Bei der Bestimmung des Wolframs in Erzen

Ohne Zusammenfassung     

On the growth of components with non-fixed excesses

Denote by an l-component a connected graph with l edges more than vertices. We prove that the expected number of creations of (l+1)-component, by means of adding a new edge to an l-component in a randomly growing graph with n vertices, tends to 1 as l,n tends to ∞ but with l=o(n^1/4). We also show, under the same conditions on l and n, that the expected number of vertices that ever belong to an l-component is (12l)^1/3n^2/3.     

Optimization of a Bonse–Hart instrument by suppressing surface parasitic scattering

An improved crystal design for a Bonse–Hart ultra‐small‐angle scattering instrument is presented. Defects at the diffracting surfaces of the conditioning crystals were found to be at the origin of diffuse scattering that enhances the intensity in the wings of the rocking curves by several orders of magnitude. In order to improve the performance of the instrument, the monolithic channel‐cut crystals were replaced by pairs of separate polished and deeply etched crystals. These crystals were mounted on a mechanical stage that allows very precise parallel alignment of the crystals to within a tiny fraction of the rocking curve width (sub‐µrad range). By using these double‐crystal set‐ups, the parasitic background scattering was reduced by more than an order of magnitude. The steps to achieve the optimum surface quality of the crystals as well as the precision mechanical design for their parallel alignment are described. Significant improvement of the signal‐to‐background ratio and the available wavevector range of the instrument make it suitable for studying the microstructure and dynamics of dilute and weakly scattering soft‐matter systems. This development also has potential applications in X‐ray optics such as low‐background and tunable monochromators and collimators.