Computer simulation of diffusion in multiphase systems
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I.
INTRODUCTION
IN binary diffusion couples, new phases form as layers perpendicular to the direction of diffusion. The growth of such layers will then be controlled by diffusion through the layers themselves. When three or more components take part in a diffusion process, the situation becomes more complex, and new phases may form also as dispersed particles in a matrix. For example, when a pure metal is oxidized, an oxide layer forms on the surface, whereas upon oxidizing an alloy, discrete oxide particles may form in the interior; so-called internal oxidation. [lj A similar behavior is observed during carburizing and nitriding. If a binary Fe-C steel is decarburized at a temperature below A t , a ferritic layer will form at the surface and grow into the steel. The fraction of cementite will drop from its initial value to zero within a very thin layer, and on a micrograph, there appears to be a sharp boundary between the two-phase mixture and the surface layer. The overall C content drops more or less discontinuously at this boundary. On the other hand, when a high-alloy steel is decarburized, there will be gradual change in the volume fraction of carbides as we approach the surface from the interior, and there will be a continuous variation in C content. The difference in behavior is related to the Gibbs phase rule, which states that under isobaric and isothermal conditions, there are no degrees of freedom left in a binary alloy when two phases coexist at equilibrium. If the interparticle spacing is small compared to the distances over which diffusion occurs, there can be no chemical-potential gradients to cause long-range diffusion in a binary two-phase mixture. Recently, models for diffusion in one-phase multicomponent systemst2~ and diffusion-controlled growth of layers and individual particles t3J were developed and implemented as a subroutine package called DICTRA. The main ambition was to base the treatment on only basic thermodynamic and kinetic data obtained independently of the transformation under consideration. The purpose A N D E R S E N G S T R O M and LARS H(3GLUND, Graduate Students, and JOHN AGREN, Professor, are with the Department of Materials Science and Engineering, Division of Physical Metallurgy, Royal Institute of Technology, S-100 44 Stockholm, Sweden. Manuscript submitted March 29, 1993. METALLURGICALAND MATERIALS TRANSACTIONS A
of the present report is to treat the problem of long-range diffusion through multiphase structures with the same ambition. This prob!em has been tackled by several authors over the years. Agren, t41 when treating C diffusion in tool steels, reduced the problem to an ordinary one-phase diffusion problem by introducing an effective diffusion coefficient. The effective diffusion coefficient was calculated from the C diffusivity in the matrix and the thermodynamic properties of the multiphase system only. In general, the effective diffusivity will be concentration dependent and numerical methods are needed to solve the diffusion equation. Quite recently, Morral e
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