Abstract
The nonlinear diffusion equation for a binary system interdiffusion was analytically solved in the previous work. The theoretical relation of Kirkendall effect was also derived in the previous work. These new results have not yet been concretely applied to actual diffusion problems. In the present work, it is revealed that the previous results reproduce the experimental concentration profile by taking account of the movement of diffusion region space. It is thus actually confirmed that any problems of binary system interdiffusion can be solved by the new analytical method if even diffusivities of self-diffusion and impurity diffusion in the materials concerned are given. The method for solving interdiffusion problems of many elements system, which is extremely important for the development of new useful materials, is also reasonably discussed. Further, it is revealed that the concept of intrinsic diffusion is unsuitable for the diffusion theory. The fundamental theory of diffusion discussed here will be useful for analyzing actual diffusion problems in future.
Highlights
The diffusion problem is one of the most fundamental and important research subjects in the material science field
Using the analytical solutions expressed by Equations ((29) and (30)), the interdiffusion problem between the pure copper and brass alloy was reasonably solved in the present study, regardless of the Darken equation
It was concretely confirmed that the Darken equation, which has been widely used for analyzing problems of binary system interdiffusion, is unnecessary and theoretically unsuitable for analyzing the interdiffusion problems
Summary
The diffusion problem is one of the most fundamental and important research subjects in the material science field. The diffusion research has been widely and actively performed in accordance with the industry requirements for the development of new useful materials [1] [2] [3] [4] [5]. The analytical method of the nonlinear diffusion equation, which is applicable to analyzing interdiffusion problems, was reported [13] [14] [15]. It does not seem that the method is really applied to analyzing results of diffusion experiments. ( ) D ∂CII ∂x =−D ∂ CI + CII ∂x =0 is valid only in the differential equation of diffusion. When we use solutions of Equations (4) for the diffusion flux J =−D ∂C ∂x , J I + J II ≠ 0 is valid . There is no doubt that the Kirkendall effect (K effect) relevant to the essence of interdiffusion mechanism is caused by J I + J II ≠ 0 [15]
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