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The problem of simultaneous growth and competition of intermediate phases during reactive diffusion is formulated and solved. In this paper, we compare existing models of steady state reaction diffusion and introduce the new one basing on the bi-velocity method. We extend old problem and propose method based on material (lattice) fixed frame of reference. It allows computing the material velocity in the reacting system in which reactions at several moving interfaces occur. All reactions lead to the lattice shift due to the difference of intrinsic diffusivities and different molar volumes. The following peculiarities are taken into account: (1) the deviation from local equilibrium at all interfaces; (2) the mobilities of the components in the bulk and interphase zone; and (3) the molar volumes of the components. We show the kinetic of the reactions, the non parabolic regime, the multiphase scale growth and present the practical application of the method. V

The biodegradable magnesium-based implants have been widely utilized in medical orthopedic applications in recent years. We have recently shown that direct culture on Pure Mg and Mg2Ag alloys lead to a progressive differentiation impairment of MC3T3-E1 pre-osteoblasts. In this study, we aimed to analyze the apoptotic reaction of MC3T3-E1 cells in response to the direct culture on Pure Mg, Mg2Ag and Extreme High Pure Mg (XHP Mg) alloy samples. Our results demonstrated that long-term culturing of MC3T3-E1 cells on Pure Mg and Mg2Ag alloys induce time-dependent expression of active caspase-3 (active casp-3) and cleaved PARP-1 (cl. PARP-1), the hallmark of apoptosis reactions concomitant with a significant increase in the number of dead cells. However, direct culture on XHP Mg material results in a lower number of dead cells in comparison to Pure Mg and Mg2Ag alloys. Furthermore, XHP Mg materials influence expression of apoptotic markers in a process resembles that of observed in osteogenic condition apparently indicative of MC3T3-E1 osteodifferentiation. This study indicates that Mg alloy samples mediated differential apoptotic reactions of MC3T3-E1 cells can be ascribed to factors such as distinct topography and hydrophobicity features of Mg material surfaces, contrasting nature/composition of corrosion products as well as different impurities of these materials. Therefore, initial Mg alloys surface preparation, controlling the growth and composition of corrosion products and Mg alloys purity enhancement are necessary steps towards optimizing the Mg alloys usage in medical orthopedic applications.Graphical Abstract

A diffusion multiple (DM) technique was applied to the Sn-Ag-Cu ternary system with the aim to determine the kinetics of formation of Cu-Sn intermetallic compounds (IMCs) and to predict properties of the interface in the solder joints. The formation and growth of the Cu-Sn intermetallics at the interface between the Cu as a base material and Sn-Ag-(Cu) solder was additionally studied during a standard reflow soldering process. Based on the experimental data, the kinetic rate constants and the respective activation energies of the Cu-Sn IMCs in the temperature range between 150 and 200°C were calculated and compared with experimental data from the literature. In this way, the mechanism of the pure solid-state reaction (DM technique) and liquid phase reaction (reflow soldering) were studied. The limitations of DM techniques for the prediction of the IMCs growth during reflow soldering process are discussed as well.