Calculation of Two‐Point Correlation Functions

Summary

This chapter provides a comprehensive study that performed to measure two‐point correlation functions, using different techniques such as transmission electron microscopy (TEM) or scanning (STEM), small‐angle X‐ray scattering (SAXS), small‐angle neutron scattering (SANS) and Monte Carlo simulations. The distribution, orientation and shape of the heterogeneous material phases are described by two‐point or higher order correlation functions, which can in general be determined from appropriate microstructure measurements. SAXS data is used to calculate two‐point correlation function correlation for two‐phase polymer composites. Two‐point correlation functions are determined based on the probability of occurrence of the head and tail of each vector in a particular phase. The Monte Carlo estimation of two‐point correlation functions are acquired by assigning large number of random vectors within the generated microstructure and examining the number fraction of the sets which satisfy the different types of correlation functions.