1 / 16

Anomalous Transport and Diffusion in Disordered Materials

This tutorial introduces the percolation concept, critical behavior, and fractal structures of anomalous diffusion in disordered materials. It explores applications in materials science, specifically composite ionic conductors.

kharman
Download Presentation

Anomalous Transport and Diffusion in Disordered Materials

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Anomalous Transport and Diffusion in Disordered Materials Armin Bunde Justus-Liebig-Universität Giessen in cooperation with Markus Ulrich (Giessen, Stuttgart) Paul Heitjans, Sylvio Indris (Hannover)

  2. (I) Tutorial introduction into the percolation concept: model, critical behavior, fractal structures anomalous diffusion (II) Applications in materials science: composite ionic conductors Outline

  3. (I) The percolation concept pc: critical concentration: spanning (“infinite”) cluster emerges p > pc: infinite cluster + finite clusters p < pc: finite clusters of occupied sites mean length of finite clusters: size of the infinite cluster:

  4. At pc: Above pc: Fractal structures:

  5. Self-similarity at pc:

  6. Self-similarity above pc:

  7. Anomalous diffusion Normal lattice A B Percolation at A B

  8. Diffusion above Nernst-Einstein: Percolation system: Relation between and : Proof:

  9. nanocrystalline Li2O:B2O3 composite II. Applications of percolation theory: Nano- and microcrystalline Li2O:B2O3 composites

  10. DC conductivity of nano- and microcrystalline Li2O:B2O3 composites Indris et al, 2000

  11. Brick-layer model Li20 grain: length a, interface l Cluster of conducting Li20 grains Bulk: normal conducting s0 Interface: highly conducting Ulrich et al, 2004

  12. Brick-layer model: connections between grains Ulrich et al, 2004

  13. Brick-layer model: Results DC conductivity for different grain sizes a and ratios t= s1/s0 between interface and bulk conductivities, l= 1 nm. Nanocrystalline grains: a = 10 nm, t = 200; a = 10 nm, t = 100; a = 20 nm, t = 200; a = 20 nm, t = 100. Microcrystalline grains: a = 10 , t = 200; a = 10 , t = 100; a = 20 , t = 200; a = 20 , t = 100. Comparison of the experimentally observed normalized dc conductivity s(p)/s(0) with the simulation results for l = 1 nm, t = 200; a = 10 nm and a = 10 , respectively. Ulrich et al, 2004

  14. log-normal distribution of grain sizes, percolation threshold: pc= 0.85 (also too small!) Voronoi-type model Ulrich et al, 2004

  15. Way out: Ionic diffusion via B2O3: B2O3 interfacesin the nanocrystalline system pc 0.95 Voronoi model Brick-layer model pc 0.93 Ulrich et al, 2004

More Related