The interaction of oxygen with polycrystalldve niobium studied using aes and low-energy sims

The interaction of oxygen with polycrystalline niobium has been studied using both Auger electron spectroscopy and low-energy secondary ion mass spectrometry in the temperature range from 300–1250 K. At higher temperatures there is oxygen dissolution into the bulk but a preferential surface segregation on recooling. Between 300 and 1250 K, there is a rapid initial adsorption into a very stable state which is associated with increases in the Nb⁺ and NbO⁺ yields that are linear with coverage. At 1250 K, further changes are very slow. At 900 K, the initial stage is followed by the adsorption with a lower sticking coefficient (<0.1) as coverage increases from θ = 0.5 to 0.7. This produces an additional larger increase in the yield of Nb⁺ but a much smaller change in NbO⁺. At 300 K, the sticking probability falls more slowly with coverage above θ = 0.5 and the amount of oxygen continues to increase slowly with exposure. The SIMS spectrum shows dramatic increases in Nb⁺, NbO⁺ and NbO⁺₂ yields and the successive appearance of small yields of ions such as Nb₂O⁺₂ and Nb₂O⁺₃ as oxide formation begins. The Nb⁺ yield slowly decreases as further oxidation occurs. Each stage of oxidation has a characteristic secondary ion mass spectrum.     

The Central Limit Problem for Random Vectors with Symmetries

Motivated by the central limit problem for convex bodies, we study normal approximation of linear functionals of high-dimensional random vectors with various types of symmetries. In particular, we obtain results for distributions which are coordinatewise symmetric, uniform in a regular simplex, or spherically symmetric. Our proofs are based on Stein’s method of exchangeable pairs; as far as we know, this approach has not previously been used in convex geometry. The spherically symmetric case is treated by a variation of Stein’s method which is adapted for continuous symmetries. This work was done while at Stanford University.     

Nanoimprinted substrates for high-yield production of topological insulator nanoribbons

We present a growth process mediated by nanoimprinted nanostructures specifically for producing bismuth selenide (Bi₂Se₃) topological insulator nanoribbons with a high yield. In this process, topological insulator nanostructures are grown on nanoimprinted gratings by using a nanoparticle-catalyzed vapor–liquid–solid mechanism. In comparison with the growth processes performed on flat and randomly rough substrates, such a nanograting-mediated growth method produces topological insulator nanoribbons with a higher yield (～15?000 nanoribbons/mm²), a narrower average ribbon width (w _avg<60 nm), and a higher uniformity in ribbon width (σ<30 nm); effectively suppresses the formation of other unwanted morphologies; and also results in the axial growth of nanoribbons along specific in-plane directions relative to pre-structured gratings. Such technical merits of nanograting-mediated growth are attributed to the preferential nucleation of Bi₂Se₃ crystal seeds and the concomitant pinning of catalytic nanoparticles at ordered grating edges. Finally, Aharonov–Bohm interference oscillations in the magnetoresistance were observed and demonstrated the coherent transport of electrons through topological surface states of Bi₂Se₃ nanoribbons. This growth process in combination with large-area nanoimprint lithography could serve as an important foundation for nanomanufacturing topological insulator nanoribbons with controllable feature size, large-area uniformity, and ordering, suitable for applications in future low-dissipation nanoelectronics.     

Computing inertia sets using atoms

We consider the problem of computing inertia sets for graphs. By using tools for combining the inertia sets of smaller graphs we can reduce this problem to understanding the inertia sets for three-connected graphs that are not joins. We term such graphs atoms and give the inertia sets for all atoms on at most seven vertices. This can be used to compute the inertia sets for all graphs on at most seven vertices.     

Moufang sets of mixed type F4

Moufang sets were introduced by Jacques Tits in order to understand isotropic linear algebraic groups of relative rank one, but the notion is more general. We describe a new class of Moufang sets, arising from so‐called mixed groups of type ${\mathsf{F}}_4$ in characteristic 2, obtained as the fixed point set under a suitable involution.     

Assessing views of coaching via a video-based tool

Mathematics coaches represent a unique group of didacticians, or individuals who work with practicing teachers. Twenty-eight mathematics coaches participated in this exploratory study, which used video viewing to examine the coach–teacher dynamic. To gather data about participants’ views of effective coaching practices, we developed the Video Assessment of Coaching instrument, which provided coaches with opportunities to express their views of effective practice and implementation. The participants expressed views of effective coaching that often did not align with those of coaching authors. The significance of this research lies in its efforts to document the views that mathematics coaches develop as practitioners, as an early step in the examination of the relationships between the views of coaches and coaches’ effectiveness in improving teacher practice, knowledge, and attitudes.     

Ultralow power continuous-wave frequency conversion in hydrogenated amorphous silicon waveguides

We demonstrate wavelength conversion through nonlinear parametric processes in hydrogenated amorphous silicon (a-Si:H) with maximum conversion efficiency of -13 dB at telecommunication data rates (10 GHz) using only 15 mW of pump peak power. Conversion bandwidths as large as 150 nm (20 THz) are measured in continuous-wave regime at telecommunication wavelengths. The nonlinear refractive index of the material is determined by four-wave mixing (FWM) to be n(2)=7.43×10(-13) cm(2)/W, approximately an order of magnitude larger than that of single crystal silicon.     

Cyclic 1,3-dipoles or acyclic phosphonium ylides? Electronic characterization of "Montréalones"

The structural features of a recently introduced class of 1,3-dipolar reagents have been computed by density functional theory and ab initio methods. The reagents are formally derived from Münchnones by replacement of the C O group with a PR3 unit. The parent species (PR3 = PH3) shows a long P...O interaction (2.55 A at the B3LYP/6-31+G(d) level), together with a nonplanar ring, and is best described as a weakly chelated acylamino-phosphonium ylide. The corresponding acyclic form, in which the P...O interaction is absent, is predicted to be 2-3 kcal mol-1 higher in enthalpy. Variation of the phosphorus substituents exerts a marked effect on the P...O distance, with electron-withdrawing groups favoring a covalent interaction [P...O 1.97 A for PR3 = PPh(catechyl)] and electron-donating groups favoring a weak interaction [P...O 3.92 A for PR3 = PPh3]. However, this variation has little effect on the relative energies of the cyclic and acyclic forms. The barriers for concerted cycloadditions with ethylene are 22.8 kcal mol-1 (PH3), 31.7 kcal mol-1 (PPh3), and 16.2 kcal mol-1 [PPh(catechyl) with axial O], which correspond with experimental observations and follow the same trend as the energies required to distort the dipole to the TS geometry.     

Organolanthanide-based synthesis of 1,2,3-triazoles from nitriles and diazo compounds

The reaction of [(C5Me5)2Ln][(mu-Ph)2BPh2] complexes with the lithium salt of (trimethylsilyl)diazomethane, Li[Me3SiCN2], gave products formulated as the dimeric isocyanotrimethylsilyl amide complexes {(C5Me5)2Ln[mu-N(SiMe3)NC]}2 (Ln = Sm, 1; La, 2). Reactions of (C5Me5)2Sm and [(C5Me5)2Sm(mu-H)]2 with Me3SiCHN2 also form 1. Complexes 1 and 2 react with Me3CCN to form the 1,2,3-triazolato complexes (C5Me5)2Ln(NCCMe3)[NNC(SiMe3)C(CMe3)N] (Ln = Sm, 3; La, 4). Complex 2 reacts with Me3SiN3 to make the isocyanide ligated azide complex {(C5Me5)2La[CNN(SiMe3)2](mu-N3)}3, 5.