Self-Diffusion of Component i in a Chemically Homogeneous Binary Solution

2 Self-Diffusion of Component i in a Chemically Homogeneous Binary Solution 

In Section 3.1.1, the self-diffusivity was obtained for a diffusion couple composed of a chemically pure material but with gradients of an isotope of that material. In this section we discuss self-diffusion of an isotopic species in a chemically homogeneous binary solution consisting of atoms of types 1 and 2 in the presence of a concentration gradient of the isotope. 

The self-diffusion of component 1 in such a system is measured by studying the diffusion of a radioactive isotope tracer of component 1 (i.e., 1) under the condition that while there is a gradient in the tracer s concentration, c i, the sum (ci +c i) and C2 are both uniform. A possible diffusion couple is shown in Fig. 3.2. 

Considering Eq. 2.21 in a case in which diffusion occurs in a crystal by the vacancy exchange mechanism, there are four components, Cj., c i, c2, and cy. Because the crystal remains fixed during the diffusion, the C-frame is again used for measuring the flux. The system is chemically homogeneous, so 

a Fick s-law expression is obtained for the self-diffusion of the radioactive component. The self-diffusivity of component 1 in a binary system of uniform chemical composition is designated by D to distinguish it from the self-diffusivity of a pure material, D. 

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