scholarly journals Compendium About Multicomponent Interdiffusion in Two Dimensions

2021 ◽  
Author(s):  
Bogusław Bożek ◽  
Lucjan Sapa ◽  
Katarzyna Tkacz-Śmiech ◽  
Marek Zajusz ◽  
Marek Danielewski
Keyword(s):  
Diffusion Coefficients ◽  
Multicomponent System ◽  
Three Dimensional ◽  
Two Dimensions ◽  
Diffusion Couples ◽  
Strongly Coupled ◽  
One Dimensional ◽  
Nonlinear Parabolic ◽  
Drift Potential ◽  
And Diffusion

AbstractInterdiffusion between dissimilar solids can change the properties of joined materials. Although much work has been done to study experimentally and theoretically interdiffusion in one-dimensional (1-D) diffusion couples, studying interdiffusion in two-dimensional (2-D) or three-dimensional (3-D) solids remains a challenge. In this article, we report an experiment and develop a model to study interdiffusion in a multicomponent system of 2-D geometry. The results (concentration maps and profiles) are compared with data obtained by modeling and numerical simulations. It is assumed that the system satisfies Vegard’s rule and diffusion coefficients are composition dependent. To model the multidimensional diffusion with a drift, we take benefit of the concept of the drift potential. A nonlinear parabolic-elliptic system of strongly coupled differential equations is formulated and the implicit difference method, preserving Vegard’s rule, is applied in the simulations.

Fo and Ni Relations in Olivine Differentiate between Crystallization and Diffusion Trends

2020 ◽  
Author(s):  
Boris Gordeychik ◽  
Tatiana Churikova ◽  
Thomas Shea ◽  
Andreas Kronz ◽  
Alexander Simakin ◽  
...  
Keyword(s):  
Diffusion Coefficients ◽  
Computational Models ◽  
Three Dimensional ◽  
Crystal Shape ◽  
Diffusion Anisotropy ◽  
Progressive Loss ◽  
Theoretical And Computational Models ◽  
Diffusion Controlled ◽  
Mafic Magmas ◽  
And Diffusion

Abstract Nickel is a strongly compatible element in olivine, and thus fractional crystallization of olivine typically results in a concave-up trend on a Fo–Ni diagram. ‘Ni-enriched’ olivine compositions are considered those that fall above such a crystallization trend. To explain Ni-enriched olivine crystals, we develop a set of theoretical and computational models to describe how primitive olivine phenocrysts from a parent (high-Mg, high-Ni) basalt re-equilibrate with an evolved (low-Mg, low-Ni) melt through diffusion. These models describe the progressive loss of Fo and Ni in olivine cores during protracted diffusion for various crystal shapes and different relative diffusivities for Ni and Fe–Mg. In the case when the diffusivity of Ni is lower than that for Fe–Mg interdiffusion, then olivine phenocrysts affected by protracted diffusion form a concave-down trend that contrasts with the concave-up crystallization trend. Models for different simple geometries show that the concavity of the diffusion trend does not depend on the size of the crystals and only weakly depends on their shape. We also find that the effect of diffusion anisotropy on trend concavity is of the same magnitude as the effect of crystal shape. Thus, both diffusion anisotropy and crystal shape do not significantly change the concave-down diffusion trend. Three-dimensional numerical diffusion models using a range of more complex, realistic olivine morphologies with anisotropy corroborate this conclusion. Thus, the curvature of the concave-down diffusion trend is mainly determined by the ratio of Ni and Fe–Mg diffusion coefficients. The initial and final points of the diffusion trend are in turn determined by the compositional contrast between mafic and more evolved melts that have mixed to cause disequilibrium between olivine cores and surrounding melt. We present several examples of measurements on olivine from arc basalts from Kamchatka, and published olivine datasets from mafic magmas from non-subduction settings (lamproites and kimberlites) that are consistent with diffusion-controlled Fo–Ni behaviour. In each case the ratio of Ni and Fe–Mg diffusion coefficients is indicated to be <1. These examples show that crystallization and diffusion can be distinguished by concave-up and concave-down trends in Fo–Ni diagrams.

Theoretical design of MoO3-based high-rate lithium ion battery electrodes: the effect of dimensionality reduction

2014 ◽  
Vol 2 (45) ◽  
pp. 19180-19188 ◽  
Author(s):  
Fengyu Li ◽  
Carlos R. Cabrera ◽  
Zhongfang Chen
Keyword(s):  
Density Functional ◽  
Three Dimensional ◽  
Lithium Ion ◽  
High Rate ◽  
Functional Theory ◽  
One Dimensional ◽  
Theoretical Design ◽  
Different Dimensions ◽  
Li Adsorption ◽  
And Diffusion

By means of density functional theory computations, we systematically investigated the behavior of lithium (Li) adsorption and diffusion on MoO3 with different dimensions: including three-dimensional (3D) bulk, two-dimensional (2D) double-layer, 2D monolayer and one-dimensional (1D) nanoribbons.

Monte Carlo algorithms for calculation of diffusive characteristics of an electron avalanche in gases

2016 ◽  
Vol 31 (6) ◽  
Author(s):  
Galiya Z. Lotova
Keyword(s):  
Monte Carlo ◽  
Diffusion Coefficients ◽  
Distribution Density ◽  
High Efficiency ◽  
Time Moment ◽  
Three Dimensional ◽  
Electron Avalanche ◽  
Monte Carlo Algorithms ◽  
And Diffusion ◽  
Projection Estimators

AbstractSome problems of the theory of electron transfer in gases under the action of a strong external electric field is considered in the paper. Based on the three-dimensional ELSHOW algorithm, samples of states of particles in an electron avalanche are obtained for a given time moment in order to calculate the corresponding ‘diffusion radii’ and diffusion coefficients. Randomized projection estimators and kernel estimators (for test purpose) are constructed with the use of grouped samples for evaluation of the distribution density of particles in an avalanche. Test computations demonstrate a high efficiency of projection estimators for calculation of diffusive characteristics.

Approximation of Euler–Maruyama for one-dimensional stochastic differential equations involving the maximum process

2020 ◽  
Vol 26 (1) ◽  
pp. 33-47
Author(s):  
Kamal Hiderah
Keyword(s):  
Differential Equations ◽  
Strong Convergence ◽  
Stochastic Differential Equations ◽  
Diffusion Coefficients ◽  
One Dimensional ◽  
Maximum Process ◽  
And Diffusion

AbstractThe aim of this paper is to show the approximation of Euler–Maruyama {X_{t}^{n}} for one-dimensional stochastic differential equations involving the maximum process. In addition to that it proves the strong convergence of the Euler–Maruyama whose both drift and diffusion coefficients are Lipschitz. After that, it generalizes to the non-Lipschitz case.

Cage correlation and diffusion in strongly coupled three-dimensional Yukawa systems in magnetic fields

2016 ◽  
Vol 93 (6) ◽  
Author(s):  
K. N. Dzhumagulova ◽  
R. U. Masheyeva ◽  
T. Ott ◽  
P. Hartmann ◽  
T. S. Ramazanov ◽  
...  
Keyword(s):  
Magnetic Fields ◽  
Three Dimensional ◽  
Strongly Coupled ◽  
And Diffusion

DIFFUSION IN THE FRENKEL–KONTOROVA MODEL WITH ANHARMONIC INTERATOMIC INTERACTIONS

1994 ◽  
Vol 08 (17) ◽  
pp. 2353-2389 ◽  
Author(s):  
OLEG M. BRAUN ◽  
IRINA I. ZELENSKAYA ◽  
YURI S. KIVSHAR
Keyword(s):  
Low Temperature ◽  
Diffusion Coefficients ◽  
Type Equation ◽  
Chemical Diffusion ◽  
Phenomenological Approach ◽  
Superionic Conductors ◽  
One Dimensional ◽  
Anisotropic Layers ◽  
And Diffusion ◽  
Kontorova Model

Low-temperature diffusion and transport properties of the generalized Frenkel–Kontorova model are investigated analytically in the framework of a phenomenological approach which treats a system of strongly interacting atoms as a system of weaklyinteracting quasiparticles (kinks). The model takes into account realistic (anharmonic) interaction of particles subjected into a periodic substrate potential, and such a generalization leads to a series of novel effects which we expect are related to the experimentally-observed phenomena in several quasi-one-dimensional systems. Analysing the concentration dependences in the framework of the kink phenomenology, we use the renormalization procedure when the atomic structure with a complex unit cell is treated as (more simple) periodic structure of kinks. Using phenomenology of the ideal kink gas, the low-temperature states of the chain are described as those consisting of "residual" kinks supplemented by thermally-excited kinks. This approach allows us to describe the ground states of the chain as a hierarchy of "melted" kink lattices. Dynamical and diffusion properties of the system are then described in terms of the kink dynamics and kink diffusion. The motion equation for a single kink is reduced to a Langevin-type equation which is investigated with the help of the Kramers theory. Susceptibility, conductivity, self-diffusion and chemical diffusion coefficients of the chain are calculated as functions of the kink diffusion coefficient. In this way, we qualitatively analyze, for the first time to our knowledge, dependence of the different diffusion coefficients on the concentration of atoms in the chain. The results are applied to describe peculiarities in conductivity and diffusion coefficients of quasi-one-dimensional systems, in particular, superionic conductors and anisotropic layers of atoms adsorbed on crystal surfaces which were earlier investigated experimentally.

Correlation between estimated diffusion coefficients from different types of diffusion couples in multicomponent system

Materialia ◽  
2021 ◽  
Vol 16 ◽  
pp. 101046
Author(s):  
Neelamegan Esakkiraja ◽  
Anuj Dash ◽  
Avik Mondal ◽  
K.C. Hari Kumar ◽  
Aloke Paul
Keyword(s):  
Diffusion Coefficients ◽  
Multicomponent System ◽  
Diffusion Couples ◽  
Different Types

Multidimensional Water Flow in Variably Saturated Soils

2003 ◽  
Author(s):  
Arthur W. Warrick
Keyword(s):  
Point Source ◽  
Three Dimensional ◽  
Practical Interest ◽  
Two Dimensions ◽  
Point Sources ◽  
Radial Coordinate ◽  
Dimensional Problem ◽  
One Dimensional ◽  
Divergent Flow ◽  
Suction Sampler

Chapters 4 and 5 dealt with one-dimensional rectilinear flow, with and without the effect of gravity. Now the focus is on multidimensional flow. We will refer to two- and three-dimensional flow based on the number of Cartesian coordinates necessary to describe the problem. For this convention, a point source emitting a volume of water per unit time results in a three-dimensional problem even if it can be described with a single spherical coordinate. Similarly, a line source would be two-dimensional even if it could be described with a single radial coordinate. A problem with axial symmetry will be termed a three-dimensional problem even when only a depth and radius are needed to describe the geometry. The pressure at a point source is undefined. But more generally, three-dimensional point sources refer to flow from finite-sized sources into a larger soil domain, such as infiltration from a small surface pond into the soil. Often, the soil domain can be taken as infinite in one or more directions. Also, a point sink can occur with flow to a sump or to a suction sampler. In two dimensions, the same types of example can be given, but we will refer to them as line sources or sinks. Practical interest in point sources includes analyses of surface or subsurface leaks and of trickle (drip) irrigation. The desirability of determining soil properties in situ has provided the impetus for a rigorous analysis of disctension and borehole infiltrometers. Also, environmental monitoring with suction cups or candles, pan lysimeters, and wicking devices all include convergent or divergent flow in multidimensions. There are some conceptual differences between line and point sources and one-dimensional sources. For discussion, consider water supplied at a constant matric potential into drier surroundings. For a one-dimensional source, the corresponding physical problem includes a planar source over an area large enough for “edge” effects to be negligible. For two dimensions, the source might be a long horizontal cylinder or a furrow of finite depth from which water flows. For three dimensions, the source could be a small orifice providing water at a finite rate or a small, shallow pond on the soil surface.

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