A random resistor model to forecast the electrical properties of crystalline ionic conductor composites

A model able to forecast the electrical properties of crystalline composites is presented. Systems having both insulating and ionic conducting phases were simulated taking into account the relative size and distribution of the particles. The model works through three steps: a suitable digital image-based representation of the material microstructure, its conversion into a 3-D electrical network and the impedance calculation. The polycrystalline microstructure of the matrix was generated using the Voronoi tessellation and the insulating phase was successively distributed along intergranular positions by a Montecarlo method. The simulated digital image was converted in a network of cubes and their edges substituted with discrete circuits. Such a procedure was performed by well defined rules; so the bulk and the grain boundary electrical behaviour of the different phases was reproduced. The electrical network thus attained was solved via a transfer-matrix method and the complex impedance spectra obtained. The model might be used to tailor the composites in order to obtain the best compromise between its electrical properties and microstructure.