Microstructural quantification of heterogeneous materials using higher-order correlation functions

Optimal design and (re)construction of heterogeneous materials, e.g. ceramics and alloys, with desired properties, e.g. conductivity and stiffness, are of crucial importance in many scientific and engineering fields. Doing so, however, requires the establishment of microstructure-property relationships. Furthermore, accurate characterization of the microstructure is possible if several n-point correlation functions that describe their statistical properties can be computed. While the limits n=1, corresponding to phase fractions, and n=2 that represents such two-point correlation functions as the radial distribution function, have yielded useful information and insights and have been utilized for reconstruction of models of heterogeneous materials, in many cases higher-order correlation functions are required in order to develop deeper understanding of materials' properties, as well as obtaining accurate estimates for them. Here, we present the results of extensive computations and analyzes of the most important third-order correlation functions for accurate quantification and characterization of the microstructure of various types of heterogeneous materials. These include three-point probability and cluster functions as well as three-point surface correlation functions. The accuracy of our simulations is tested against theoretical predictions for some basic models.