PNNL

Abstract

We describe a simple finite difference approach for the calculation of the bulk electrical conductivity and the spatially-dependent current density of polycrystalline materials. These calculations can be applied to account for changes in grain structure, grain size, grain boundary character, temperature, and the presence of defects within the microstructure. As an example case, we demonstrate the application of our method for calculations of the bulk electrical conductivity of copper, as well as the current density and charge density within the copper microstructure. The bulk electrical conductivity of copper calculated using our model as a function of grain size indicated that when average grain diameter decreased from 100 µm to 100 nm, the conductivity decreased by a factor of approximately 25%. This is consistent with previous experimental studies from the literature, which reported similar decreases in electrical conductivity. Effects of variations in texture, twinned grain boundary density, and temperature on the conductivity of the copper microstructure are explored in order to further demonstrate the predictive capability of our model.