Modelling Study on the Electrical Behaviour of YSZ-BASED Composites
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INTRODUCTION It is well known that high ionic conductivity (>10"1 S/cm at 1000 'C) of fully stabilised Y 20 3-ZrO2 (YSZ) makes it suitable for application in solid oxide fuel cells (SOFC) [1]. However, its relatively poor bending strength is a source of problems when shaped as thin sheets. It has recently been demonstrated that the addition of alumina (ot-A120 3) as secondary phase improves the YSZ mechanical properties; so the use of these composites has been suggested in planar configuration SOFC [2-5]. Unfortunately, the total electrical conductivity largely decreases as the amount of insulating materials increases. This general trend however might be smoothed in view of recent results [6,7]; the same total amount of alumina having different grain sizes induces different changes in total electrical conductivity. A full understanding of the electrical behaviour of these composites is still lacking but the possibility to partially forecast it, suggested the development of a digital image-based model able to simulate both the material polycrystalline microstructure and its a.c. electrical response. In the present paper the complex impedance spectra of YSZ/AI20 3 composites have been simulated; the obtained bulk and grain boundary electrical conductivities were compared with the experimental ones [8] and the usefulness of the model evaluated.
331 Mat. Res. Soc. Symp. Proc. Vol. 575 ©2000 Materials Research Society
MODELLING AND SIMULATION The random resistor network approach [9] has been adopted to develop a digital imagebased model able to simulate the electrical behaviour of YSZ/A120 3 composites [ 10,11 ]. The model works through three steps: a suitable representation of the material microstructure, its conversion into a 3-D electrical network and the successive solution of the electrical circuit obtained via an iterative procedure [12]. Details of the model were discussed elsewhere [10,11 ], so that here only the main features will be given. Pixel units were used in the simulation and only before solving the electrical network were they converted into physical quantities. Microstructure simulation The spatial Voronoi tessellation [13] was used to simulate the polycrystalline microstructure of YSZ: crystallites were obtained dividing a defined rectangular prism into convex hulls. The uniformity of the grain size distribution was enhanced, generating the tessellation by a MonteCarlo algorithm and ad hoc modified, where a minimum distance among the sites was imposed. The alumina particles (represented as constant diameter spheres) were then randomly placed along the YSZ grain boundaries to build up the composite, in accordance with previuos findings [14]. Figure 1 shows a planar section of the YSZ (a) and of the composite YSZ/10%wt A120 3 (b).
a)
b)
Figure 1. Planar section of simulated polycrystalline YSZ (a) and composite (b) The simulation volume size (500x500x20,000 pixel), the grains number (about 800) and their average diameter [15] (about 360 pixel) were the result of a careful compromise between good
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