Characterization of rough interfaces obtained by boriding

This study evaluates the morphology of borided interfaces by means of the fractal theory. The boride layers were formed in the AISI M2 steel by applying the paste boriding treatment at temperatures of 1253 and 1273 K and treatment times of 2 and 6 h, while a boron carbide paste thickness of 4 or 5 mm covered the samples surface in order to produce the boron diffusion. The morphology of interfaces formed between FeB and Fe ₂ B layers and between Fe ₂ B layer and steel substrate was analyzed by the rescaled-range (R/S), root-mean-square (RMS), and Fourier power spectrum (FPS) methods. Moreover, the multi-affine spectra of roughness exponent were obtained by calculating the q-order height-height correlation functions. We found that both interfaces are multi-affine, rather than self-affine. The multi-affine spectra of roughness exponents are found to be different for FeB/Fe ₂ B and Fe ₂ B/substrate interfaces, but independent on the treatment parameters (boron carbide paste thickness, temperature, and boriding time). Furthermore, we found that the multi-affine spectra of both interfaces behave as it is expected for "universal multi-fractals" with the Lévy index γ = 1, associated with the multiplicative cascades with a log-Cauchy distribution. Furthermore, our data suggest a great homogeneity of the boron diffusion field, characterized by universal fractal dimension D _diff = 2.90 ± 0.01. These findings provide a novel insight into the nature of phase formation during the boriding treatment.