Multifractal properties of Pyrex and silicon surfaces blasted with sharp particles

Abstract

The blasting of brittle materials with sharp particles is an important fabrication technology in many industrial processes. In particular, for microsystems, it allows the production of devices with feature sizes down to few tens of microns. An important parameter of this process is the surface roughness of post-blasted surfaces. In this work the scaling properties of Pyrex glass and silicon surfaces after bombardment with alumina particles are investigated. The targets were bombarded at normal incidence using alumina particles with two different average sizes, 29 µm and 9 µm. This investigation indicates that the resulting surfaces are multifractal. Applying multifractal detrended fluctuation analysis (MFDFA) allowed us to determine the singularity spectrum of the surfaces. This spectrum did not depend on the target material or on the size of the particles. Several parameters quantifying relevant quantities were determined. It was found that long range correlations are responsible for the observed multifractal behaviour.

Multifractality in dilute magnetorheological fluids under an oscillating magnetic field

“…The width of the f (α) spectrum = α max − α min can be used to indicate the complexity of a structure: Monofractal structures give narrow spectra, whereas multifractal distributions give broader spectra [34,35]. The degree of multifractality of the structures in MR fluids for different (a) particle concentrations and different (b) frequencies is shown in Table I.…”

Multifractal analysis of the fracture surfaces of foamed polypropylene/polyethylene blends

“…The observed multifractal behaviour can be partly interpreted in terms of the spatial intermittency [54,55] and the origin of the multifractal hidden in the fracture surface may be the long range correlations of the intermittent fluctuation [41,56]. A basic foaming process can be divided into three steps [4]: (1) temperature increase or a pressure decrease; (3) cell growth and coalescence, a combination of mass transfer and fluid dynamics.…”

“…Raoufi et al analyzed the multifractal spectrum of ITO thin films prepared by electron beam deposition method and the f (α) shapes of ITO thin films remained left hooked after annealing at 200 • C and 300 • C [40]. Moktadir et al researched the multifractal properties of Pyrex and silicon surfaces blasted with sharp particles, and found that the long-range correlations were the origin of the multifractal behaviour [41].…”