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Tham khảo tài liệu 'kinetics of materials - r. balluff s. allen w. carter (wiley 2005) ww part 5', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | 140 CHAPTER 6 DIFFUSION IN MULTICOMPONENT SYSTEMS Ni Figure 6.3 Diffusion path for ternary diffusion profiles shown in Fig. 6.2. From Vignes and Sabatier 2 . Consider a ternary diffusion couple in which each component has an initial stepfunction profile and boundary conditions similar to those given by Eq. 4.44. Integrating and changing variables as in the development leading up to Eqs. 4.48 and 4.49 for the binary case wb d C1G c2 v __ -2 _ 5i2 6.52 ycH drj CR dĩ CR and 1 dci dc2 r xdCi 2-77 Ji 6-53 2r Jcr dx dx Because the diffusion profiles Cl a and c2 x are known the fluxes J and J2 can be determined at any X by inverting Cl ar and 02 2 and evaluating the integrals in Eqs. 6.53 for i 1 2. Because dci dx and dc Ịdx are known at the selected X two equations relating the four diffusivities are obtained. Therefore if two ternary diffusion experiments are analyzed at a point of common concentration four equations relating the four diffusivities at those common concentrations will be obtained and all four diffusivities can be determined. However use of this method to derive diffusivities from experimental results is highly labor intensive and subject to significant error 3 . Alternatively coupled diffusion equations with concentration-dependent diffusivities and comparison with experimental results can be solved with numerical methods see Kirkaldy and Young 1 and Glicksman 4 . In many systems complex particle-particle interactions can produce a plane inside the diffusion zone where the flux of one of the components is zero. Such planes can be found by evaluating the integral in Eq. 6.53 along the diffusion profile to find 6.3 MEASUREMENT OF DIFFUSIVITIES 141 points where Ji 0. This approach can be used to obtain information regarding diffusion in the system 5 Exercise 6.3 provides an illustration. 6.3 MEASUREMENTS AND INTERPRETATIONS OF DIFFUSIVITIES There are extensive reviews of the many measurements of the Dij particularly in ternary systems 1 . Numerous .