A study of the effect of an intermediate phase on the dissolution and homogenization characteristics of binary alloys
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R. W. HECKEL
The effect of an intermediate phase on the dissolution and homogenizationcharacteristics of binary alloys was studied by mathematically modeling finite, three-phase, diffusion-controlled, binary systems for planar, cylindrical, and spherical interfaces with the mean composition in a terminal solid solution (~). Calculations were carried out using numerical methods and computer techniques. The major variables affecting the dissolution of the unstable terminal solid solution (~) and the intermediate phase ~3) were found as well as the variables affecting the homogenization process. Comparison of the results to existing solutions for one-phase (Heckel '8) and two-phase (Tanzilli and Heckelxr) binary systems led to predictions for the behavior of n-phase binary systems. Calculations based on the spherical model were successfully compared to existing literature data for dissolution in a compacted blend of W-Re powders and for the formation of austenife from ferrite and cementite.
O OINCE intermediate phases occur in the majority of binary systems, a knowledge of their effect on dissolution and homogenizationcharacteristics of alloys is important in many applications. Specific applications include the production of alloys from blends of elemental powders, the stability of metal-matrix composites, the stability of protective coatings and the formation of austenite from ferrite and cementite. The natural starting point for a study concerning intermediate phases is a system in which one intermediate phase is formed between the parent metals, i.e., a three-phase, binary system. The ideal type of mathematical solution to the three-phase problem is an exact, closed-form solution. Solutionsof this type were carried out by Wagner as reported by Jost I for two-phase, binary systems. Similar solutions exist in the literature for the three-phase, binary, diffusion-controlled problem2 and for the general, n-phase problem.~'4 Gibbss examined the limiting cases of the closed-form solutions when the interdiffusion coefficients were significantly different. The treatment led to simplified forms of the solution for specific situations. Solutions of this type are applicable to problems with a planar geometry (e.g., coatings and cladding) when the interdiffusion distances are small compared with the thickness of the material. Hurley and Dayananda6 obtained a closed-form solution for vapor-solid diffusion couples in which an intermediate phase was formed between the vapor phase and the initial metallic phase. The expansion of the couple due to the diffusion of the solute atoms was considered. Assumptions made were: I) the concentration at the surface and the interface concentrations were time-independent, 2) the interdiffusion coefficients were concentration-independent, R. D. LANAM and R. W. HECKEL are Graduate Student in Materims Engineering and Professor of Metallurgical Engineering, respectively, Drexel University, Philadelphia, Pa. Manuscript submitted August 10, 1970. METALLURGICAL TRANSACTIONS
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