Download presentation

Presentation is loading. Please wait.

Published byLeslie Bickmore Modified over 2 years ago

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

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

4
Fractal structures: ● At p c : ● Above p c :

5
Self-similarity at p c :

6
Self-similarity above p c :

7
A B A B Anomalous diffusion Normal lattice Percolation at

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

9
nanocrystalline Li 2 O:B 2 O 3 composite II. Applications of percolation theory: Nano- and microcrystalline Li 2 O:B 2 O 3 composites

10
DC conductivity of nano- and microcrystalline Li 2 O:B 2 O 3 composites Indris et al, 2000

11
Brick-layer model Cluster of conducting Li 2 0 grains Li 2 0 grain: length a, interface Bulk: normal conducting 0 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 = 1 / 0 between interface and bulk conductivities, 1 nm. Nanocrystalline grains: a = 10 nm, = 200; a = 10 nm, = 100; a = 20 nm, = 200; a = 20 nm, = 100. Microcrystalline grains: a = 10, = 200; a = 10, = 100; a = 20, = 200; a = 20, = 100. Comparison of the experimentally observed normalized dc conductivity (p)/ (0) with the simulation results for = 1 nm, = 200; a = 10 nm and a = 10, respectively. Ulrich et al, 2004

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

15
Way out: Ionic diffusion via B 2 O 3 : B 2 O 3 interfaces in the nanocrystalline system p c 0.95p c 0.93 Brick-layer model Voronoi model Ulrich et al, 2004

Similar presentations

Presentation is loading. Please wait....

OK

FRACTAL DIMENSION OF BIOFILM IMAGES

FRACTAL DIMENSION OF BIOFILM IMAGES

© 2017 SlidePlayer.com Inc.

All rights reserved.

Ads by Google

Interactive ppt on male reproductive system Ppt on exploitation of child labour Ppt on human body Ppt on properties of different quadrilaterals Ppt on ready to serve beverages menu Ppt on total internal reflection in diamond Ppt on electronic payment systems Ppt on renewable energy sources in india Ppt on reuse of waste material Ppt on cross-sectional study strengths and weaknesses