The lattice shift generated by two dimensional diffusion process

Wierzba, Bartek�; Danielewski, Marek

doi:10.1016/j.commatsci.2014.07.015

Cited by 6 publications

(3 citation statements)

References 21 publications

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“… v d = − ∇ F . An attempt to construct a model with the potential drift field has been made in [18]. Unfortunately, in that study, the idea of deriving formulae is not correct because the rotation of a scalar potential is considered.…”

Section: Introductionmentioning

confidence: 99%

Interdiffusion in many dimensions: mathematical models, numerical simulations and experiment

Sapa

Bożek

Tkacz–Śmiech

et al. 2020

Mathematics and Mechanics of Solids

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Over the last two decades, there have been tremendous advances in the computation of diffusion and today many key properties of materials can be accurately predicted by modelling and simulations. In this paper, we present, for the first time, comprehensive studies of interdiffusion in three dimensions, a model, simulations and experiment. The model follows from the local mass conservation with Vegard’s rule and is combined with Darken’s bi-velocity method. The approach is expressed using the nonlinear parabolic–elliptic system of strongly coupled differential equations with initial and nonlinear coupled boundary conditions. Implicit finite difference methods, preserving Vegard’s rule, are generated by some linearization and splitting ideas, in one- and two-dimensional cases. The theorems on the existence and uniqueness of solutions of the implicit difference schemes and the consistency of the difference methods are studied. The numerical results are compared with experimental data for a ternary Fe-Co-Ni system. A good agreement of both sets is revealed, which confirms the strength of the method.

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Section: Introductionmentioning

confidence: 99%

Interdiffusion in many dimensions: mathematical models, numerical simulations and experiment

Sapa

Bożek

Tkacz–Śmiech

et al. 2020

Mathematics and Mechanics of Solids

Self Cite

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“…In the paper we study the model of interdiffusion introduced in [22] and in some special case in [24], in the one-dimensional and the multidimensional cases. The model is expressed by the strongly coupled nonlinear parabolic-…”

Section: Introductionmentioning

confidence: 99%

Difference Methods to One and Multidimensional Interdiffusion Models With Vegard Rule

Bożek

Sapa

Danielewski

2019

Mathematical Modelling and Analysis

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In this work we consider the one and multidimensional diffusional transport in an s-component solid solution. The new model is expressed by the nonlinear parabolic-elliptic system of strongly coupled differential equations with the initial and the nonlinear coupled boundary conditions. It is obtained from the local mass conservation law for fluxes which are a sum of the diffusional and Darken drift terms, together with the Vegard rule. The considered boundary conditions allow the physical system to be not only closed but also open. We construct the implicit finite difference methods (FDM) generated by some linearization idea, in the one and two-dimensional cases. The theorems on existence and uniqueness of solutions of the implicit difference schemes, and the theorems concerned convergence and stability are proved. We present the approximate concentrations, drift and its potential for a ternary mixture of nickel, copper and iron. Such difference methods can be also generalized on the three-dimensional case. The agreement between the theoretical results, numerical simulations and experimental data is shown.

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“…This implies that modelling inter diffusion phenomena in fluid mixtures is far from being considered as an established theory. Following the recent introduction of the bi-velocity hydrodynamic theory [4,5], new models for mixtures have been proposed [6,7,8]. Here we developed a single fluid kinetic equation model for gas mixtures in which, each species is associated with a new form of 'volume velocity'.…”

Section: Introductionmentioning

confidence: 99%

A single fluid kinetic and continuum model in multicomponent gas mixtures

Dadzie¹

2015

AIP Conference Proceedings

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A single fluid kinetic and continuum model in multicomponent gas mixtures Dadzie, Kokou Sename EnyonamAbstract. We present a new single fluid kinetic equation and accompanying continuum hydrodynamic model for multicomponent gases. The new model follows the volume diffusion (bi-velocity hydrodynamics) concept involving each gaseous species. A method to derive accompanying constitutive equations is presented. It is shown that the new mixture continuum model alleviates some of the problems related to other standard approaches and may be better suited to deal with complex fluids involving large number of species.

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The lattice shift generated by two dimensional diffusion process

Cited by 6 publications

References 21 publications

Interdiffusion in many dimensions: mathematical models, numerical simulations and experiment

Interdiffusion in many dimensions: mathematical models, numerical simulations and experiment

Difference Methods to One and Multidimensional Interdiffusion Models With Vegard Rule

A single fluid kinetic and continuum model in multicomponent gas mixtures

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