A coupled electron diffraction and rigid unit mode (RUM) study of the crystal chemistry of some zeotypic AlPO4 compounds

Electron diffraction and lattice dynamical calculations are used to investigate the unit cells, space group symmetries and inherent displacive flexibility of the room-temperature average structures of AlPO₄-8, AlPO₄-16 and AlPO₄-tridymite. The zero-frequency rigid unit modes (RUMs) of the idealized high-symmetry polymorphs thereof are also investigated along with their relationship to the lower-temperature polymorphism of these zeotypic aluminophosphates. The clear presence of satellite reflections in addition to the Bragg reflections (G) of the underlying Cmc2₁ parent structure in the case of AlPO₄-8 shows that the true unit cell of the room-temperature polymorph has a doubled c-axis due to a condensed RUM mode. Structured diffuse scattering is also observed which can be related to the thermal excitation of RUM modes. In the case of AlPO₄-tridymite, a complex F1 triclinic polymorph is observed and related to soft RUM modes while, in the case of AlPO₄-16, a soft q=0 RUM mode is shown to be responsible for an observed phase transition in the case of the all SiO₂ analogue of AlPO₄-16. A large number of additional zero-frequency RUM modes also exist in the case of AlPO₄-16.     

Identification of defect sites on oxide surfaces by metastable impact electron spectroscopy

In this review, thin films of SiO₂ on Mo(1 1 2) and MgO(1 0 0) on Mo(1 0 0) have been characterized using metastable impact electron and ultraviolet photoelectron spectroscopies (metastable impact electron spectroscopy (MIES) and ultraviolet photoelectron spectroscopy). The electronic and chemical properties of the thin films are identical to those of the corresponding bulk oxides. For different prepared defective SiO₂ surfaces, additional features are observed in the band-gap region. These features arise from vacancies or excess oxygen and are consistent with theoretical predictions of additional occupied states in the band-gap due to point defects. Extended defect sites on SiO₂ and MgO are identified using MIES by a narrowing of the O(2p) features with a reduction in the density of extended defect sites. MIES of adsorbed Xe (MAX) is also used to estimate the density of extended defect sites. Furthermore, it is shown that CO is an appropriate probe molecule for estimating the defect density of MgO surfaces. Upon Ag exposure, the change in the work function of a low defect MgO(1 0 0) versus a high defect surface is markedly different. For a sputter-damaged MgO(1 0 0) surface, an initial decrease of the work function was found, implying that small Ag clusters on this surface are electron deficient. In contrast, for SiO₂ no significant change of the work function upon Ag exposure with increasing defect density was observed. On MgO(1 0 0), the presence of defect sites markedly alter the electronic and chemical properties of supported Ag clusters. Such a strong influence of defect sites was not found for Ag clusters on SiO₂.     

A modified steepest descent method with applications to maximizing likelihood functions

In maximizing a non-linear function G(), it is well known that the steepest descent method has a slow convergence rate. Here we propose a systematic procedure to obtain a 1–1 transformation on the variables , so that in the space of the transformed variables, the steepest descent method produces the solution faster. The final solution in the original space is obtained by taking the inverse transformation. We apply the procedure in maximizing the likelihood functions of some generalized distributions which are widely used in modeling count data. It was shown that for these distributions, the steepest descent method via transformations produced the solutions very fast. It is also observed that the proposed procedure can be used to expedite the convergence rate of the first derivative based algorithms, such as Polak-Ribiere, Fletcher and Reeves conjugate gradient methods as well.     

Rates of convergence of α-stable random motions

The rate-of-convergence problem in the central limit theorem is considered for -stable distributions on the noncommutative group of motions in ^d. The method used here is based on the theory of probability metrics.     

X-ray spectroscopic characterization of Cu2+-phenanthroline complexes intercalated in α-zirconium phosphate

X-ray photoelectron spectroscopy provides evidence that when [Cu(phen)₂]²⁺(phen = 1,10-phenanthroline) is diffused between the layers of -zirconium phosphate, the complex species does not remain intact after intercalation, but some Cu-N bonds are broken, replaced with Cu-O bonds and the released nitrogen atoms can now interact with the PO₃-OH groups of the host. XPS also provides evidence for coordination of the Cu²⁺ ions when they are diffused by ion exchange in the phenanthroline--zirconium phosphate intercalation compound. Although Cu²⁺ and phen are in a 1 : 1 molar ratio in the interlayer region of the host, so that a 1 : 1 coordination could be expected between the two species, the characteristic peaks of the uncoordinated phenanthroline, even though at a low intensity, are still present. The differences between the two Cu(II)-intercalation compounds are discussed.     

Supercritical Propanol-Water Synthesis and Comprehensive Size Characterisation of Highly Crystalline anatase TiO2 Nanoparticles

Highly crystalline anatase TiO₂ nanoparticles have been synthesised in less than 1 min in a supercritical propanol-water mixture using a continuous flow reactor. The synthesis parameter space (T, P, concentration) has been explored and the average particle size can be accurately controlled within 10-18 nm with narrow size distributions (2-3 nm). At subcritical conditions amorphous products are obtained, whereas a broad range of T and P in the supercritical regime gives 11-14 nm particles. At high temperature and pressure, the particles size increase to 18 nm. The nanoparticles have been extensively characterised with powder X-ray diffraction (PXRD), transmission electron microscopy (TEM) and small-angle X-ray scattering (SAXS) with excellent agreement on size and size distribution parameters. The SAXS analysis suggests disk-shaped particles with diameters that are approximately double the height. For comparison, a series of conventional autoclave sol-gel syntheses have been carried out. These also produce phase-pure anatase nanoparticles, but with much broader size distributions and at much longer synthesis times (hours). The study demonstrates that synthesis in supercritical fluids is a very promising method for manipulating the size and size distribution of nanoparticles, thus removing one of the key limitations in many applications of nanomaterials.     

Degradation in gain for a free electron laser amplifier due to electron momentum spread

A finite spread in axial momentum for the electron beam in a free electron laser amplifier is shown to decrease the small-signal gain. For millimeter and sub-millimeter wave amplifiers, where exponential growth dominates the gain, it is shown that the gain is approximately 3 db below that for a cold beam if the relative momentum spread (u/u)_1/2 = (G_o/248)^1/2 (_o/L), where G_o1 is the gain in db for the cold-beam case, _o is the magnetic wiggler period, and L is the amplifier length. Exact numerical examples are given for representative FEL amplifiers at 35 and 550 GHz.This research was sponsored by the U.S. Office of Naval Research, and by the U.S.-Israel Binational Science Foundation.     

同分布NA列Jamison型加权和强稳定的充要条件

本文将Ｊａｍｉｓｏｎ等（１９６５）关于ｉｉｄ列加权和强稳定的充分性结果推广到ＮＡ列的场合并且得到了ＮＡ列Ｊａｍｉｓｏｎ型加权和强稳定的必要性结果。     

Quantum Information Entropies on Hyperbolic Single Potential Wells

In this work, we study the quantum information entropies for two different types of hyperbolic single potential wells. We first study the behaviors of the moving particle subject to two different hyperbolic potential wells through focusing on their wave functions. The shapes of these hyperbolic potentials are similar, but we notice that their momentum entropy densities change along with the width of each potential and the magnitude of position entropy density decreases when the momentum entropy magnitude increases. On the other hand, we illustrate the behaviors of their position and momentum entropy densities. Finally, we show the variation of position and momentum entropies Sx and Sp with the change of the potential well depth u and verify that their sum still satisfies the BBM inequality relation.     

基于机器学习的直接电离质谱爆炸物检测方法

直接电离质谱系统在现场快速检测中的应用日益广泛,主要用于爆炸物、毒品、食品添加剂等的检测.然而,直接电离质谱系统中质谱信号波动大且同一浓度样品峰强呈现对数正态分布,严重影响了检出限附近低浓度样品的检测准确性.该研究将乙酰水杨酸(115个样品)作为爆炸物模拟物,利用介质阻挡放电离子源与质谱系统,研究了基于机器学习的直接电...