Grain boundary thickness

L = average grain diameter S = grain boundary thickness... 

In order to determine the grain boundary thickness, C2-values have to be analyzed according to Eq. (44). As for R2, the specific geometry of the investigated grain boundary and its surroundings affects the analysis since only estimates of the grain boundary area and the /c-factor are available. Hence, a relatively broad distribution... 

In common cases, the grain-boundary thickness is close to a few nanometers the overall volume fraction of the boundaries is very small. The opposite situation is observed in nano crystalline solids, with profound effects on defect - thermodynamics and transport. 

Budai, J., Gaudig, W., Sass, S. L. (1979). Measurement of grain boundary thickness using x-ray diffraction techniques. Phil. Mag., 39, 533-49. 

Figure 10.16 Equilibrium grain boundary thickness measured by HREM plotted versus the bulk calcium doping level in silicon nitride. (Erom Ref. 37.)...

Fig. 1. The effect of grain size on the volume fractions of interaystalline region, grain boimdaries and triple points calculated from equations 2-5 and assuming the grain boundary thickness to be 1 nm [2].

Fig.3 (a) Schematic diagram showing the ionic conduction in polycrystalline stabilized zirconia specimen with a resistive grain boxmdary and (b) its simplification by the brick layer model, (d electrode area, / specimen thickness, dgi average grain size, <%4 grain boundary thickness)... 

Grain boundary self-diffusion prefactor times the grain boundary thickness 5, m /s... 

Table 6.5 shows the different parameters used in the Riedel model equation with G the atomic volume, D, S the grain boundary self-diffusion coefficient times the grain boundary thickness, S and gb the activation energy for grain boundary self-diffusion. The parameters D, 8 and gb describe the grain boundary diffusion for... 

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