Defect and Diffusion Forum Vols. 323-325

Abstract: Simultaneous ¹⁸O and ²⁶Al tracer diffusion experiments were performed in nominally undoped single crystalline α-Al₂O₃. The results clearly show that the bulk diffusivity of aluminium is much higher than the bulk diffusivity of oxygen in nominally undoped alumina. Comparing the ²⁶Al tracer diffusivities of Ti doped (300-400 wt. ppm Ti) and nominally undoped single crystalline α-Al₂O₃ one finds that the aluminium bulk diffusivity is insensitive to the Ti doping.

Abstract: Motivation for this work comes from the application of the inverse method to electrochemical systems. The basic process operating in these systems is electrodiffusion, which can be described by the full form of the Nernst-Planck and Poisson equations. No simplification like electroneutrality assumption is used. Numerical procedure based on the method of lines (MLs) for time dependent electrodiffusion transport is presented with any number of ionic species. The resulting system of ODEs is effectively solved by employing different integrators (Radau IIA, Rosenbrock, SEULEX). Selected electrochemical systems (liquid junction, bi-ionic case, ion selective electrodes (ISE)) are treated. Performance of the integrators is compared.

Abstract: A molecular dynamics study of a layered Ni-Al-Ni system is developed using an embedded atom method potential. The specific geometry is designed to model a Ni-Al nanometric metallic multilayer. The system is initially thermalized at the fixed temperature of 600 K. We first observe the interdiffusion of Ni and Al at the interfaces, which is followed by the spontaneous phase formation of B2-NiAl in the Al layer. The solid-state reaction is associated with a rapid system's heating which further enhances the diffusion processes. NiAl phase is organized in small regions separated by grain boundaries. This study confirms the hypothesis of a layer-by-layer development of the new phase. For longer times, the temperature is notably higher (> 1000 K) and the system may partly lose some its B2-NiAl microstructure in favor of the formation of Ni₃Al in L12 configuration. This work shows the spontaneous development of a real exothermic solid-state reaction in metallic nanosystems mostly constituted by interfaces.

Abstract: Evolution of a molybdenum system containing self-interstitials and vacancies was studied by molecular dynamics simulation using a new molybdenum interatomic potential. The potential was parameterized by using formation and migration energies of the defects. Clustering and annihilation of the defects were investigated in terms of the defect concentration changes during the calculation. The rate constants were evaluated and compared with the diffusion coefficients. Also investigated was the influence of one-dimensional diffusion on kinetics, as well as the effects of temperature and defect concentrations on the reaction rates.

Abstract: Fractal functions are used to model a metallic interface. An analytical model described by three partial differential equations is built to model time evolution of the surface during heating including three different mechanisms of diffusion: superficial diffusion (SD), volume diffusion (VD) and diffusion by evaporation-condensation (DEC). Initial topographies are modeled by Stochastic Weierstraβ functions because of their ability to reproduce experimental roughness profiles. Applied to an aluminum alloy at 550°C, a high number of roughness parameters and their variance are calculated. A classification method shows that the best geometrical approach that discriminates heat effect is the fractal dimension. The most popular parameter, R_a, badly discriminates processes (classification number = 58). The four order spectral moments of the roughness profile are correlated with the evolution of profile. It is shown theoretically that the superficial diffusion depends directly to the fourth spectral moment of the roughness profile.

Abstract: During the last decade, an increasing importance has been given to the feedback of mechanical stresses on the chemical diffusion and, further, on corrosion. Many works point the active role of stresses on the material ageing especially on their negative consequences leading to the damaging of structures. Based on a theoretical study and using numerical tools and experimental results our previous works [1, on stress/diffusion coupling, highlight the strong influence of stress field on the diffusion process. The aim of the present paper is to describe the influence of some particular morphologies of the metal/oxide interface on both diffusion and oxidation process. The oxidation is assumed to be driven by a mass conservation law (Stefan's law) while the diffusion coefficient of oxygen in metal is locally influenced by the stress field. The stability of a waved-shape interface is studied in both cases: simple diffusion and coupled stress/diffusion process. In this purpose we have developed an original numerical model using a virtual metal/oxide interface of a mono-material with oxygen concentration-dependent parameters, which allows to operate easily with any shape of interface and to use simple finite element meshes. Furthermore, in order to underline in a more obvious way the consequences of mechanical stress on the diffusion process, a particular geometry is studied.

Abstract: The interface metal/molten oxide is of interest for several high temperature processes (metallurgy, gasification). The exchange reactions occurring at the interface between the metal and the molten slag are complex and up to date not well understood. More generally, this is of importance for the understanding of the exchange reaction kinetics between one metallic compound (solid or liquid) and an ionic one (slag). This work proposes a theoretical approach which takes into account the effect of speciation in the slag on the diffusion process of the species in the two phases and the redox reaction occurring within the vicinity of the interface. The systems investigated consist of Fe and CaO-SiO₂ without convection. The concentration profiles of silicon and iron oxide in both parts were calculated. The effect of impurities present in metal phase such as sulphur in the molten slag was investigated. This provides a basis of comprehensive approach for the purification of metal and a better understanding of processes at metal/oxide interface.

Abstract: Coupling diffusion and convection of species is relevant for optimization of diverse engineering processes, especially when chemical reactions are involved. In particular, the problem of predicting the flow of species into a particle is of large importance in the design of catalytic particles. A numerical framework using the Least Squares Spectral Element Method is implemented in order to analyze the species transport from a flow into a particle by a fractional constitutive law. The aim of this work is to investigate the qualitative change in the concentration profiles in the transition from Fickian to fractional anomalous transport inside the particle. A sample case is provided corresponding to a flow between two parallel plates and around a cylinder, coupled with species transport into the cylinder.

Abstract: The formation of intermetallic compounds (IMC) at the solder-substrate interface is required to initiate the metallurgical bond. However, rapid growth of IMCs may degrade joint strength through i) the increased presence of a low toughness phase, ii) the consumption of the solderable surface (void formation) and iii) generation of primary and secondary stresses. Knowledge of mass transport and reaction processes during joint formation and service life are essential for solder system design. The mathematical description of inter-and reactive diffusion in open system presented here is based on Darken method (bi-velocity), involving the different molar volumes in the system and Wagner boundary conditions. It combines the interdiffusion, reactive diffusion and the effective flux constraints to couple processes occurring at different time scales. The rCADiff software serves as a tool to simulate simultaneous growth of the two Cu-Sn IMCs.

Abstract: There are few articles that mention fractal dimension in grain growth mechanism. Some authors build a simplified analytic model showing that initial fractal dimension of grain boundary has an influence on interface modification velocity. Nevertheless they postulate the relation where L is the grain length, c is a constant, s is grain size and the fractal dimension. The aims of this paper is to experimentally analyze by image analysis the fractal dimension of A5 aluminum sheet grain boundaries during heating and to simulate their evolution by a Monte Carlo method to validate experimental data.. It is shown by Monte-Carlo simulation and confirmed experimentally that the grain growth process decreases the fractal dimension of grain border. It can be concluded that it is very hazardous to build a model of grain growth without including the effect of grains morphology. The macroscopic fractal morphology of the grain structure could then be used to validate microscopic relation between Monte Carlo Steps time and real time.