Grain Boundary Diffusion, Stresses and Segregation

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Authors: Sergiy V. Divinski, Boris S. Bokstein
Abstract: Some unresolved problems of grain boundary diffusion – restrictions of Fisher-Gibbs model, refinement of the conditions for B- and C-regimes, relation between segregation (s) and enrichment (b) coefficients, grain boundary width, non-linear segregation effects on grain boundary diffusion – are discussed.
Authors: Irina V. Belova, Graeme E. Murch, Thomas Fiedler
Abstract: The location of the transition points for the three main Harrison’s kinetics regimes (Type-A, B and C) for the measurement of grain boundary diffusivities from tracer concentration depth profiles (self-diffusion) has been extensively studied in (Divinski et al. Zeit. Metallk, 2002, Belova and Murch, Phil. Mag, 2001, 2009; Defect and Diffusion Forum, 2006, 2008, 2009) by making use of the phenomenological Lattice Monte Carlo numerical method. Those locations are mainly dependent on the dimensionality of the problem. For the case of impurity grain boundary diffusion, the segregation effect is very important. In the present study, the influence of segregation on the transition points is investigated for the parallel slab model (2-dimensional) of the grain boundary diffusion problem by making use of the tracer-type solution to the equivalent diffusion problem. It is shown that the Type-B regime is most likely not realized for the cases of fine-grain material with a strong segregation effect present.
Authors: Leonid Klinger, Eugen Rabkin
Abstract: A grain boundary interdiffusion in a semi-infinite bicrystal under the conditions of negligible bulk diffusion is considered. We show that the inequality of intrinsic grain boundary diffusion coefficients of the two components leads to plating out of additional material at the grain boundary in the form of extra material wedge, which generates an elastic stress field in the vicinity of the grain boundary. We solved a coupled diffusion/elasticity problem and determined the time-dependent stress field and concentration distribution in the vicinity of the grain boundary.
Authors: Vladimir Esin, Boris S. Bokstein, Alexey Rodin
Abstract: Thermodynamics of the atomic complexes formation in a grain boundary (GB) is discussed applying to AB complex. It is shown that the AB complex formation leads to the nonlinearity of segregation isothermes. Consequently, the concentration profiles for GB diffusion are nonlinear. The total (free and bound into complexes) concentration of diffusant B decreases at the given depth as the molar fraction of the complexes increases.
Authors: Pawel Nowakowski, Frédéric Christien, Marion Allart, René Le Gall
Abstract: It was recently shown [1] that EMPA-WDS (Electron Probe MicroAnalysis by Wavelength Dispersive X-ray Spectroscopy) can be used to detect and to accurately quantify monolayer surface and grain boundary segregation. This paper presents the last developments of this application. It focuses on the measurement of sulphur grain boundary segregation in nickel on fractured surfaces. A special attention was paid to the quantification of the sulphur coverage, taking into account the non-normal incidence of the electron beam on a fracture surface. Sulphur grain boundary segregation kinetics was measured at 750°C in nickel to document the quantitative possibilities of the technique.
Authors: Aleksey Lipnitskii, I.V. Nelasov, Yurii Kolobov
Abstract: Suggested methods describe the process of self-diffusion along grain boundaries and triple junctions in polycrystals without using geometric models of the grain boundaries structure. The calculation method introduced diffusion characteristics along grain boundaries derived from the results of molecular dynamic simulations of nanocrystalline materials. The diffusion experiments were imposed to establish relationship between introduced diffusion characteristics and the diffusion parameters along grain boundaries and triple junctions of the Fisher’s grain boundary diffusion model. By the example of copper for the first time the characteristics of self-diffusion along grain boundaries of nanocrystalline materials and coarse grained analog defined in the same temperature range was compared for the first time. It was found that values of the self-diffusion characteristics along grain boundaries in high purity nanocrystalline and polycrystalline copper are equal at the same temperatures.
Authors: Boris Straumal, A.O. Rodin, A.L. Petelin, Brigitte Baretzky, Svetlana Protasova, S.V. Dobatkin, J. Dutta Majumdar, I. Manna
Abstract: The microstructure, phase composition, Mössbauer spectra, grain boundary segregation and magnetic properties of binary Fe–C alloys with carbon concentration of 0.05, 0.10, 0.20, 0.25, 0.45, 0.60, 1.3, 1.5 and 1.7 wt. % were studied in the as-cast state, after a long annealing at 725°C and after high-pressure torsion (HPT) at the ambient temperature and 5 GPa with 5 anvil rotations (shear strain about 6). The grain size after HPT was in the nanometer range. Only Fe3C (cementite) and -Fe remain in the alloys after HPT. It was also shown that the less stable Hägg carbide (Fe5C2) and retained austenite disappear, and phase composition closely approaches the equilibrium corresponding to the HPT temperature and pressure. Measurements of saturation magnetization and Mössbauer effect reveal that the amount of cementite decreases after HPT. The reason for partial cementite dissolution is the formation of the carbon-rich segregation layers in the ferrite grain boundaries.
Authors: Alain Portavoce, Ivan Blum, Lee Chow, Jean Bernardini, Dominique Mangelinck
Abstract: The measurement of diffusion coefficients in today’s materials is complicated by the down scaling of the studied structures (nanometric effects in thin films, nano-crystalline layers, etc.) and by the complex production process conditions of industrial samples or structures (temperature variations, complex solute and point defect distributions, stress gradients, etc.). Often diffusion measurements have to be performed in samples for which initial experimental conditions do not offer the possibility of using conventional diffusion analytical solutions. Furthermore, phenomena involved with diffusion are sometimes so numerous and complex (stress, matrix composition inhomogeneities, time dependence of point defect generation sources, electrical effects, clustering effects, etc…) that the use of analytical solutions to solve the observed diffusion behavior is difficult. However, simulations can be of use in these cases. They are time consuming compared to the use of analytical solutions, but are more flexible regarding initial conditions and problem complexity. The use of simulations in order to model physical phenomena is quite common nowadays, and highly complex models have been developed. However, two types of simulations have to be considered: i) simulations aiming to understand and predict phenomena, and ii) simulations for measurement purposes, aiming to extract the (average) value of a physical parameter from experimental data. These two cases have different constrains. In the second case, that is the subject of this article, one of the most important stress is that the simulation has to precisely scale the experiment (sample size, experiment duration, etc.), sometimes preventing the measurement due to computational time consumption. Furthermore, the simpler the model (small number of parameters) used in the simulation, the more relevant the measurement (minimum error). In this paper, examples of recent works using two- and three-dimensional finite element simulations for diffusion coefficient measurements in thin polycrystalline films and nano-crystalline layers are presented. The possible use of simulations for diffusion coefficient measurements considering GB migration, GB segregation, or triple junctions is also discussed.
Authors: Alexey Rodin, Nikolai Dolgopolov, Andrei Simanov, Alla Zaytseva
Abstract: The diffusion of Cu in Al and Al based alloys was studied. It was shown the great scattering of triple product values, measured for different grain boundaries (GB) at the same samples. It was discussed in the terms of GB energy difference. It was also shown that GB triple product can be varied significantly by preliminary alloying of Al by 0.1% Cu. However, the alloying of Al by 0.5% Cu leads to disappearing of the effect of accelerated diffusion in GB in comparison with the bulk.

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