Inhomogeneous Bulk Conductivities

Owing to several reasons, bulk conductivities in ceramics are frequently inhomogeneous  

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Fleig reviews fundamental aspects of solid state ionics, and illustrates many similarities between the field of solid state electrochemistry and liquid electrochemistry. These include the consideration of mass and charge transport, electrochemical reactions at electrode/solid interfaces, and impedance spectroscopy. Recent advances in microelectrodes based on solid state ionics are reviewed, along with their application to measuring inhomogeneous bulk conductivities, grain boundary properties, and electrode kinetics of reactions on anion conductors. 

Electrical bulk properties of ionic solids can be rather inhomogeneous (Sec. 3.1). In the following it is shown that microelectrodes are a very useful tool to gain spatially resolved information on the conductivity of such inhomogeneous solids. Let us first consider the case of a spherical microelectrode (radius rme) atop a sample with homogeneous bulk conductivity Ubuik- The bulk resistance R between the microelectrode and a hemispherical counter-electrode of radius rce (Fig. 12a) can be calculated by integrating the infinitesimal resistances of hemispherical shells according to... 

In the following section, a new bulk conductivity cell is described that significantly reduces the contact resistance to a level where the measurements of paper bulk conductivity can be made with an accuracy that is limited primarily by the anisotropic structure of the paper itself. A small uncertainty in the measured conductivity arises from compaction ( 10%) of the paper sample in the apparatus caused by the application of 13-8 MPa pressure to the stainless steel electrode system in the cell. This pressure is used to eliminate contact resistance. Despite this uncertainty, measurement errors in the new cell are significantly less than the spread in the conductivity values ( 200)t) determined at different points in a single paper sheet. The variability arises from inhomogeneities in the cellulose fiber network within the sheet. 

Figure 7. Nonequilibrium Monte Carlo results for the thermal conductivity (To = 2). The circles and squares are the present steady-state results for bulk and inhomogeneous systems, respectively (horizontally offset by 0.015 for clarity), and the triangles are NEMD results [89, 91]. (From Ref. 5.)...

Figure 7 also shows results for the thermal conductivity obtained for the slit pore, where the simulation cell was terminated by uniform Lennard-Jones walls. The results are consistent with those obtained for a bulk system using periodic boundary conditions. This indicates that the density inhomogeneity induced by the walls has little effect on the thermal conductivity. 

The electron mobilities at 296 and 420°K are given for several Cr-doped and -doped samples in Table II. The data for the Cr-doped crystals should be considered less accurate since a mixed-conductivity analysis was necessary in most cases (Look, 1980). However, the temperature dependences are not unlike those of conductive GaAs samples with similar impurity concentrations (1016—1018 cm-3). At least two of the crystals (MA 287/80 and MOR 56/76) appeared to be inhomogeneous, as evidenced by nonlinear Arrhenius plots. However, it is doubtful that the bulk of the data require a percolation-type conduction mechanism to be operative, as has been suggested (Robert et ai,... 

The magnitude of the errors in determining the flat-band potential by capacitance-voltage techniques can be sizable because (a) trace amounts of corrosion products may be adsorbed on the surface, (b) ideal polarizability may not be achieved with regard to electrolyte decomposition processes, (c) surface states arising from chemical interactions between the electrolyte and semiconductor can distort the C-V data, and (d) crystalline inhomogeneity, defects, or bulk substrate effects may be manifested at the solid electrode causing frequency dispersion effects. In the next section, it will be shown that the equivalent parallel conductance technique enables more discriminatory and precise analyses of the interphasial electrical properties. 

The fact that in the case of the bicrystal in Figure 54 the effective thickness calculated from the low-frequency semicircle is very much greater than expected from the width of the boundary, while the activation energy is almost equal to that of the bulk, points towards a frequently overlooked complication, namely to current-constriction effects. Such constriction effects occur287 when the crystal grains are not ideally sintered together, if pores or second phases are included, and interrupt the lateral conductivity of boundaries, as is the case for inhomogeneous electrode contacts. 

This Section examines the dielectric and conduction mechanisms in bulk materials, assuming that the medium is linear (at the applied electric field strength) and homogeneous. Effects of interfaces and inhomogeneities are discussed in Section 3.2. Additional discussion can be found in basic texts 21 23). 

GD-MS is of use for the direct determination of major, minor and trace bulk concentrations in electrically-conductive and semi-conductor solids down to concentrations of 1 ng/g. Because of the limited ablation (10-1000 nm/s), the analysis times especially when samples are inhomogeneous are long. It has been applied specifically to the characterization of materials such as Al, Cd, Ga, In, Si, Te, GaAs and CdTe. 

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