Optical transitions,XPS, electronic states in NiPS3

We have measured the optical absorption below the fundamental threshold, the normal-incidence reflectivity between 1.5 and 30 eV and the X-ray photoemission spectra of NiPS₃. Shake-up satellites present at the Ni 2p and 3p core levels are strong evidence for the ionicity of the NiS bonds. We have also derived a qualitative molecular orbital model of NiPS₃ in which the trigonal crystal field splits the P and S 3p_xp_y-3p_a states, and strong covalent hybridization between P and S p_xp_y orbitals leads to covalent electronic bonding. Ni is envisaged as a divalent ion which plays little role in the electronic bonding and its 3d levels are localized, lying near the top both of the valence states. This model accounts well for both the valence band XPS data and the low energy optical transitions. Our model should represent, at the center of the Brillouin zone but not at the boundaries, the energy level sequence in NiPS₃ and other related MPX₃ layer-type compounds where M Co²⁺, Mn²⁺, Fe²⁺, Zn²⁺ and X is sulfur or selenium.The XPS spectra and optical properties of NiPS₃ have been obtained and interpreted on a qualitative molecular orbital model in which the Ni is a divalent positive ion which plays little role in the bonding. Evidence for such ionicity appears in the optical properties and XPS satellite structures, as well as in the magnetic properties. The model should represent qualitatively the band structure at the center of the Brillouin zone, but not at the boundaries. It should also be valid for other compounds similar to NiPS₃, i.e. those with other metals in place of Ni and those with Se in place of S.     

Detection of laser induced dielectric breakdown in water using a laser doppler vibrometer

This study is focused on exploring the feasibility of an all-optic surface scanning method in determining the size and position of a submerged, laser generated, optoacoustic (OA) source. The optoacoustic effect in this case was generated when the absorption of a short electromagnetic pulse in matter caused a dielectric breakdown, a plasma emission flash and a subsequent acoustic wave. In the experiment, a laser pulse with λ = 1064 nm and 12 ns pulse length was aimed at a volume of deionized water. When the laser beam was focused by a f = 16 mm lens, a single dielectric breakdown spot occurred. When a f = 40 mm was used several breakdowns in a row were induced. The breakdowns were photographed using a double shutter camera. The acoustic wave generated by the dielectric breakdowns were detected at a point on the water surface using a laser Doppler vibrometer (LDV). First, the LDV signal was used to calculate the speed of sound with an accuracy of 10 m/s. Secondly, the location and length of the dielectric breakdown was calculated with an accuracy of 1 mm. The calculated position matched the breakdown location recorded by a camera. The results show that it is possible to use LDV surface measurements from a single spot to determine both the position and length of the OA source as well as the speed of sound in the medium. Furthermore, the LDV measurements also show a secondary peak that originates from the OA source. To unravel the origin and properties of this interesting feature, further investigations are necessary     

Realizing colloidal artificial ice on arrays of optical traps

We demonstrate how a colloidal version of artificial ice can be realized on optical trap lattices. Using numerical simulations, we show that this system obeys the ice rules and that for strong colloid-colloid interactions, an ordered ground state appears. We show that the ice-rule ordering can occur for systems with as few as 24 traps and that the ordering transition can be observed at constant temperature by varying the barrier strength of the traps.     

On the 1/3–2/3 Conjecture

Let (P, ≤) be a finite poset (partially ordered set), where P has cardinality n. Consider linear extensions of P as permutations x₁x₂?x_n in one-line notation. For distinct elements x, y ∈ P, we define ?(x ? y) to be the proportion of linear extensions of P in which x comes before y. For \(0\leq \alpha \leq \frac {1}{2}\), we say (x, y) is an α-balanced pair if α ≤ ?(x ? y) ≤?1 ? α. The 1/3–2/3 Conjecture states that every finite partially ordered set which is not a chain has a 1/3-balanced pair. We make progress on this conjecture by showing that it holds for certain families of posets. These include lattices such as the Boolean, set partition, and subspace lattices; partial orders that arise from a Young diagram; and some partial orders of dimension 2. We also consider various posets which satisfy the stronger condition of having a 1/2-balanced pair. For example, this happens when the poset has an automorphism with a cycle of length 2. Various questions for future research are posed.     

Defect chemistry, surface structures, and lithium insertion in anatase TiO2

Atomistic simulation techniques are used to investigate the defect properties of anatase TiO(2) and Li(x)TiO(2) both in the bulk and at the surfaces. Interatomic potential parameters are derived that reproduce the lattice constants of anatase, and the energies of bulk defects and surface structures are calculated. Reduction of anatase involving interstitial Ti is found to be the most favorable defect reaction in the bulk, with a lower energy than either Frenkel or Schottky reactions. The binding energies of selected defect clusters are also presented: for the Ti(3+)-Li(+) defect cluster, the binding energy is found to be approximately 0.5 eV, suggesting that intercalated Li ions stabilize conduction band electrons. The Li ion migration path is found to run between octahedral sites, with an activation energy of 0.45-0.65 eV for mole fractions of lithium in Li(x)TiO(2) of x < or = 0.1. The calculated surface energies are used to predict the crystal morphology, which is found to be a truncated bipyramid in which only the (101) and (001) surfaces are expressed, in accord with the available microscopy data. Calculations of defect energies at the (101) surface suggest that single Ti(3+) defects and neutral Ti(3+)-Li(+) pairs tend to segregate to the surface.     

Influence of cation on charge recombination in dye-sensitized TiO2 electrodes

The reaction of a dye cation recombining with an electron in TiO(2), in the presence of Li(+), Ca(2+), and TBA(+) cations, was studied with laser-induced transient absorption measurements. The active cations, Li(+) and Ca(2+), shorten the dye cation lifetime on sensitized TiO(2) but not ZnO electrodes. By combining the absorbance measurements of the dye cation with simultaneous measurements of the current transient, the contribution of the recombination reaction to the current is identified. Furthermore, classical porous electrode theory is used to quantify the behavior of the heterogeneous electrode, and in doing so, the processes contributing to photoinduced current are identified as Helmholtz layer charging, porous electrode charging, recombination reactions, and surface diffusion of the active cations. The rate of charge recombination is proportional to the concentration of initially deposited active cations. The effect of water on the recombination rate and the current is also observed.     

Synthesis, characterization, and tunable optical properties of hollow gold nanospheres

Nearly monodisperse hollow gold nanospheres (HGNs) with tunable interior and exterior diameters have been synthesized by sacrificial galvanic replacement of cobalt nanoparticles. It is possible to tune the peak of the surface plasmon band absorption between 550 and 820 nm by carefully controlling particle size and wall thickness. Cobalt particle size is tunable by simultaneously changing the concentration of sodium borohydride and sodium citrate, the reducing and capping agent, respectively. The thickness of the gold shell can be varied by carefully controlling the addition of gold salt. With successful demonstration of ensemble as well as single HGN surface-enhanced Raman scattering, these HGNs have shown great potential for chemical and biological sensing applications, especially those requiring nanostructures with near-IR absorption.     

The negative sign and exponential expressions: Unveiling students’ persistent errors and misconceptions

The purpose of this study was to determine whether or not certain errors made when simplifying exponential expressions persist as students progress through their mathematical studies. College students enrolled in college algebra, pre-calculus, and first- and second-semester calculus mathematics courses were asked to simplify exponential expressions on an assessment. Persistent errors are identified and characterized. Using quantitative and qualitative methods, we found that the concept of negativity played a prominent role in most of the students’ errors. We theorize that an underdeveloped conception of additive and multiplicative inverses is the root of these errors.     

Radial basis function (RBF)‐based parametric models for closed and open curves within the method of regularized stokeslets

The method of regularized Stokeslets (MRS) is a numerical approach using regularized fundamental solutions to compute the flow due to an object in a viscous fluid where inertial effects can be neglected. The elastic object is represented as a Lagrangian structure, exerting point forces on the fluid. The forces on the structure are often determined by a bending or tension model, previously calculated using finite difference approximations. In this paper, we study spherical basis function (SBF), radial basis function (RBF), and Lagrange–Chebyshev parametric models to represent and calculate forces on elastic structures that can be represented by an open curve, motivated by the study of cilia and flagella. The evaluation error for static open curves for the different interpolants, as well as errors for calculating normals and second derivatives using different types of clustered parametric nodes, is given for the case of an open planar curve. We determine that SBF and RBF interpolants built on clustered nodes are competitive with Lagrange–Chebyshev interpolants for modeling twice‐differentiable open planar curves. We propose using SBF and RBF parametric models within the MRS for evaluating and updating the elastic structure. Results for open and closed elastic structures immersed in a 2D fluid are presented, showing the efficacy of the RBF–Stokeslets method. Copyright © 2015 John Wiley & Sons, Ltd.     

Novel tricyclic diamines 2. Synthesis of 1,7-diazaisoadamantane, 1,5-diazaisoadamantane and 1,6-diazahomobrendane

Three novel tricyclic diamines (1,7-diazaisoadamantane, 1,5-diazaisoadamantane and 1,6-diazahomobrendane) were prepared. A flexible synthetic strategy was employed which used flat, aromatic azaindoles as the starting materials. The requisite azaindoles were prepared by a tandem Sonogashira coupling/intramolecular cyclization reaction. Ring saturation, appropriate functionalization and intramolecular alkylation provided the three novel tricyclic diamines cores.