Exploring the proper statistical proxy to distinguish random structures

Abstract The canonical description of structures comprises two aspects: (1) basic structural elements and (2) arrangement pattern between those elements. This tidy description has been very successful and facilitates the development of structural physics tremendously, enabling the classification, comparison and analysis of an extremely wide range of structures, including crystals, quasi-crystals, liquid crystals, semi-crystalline materials and so on. However, it has been gradually realized that many novel materials and devices exhibit random structures in which either basic elements or arrangement patterns may not exist. With the rapid development of modern advanced materials, this type of apparently random structure pops up frequently, leaving researchers struggling with how to describe, classify and quantitatively compare them. This paper proposes the utilization of statistical characteristics as the major indicators for the description of apparently random structures. Specifically, we have explored many statistical properties, including power spectral density, histograms, structural complexity, entropic complexity, autocorrelation, etc., and found that autocorrelation may serve as a promising statistical proxy to distinguish similar-looking random structures. We discuss eight atomic force microscope images of random structures, demonstrating that autocorrelation can be used to distinguish them. In addition, 14 more diverse datasets are used to support this conclusion, including atomic force microscopy images of polymers and non-polymers, transmission electron microscopy images of nanocomposite layers and scanning electron microscopy images of non-polymers.