Regimes of Grain-Boundary Short-Circuit Diffusion in a Polycrystal

1 Regimes of Grain-Boundary Short-Circuit Diffusion in a Polycrystal 

The quantity ( D) is the average effective diffusivity, which describes the overall diffusion in the system. The diffusion in the system therefore behaves macroscopically as if bulk diffusion were occurring in a homogeneous material possessing a uniform diffusivity given by Eq. 9.4. The situation is illustrated schematically in Fig. 9.4a, and experimental data for diffusion of this type are shown in Fig. 9.5. This diffusion regime is called the multiple-boundary diffusion regime since the diffusion field 

At the opposite extreme when essentially no diffusion occurs in the grains but significant diffusion still occurs along the boundaries, the overall diffusion will consist of only diffusion penetration along the boundaries, as illustrated in Fig. 9.4c. This will tend to occur at low temperatures or short times under the conditions DXLt A2 and DBt A2, where A is the interatomic distance. 

The various regimes of possible diffusion behavior can be represented graphically in an approximate manner, as shown in Fig. 9.6 [8]. The axes are taken to be log( DXLt) and log(uf) logarithmic scales have been used to show the details near the origin because s/A is typically 103 or more. The stationary-boundary regimes 

Atoms are diffusing into the boundary laterally from its edges and can diffuse out through its front face into the forward grain. At the same time, atoms will be deposited in the backward grain in the wake of the boundary. In the quasi-steady state in a coordinate system fixed to the moving boundary, the diffusion flux in the forward grain is J = — DXL(dc/dx) — vc and the diffusion equation is 

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