Modeling the Interdiffusion and Reactive-Diffusion Processes in Multicomponent Systems
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he processes and material behavior can be very useful in testing material stability, estimating required properties, and predicting their ‘‘life time.’’ The reliable and simple simulation software considerably accelerates both the research and the development. It helps in the design and production of new materials. Within the last few decades, it was documented that the chemistry within the solid state is similar to the chemistry in the liquid state. The departures from the ideal solid structure are thermodynamically unavoidable, and very often diffusion determines the overall reaction rate. Materials science widely uses this area of chemistry to describe and treat in a unified way such different phenomena as the kinetics of the synthesis and sintering of solid materials, the processes in gas sensors and high temperature fuel cells, the corrosion, etc. In this article, we show the method to model the heterogeneous reaction, i.e., to combine the fundamental formulas of the diffusive mass transport in solutions (interdiffusion) with kinetic processes (reactive diffusion). The heterogeneous reactions in the binary system were analyzed by Wagner.[1–4] These are essentially the quasi-equilibrium processes (chemical diffusion and reactions at interfaces) that take place under the influence of the chemical potential gradient.[5,6] Wagner studied the conditions necessary for selective oxidation MAREK DANIELEWSKI, Professor, and BARTLOMIEJ WIERZBA, Doctor, are with the Interdisciplinary Centre for Materials Modeling, Faculty of Materials Science and Ceramics, AGH University of Science and Technology, 30-059 Cracow, Poland. Contact e-mail: bwierzba@ agh.edu.pl Manuscript submitted March 4, 2008. Article published online August 12, 2008. METALLURGICAL AND MATERIALS TRANSACTIONS B
of the ideal binary alloy, derived an appropriate analytical expression, and obtained the qualitative agreement between the experimental and calculated values of the reaction rate. He was first to notice that the oxidized component enters the oxide phase as a result of the surface reaction and of the diffusion through the alloy/oxide interface. The nonreacting elements diffuse into the interior of the alloy.[3] Both the Onsager[7,8] and the Darken[9] methods are commonly used in nonequilibrium thermodynamics to describe the diffusion in solids. The key Darken postulate that the total mass flow is a sum of the diffusion and drift flows was applied for the description of the diffusion in the multicomponent solid solution.[10,11] The equations of mass conservation, the appropriate expressions describing the fluxes, and the postulate of constant molar volume of the system allowed the quantitative description of the diffusion transport process in the open as well as closed systems. This method describes the interdiffusion when intrinsic diffusivities depend on composition and allows inclusion of the activities of components.[10] In this article, the Darken method is further extended to include the variable or different molar volumes, e.g., the Vegard law.[12] Moreover, we rigo
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