Diffusion kinetics in a multicomponent thermodynamic system at small deviations from the equilibrium state
DOI:
https://doi.org/10.15330/pcss.25.2.406-412Keywords:
non-equilibrium thermodynamics, variational principles, diffusion fluxes, equations of motion, carbide transformations, chromium steelAbstract
The theory of diffusion processes in solids has achieved significant results in recent decades, but the development of methods for calculating diffusion in a multicomponent thermodynamic system is still an urgent task. Problems of diffusion in solid and liquid solutions with small deviations from the equilibrium state, or fluctuations, are of significant interest. The work develops a general methodology for calculating diffusion flows in a multicomponent thermodynamic system for small deviations from the equilibrium state. A connection has been established between the mechanical approach to the analysis of generalized systems and the phenomenological equations of nonequilibrium thermodynamics. Examples are given of the use of the developed methodology for the analysis of carbide transformations in chromium steel.
References
S. Bokstein, Thermodynamics and kinetics in materials science: a short course. (Oxford University Press, 2005).
O. Penrose and J.W. Cahn. On the mathematical modelling of cellular (discontinuous) precipitation. Discrete and continuous Dynamical System, 37, 963 (2017); https://doi.org/10.3934/dcds.2017040.
S.V. Bobyr. Using the principles of nonequilibrium thermodynamics for the analysis of phase transformations in iron-carbon alloys. Non-Equilibirum Particle Dynamics (Intechopen, London, May 2019); https://doi.org/10.5772 /Intechopen.83657.
L.S. Darken. Diffusion, Mobility and Their Interrelation through Free Energy in Binary Metallic Systems. Trans. AIME, 175, 184 (1948).
D. Arovas. Lecture Notes on Thermodynamics and Statistical Mechanics (A Work in Progress) (Department of Physics University of California, San Diego, October 2015).
V.S. Eremeev. Calculation of flows in a thermodynamic system taking into account the non-diagonal elements of the Onsager matrix. Physics of Metals and Material Science, 45(1), 19 (1978).
M. Hillert. On the driving force for diffusion Induced Grain Boundary Migration. Scripta metallurgica Materiala, 17 (1), 237 (1983).
S.V. Bobyr. Calculation of Diffusion Flows for the Formation of Phases in Alloys Iron-Carbon-Alloying Element. Physics and Chemistry of Solid State, 20(2), 196 (2019); https://doi.org/10.15330/pcss.20.2.196-201.
S.V. Bobyr. Non-equilibrium thermodynamics model for calculating diffusion fluxes under phase transformations in alloy steels. Proceedings of the National Academy of Sciences of Belarus. Physical-technical series, 66(1), 28 (2021); https://doi.org/10.29235/1561-8358-2021-66-1-28-36.
S.V. Bobyr, P.V. Krot. Nonequilibrium Thermodynamic Analysis of Diffusion Processes in the Steel - Carbon Thin Film Tribological System. Material Science & Engineering International Journal, 6(1), 14 (2022); http://dx.doi.org/10.15406/mseij.2022.06.00174.
N. Lecoq, H. Zapolsky, and P. Galenko, Evolution of the structure factor in spinodal decomposition. Eur. Phys. J. Spec. Top., 177, 165 (2009).
D. Jou, J. Cases-Vezquez, G. Lebon. Extended Irreversible Thermodynamics. T. XVIII (Springer, London, 2010).
T. Barkar, L. Hoglund, J. Odqvist and J. Agren. Effect of concentration dependent gradient energy coefficient on spinodal decomposition n the Fe-Cr system. Computational Material Science, 143, 446 (2018); http://dx.doi.org/10.1016/j.commatsci.2017.11.043.
D. Mukherjee, H. Larsson, and J. Odqvist. Phase-field modeling of diffusion induced grain boundary migration in binary alloys. Computational Material Science, 184, 1 (2020); http://dx.doi.org/10.1016/j.commatsci.2020.109914.
A. Finel, Y. L. Bouar, B. Dabas, B. Appolaire, Y. Yamada, and T. Mohri. Sharp Phase Field Method. Phys. Rev. Let., 121(2), 025501 (2018); https://doi.org/10.1103/PhysRevLett.121.025501.
Chia-Ying Chou, N.H. Petterson, A. Durga, F. Zhang, Ch. Oikinomou, A. Borgenstam, J. Odqvist, G. Lindwall. Precipitation Kinetics during Post-heat Treatment of an Additively Manufactured Hot-work Tool Steel. Chia-Ying Chou. Doctoral Thesis in Material Science and Engineering (KTH Royal Institute of Technology, Stockholm, 2023).
R. Kozubski, G. E. Murch, I. V. Belova. Vacancy-Mediated Diffusion and Diffusion-Controlled Processes in Ordered Binary Intermetallics by Kinetic Monte Carlo Simulations, Diffusion Foundations, 29, 95 (2021); http://dx.doi.org/10.4028/www.scientific.net/DF.29.95.
A.N. Gorban, H.P. Sargsyan, H.A. Wahab. Quasichemical Models of Multicomponent Nonlinear Diffusion. Mathematical Modelling of Natural Phenomena, 6(5),184 (2011); https://doi.org/10.1051/mmnp/20116509.
M. Hellmuth. Diffusion in solids (Intellect Publishing House, Moscow, 2011).
Landau L. D., Lifshits E. M. Statistical physics. Part 1. 5th edition (Fizmatlit, Moscow, 2005).
D. ter Haar. Fundamentals of Hamiltonian mechanics (Nauka, Moscow, 1974).
B. B. Vinokur. Carbide transformations in structural steels. Monograph (Naukova Dumka, Kyiv, 1988).
L.N. Larikov, V.I. Isachev. Diffusion in metals and alloys/Structure and properties of metals and alloys Directory (Naukova Dumka, Kyiv, 1987).
K. J. Homan. Diffusion of carbon in α-iron. Diffusion in metals with a body-centered lattice. Ed. S. Z. Bokshtein (Metallurgy, Moscow,1969).
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