Structural characterization of supported nanocrystalline ZnO thin films prepared by dip-coating

Nanocrystalline ZnO thin films prepared by the sol-gel dip-coating technique were characterized by grazing incidence X-ray diffraction (GIXD), atomic force microscopy (AFM), X-ray reflectivity (XR) and grazing incidence small-angle X-ray scattering (GISAXS). The structures of several thin films subjected to (i) isochronous annealing at 350, 450 and 550 degrees C, and (ii) isothermal annealing at 450 degrees C during different time periods, were characterized. The studied thin films are composed of ZnO nanocrystals as revealed by analysing several GIXD patterns, from which their average sizes were determined. Thin film thickness and roughness were determined from quantitative analyses of AFM images and XR patterns. The analysis of XR patterns also yielded the average density of the studied films. Our GISAXS study indicates that the studied ZnO thin films contain nanopores with an ellipsoidal shape, and flattened along the direction normal to the substrate surface. The thin film annealed at the highest temperature, T = 550 degrees C, exhibits higher density and lower thickness and nanoporosity volume fraction, than those annealed at 350 and 450 degrees C. These results indicate that thermal annealing at the highest temperature (550 degrees C) induces a noticeable compaction effect on the structure of the studied thin films. (C) 2011 Elsevier B.V. All rights reserved.

Billiards in a General Domain with Random Reflections

We study stochastic billiards on general tables: a particle moves according to its constant velocity inside some domain D R(d) until it hits the boundary and bounces randomly inside, according to some reflection law. We assume that the boundary of the domain is locally Lipschitz and almost everywhere continuously differentiable. The angle of the outgoing velocity with the inner normal vector has a specified, absolutely continuous density. We construct the discrete time and the continuous time processes recording the sequence of hitting points on the boundary and the pair location/velocity. We mainly focus on the case of bounded domains. Then, we prove exponential ergodicity of these two Markov processes, we study their invariant distribution and their normal (Gaussian) fluctuations. Of particular interest is the case of the cosine reflection law: the stationary distributions for the two processes are uniform in this case, the discrete time chain is reversible though the continuous time process is quasi-reversible. Also in this case, we give a natural construction of a chord ""picked at random"" in D, and we study the angle of intersection of the process with a (d - 1) -dimensional manifold contained in D.