Simulation of the influence of particle size distribution and grain boundary resistance on the electrical response of 2D polycrystals

Nanostructured polycrystalline materials have reached an increasing technological importance during the last years in topical fields, such as gas sensors and fuel cells. For these applications, the understanding of transport properties is of primer importance since they directly influence the efficiency of the devices. In this respect, impedance spectroscopy is a widely used tool in the analysis of the material conductivity. It involves the measurement of the impedance of the studied sample in a range of frequencies. A suitable representation of the impedance values allows separating the contribution of the bulk and the grain boundaries. The implementation of this technique is usually combined with the statement of some hypothesis, usually summarized in the so called brick layer model (BLM) which consists on the idealisation of the studied polycrystal as made up of regular and cubic-shaped grains. Nevertheless, in the real case, the crystal growth is not homogeneous, but a wide range of grain sizes is present. This may lead to a lack of accuracy in the obtained results when applying the aforementioned suppositions, as shown by Fleig et al. [1]. In the present study, the influence of the grain size distribution in the conductivity of 2D polycrystals is modelized considering the nanocrystalline case. With this aim, artificial 2D polycrystal images were simulated with different grain size distributions. From those images, equivalent RC impedance networks were built. The electrical response of the constructed circuit is calculated for various frequencies. The results obtained allow the discussion of the validity of the brick layer model as a function of grain size distribution and grain boundary-to-bulk conductivity ratios. We show that, when starting from a brick layer model, a progressive disordering of the structure is accompanied by a diminution of the overall resistance. This decrease is directly correlated to the augmentation of the linear density of grain boundary. In other words, for a given crystal size, a greater specific surface leads to a lowering of the grain boundary resistance. For high levels of disorders i.e. for wide grain size distributions, another effect becomes predominant. It consists on the appearance of some very conductive pathways associated with big grains and a few number of grain boundaries to cross. This leads to a strong inhomogeneity of current flows as shown on figure 5. Such observation may have some great importance in devices in which a high conduction is needed, or in which a concentration of current flow in one region of the material may lead to its proper destruction.