najoNanosystems: Physics, Chemistry, MathematicsНаносистемы: физика, химия, математика2220-80542305-7971Университет ИТМО10.17586/2220-8054-2019-10-1-42-49najo-531Research ArticlePHYSICSФИЗИКАFractal characterization of nanostructured materialsKovalenkoA. N.

26 Politekhnicheskaya, St. Petersburg 194021

ras-kan@mail.ruIoffe InstituteRussian Federation2019060820251014249Copyright © Kovalenko A.N., 20252025Kovalenko A.N.Kovalenko A.N.This work is licensed under a Creative Commons Attribution 4.0 License.https://nanojournal.ifmo.ru/jour/article/view/531

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 Renyi generalized equation.

nanostructured materialsSEM micrographs of chipsfractal analysisgradient-pixel methodspectrum of multifractal dimensionsReferencesKohler M., Fritzsche W. Nanotechnology: An Introduction to Nanostructuring Techniques. Wiley, John & Sons, Incorporated, 2004, 284 pp.Kohler M., Fritzsche W. Nanotechnology: An Introduction to Nanostructuring Techniques. Wiley, John & Sons, Incorporated, 2004, 284 pp.Zhabrev V.A., Kalinnikov V.T., Margolin V.I., Nikolaev A.I., Tupik V.A. Physico-chemical processes of nanoscale objects synthesis. St. Petersburg: Elmor Publishing House, 2012 (in Russian).Zhabrev V.A., Kalinnikov V.T., Margolin V.I., Nikolaev A.I., Tupik V.A. Physico-chemical processes of nanoscale objects synthesis. St. Petersburg: Elmor Publishing House, 2012 (in Russian).Ivanov V.K., Kopitsa G.P., Ivanova O.S., Baranchikov A.Ye., Pranzas K., Grigoriev S.V. Complete inheritance of fractal properties during first-order phase transition. Journal of Physics and Chemistry of Solids, 2014, 75(2), P. 296–299.Ivanov V.K., Kopitsa G.P., Ivanova O.S., Baranchikov A.Ye., Pranzas K., Grigoriev S.V. Complete inheritance of fractal properties during first-order phase transition. Journal of Physics and Chemistry of Solids, 2014, 75(2), P. 296–299.Jens Feder. Fractals. Plenum Press. New York and London, 1988, 284 pp.Jens Feder. Fractals. Plenum Press. New York and London, 1988, 284 pp.Mandelbrot B.B. The fractal geometry of nature. San Francisco, Freeman, 1982.Mandelbrot B.B. The fractal geometry of nature. San Francisco, Freeman, 1982.Roldughin V.I. Self-assembly of nanoparticles at interfaces. Russian Chemical Reviews, 2004, 73(2), P. 115–145.Roldughin V.I. Self-assembly of nanoparticles at interfaces. Russian Chemical Reviews, 2004, 73(2), P. 115–145.Krasilin A.A., Almjasheva O.V., Gusarov V.V. Effect of the structure of precursors on the formation of nanotubular magnesium hydrosilicate. Inorganic Materials, 2011, 47(10), P. 1111–1115.Krasilin A.A., Almjasheva O.V., Gusarov V.V. Effect of the structure of precursors on the formation of nanotubular magnesium hydrosilicate. Inorganic Materials, 2011, 47(10), P. 1111–1115.Ivanov V.K., Kopitsa G.P., Baranchikov A.E., Grigoriev S.V., Runov V.V., Garamus V. Hydrothermal growth of ceria nanoparticles. Russian Journal of Inorganic Chemistry, 2009, 54(12), P. 1939–1943.Ivanov V.K., Kopitsa G.P., Baranchikov A.E., Grigoriev S.V., Runov V.V., Garamus V. Hydrothermal growth of ceria nanoparticles. Russian Journal of Inorganic Chemistry, 2009, 54(12), P. 1939–1943.Vasilevskaya A., Almjasheva O.V., Gusarov V.V. Peculiarities of Structural Transformations in Zirconia Nanocrystals. Journal of Nanoparticle Research, 2016, 18(188), P. 1-11.Vasilevskaya A., Almjasheva O.V., Gusarov V.V. Peculiarities of Structural Transformations in Zirconia Nanocrystals. Journal of Nanoparticle Research, 2016, 18(188), P. 1-11.Korytkova E.N., Pivovarova L.N., Drosdova I.A., Gusarov V.V. Hydrothermal synthesis of nanotubular Co-Mg hydrosilicates with the chrysotile structure. Russ. J. Gen. Chem., 2017, 77(10), P. 1669–1676.Korytkova E.N., Pivovarova L.N., Drosdova I.A., Gusarov V.V. Hydrothermal synthesis of nanotubular Co-Mg hydrosilicates with the chrysotile structure. Russ. J. Gen. Chem., 2017, 77(10), P. 1669–1676.Prigogine I., Defay R. Chemical thermodynamics. Longman Green and Co. London-New York - Toronto, 1954.Prigogine I., Defay R. Chemical thermodynamics. Longman Green and Co. London-New York - Toronto, 1954.Kovalenko A.N., Tugova E.A. Thermodynamics and kinetics of non-autonomous phases formation in nanostructured materials with variable functional properties. Nanosystems: physics, chemistry, mathematics, 2018, 9(5), P. 641–662.Kovalenko A.N., Tugova E.A. Thermodynamics and kinetics of non-autonomous phases formation in nanostructured materials with variable functional properties. Nanosystems: physics, chemistry, mathematics, 2018, 9(5), P. 641–662.Emets E.P., Novoselova A.E., Poluektov P.P. In situdetermination of the fractal dimensions of aerosol aggregates. Physics-Uspekhi (Advances in Physical Sciences), 1994, 37(9), P. 881–887.Emets E.P., Novoselova A.E., Poluektov P.P. In situdetermination of the fractal dimensions of aerosol aggregates. Physics-Uspekhi (Advances in Physical Sciences), 1994, 37(9), P. 881–887.Swapna M.S.,Sankararaman S. Fractal analysis - a surrogate technique for material characterization. Nanosystems: physics, chemistry, mathematics, 2017, 8(6), P. 809–815.Swapna M.S.,Sankararaman S. Fractal analysis - a surrogate technique for material characterization. Nanosystems: physics, chemistry, mathematics, 2017, 8(6), P. 809–815.Stryapunina K.A., Makarova L.E., Degtyarev A.I., Karavayev D.M., Matygullina E.V., Sirotenko L.D. The multifractal analysis of the composite material on the basis of thermoexpanded graphite. Izvestia of Samara Scientific Center of the Russian Academy of Sciences, 2014, 16(2), P. 552–556.Stryapunina K.A., Makarova L.E., Degtyarev A.I., Karavayev D.M., Matygullina E.V., Sirotenko L.D. The multifractal analysis of the composite material on the basis of thermoexpanded graphite. Izvestia of Samara Scientific Center of the Russian Academy of Sciences, 2014, 16(2), P. 552–556.Lomanova N.A., Tomkovich M.V., Ugolkov V.L., Volkov M.P., Pleshakov I.V., Panchuk V.V., Semenov V.G. Formation mechanism, thermal and magnetic properties of (Bi1−xSrx)m+1Fem−3Ti3O3(m+1)−δ (m=4-7) ceramics. Nanosystems: physics, chemistry, mathematics, 2018, 9(5), P. 676–687.Lomanova N.A., Tomkovich M.V., Ugolkov V.L., Volkov M.P., Pleshakov I.V., Panchuk V.V., Semenov V.G. Formation mechanism, thermal and magnetic properties of (Bi1−xSrx)m+1Fem−3Ti3O3(m+1)−δ (m=4-7) ceramics. Nanosystems: physics, chemistry, mathematics, 2018, 9(5), P. 676–687.Oksengendler B.L., Ashurov N.R., Maksimov S.E., Uralov I.Z., Karpova O.V. Fractal structures in perovskite-based solar cells. Nanosystems: physics, chemistry, mathematics, 2017, 8(1), P. 92–98.Oksengendler B.L., Ashurov N.R., Maksimov S.E., Uralov I.Z., Karpova O.V. Fractal structures in perovskite-based solar cells. Nanosystems: physics, chemistry, mathematics, 2017, 8(1), P. 92–98.Ivanov V.K., Baranov A.N., Oleinikov N.N., Tretyakov Yu.D. Fractal surfaces of ZrO2, WO3, and CeO2 powders. Inorganic Materials, 2002, 38(12), P. 1224–1227.Ivanov V.K., Baranov A.N., Oleinikov N.N., Tretyakov Yu.D. Fractal surfaces of ZrO2, WO3, and CeO2 powders. Inorganic Materials, 2002, 38(12), P. 1224–1227.

The authors declare that there are no conflicts of interest present.