Grain boundary width

Fig. 7.37 Diffusion coefficients for some impurities in NiO grain boundaries compared with the corresponding lattice diffusivities (the grain boundary width is assumed to be I nm) (after...

Radioactive 180 was diffused into a poly crystalline pellet of ZnO at 900°C for 48 h. The diffusion profile had a marked tail showing that extensive grain boundary diffusion had occurred. The variation of the concentration of the radioactive isotope with depth for the tail of the penetration profile is given in the following table. Calculate the grain boundary diffusion coefficient, Dgb, of 180 if the bulk diffusion coefficient at 900°C is 5.53 x 10-21 m2 s-1 and the grain boundary width is taken as 1 nm. 

The fabrication procedure affects the product s microstructure including grain size, grain-boundary width, and porosity. In addition, different procedures introduce various amounts of impurities to the product. Therefore, the electrical conductivity and activation energy are affected by the fabrication procedure since, as mentioned above,... 

Nanosized particles have high ratios of surface area to volume, and it is expected that surface diffusion is of importance. The driving force for. surface diffusion is the gradient of the chemical potential along the surface. The fonn of the diffusion coefficient for surface diffusion is similar to that for grain boundary diffu.sion. except that the grain boundary width h is replaced by the width of the surface layer. Because of the similarity between the forms of the diffusion coefficient, surface diffusion can sometimes he treated in a manner equivalent to grain boundary diffusion. 

Fig. 11.13. Experimental observations of (T = 4.2 K) as a function of misorientation angle from the results of several groups [11.1-11.3] show an exponential dependence. Where the results were reported at E = 77 K, the values at 4.2 K were extrapolated from the temperature dependence of Jq [11.45]. The grain boundary tunneling current calculated from eq. 11.2 using the grain boundary widths from Fig. 11.12 shows excellent quantitative agreement for a width defined by a copper(I) valence between 1.5 and 1.9. This copper valence corresponds to the copper(I) valence in bulk YBCO when it becomes non-superconducting. The predicted drop in due to the symmetry of the superconducting order parameter is insufficient by two orders of magnitude to account for the observed behavior.

Fig. 2. (a) Synthetic plot of grain boundary width as a function of time for growth by volume diffusion, assuming no initial width (b) synthetic plot of grain boundary width as a function of time for growth by volume diffusion, assuming an initial rapid growth. 

The subscripts refer to the grain boundaries, Q is the atomic volume (of a vacancy), S is the grain-boundary width and 1 is the grain size. (In Nabarro-Herring, grain size was denoted by d). The Ds in Eqs. (6.47) and (6.48) is replaced, in Coble s equation, by Dgb. Factor 1/1 represents the density of the cross-section... 

At a given temperature and external oxygen partial ptressure, Nb (critl) and Nb (crit2) are a function of only grain size (d) of the alloy, diffusion coefficients (Dgi, and D(,) and grain boundary width (5) of the alloy. 

Dgb grain boundary diffusivity 5 grain boundary width A dimensionless constant D diffusion coefficient... 

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