Impedance/Dielectric Spectroscopy of Electroceramics in the Nanograin Regime
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Impedance/Dielectric Spectroscopy of Electroceramics in the Nanograin Regime N. J. Kidner, B. J. Ingram, Z. J. Homrighaus, T. O. Mason, and E. J. Garboczi1 Department of Materials Science and Engineering and Materials Research Center, Northwestern University, Evanston, IL 60208, U.S.A. 1 Materials and Construction Research, Building and Fire Research Laboratory, National Institute of Standards and Technology, Gaithersburg, MD 20899, U. S. A. ABSTRACT In the microcrystalline regime, the behavior of grain boundary-controlled electroceramics is well described by the “brick layer model” (BLM). In the nanocrystalline regime, however, grain boundary layers can represent a significant volume fraction of the overall microstructure and simple layer models are no longer valid. This work describes the development of a pixel-based finite-difference approach to treat a “nested cube model” (NCM), which more accurately calculates the current distribution in polycrystalline ceramics when grain core and grain boundary dimensions become comparable. Furthermore, the NCM approaches layer model behavior as the volume fraction of grain cores approaches unity (thin boundary layers) and it matches standard effective medium treatments as the volume fraction of grain cores approaches zero. Therefore, the NCM can model electroceramic behavior at all grain sizes, from nanoscale to microscale. It can also be modified to handle multi-layer grain boundaries and property gradient effects (e.g., due to space charge regions). INTRODUCTION There are a number of existing and proposed applications of electroceramics in nanocrystalline form, including batteries, fuel cells, gas separation membranes, solar cells, etc. [1] Nanoceramics are utilized as chemical catalysts and as chemical sensors. Their microcrystalline counterparts are often used as active electrical devices (e.g., varistors and thermistors). In certain cases, like the latter, grain boundaries are necessary to impart the required electro-active or thermo-active responses. In other cases, grain boundaries act as undesirable barriers limiting transport (e.g., in ionic conductors). In still others, boundaries between dissimilar ceramics can impart enhanced ion transport due to high mobility space charge regions (e.g., in “dispersed ionic conductors”) [2,3]. Given the high surface-to-volume ratios in nanoceramics, grain boundaries can be expected to exert greater influence over electrical/dielectric properties than in conventional microcrystalline ceramics. There are several problems with existing grain boundary layer models (see below) insofar as describing the electrical/dielectric response of nanoceramics is concerned. First, in the nanograin regime, boundary layers such as space-charge regions or local oxidation layers can represent a significant volume fraction of the overall microstructure (see Figure 1). Conventional layer models, such as the “brick layer model” (BLM), are hardly adequate for such a situation. Second, as pointed out by Maier [4], there can be differential transp
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