Vibrational fluorescence of CN− centers in KCl by electronic excitation of neighbouring Tl+ centers

Abstract

Infrared emission from higher vibrational states of CN^? in KCl has been achieved by optically exciting nearby Tl⁺ ions with an excimer laser. The electronic vibrational energy transfer, already known from F_H(CN^?) in alkali halides, leads to population of vibrational states up to at least the tenth level.     

Pressure Studies on Fe 1−x Si 1+x Single Crystals (−0.003≤ x ≤0.025)

A study of the pressure response of single crystalline Fe 1 m x Si 1+x samples revealed beyond an initial increase a pressure driven reduction of the band gap E g . Concomitantly, there is a well resolvable change of the variable range hopping conductivity, presumably caused by an increase of the characteristic temperature of the system due to band broadening effects in the electronic density of states.     

The Formation of Large‐Area Conducting Graphene‐Like Platelets

The treatment of a suspension of graphite oxide (GO) with sodium azide leads to a material that, after reduction, features amino groups at the top and bottom of the sheets. These groups react through microcontact printing with an isothiocyanate monolayer on a silicon oxide substrate to form covalent bonds that strongly attach to the particles on the surface. With ultrasonication it is possible to obtain exfoliation of the sheets that are not covalently bound to the surface leaving single‐layer platelets attached to the substrate. The azido derivative can be also used to functionalize the graphene oxide with long alkylic chains through a click chemistry approach. This functionalization results in the exfoliation of this material in dimethylformamide. The novel materials were fully characterized by different techniques including IR spectroscopy, thermogravimetric analysis (TGA), scanning and transmission electron microscopy (SEM and TEM), X‐Ray photoelectron spectroscopy (XPS), and solid state NMR spectroscopy. The material with amino groups, after the reduction step, is conductive with a resistivity only approximately seven times larger than that of unprocessed graphite. This implies that after reduction of the GO, the conjugated sp² network is largely restored. We consider this to be an important step towards a chemical approach for forming conducting large‐area platelet films of single‐layer graphene.     

Lower bounds on Ricci curvature and quantitative behavior of singular sets

Let Y ⁿ denote the Gromov-Hausdorff limit $M^{n}_{i}\stackrel{d_{\mathrm{GH}}}{\longrightarrow} Y^{n}$ of v-noncollapsed Riemannian manifolds with ${\mathrm{Ric}}_{M^{n}_{i}}\geq-(n-1)$ . The singular set $\mathcal {S}\subset Y$ has a stratification $\mathcal {S}^{0}\subset \mathcal {S}^{1}\subset\cdots\subset \mathcal {S}$ , where $y\in \mathcal {S}^{k}$ if no tangent cone at y splits off a factor ? ^k+1 isometrically. Here, we define for all η>0, 0<r≤1, the k-th effective singular stratum $\mathcal {S}^{k}_{\eta,r}$ satisfying $\bigcup_{\eta}\bigcap_{r} \,\mathcal {S}^{k}_{\eta,r}= \mathcal {S}^{k}$ . Sharpening the known Hausdorff dimension bound $\dim\, \mathcal {S}^{k}\leq k$ , we prove that for all y, the volume of the r-tubular neighborhood of $\mathcal {S}^{k}_{\eta,r}$ satisfies ${\mathrm {Vol}}(T_{r}(\mathcal {S}^{k}_{\eta,r})\cap B_{\frac{1}{2}}(y))\leq c(n,{\mathrm {v}},\eta)r^{n-k-\eta}$ . The proof involves a quantitative differentiation argument. This result has applications to Einstein manifolds. Let $\mathcal {B}_{r}$ denote the set of points at which the C ²-harmonic radius is ≤r. If also the $M^{n}_{i}$ are Kähler-Einstein with L ₂ curvature bound, $\| Rm\|_{L_{2}}\leq C$ , then ${\mathrm {Vol}}( \mathcal {B}_{r}\cap B_{\frac{1}{2}}(y))\leq c(n,{\mathrm {v}},C)r^{4}$ for all y. In the Kähler-Einstein case, without assuming any integral curvature bound on the $M^{n}_{i}$ , we obtain a slightly weaker volume bound on $\mathcal {B}_{r}$ which yields an a priori L _p curvature bound for all p<2. The methodology developed in this paper is new and is applicable in many other contexts. These include harmonic maps, minimal hypersurfaces, mean curvature flow and critical sets of solutions to elliptic equations.