Multifractal Analysis of Disperse Polymetallic Systems

Abstract

Multifractal analysis is one of the tools for studying complex systems with a self-similar structure, e.g., disperse polymetallic systems. This paper studied the application of multifractal analysis to describe and evaluate the characteristics of disperse polymetallic systems (Fe–Al–Co, Fe–Al–Cr, Fe–Al–Mo) obtained by galvanic substitution. The study resulted in the identification of important aspects, such as the distribution of fractal dimensions, which allows for a deeper understanding of the mechanisms of formation and development of structures in polymetallic systems. The presented results can be useful for the development of new materials and technologies, as well as for improving existing methods of analysis and quality control of polymetallic systems. It was shown that the spectrum of generalized fractal dimensions of Fe–Al–Co is similar to the spectrum of the Sierpinski dodecahedron—an S-shaped descending curve. The calculated generalized fractal dimension is 1.662, which indicates a lower complexity of the structure of the Fe–Al–Co sample compared to the model Sierpinski dodecahedron. A micrograph of a particle of a synthesized dispersed sample of the Fe–Al–Cr system shows an agglomerated structure of micron sizes, which, in turn, is formed from interconnected spherical formations with a size of 50–200 nm. The spectrum of generalized fractal dimensions of Fe–Al–Cr also represents an S-shaped ascending curve. The generalized fractal dimension in this case is 1.881, which is higher than that of the sample of the disperse Fe–Al–Co system. The results obtained showed that the multifractal spectrum and the distribution of fractal dimensions can serve as tools for analyzing the mechanisms of formation and evolution of the structure of polymetallic systems. This opens new opportunities for the development of innovative materials with specified properties and the improvement of existing technologies and quality control of materials.