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Authors: Irina V. Belova, Graeme E. Murch
Abstract: In this paper, we show how lattice–based random walks of virtual particles directed by Monte Carlo methods (Lattice Monte Carlo) can be used to address a variety of complex phenomenologically mass diffusion problems. Emphasis is put on the practical details of doing the calculations. It is shown how concentration depth profiles can be determined: this is exemplified with diffusion in the presence of isolated dislocation pipes, grain boundary slabs, and oxygen segregation at interfaces in metal-ceramic oxide composites. It is also shown how effective diffusivities can be determined in materials. We also show how temperature profiles and the effective thermal conductivity can be determined for the thermal diffusion analogue of mass diffusion. A detailed comparison is made in one case with the results of the Finite Element method.
Authors: Marek Danielewski, Maciej Pietrzyk, Bartłomiej Wierzba
Abstract: The mass transport in the presence of stress, electrical, mechanical and chemical potential gradients in multicomponent solid solution is analyzed. The method bases on the Darken concept and the calorimetric equation of state. We effectively coupled the conservation of the mass (continuity equations), energy, momentum and Gauss equations. The diffusion fluxes of the components are given by the Nernst-Planck formulae and take into account the electro-chemical and mechanical potentials. We simulate the deformation field during the diffusion caused by the gradients of the chemical potential of all elements in non-ideal Fe-Cu-Ni alloy. The simulations show that the model is compatible with experimental results, and can be effectively used for modelling the energy, momentum and mass transport problems in compressible multicomponent solid solutions. The numerical problems and methods of solution are presented.
Authors: Simon P.A. Gill, Paul E. Spencer
Abstract: A kinetic Monte Carlo (KMC) model for surface diffusion on a 2D lattice is proposed. An equivalent continuum cellular automaton (CA) model is derived from this. These models are shown to produce similar results at high temperatures. A hybrid KMC-CA model is derived which consistently allows material to transfer between a deterministic CA model and a stochastic KMC model concurrently embedded within it. The quality of the model is demonstrated by simulating the flattening of a sinusoidal surface profile and the evolution of an elliptical body into a circular one.
Authors: Łukasz Madej, Peter D. Hodgson, Maciej Pietrzyk
Abstract: An investigation of the application of a multi scale CAFE model to prediction of the strain localization phenomena in industrial processes, such as extrusion, is presented in this work. Extrusion involves the formation of a strong strain localization zone, which influences the final product microstructure and may lead to a coarse grain layer close to the surface. Modelling of the shape of this zone and prediction of the strain magnitude will allow computer aided design of the extrusion process and optimisation of the technological parameters with respect to the microstructure and properties of the products. Thus, the particular objective of this work is comparison of the FE and CAFE predictions of strain localization in the shear zone area in extrusion. Advantages and disadvantages of the developed CAFE model are also discussed on the basis of the simulation results.
Authors: Frédéric Soisson, Chu Chun Fu
Abstract: The thermodynamic and kinetic properties of Fe-Cu alloys are studied by ab initio calculations, in the framework of a multiscale modeling of precipitation kinetics. The configuration energies at various compositions, the solute migration and binding energies, as well as the vacancy formation and binding energies are computed. The effects of the local copper distribution on the migration barriers are considered. We show that a simple diffusion model with effective interactions on a rigid lattice, which includes a description of the saddle-point configurations, captures the main features of the energetic landscapes explored by the vacancy during its diffusion in dilute and concentrated configurations.
Authors: C. Bos, F. Sommer, Eric J. Mittemeijer
Abstract: A kinetic Monte Carlo method has been developed for the simulation of interface controlled solid-state transformations to overcome timescale limitations associated with other atomistic simulation methods. In the simulation method the atoms can take place on sites from (at least) two intertwining crystal lattices. To enable the atoms to also take positions between the ideal lattice sites, a collection of randomly placed sites can be included. These ‘random sites’ have a realistic chance to be occupied at the location of the transformation interface and thus allow for irregularities in the atomic structure of the transformation interface. The atoms move by independent, thermally activated jumps. The activation energy for the atomic jumps can be determined for every jump separately based on the arrangement of the neighbouring atoms. The simulation method has been used to study the interface mobility in the austenite to ferrite transformation in iron for different interface orientations. The results obtained indicate that the excess volume associated with the interface plays a key role for the activation enthalpy for the interface mobility. The rate controlling process is the rearrangement of free space at the interface by series of (unfavourable) jumps by different atoms to create a path from the parent to the product phase.
Authors: Alain Barbu, Emmanuel Clouet
Abstract: The aim of this paper is to give a short review on cluster dynamics modeling in the field of atoms and point defects clustering in materials. It is shown that this method, due to its low computer cost, can handle long term evolution that cannot, in many cases, be obtained by Lattice Kinetic Monte Carlo methods. Indeed, such a possibility is achieved thanks to an important drawback that is the loss of space correlations of the elements of the microstructures. Some examples, in the field of precipitation and irradiation of metallic materials are given. The limitations and difficulties of this method are also discussed. Unsurprisingly, it is shown that it goes in a very satisfactory way when the objects are distributed homogeneously. Conversely, the source term describing the primary damage under irradiation, by nature heterogeneous in space and time, is tricky to introduce especially when displacement cascades are produced.

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