Numerical Calculation of Electrical Conductivity of Porous Electroceramics

A numerical method for the calculation of the electrical conductivity of porous ceramics for gas sensing applications is developed, which takes into account detailed microstructural features by mapping a mesoscopic irregular resistor network onto the microstructure. The overall conductance of the ceramic sample is obtained by solving the Kirchhoff equations for the irregular network using an efficient iterative algorithm. The method is designed to handle the widely varying conductivities of different microstructural components present in ceramic gas sensors. The evolution of the macroscopic conductance of the model systems during a phase field simulation of sintering is obtained and several characteristic stages are distinguished. The potential applications of the method in computer aided microstructural optimization for ceramic gas sensors is discussed.