In this article, an alloy of the Finemet type Fe77Cu1Si16B6 obtained by quenching from a liquid state (spinning method) in the initial state is investigated. The main research methods were scanning and transmission electron microscopy. Methods for describing multiscale structural heterogeneities in amorphous-nanocrystalline alloys have been developed, allowing the structural state to be described and its influence on the physicochemical and technical properties to be determined depending on the technological conditions for obtaining these alloys. Representation of electron microscopic images in the form of Fourier spectra made it possible to reveal the nature of the formation of short- and middle-order in amorphous-nanocrystalline alloys according to the principle of self-similar spatial structures. The analysis of electron microscopic images by integral Lebesgue measures revealed density fluctuations over the alloy volume, which corresponds to the hierarchical representation of structural inhomogeneities in amorphous metallic alloys.

Using the methods of spectral analysis with application of the formalism of the integral function of Lebesgue measures and Kullback's divergence, the structural features of the interfaces of spinning Fe- (Cu, Nb) - (Si, B) tapes with different metalloid contents are investigated. An increase in the total concentration of the metalloid ambiguously affects the nature of the morphology of rapidly quenched alloys. The minimum difference in the statistics of contact and free surfaces, formed in the spinning process, is demonstrated by fusionFe74Cu1Nb3Si16B6.