The Laplace transformed diffusion equation is solved for finite diffusion in planar, cylindrical and spherical geometry with a Nemstian or an impermeable diffusion layer boundary condition. Analytical expressions are presented generalized as the Laplace transformed concentration to flux ratio at the
Reactive diffusion in nanostructures of spherical symmetry
β Scribed by Guido Schmitz; Constantin-Buzau Ene; Carsten Nowak
- Publisher
- Elsevier Science
- Year
- 2009
- Tongue
- English
- Weight
- 690 KB
- Volume
- 57
- Category
- Article
- ISSN
- 1359-6454
No coin nor oath required. For personal study only.
β¦ Synopsis
To investigate reactive diffusion in nanosized spherical geometries, a clear model experiment has been designed. Thin film {Al/Cu/Al} and {Cu/Al/Cu} triple layers were deposited on tips of 25 nm apex radius and investigated by atom probe tomography (APT). At the interfaces within both samples, the growth of the reaction product proceeds parabolically from the very beginning but with remarkably different rates. Growth appears to be always faster if Cu is stacked to the outer side of Al. The complex quantitative analysis of reactioninduced stress, surface tensions and partial mobilities suggests that the different growth rates represent the Darken and the Nernst-Planck limits of interdiffusion. Since the curvature radius of the model samples ranges down to a few tens of nanometers, it is anticipated that an analogous effect may play a role in the oxidation of nanospheres or in chemical reactions of core-shell structures.
π SIMILAR VOLUMES
## Abstract A previously developed model for active species concentration profiles in infinite cylindrical systems has been extended to include the spherical system. The model couples the processes of diffusion to and reaction at the wall. Predictions of time buildup under conditions of homogeneous