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Anomalous Transport and Diffusion in Disordered Materials Armin Bunde

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). (I) Tutorial introduction into the percolation concept:

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Anomalous Transport and Diffusion in Disordered Materials Armin Bunde

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  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

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