Diffusion Coefficients of Single and Many Particles in Lattices with Different Forms of Disorder

Kehr, K. W.; Wichmann, Thomas

doi:10.4028/www.scientific.net/msf.223-224.151

Cited by 20 publications

(24 citation statements)

References 25 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In a random trap model shown in Fig. 1 (B), the transition occurs with equal rate from the site denoted by i to one of the nearest neighbor site j and the rate is given by [12][13][14] …”

Section: Quantitative Models Of Rugged Energy Landscapementioning

confidence: 99%

“…(8) in the absence of the spatial correlation. In general, the mean first passage time can be expressed as [11][12][13]15,37] …”

Section: Treatment Of Diffusion In One Dimensional Rugged Energymentioning

confidence: 99%

“…As shown previously, the effective diffusion constant can be obtained using the mean first passage time ! τ mft as [11][12][13] ! !…”

Section: Treatment Of Diffusion In One Dimensional Rugged Energymentioning

confidence: 99%

“…In an influential early paper, Scher and Lax introduced the use of the formalism of waiting time distribution to explain the observed power law decay of current in disordered materials [4][5][6]. Kehr and Haus [11][12][13] used "hopping over barriers" model to take into account randomly placed barriers and traps. Subsequently, many different theoretical studies were carried out in different areas of condensed matter physics and chemistry to include effects of complex environments on diffusion.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Anomalous dimensionality dependence of diffusion in a rugged energy landscape: How pathological is one dimension?

Seki

Bagchi²,

Bagchi

2016

The Journal of Chemical Physics

View full text Add to dashboard Cite

Diffusion in one dimensional rugged energy landscape (REL), is predicted to be pathologically different (from any higher dimension) with much larger chance of encountering broken ergodicity (D. L. Stein and C. M. Newman, AIP Conf. Proc. 1479Proc. , 620 (2012). However, no quantitative study of this difference has been reported, despite prevalence of multidimensional physical models in literature (like a high dimensional funnel guiding protein folding/unfolding). Paradoxically, some theoretical studies of these phenomena still employ a one dimensional diffusion description for analytical tractability. We explore the dimensionality dependent diffusion on REL by carrying out an effective medium approximation based analytical calculations and compare them with the available computer simulation results. We find that at intermediate level of ruggedness (assumed to have 2 a Gaussian distribution), where diffusion is well-defined, the value of the effective diffusion coefficient depends on dimensionality and changes (increases) by several factors (~5-10) in going from 1d to 2d. In contrast, the changes in subsequent transitions (like 2d to 3d and 3d to 4d and so on) are far more modest, of the order of 10-20% only. When ruggedness is given by random traps with an exponential distribution of barrier heights, the mean square displacement is sub-diffusive (a well-known result), but the growth of MSD is described by different exponents in one and higher dimensions.The reason for such strong ruggedness induced retardation in the case of one dimensional REL is discussed. We also discuss the special limiting case of infinite dimension (d= ∞ ) where the effective medium approximation becomes exact and where theoretical results become simple. We discuss, for the first time, the role of spatial correlation in the landscape on diffusion of a random walker.

show abstract

“…In a random trap model shown in Fig. 1 (B), the transition occurs with equal rate from the site denoted by i to one of the nearest neighbor site j and the rate is given by [12][13][14] …”

Section: Quantitative Models Of Rugged Energy Landscapementioning

confidence: 99%

“…(8) in the absence of the spatial correlation. In general, the mean first passage time can be expressed as [11][12][13]15,37] …”

Section: Treatment Of Diffusion In One Dimensional Rugged Energymentioning

confidence: 99%

“…As shown previously, the effective diffusion constant can be obtained using the mean first passage time ! τ mft as [11][12][13] ! !…”

Section: Treatment Of Diffusion In One Dimensional Rugged Energymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Anomalous dimensionality dependence of diffusion in a rugged energy landscape: How pathological is one dimension?

Seki

Bagchi²,

Bagchi

2016

The Journal of Chemical Physics

View full text Add to dashboard Cite

show abstract

“…From the physical point of view, diffusion of lattice gases in systems with site disorder has been studied mainly by means of simulations and more or less rough approximations like mean field . We refer the interested reader to [19], [20], [21], [22], [24] and to [17] for an iterative procedure to compute corrections to the mean-field approximation.…”

Section: Introductionmentioning

confidence: 99%

Hydrodynamic limit of a disordered lattice gas

Faggionato

Martinelli

2003

Probab. Theory Relat. Fields

View full text Add to dashboard Cite

ABSTRACT. We consider a model of lattice gas dynamics in Z d in the presence of disorder. If the particle interaction is only mutual exclusion and if the disorder field is given by i.i.d. bounded random variables, we prove the almost sure existence of the hydrodynamical limit in dimension d ≥ 3. The limit equation is a non linear diffusion equation with diffusion matrix characterized by a variational principle. MSC: 60K40, 60K35, 60J27, 82B10, 82B20

show abstract

Ag diffusion in SiC high-energy grain boundaries: Kinetic Monte Carlo study with first-principle calculations

Deng

Szlufarska

et al. 2016

Computational Materials Science

View full text Add to dashboard Cite

The diffusion of silver (Ag) impurities in high energy grain boundaries (HEGBs) of cubic (3C) silicon carbide (SiC) is studied using an ab initio based kinetic Monte Carlo (kMC) model. This study assesses the hypothesis that the HEGB diffusion is responsible for Ag release in TristructuralIsotropic (TRISO) fuel particles, and provides a specific example to increase understanding of impurity diffusion in highly disordered grain boundaries. The HEGB environment was modeled by an amorphous SiC (a-SiC), which approximately represents the local environments of HEGBs. The structure and stability of Ag defects were calculated using ab initio methods based on Density Functional Theory (DFT). The defect energetics suggested that the fastest diffusion takes place via an interstitial mechanism in a-SiC and that is what is modeled. Interstitial sites were identified by a gridded search and transition states were computed using the climbing image nudged elastic band method. The formation energy of Ag interstitials (relative to bulk Ag) and the Kinetic Resolved Activation (EKRA) energies between them were well approximated with Gaussian distributions that were then sampled in the kMC. The diffusion of Ag was simulated with the effective medium model using kMC. Ag diffusion coefficients were estimated for the temperature range of 1200-1600°C. Ag in a HEGB is predicted to exhibit an Arrhenius type diffusion and with a diffusion prefactor and effective activation energy of (2.73 ± 1.09) × 10 −10 m 2 s −1 and 2.79 ± 0.18 eV, respectively. The comparison between HEGB results to other theoretical studies suggested not only that GB diffusion is predominant over bulk diffusion, but also that the HEGB is one of fastest grain boundary paths for Ag diffusion in SiC. The Ag diffusion coefficient in the HEGB shows a good agreement with ionimplantation measurements, but is 2-3 orders of magnitude lower than the reported diffusion coefficient values extracted from integral release measurements on in-and out-of-pile samples. The discrepancy between GB diffusion and integral release measurements suggests that other contributions are responsible for fast release of Ag in some experiments and we propose that these contributions may arise from radiation enhanced diffusion.

show abstract

Diffusion Coefficients of Single and Many Particles in Lattices with Different Forms of Disorder

Cited by 20 publications

References 25 publications

Anomalous dimensionality dependence of diffusion in a rugged energy landscape: How pathological is one dimension?

Anomalous dimensionality dependence of diffusion in a rugged energy landscape: How pathological is one dimension?

Hydrodynamic limit of a disordered lattice gas

Ag diffusion in SiC high-energy grain boundaries: Kinetic Monte Carlo study with first-principle calculations

Contact Info

Product

Resources

About