عنوان مقاله [English]
N-point correlation functions are used for calculating properties of heterogeneous systems. Power and main advantage of statistical continuum technique is the direct link to statistical information of microstructures. Two-point correlation functions are the lowest order of correlation functions that can describe the relationship between morphology and properties of microstructures. Statistical pair correlation functions are achieved by scattering electron microscopy or small-angle X-ray scattering experimentally.
Higher order correlation functions must be calculated or measured to increase the accuracy statistical continuum approach. Microstructure two-point correlation functions are well-known class of statistical descriptors for characterization and reconstruction of heterogeneous microstructures. In this study, a comprehensive review on statistical correlation functions that are used in micro and nanostructures is done and then, focused on reconstruction of these structures by using numerical and experimental approaches. Description and characterization of heterogeneous systems had high importance for scientists for last decades and different approaches have been developed for determining 3D descriptors of heterogeneous systems. Statistical continuum mechanics provided alternative approach for reconstruction and characterization of heterogeneous systems. Reconstruction approaches have been improved by developing of numerous simulation techniques in recent years. Anisotropic structures, orientation distribution, shape, and geometrical features can be extracted from statistical correlation functions. 3D reconstruction of microstructures and nanostructures is a new way to investigate the behavior of these structures precisely. In this method the distribution of nanoparticles is determined, and their coordinates are saved which is very helpful for determination of their treatment. Mani different researches have used reconstruction approach to enter their experimental samples to finite element software. Then, by applying the properties of each phase they investigate about different behavior of their experimental samples. Depended on samples different approaches are used for reconstruction and researches have tried different ways to reduce reconstruction error. In this study, different approaches are discussed, and the calculation of error is presented.