Diffusion in Materials

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Authors: Yuri Mishin
Abstract: This paper presents an overview of recent computer simulations of grain boundary (GB)diffusion focusing on atomistic understanding of diffusion mechanisms. At low temperatures when GBstructure is ordered, diffusion is mediated by point defects inducing collective jumps of several atomsforming a chain. At high temperatures when GB structure becomes highly disordered, the diffusionprocess can be analyzed by statistical methods developed earlier for supercooled liquids and glasses.Previous atomistic simulations reported in the literature as well as the new simulations presented in thispaper reveal a close similarity between diffusion mechanisms in GBs and in supercooled liquids. GBdiffusion at high temperatures is dominated by collective displacements of atomic groups (clusters),many of which have one-dimensional geometries similar to strings. The recent progress in this fieldmotivates future extensions of atomistic simulations to diffusion in alloy GBs, particularly in glassformingsystems.
Authors: Alain Portavoce, Khalid Hoummada, Franck Dahlem, Christophe Girardeaux, Boubekeur Lalmi
Abstract: Silicide growth via reaction between a metallic film and a Si substrate has been well documented. In general, atomic transport kinetic during the growth of silicides is considered to be the same as during equilibrium diffusion, despite the reaction and its possible injection of point-defects in the two phases on each side of the interface. To date, the main studies aiming to investigate atomic transport during silicide growth used immobile markers in order to determine which element diffuses the fastest during growth and in which proportion. The quantitative measurements of effective diffusion coefficients during growth was also performed using Deal-and-Groove-type of models, however, these effective coefficients are in general not in agreement with the interdiffusion coefficients calculated using the equilibrium diffusion coefficients measured during diffusion experiments. In general, atomic transport kinetic measurements during growth and without growth are performed using different types of samples for experimental reasons. In this paper, we discuss the possible use of ultrahigh vacuum in situ Auger electron spectroscopy in order to measure the effective diffusion coefficient during growth, as well as the equilibrium self-diffusion coefficients, in the same samples, in the same experimental conditions. The first results on the Pd-Si system show that atomic transport during Pd2Si growth is several orders of magnitude faster than at equilibrium without interfacial reaction.
Authors: Vladimir V. Popov, A.V. Sergeev, A.Yu. Istomina
Abstract: Grain boundary diffusion of Co in Mo has been studied by radiotracer analysis and emission Mössbauer spectroscopy. The experimental results are treated based on the specified Fisher model. The mechanism of grain boundary diffusion of Co in Mo and temperature dependences of segregation factor and grain boundary diffusivity have been determined.
Authors: J. Dąbrowa, Witold Kucza, Katarzyna Tkacz-Śmiech, Bogusław Bożek, Marek Danielewski
Abstract: The Nernst-Planck flux formula is used in Darken's method to obtain the interdiffusion fluxes. The effective interdiffusion potentials, derived for the independent components in the system, allow obtaining the symmetrical matrix of the interdiffusion coefficients. The transport coefficients for 2, 3 and r-component system are presented. Interpretation of obtained matrixes in the light of Onsager's theory of irreversible thermodynamics is shown. Equation for the entropy production in the interdiffusion process is displayed. The presented approach allows calculation of entropy production during interdiffusion, as well as formulating Onsager's phenomenological coefficients for the interdiffusion in an explicit form, a form which is directly correlated with the mobilities of the atoms present in the system.
Authors: Alexey O. Rodin, D. Prokoshkina, A. Itckovitch, N. Dolgopolov
Abstract: It is generally agreed that during diffusion process between two phases e.g. matrix/diffusant layer the thermodynamic equilibrium state is fulfilled and the supersaturated solid solutions can not formed by diffusion. Nevertheless, in many cases the formation of equilibrium phases does not occur due to kinetic and other reasons, and metastable phases can be formed. The analysis of the concentration profiles for bulk diffusion obtained at low temperatures consistent with B-regime for grain boundary diffusion in systems Cu/Al, Fe and Co/Cu is performed. It is shown that in these systems the supersaturated solutions are formed and the extent of supersaturation is the more as the diffusion temperature is lower. The concentration of diffusant may be 5-10-times greater than solubility according to phase diagram.
Authors: Bartek Wierzba, Wojciech Skibiński
Abstract: In this paper three methods for calculating Kirkendall plane position after diffusion process are described. Bifurcation of K-plane is discussed. Kirkendall planes shift is simulated in hypothetical binary system where solid solution occur and binary system, where two interphases occur. Kirkendall plane shift was estimated by marker conservation method, which is described. It was shown that bifurcation of Kirkendall plane can occur in multiphase systems.
Authors: Erwin Hüger, Lars Dörrer, Jochen Stahn, Thomas Geue, Harald Schmidt
Abstract: Lithium transport through ultrathin silicon layers can be measured non-destructively by neutron reflectometry (NR) using a multilayer composed of silicon layers embedded between solid state Li reservoirs. An established model system is a multilayer with a repetition of five [Si / natLiNbO3 / Si / 6LiNbO3] units. Two types of Bragg peaks are detectable in reflectivity patterns. These Bragg peaks result from the interference of neutrons reflected at periodic interfaces. One type of Bragg peak originates from the periodicity of the LiNbO3/Si chemical contrast (first order peak), while the other Bragg peak results from a superstructure with double periodicity. This superstructure may arise from 6Li/7Li isotope contrast or alternatively from periodic thickness variations, as shown by simulations based on the Parratt algorithm. The intention of the present paper was to elucidate the origin of the second Bragg peak. Experiments done by Secondary Ion Mass Spectrometry (SIMS) isotope sensitive depth profiling showed in a direct way that annealing at 360 °C destroys indeed the 6Li/7Li contrast, whereas the LiNbO3/Si chemical contrast remains unchanged. This evidences that the experimentally observed decrease of the second Bragg peak in the reflectivity pattern during annealing is a measure for Li transport through the Si layer.
Authors: Alain Portavoce, Omar Abbes, Sylvain Bertaina, Yauheni Rudzevich, Lee Chow, Vinh Le Thanh, Christophe Girardeaux, Lisa Michez
Abstract: In this paper, we report investigations concerning the fabrication of a diluted Ge (Mn) solution using solid state Mn diffusion, and Mn/Ge reactive diffusion for spintronic applications. The study of Mn diffusion shows that the quasi-totality of the incorporated Mn atoms occupies Ge substitutional sites and probably exhibits two negative elementary charges. The solubility limit of Mn in Ge is comprised between 0.7 and 0.9 % (T  600 °C). We show that substitutional Mn atoms are not ferromagnetic in Ge and consequently that Ge (Mn) diluted magnetic semiconductor can not be produced. Beside the ferromagnetic signal from Mn5Ge3, ferromagnetic signals detected in the samples could be always attributed to surface or bulk Mn-Ge clusters. Furthermore, we show that the CMOS Salicide process is potentially applicable to Mn5Ge3 nanolayer fabrication on Ge for spintronic applications. During Mn (thin-film)/Ge reaction, Mn5Ge3 is the first phase to form, being thermally stable up to 310 °C and exhibiting ferromagnetic properties up to TC ~ 300 K.
Authors: Johanna Rahn, Benjamin Ruprecht, Paul Heitjans, Harald Schmidt
Abstract: The diffusion of lithium in amorphous lithium niobate layers is studied as a function of temperature between 293 and 423 K. About 800 nm thick amorphous 7LiNbO3 layers were deposited on sapphire substrates by ion-beam sputtering. As a tracer source about 20 nm thin 6LiNbO3 layers were sputtered on top. Isotope depth profile analysis is done by secondary ion mass spectrometry. Compared are amorphous samples which show a ratio of Li : Nb < 1 (Li-poor) and of Li : Nb > 1 (Li-rich) close to the stoichiometric composition of Li : Nb = 1 for crystalline LiNbO3. The results reveal that the diffusivities of both types of samples obey the Arrhenius law with an activation enthalpy of 0.70 eV and 0.83 eV, respectively. The diffusivities of the sample containing a higher amount of Li are lower by a factor of about two to ten. This demonstrates that variation of the Li content in amorphous samples over the stability range of the crystalline LiNbO3 phase has only a modest influence on diffusivities and activation enthalpies.

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