KRASIKOVA I. New quantitative methods for determining the structure of materials in electron microscopy

The dissertation work is devoted to the development of a methodology for a mathematically defined quantitative characterization of the structure of a material based on its electron microscopic image. In the dissertation work, the adaptation of the mathematical model of the multifractal formalism to determine the quantitative characteristics of images of the structure of materials is carried out. The corresponding software, which gives stable calculation results, has been developed based on this adaptation. The high performance of the developed software makes it possible, in principle, to include it in existing software packages for processing electron microscopic images in real time, including the embedded software of electron microscopes. Using the presented technique, a study of the obtained multifractal and physical characteristics of hot-pressed AlB12–AlN composites was carried out in order to verify the adaptation of models and the developed software. These studies allows to draw an important conclusion that physical characteristics can be associated not only with the multifractal characteristics of images of the phase structure, but also multifractal characteristics of the boundaries cut out on them (boundaries grains, phase boundaries — depending on the test material). The results of calculations of the fractal characteristics of chromium films deposited in argon with a change in the deposition temperature and depending on the addition of oxygen are presented. It is shown that there is a correlation between the fractal dimension and the physical characteristics of chromium films — the hardness H and the reduced modulus of elasticity (1 2 ) r E = E − ν . A high degree of correlation is observed both for calculating the fractal dimension of the micrographs themselves, and for systems of distinguished boundaries. Keywords: electron microscopic image, material structure, grain boundaries, quantitative characterization, fractal dimension, multifractal characteristics