Determination of local fractal dimension of the catalyst support MgAl2O4 surface

In this paper, a procedure for estimating local fractal dimensionality values for greyscale images was developed. This procedure was tested on synthesised fractal and multifractal Brownian surfaces. The use of the method of detrended fluctuation analysis to determine the Hurst index for samples with a size not exceeding 2000 points was analysed. The optimal values of the sample size and the scale parameter have been obtained, allowing the Hurst index to be calculated with an error of less than 20%. The procedure was also tested on greyscale images, which are 8-bit representations of a synthesised fractal surface. The peculiarities of the application of the procedure for calculating the local fractal dimension for images obtained by scanning electron microscopy have been analysed. The values of the local fractal dimension of the oxide support MgAl₂O₄ are calculated using SEM images at different magnifications. It has been shown that, taking into account the fractal dimensionality calculation, different morphologies of the particle surface are observed at different scales of image magnification. At the highest magnification, the particle surface is found to consist of embedded smooth micron particles. The surface morphology of the MgAl₂O₄ particle depends on the micro- and mesopores between the embedded particles, this surface can be characterised by a fractal surface with FD₂ = 2.3–2.4.