Determining the representative volume element size for three-dimensional microstructural material characterization. Part 1: Predictive models

Recent advances in microstructural imaging and characterization tools have led to an increase in the direct examination of 3-D microstructures of composite materials in devices such as solid oxide fuel cells, battery electrodes, and composite gas separation membranes. In particular, focused ion beam-scanning electron microscopy and x-ray nanotomography methods have opened the door for materials characterization at the tens of nanometer scale. These experimental methods have enabled the quantitative evaluation of microstructures for a variety of important parameters. However, there is often uncertainty in the literature regarding the necessary size of a representative volume element (RVE) in order to capture an accurate description of the structure. In an effort to provide guidance for the field, in this work simplified geometric models are presented to provide basis for the a priori estimation of RVE size for three common microstructural parameters: volume fraction, particle size, and network contiguity. In a second and complementary paper (Part 2), the results of the model will be compared to experimental data obtained from the extensive imaging of a multiphase composite membrane material using x-ray nanotomography.