Interface Depinning in the Absence of External Driving Force

We study the pinning-depinning phase transition of interfaces in the quenched Kardar-Parisi-Zhang model as the external driving force $F$ goes towards zero. For a fixed value of the driving force we induce depinning by increasing the nonlinear term coefficient $\lambda$, which is related to lateral growth, up to a critical threshold. We focus on the case in which there is no external force applied (F=0) and find that, contrary to a simple scaling prediction, there is a finite value of $\lambda$ that makes the interface to become depinned. The critical exponents at the transition are consistent with directed percolation depinning. Our results are relevant for paper wetting experiments, in which an interface gets moving with no external driving force.Comment: 4 pages, 3 figures included, uses epsf. Submitted to PR

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 Fe2B layers and between Fe2B 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/Fe2B and Fe2B/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 Ddiff = 2.90 ± 0.01. These findings provide a novel insight into the nature of phase formation during the boriding treatment