Conductivity grain-boundary effect

T. Van Dijk and A.J. Burggraaf, Grain boundary effects on ionic conductivity in ceramic GdxZri-x02-x/2 solid solutions. Phys. Stat. Sol (A), 63 (1981) 229-240. 

Single crystals are the most valuable subjects for investigating the bulk properties of materials. In particular, they clearly demonstrate the conduction anisotropy (if any), and are free from grain-boundary effects. For technical utilization, however, they are usually impractical due to their unsuitable shape and size, and high cost of production. 

The determination of dc ionic conductivity is perhaps the most widespread and also the simplest application of impedance spectroscopy. By using ac methods, electrode polarization can be correctly eliminated from an electrochemical system, and other sources of spurious frequency dispersion, such as grain boundary effects, may also be removed under certain circumstances. Electrodes may be inert foreign metals, thus eliminating the need for demonstrating the reversibility of parent metal electrodes. 

T. van Dijk and A. J. Burggraaf [1981] Grain Boundary Effects on Ionic Conductivity in Ceramic Gd.fZxi x02-(xi2i Solid Solutions, Phys. Stat. Sol. (a) 63, 229-240. 

A third area in which film crystallinity is proving to be important is that of insulating and tunnelling layers (21,22,23). Recent work at Lancaster University (24,25) has demonstrated that conduction through LB films is normally dominated by grain boundary effects. In all three areas, then, practical exploitation of the LB technique is waiting on substantial improvements in film crystallinity. 

Suppose that we know the conductivities Kj of each phase i and their volume fractions /) with Lfi = 1. Further, neglect any grain boundary effects. The overall conductivity is always bounded from above and below by the conductivities of a corresponding material in which the same amounts of the phases are arranged in a series or parallel coupling, as in lamellar or fiber composites. Another, and nontrivial, geometry is one in which the phases are distributed so as to make Keff isotropic, in a statistical sense. This would be the case in a random distribution of inclusions in a matrix. Then K ff is bounded from above and below by the Hashin-Shtrikman (27) bounds Khs and Khs-. With two phases, i = 1 and 2, one has... 

---