A Numerical Model Describing Multiphase Binary Diffusion in Liquid Metal/Solid Metal Couples
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MULTIPHASE diffusion in a semi-infinite solid metal frequently occurs in the metallurgical processes for oxidizing, carburizing, soldering, and hot dipping. In a metallurgical process, such as soldering, the occurrence and layer growth of intermediate phases provide reliable bonding of dissimilar metals, whereas too thick intermediate layers lead to the deterioration of the joining strength. It is of great practical importance to estimate the layer growth of the intermediate phases formed in the semi-infinite solid metal. The layer growth rate of an intermediate phase in a semi-infinite solid metal can be evaluated from the relations for a two-phase system.[1] Metin et al.[2] developed general analytical expressions for multiphase binary diffusion in a semi-infinite solid metal and examined the validity of these solutions by application to the Zr-O and Fe-N systems. Engstro¨m et al.[3] presented a general numerical model based on diffusion data and basic thermodynamic data for treating multiphase diffusion in a multicomponent system. It is tacitly assumed in the above models that the plane x = 0 which is initially placed at the surface is fixed with respect to the non-diffused end of a semi-infinite solid metal for all diffusion zone. In such gas/solid couples as carburizing and nitriding, the molar flux of the solid component into the gas generally is negligible small, but that of the gas component into the solid is much greater. On the other hand, the atomic volumes for C, N, and O are extremely smaller than those of metal elements. This means that the solid undergoes little change in length perpendicular to the solid surface, and the assumption where the surface of the semi-infinite solid is located at the position SHINJI TSUJI, formerly Professor with the Department of Mechanical and Precision Systems, Teikyo University, 1-1 Toyosatodai, Utsunomiya, Tochigi 320-8551, Japan, is now Senior Researcher with the Ibaraki Laboratory of Diffusion Alloys, 3-22-16, Yamatedai, Ibaraki City, Osaka 567-0009, Japan. Contact e-mail: sm-tsuji@ coast.ocn.ne.jp Manuscript submitted February 23, 2012. Article published online August 26, 2014 METALLURGICAL AND MATERIALS TRANSACTIONS A
x = 0 may be used validly. In liquid metal/solid couples, however, there are both the molar flux of the liquid component from the liquid into the solid and that of the solid component in the opposite direction, and either of the fluxes should not be disregarded. As a result, the solid expands or contracts depending mainly on the composition of the solid component in the liquid. The resultant displacement of the solid surface from the x = 0 plane which is fixed to the non-diffused end of a solid metal should not be ignored in the simulation of multiphase diffusion in liquid metal/solid metal couples. The author[4–6] presented the numerical model for obtaining the composition profile and the displacement of all the phase interfaces containing the surface in a multiphase binary type of semi-infinite solid metal in the diffusion-controlled stage. The object of the pre
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