metallogr. 91, 433–441 (2001).
M. A. Ivanov and V. I. Glushchenko, “Rate of freeenergy change upon the motion of an interphase boundary,” Phys. Met. Metallogr. 110, 415–422 (2010).
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.
N. V. Pertsov, V. A. Prokopenko, V. V. Zozulya, and M. A. Ivanov, “Processes of self-organization in ultradispersed structures upon the electrochemical dissolution of alloys, in Colloid-Chemical Nanoscience Foundations, Ed. by A. P. Shpak and Z. R. Ul’berg, (Akademperiodika, Kiev, 2005), pp. 413–423 [in Russian].
L. M. Martyushev, V. D. Seleznev, and I. E. Kuznetsova, “Application of the principle of maximum entropy production to the analysis of the morphological stability of a growing crystal,” J. Exper. Theor. Phys. 91, 132–143 (2000).
L. M. Martyushev and V. D. Seleznev, “Maximum Entropy Production Principle in Physics, Chemistry and Biology,” Phys. Rep. 426, 1–45 (2006).
M. Fleming, Solidification Processing (McGraw-Hill, New York, 1974).
B. Chalmers, Principles of Solidification (Wiley, New York, 1964).
R. Elliott, Eutectic Solidification Processing: Crystalline and Glassy Alloys (Butterworth, London, 1983).
A. J. Kenneth, Kinetic Processes: Crystal Growth, Diffusion, and Phase Transitions in Materials (Wiley, Weinheim, 2004).
H. Deng, E. C. Dickey, Y. Paderno, V. Paderno, V. Filippov, and A. Sayir, “Crystallographic characterization and indentation mechanical properties of LaB6-ZrB2 directionally solidified eutectics,” J. Mater. Sci. 39, 5987–5994 (2004).
S. Milenkovic and R. Caram, “Effect of the growth parameters on the Ni-Ni3Si eutectic microstructure,” J. Crystal Growth 237–239, 95–100 (2002).
V. S. Vladimirov, Equations of Mathematical Physics (Nauka, Moscow, 1981) [in Russian].
G. V. Kurdyumov, L. M. Utevskii, R. I. Entin, Transformations in Iron and Steel (Nauka, Moscow, 1977) [in Russian].
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Original Russian Text © M.A. Ivanov, A.Yu. Naumuk, 2014, published in Fizika Metallov i Metallovedenie, 2014, Vol. 115, No. 5, pp. 502–511.
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Ivanov, M.A., Naumuk, A.Y. Kinetics of eutectic solidification. Phys. Metals Metallogr. 115, 471–480 (2014). https://doi.org/10.1134/S0031918X14050056
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DOI: https://doi.org/10.1134/S0031918X14050056