Grain boundary transport

Haile, S. M., Staneff, G., and Ryu, K. H. Non-stoichiometry, Grain Boundary Transport and Chemical Stability of Proton Conducting Perovskites, Journal of Materials Science, 36, 1149 (2001). 

Percolation theory is helpful for analyzing disorder-induced M-NM transitions (recall the classical percolation model that was used to describe grain-boundary transport phenomena in Chapter 2). In this model, the M-NM transition corresponds to the percolation threshold. Perhaps the most important result comes from the very influential work by Abrahams (Abrahams et al., 1979), based on scaling arguments from quantum percolation theory. This is the prediction that no percolation occurs in a one-dimensional or two-dimensional system with nonzero disorder concentration at 0 K in the absence of a magnetic field. It has been confirmed in a mathematically rigorous way that all states will be localized in the case of disordered one-dimensional transport systems (i.e. chain structures). 

Finally, considering what was discussed previously, when dealing with nanosized materials and nanostructured electrodes for electrochemistry, it is important to separate the different effects of interface on the electronic and ionic transport the kinetics and mechanisms of transport along and across interfaces. The literature commonly considers transport along interfaces as grain boundary transport, corresponding to diffusion parallel to interfaces, as in grain boundaries of polycrystalUne materials or in nanoscale materials, as across nanostructures limited to a thin layer of nanometric thickness. In contrast, transport across interfaces involves transport perpendicular to the interface. 

Swinkels FB, Ashby MF (1980) Role of surface redistribution in sintering by grain-boundary transport. Powder Metall 23 1-7... 

Tsuru T, Latanision RM. Grain boundary transport of hydrogen in nickel. Scr. Metall. 1982 16 575-578. 

For a specified shape of the surface S and a prescribed chemical potential field X over S, this functional is maximum when the trial velocity field n is in fact that actual velocity field Vn defined by (9.9). The variational approach in terms of surface flux was introduced in a numerical study of grain boundary transport and cavitation by Needleman and Rice (1980), for which the grain boundary chemical potential is given by (8.14). It was introduced in the way as described here by Suo (1997) and Zhang et al. (1999) as a basis for study of surface evolution. 

A5 B. Holzapfel, D. Verebelyi, C. Cantoni, M. Paranthaman, B. Sales, R. Feenstra, D. Christen, D. P. Norton Low angle grain boundary transport properties 2.60 of undoped and doped Y123 thin film bicrystals,... 

Grain boundary transport is the subject of several fundamental pubhcations of Kaur and Gust, Atkinson and Taylor, Deschamps and Barbier, and Moya et al. ... 

If the neck has grown as a result of grain boundary transport of material away from the interface between the spheres, the tracer should be depleted in the center of the neck and piled up around its rim. 

---