Geodesic
Fractal characterization of nanostructured materials
Nanosistemy: fizika, himiâ, matematika, Tome 10 (2019) no. 1, pp. 42-49.

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The article presents a developed gradient-pixel method of fractal analysis and results of multifractal characterization of nano- structured materials with a high proportion of non-autonomous phases obtained from micrographs of their surface chips with high-resolution scanning microscopes. Compared with the black and white binarization option, the gray gradation improves the quality of multifractal analysis of nanostructured materials and expands its capabilities, in particular, the selection of multi-scale composite inclusions in the structure of the material and nano-objects on transparent or opaque basis. Establishing the characteristics of these dependencies permits linking the indicators of structural and phase nonuniformity in the development of new materials with changes in their physicochemical properties. In comparison with the fractal dimension of the Sierpinski carpet as a classic regular monofractal computed on the outlined basis, quite accurately coinciding with the known analytical value, the resulting spectrum of fractal dimensions of the synthesized chemical-catalytic and thermoelectric nanomaterials indicates the multifractal nature of their structural and phase nonuniformity according to the Rényi generalized equation.
Keywords: nanostructured materials, SEM micrographs of chips, fractal analysis, spectrum of multifractal dimensions.
Mots-clés : gradient-pixel method 
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     author = {A. N. Kovalenko},
     title = {Fractal characterization of nanostructured materials},
     journal = {Nanosistemy: fizika, himi\^a, matematika},
     pages = {42--49},
     publisher = {mathdoc},
     volume = {10},
     number = {1},
     year = {2019},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/NANO_2019_10_1_a4/}
}
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A. N. Kovalenko. Fractal characterization of nanostructured materials. Nanosistemy: fizika, himiâ, matematika, Tome 10 (2019) no. 1, pp. 42-49. http://geodesic.mathdoc.fr/item/NANO_2019_10_1_a4/