Fractal Characterization of Microstructure of Materials and Correlation with Their Properties on the Basis of Digital Materials Science Concept

Abstract

The concept of Digital Materials Science supposes that materials are designed, fabricated, tested, studied, characterized, and optimized on the basis of digital technologies, including the analysis of fractal parameters (fractal dimension, lacunarity, scale invariance, Voronoi entropy, etc.) of materials’ microstructure. Many classes of materials may be considered as composites: polymer composites with inorganic fillers, alloys containing nonmetallic inclusions (oxides, carbides, nitrides, intermetallic ones, etc.), ceramic materials with pores and sintering additives, etc. The analysis of composition-technology-structure-properties relationships for such non-ordered composite materials requires the development of numerical tools for the characterization of their structure, including the interposition of phases. This chapter presents several examples of the implementation of this concept, including the study of filler distributions in dielectric composites, interposition of phases in special ceramic materials, distribution of nonmetallic inclusions in additively manufactured stainless steel, and structural features of tungsten oxide-based electrochromic materials. Based on the analysis of such characteristics as lacunarity and surface functionality, interrelations are established between technical properties of the studied materials and their structure providing approaches to the prediction and optimization of their target performances.