Multiscale Modelling of Diffusion-Controlled Phenomena in Condensed Matter

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Authors: Jan S. Wróbel, Duc Nguyen-Manh, Krzysztof Jan Kurzydlowski
Abstract: In this chapter, we present the basic principles and methods for modelling of diffusion and phase stability of alloys using ab-initio methods. We review briefly first-principles methods and their most important approximations. The direct and approximated methods of prediction of migration energies are shown both for pure metals and for alloys. The cluster expansion method is described in more detail. We show that it can be applied to understand interactions in the alloys, to generate the representative structures of alloys and to predict migration barriers in alloys. We describe the methods to compute the effective cluster interactions and to assess the accuracy of the model. Finally, we present the examples of Monte Carlo simulations with parameters obtained from cluster expansion method. We show that the ordering in alloys can be predicted by the calculations of Warren-Cowley parameters. We investigate also the role of entropy in the stability of alloys at elevated temperatures.
Authors: Riccardo Ferrando
Abstract: The diffusion of atoms in nanoparticles can be studied computationally by Molecular Dynamics simulations, a simulation method which allow to follow the actual trajectories of the diffusing atoms. Here we focus on the simulation of diffusion in metallic nanoparticles, first considering the case of single impurity atoms in matrix clusters, and then on the simulation of the growth in gas phase. We show that diffusion of atoms in nanoparticles can take place by a variety of different mechanisms, which very often involve collective displacements. These collective displacements are facilitated in the vicinity of the cluster surface, which, in small nanoparticles, includes a large portion of the nanoparticle itself.
Authors: Tomasz Wejrzanowski, Krzysztof Jan Kurzydlowski
Abstract: The results of the studies presented here are devoted to understanding of microstructure effect on the processes and properties driven by diffusion. The role of various interfaces (intergranular, phase, free surface), as the high-energy defects, is underlined and investigated with special attention. The methodology relevant to analyses of the microstructural processes is first briefly presented. The capability and limitations of classical molecular dynamics, mesoscale Monte Carlo and cellular automaton techniques are described. Two examples of the diffusion driven processes analyzed at various length and time scale are shown: namely, grain growth in nanometallic materials and melting of thin embedded films. The modeling results are also accompanied with experimental studies. Thanks to application of numerical methods, models of relevant processes were proposed, which enabled to provide quantitative relationships between microstructure and the process kinetics. Such relationships can be later used for design of optimized materials for wide range of applications.
Authors: Miroslaw Kozlowski, Daniele Scopece, Jolanta Janczak-Rusch, Lars P.H. Jeurgens, Rafal Abdank-Kozubski, Daniele Passerone
Abstract: The validation of classical potentials for describing multicomponent materials in complex geometries and their high temperature structural modifications (disordering and melting) requires to verify both a faithful description of the individual phases and a convincing scheme for the mixed interactions, like it is the case of the embedded atom scheme. The present paper addresses the former task for an embedded atom potential for copper, namely the widely adopted parametrization by Zhou, through application to bulk, surface and nanocluster systems. It is found that the melting point is underestimated by 200 degrees with respect to experiment, but structural and temperature-dependent properties are otherwise faithfully reproduced.
Authors: Tanvir Ahmed, Elena V. Levchenko, Alexander V. Evteev, Zi Kui Liu, William Yi Wang, Rafal Abdank-Kozubski, Irina V. Belova, Graeme E. Murch
Abstract: The influence of composition on thermotransport (coupling between mass and heat transport) in Ni-Al melts is investigated by making use of equilibrium molecular dynamics simulations in conjunction with the Green-Kubo formalism. To describe interatomic interactions in Ni-Al melt models, we employ the embedded-atom method potential developed in [G.P. Purja Pun, Y. Mishin, Phil. Mag., 2009, 89, 3245]. It is demonstrated that the employed interatomic potential gives good agreement with the recent experimental study [E. Sondermann, F. Kargl, A. Meyer, Presented at the 12th International Conference on Diffusion in Solids and Liquids (DSL-2016), 26-30 June 2016, Split, Croatia] regarding the direction of thermotransport in Al-rich liquid Ni-Al alloys. Moreover, the predicted values of the reduced heat of transport (the quantity which explicitly characterizes both the magnitude and direction of thermotransport) in Ni-Al melts, reveal fairly weak composition dependence while being practically independent of temperature at all. Accordingly, in the presence of a temperature gradient, our simulation results for the models of liquid Ni25Al75, Ni50Al50 and Ni75Al25 alloys predict consistently Ni and Al to migrate to the cold and hot ends, respectively. Meanwhile, the highest value, about eV, of the reduced heat of transport is observed for Ni50Al50 alloy model and it slightly decreases towards Al-rich and Ni-rich compositions.
Authors: H. Zapolsky, G. Demange, Rafal Abdank-Kozubski
Abstract: The phase-field method is a very powerful tool to model the phase transformation and microstructural evolution of solids at mesoscopic scale. However, several important phenomena, like defect formation, grain boundary motion, or reconstructive phase transitions require an atomic scale study. Recently an approach called the quasi-particle approach, based on the Atomic Density Function theory was developed to incorporate the atomic-level crystalline structures into standard continuum theory for pure and multicomponent systems. This review focuses on the description of different computational methods used to model microstructural evolution and self-assembly phenomena at mesoscopic and atomistic scales. Various application examples of these methods are also presented.
Authors: Romuald Dobosz, Krzysztof Jan Kurzydlowski
Abstract: In this Chapter, the finite element simulations of diffusion processes in homogeneous and polycrystalline materials are presented as well as some analytical solutions and implementations of basic diffusion relations. For the homogeneous materials the presented examples show the changes in time of the concentration of diffusing matter within the semi-infinite system and simulation of anisotropic nature of diffusion processes.The polycrystalline materials have been analysed for three cases, namely influence of average grain size and the homogeneity of grain size on the macroscopic diffusivity as well as simulation of the diffusion strains. The homogenisation technique has been used to estimate the diffusion property of grains aggregates.

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