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When a Surface Becomes a Network
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Orientador(es)
Resumo(s)
The morphology of solid surfaces encodes fundamental information about the physical mechanisms that govern their formation. Here, we reinterpret scanning electron microscopy (SEM) micrographs of oxide thin films as two-dimensional self-affine morphology fields (not height-metrology) and analyze them using a multiscale statistical-physics framework that integrates spectral, multifractal, geometric, and topological descriptors. Fourier-based power spectral density (PSD) provides the spectral slope (Formula presented.) and apparent Hurst exponent (Formula presented.), while multifractal scaling yields the information dimensions (Formula presented.), the singularity spectrum (Formula presented.), and its width (Formula presented.), which quantify scale hierarchy and intermittency. Lacunarity captures intermediate-scale heterogeneity, and Minkowski functionals—especially the Euler characteristic (Formula presented.) —probe connectivity and identify the onset of a percolation-like network structure. Two representative surfaces with contrasting morphologies are used as model systems: one exhibiting an anisotropic, porous, strongly multifractal structure with fragmented domains; the other showing a compact, nearly isotropic, and nearly monofractal organization. The porous surface/topography displays steep PSD decay, broad multifractal spectra, and positive (Formula presented.), consistent with a sub-percolated, diffusion-limited, Edwards–Wilkinson-like (EW-like) growth regime. Conversely, the compact surface/topography exhibits gentler spectral slopes, narrower (Formula presented.), enhanced lacunarity at intermediate scales, and a (Formula presented.) zero-crossing indicative of a connectivity transition where a surface becomes a percolating network, consistent with a Kardar–Parisi–Zhang-like (KPZ-like) correlated growth regime. These results demonstrate that individual SEM micrographs encode quantitative fingerprints of nonequilibrium universality classes and topology-driven transitions from fragmented surfaces to connected networks, showing that SEM intensity maps can serve as a quantitative probe for testing theories of rough surfaces and kinetic growth in experimental thin-film systems.
Descrição
Copyright: © 2026 by the authors. Licensee MDPI, Basel, Switzerland
Palavras-chave
Euler characteristic χ(θ) EW/KPZ universality classes Hurst exponent (H) lacunarity Minkowski functionals multifractal analysis percolation threshold power spectral density (PSD) scanning electron microscopy (SEM) self-affine morphology thin-film surfaces Chemistry (miscellaneous) Materials Science (miscellaneous) Surfaces and Interfaces Surfaces, Coatings and Films