Diffusion in Solids - Past, Present and Future

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Authors: Jean Philibert
Abstract: After some biographical notes, Fick’s 1855 seminal paper is analysed and the contributions of Stefan and Roberts-Austen are briefly mentioned.
Authors: Lasar S. Shvindlerman
Abstract: The story of the creation of Einstein’s theory of Brownian motion is considered to the background of Einstein private life and understanding of science at the end of the 19th and the very beginning of the 20th century.
Authors: Irina V. Belova, Graeme E. Murch
Abstract: In this overview, we discuss the sum-rule relating phenomenological coefficients in randomly mixed systems and consider several applications to collective diffusion problems. These applications include intrinsic diffusion multicomponent alloys, chemical diffusion in strongly ionic mixed cation crystals and demixing of cations in randomly mixed quaternary transition metal oxides. In each case a substantial simplification is possible as a result of the sum-rule.
Authors: Irina V. Belova, M.J. Brown, Graeme E. Murch
Abstract: In this paper we first review the principal indirect and direct Monte Carlo methods for calculating the Onsager phenomenological transport coefficients in solid state diffusion. We propose a new Monte Carlo method that makes use of a steady state calculation of a flux of atoms that is driven by a difference in chemical potential of the atoms between a source and a sink plane. The method is demonstrated for the simple cubic one component lattice gas with nearest neighbour interactions. The new method gives results in good agreement with a Monte Carlo method based on Einsteinian expressions for the phenomenological coefficients.
Authors: Andreas Öchsner, Michael Stasiek, José Grácio
Abstract: A numerical approach for the segregation of atomic oxygen at Ag/MgO interfaces is presented. A general segregation kinetics is considered and the coupled system of partial differential equations is solved due to a one-dimensional finite difference scheme. Based on a model oxide distribution, the influence of the oxide distribution is numerically investigated and compared with the solution for equidistant arrangements. The numerical approach allows for the consideration of general boundary conditions, specimen sizes and time-dependent material and process parameters. Furthermore, a numerical procedure to convert two-dimensional microstructures into representative one-dimensional distributions is described.
Authors: Andrey S. Chirkov, Andrei V. Nazarov
Abstract: This work is devoted to simulation of the diffusion features of point defects in bcc metals. The properties of point defects have been investigated with the usage of many-body interatomic potentials. This approach, based on the density-functional theory, permitted us to derive more adequate diffusion features of solids. This investigation is carried out within the framework of the Finnis-Sinclair formalism, developed for an assembly of N atoms and represents the secondmoment approximation of the tight-binding theory. We used a new model, based on the molecular static method for simulating the atomic structure near the defect and vacancy migration in pure metals. This approach gives the opportunity to simulate the formation and the migration volumes of the point defects, taking into consideration the influence of pressure on structure and consequently on energy. The diffusion characteristics of bcc α-Fe and anomalous β-Zr have been investigated.
Authors: E. Jannot, Volker Mohles, Günter Gottstein, B. Thijsse
Abstract: Activation energies for solute diffusion along dislocations are difficult to measure experimentally. The aim of this work is to provide insight into pipe diffusion with the help of atomistic simulations. The distribution of vacancy formation energy and the activation energy for copper migration are determined in the core of an edge dislocation in aluminum. The Dimer method is used to find activation energies for vacancy migration. The activated region around the dislocation where a very high diffusivity is observed and the activation energy for copper diffusion associated with this region are interpreted with regard to the contribution of the dislocation and the contribution of the alloying.
Authors: Irina Valikova, Andrei V. Nazarov, Alexandr A. Mikheev
Abstract: This work is devoted to the simulation of atom configurations in bcc metals near the point defect using the molecular static method. The values of migration and formation volumes are very sensitive to the atomic structure in the vicinity of a defect, which makes it necessary to consider a large number of atoms in the computation cell and to take into account an elastic matrix around the cell. We have developed the new model taking into consideration these factors. It allows defining the “fine structure” of displacement atoms near the point defect. The atoms of third zone were embedded in an elastic continuum. The displacement of each atom embedded in an elastic continuum was defined as the first and the second terms in solution of elastic equation. In the framework of this model we calculated the formation and migration energies and volumes of defect. Also we take into consideration that the energy of system (in particular the system with defect) depends on the external pressure. This dependence gives an addition to the values of migration and formation volumes.
Authors: Jean Philibert
Abstract: The first part of this paper presents a brief historical account of the Arrhenius law, starting from the seminal paper by Arrhenius (1889) up to theoretical developments mainly based on the rate theory. The second part describes the so called compensation rule (Meyer-Neldel rule), a correlation between activation enthalpy and entropy (or between pre-exponential factor and activation energy) , and discusses whether this correlation is trivial or bears some physical meaning.
Authors: Lyudmila N. Paritskaya
Abstract: The importance and generality of Kirkendall discovery, which opened new area in diffusion science, have been discussed. The developments of Kirkendall’s idea for sub-surface (SS) and grain boundary (GB) interdiffusion have been considered and applied for the advanced structural materials, such as thin films and nano-composites. The kinetics and mechanisms of SS and GB Kirkendall effects have been analyzed theoretically and studied experimentally.

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