Investigation of the three-dimensional microstructure of Cu-Sn(Pb) diffusion zones by means of ion beam sputtering, scanning electron microscopy and lattice source interferences

On model substances of Cu-Sn(Pb) solders it is shown by the combined use of several physical analytical methods that the intermetallic compounds formed during the annealing process have a crystalline structure, which can be observed also three-dimensionally by ion etching. Moreover, grain boundaries as well as phases become visible, and it is possible to determine the crystallographic orientation of the individual crystals in the Cu starting material and in the diffusion zones by means of the Kossel technique. As a result of the investigations, conclusions can be drawn with respect to the diffusion process, especially also to the crystallographic structure of the diffusion zones and the dendritic growth.Dedicated to Professor Dr. rer. nat. Dr. h.c. Hubertus Nickel on the occasion of his 65th birthday     

The connectivity of a graph on uniform points on [0,1]

A random graph G_n(x) is constructed on independent random points U₁,…,U_n distributed uniformly on [0,1]^d, d1, in which two distinct such points are joined by an edge if the l_∞-distance between them is at most some prescribed value 0<x<1. The connectivity distance c_n, the smallest x for which G_n(x) is connected, is shown to satisfy

(1)

For d2, the random graph G_n(x) behaves like a d-dimensional version of the random graphs of Erdös and Rényi, despite the fact that its edges are not independent: c_n/d_n→1, a.s., as n→∞, where d_n is the largest nearest-neighbor link, the smallest x for which G_n(x) has no isolated vertices.     

Convex bodies of constant width and constant brightness

In 1926 Nakajima (= Matsumura) showed that any convex body in R³ with constant width, constant brightness, and boundary of class C² is a ball. We show that the regularity assumption on the boundary is unnecessary, so that balls are the only convex bodies of constant width and brightness.     

Solvation dynamics in methanol: Experimental and molecular dynamics simulation studies

We have investigated the ultrafast dynamics of methanol by time dependent fluorescent shift experiments and molecular dynamic simulations. The experiments were performed with two different probe molecules, 1-aminonaphthalene and coumarin 153. The molecular dynamic simulations employed these probes as well as small atomic and diatomic solutes. We find a previously unobserved fast decay component in the solvation response of methanol. The molecular dynamics results are in good agreement with this experimental result. The origin of this fast response and the linearity of the solvent response are discussed.     

Ultrafast experiments on intermolecular electron transfer in the benzene - bromine atom charge transfer complex

Ultrafast pump - probe measurements have been made on the benzene - bromine atom charge transfer (CT) complex in CCl₄ and cyclohexane solutions. Ultrafast optical excitation of the CT band of the complex yields an ion pair, which is comprised of a benzene cation and a bromide anion. The rate of charge recombination between the bromide and the benzene cation in the ion pair has been observed to be much faster than the rate of diffusion apart. The charge recombination rate is accelerated at high benzene concentrations as a result of the formation of a benzene dimer cation - bromide ion pair which undergoes much faster charge recombination than the benzene cation - bromide ion pair.     

The Circle of Apollonius: A Discovery Activity

The works of the Greek mathematician Apollonius offer many opportunities for conjecture regarding the discovery of geometric relationships. The “circle of Apollonius” can provide students a chance to use simple constructions and knowledge of proportions to discover an unexpected result, and, if desired, a chance to follow that discovery with a proof that what appears to be so is, indeed, the case. A minimum of prior knowledge is needed for the conjecturel discovery phase of this activity, while the proof requires a more solid background of Euclidean geometry. This exercise can lead to a number of other relationships and constructions found in the works of Apollonius.     

Infrared studies of the effect of acetylene, hydrogen, and oxygen on CO adsorption on platinum hydrosols

Infrared spectra of CO-treated platinum hydrosols subsequently treated with acetylene, hydrogen, and oxygen reveal that v(CO)_ads decreases from 2070 cm⁻¹ with increasing gas-treatment time. This has been attributed to a reduction in the coverage of adsorbed CO. In Pt sol/CO/C₂H₂ systems, v(CO)_ads decreases to a limiting value of ca. 2060 cm⁻¹ after exposure to acetylene. In the Pt sol/CO/H₂ systems, v(CO)_ads decreases to ca. 2050 cm⁻¹ after exposure to hydrogen gas. The lower frequency in the Pt sol/CO/H₂ system has been attributed to CO adsorption on more active metal sites formed from the reduction of surface platinum oxides. Exposure of the CO-treated platinum hydrosols to O₂ gas was found to cause the eventual disappearance of the v(CO)_ads band in infrared spectra, which was attributed to oxidation of adsorbed CO to CO₂ by weakly bound surface layers of platinum oxides formed by the oxygen treatment.