X-ray determination of the mean amplitudes of vibration and debye temperatures of some rare earth monochalcogenides

The x-ray diffraction intensities of Bragg reflections have been measured at room temperature for thulium selenide, samarium sulphide, samarium selenide and samarium telluride. On the basis of a common amplitude approximation, the Debye-Waller factor, the mean amplitude of vibration and the Debye temperature have been evaluated. The values of the Debye temperatures and mean amplitudes of vibration are 176±16°K, 0·185 ± 0·017 Å (TmSe), 155 ± 7°K, 0·244 ± 0·012 Å (SmS), 153 ± 14°K, 0·221 ± 0·020 Å (SmSe) and 151 ± 20°K, 0·204 ± 0·027 Å (SmTe).     

Nanoparticle-Coated Silicon Nanowires

The synthesis of silicon nanowires that are densely coated with silicon nanoparticles is reported. These structures were produced in a two-step process, using a method known as hypersonic plasma particle deposition. In the first step, a Ti–Si nanoparticle film was deposited. In the second step the Ti-source was switched off, and nanoparticle-coated nanowires grew under the simultaneous action of Si vapor deposition and bombardment by Si nanoparticles. Total process time, including both steps, equaled 5 min, and resulted in formation of a dense network of randomly oriented nanowires covering1.5 cm² of substrate area. The nanowires are composed of single-crystal Si. The diameters of the nanowires vary over the range 100–800 nm. Each nanowire has a crystalline TiSi₂ catalyst particle, believed to have been solid during nanowire growth, at its tip.     

Analysis of coefficient identification problems associated to the inverse Euler-Bernoulli beam theory

A rigorous investigation of the identification of a heterogeneousflexural rigidity coefficient in the Euler-Bernoulli steady-statebeam theory in the presence of a prescribed load is presented.Mathematically, this study is an extension to higher-order differentialequations of the coefficient identification problem analysedby Marcellini (1982) for the one-dimensional Poisson equation.In addition, various types of boundary conditions are discussed.Conditions for the well-posedness of these inverse problemsare established and, furthermore, numerical results obtainedusing a regularization algorithm are presented.     

A critical investigation of the effects of the radio frequency potential on the trapping of externally injected ions in ion trap mass spectrometry

The sensitivity of all ion trap mass spectrometry (ITMS) methods is dependent on the trapping efficiency of the instrument. For ITMS instruments utilizing external ion sources, such as laser desorption, trapping efficiency is known to depend on the phase and amplitude of the radio frequency (RF) potential applied to the ring electrode at the time of ion introduction. It is remarkable that, in a considerable body of literature, no consensus exists regarding the effects of these parameters on the efficacy of trapping externally generated ions. In this paper, a summary of the literature is presented in order to highlight significant discrepancies. New laser desorption ion trap mass spectrometry (LD-ITMS) data are also presented, from which conclusions are drawn in our effort to clarify some of the confusion. Copyright 1999 John Wiley & Sons, Ltd.     

On the Galois groups of Legendre polynomials

Ever since Legendre introduced the polynomials that bear his name in 1785, they have played an important role in analysis, physics and number theory, yet their algebraic properties are not well-understood. Stieltjes conjectured in 1890 how they factor over the rational numbers. In this paper, assuming Stieltjes’ conjecture, we formulate a conjecture about the Galois groups of Legendre polynomials, to the effect that they are “as large as possible,” and give theoretical and computational evidence for it.     

Purity analysis of hydrogen cyanide, cyanogen chloride and phosgene by quantitative (13)C NMR spectroscopy

Hydrogen cyanide, cyanogen chloride and phosgene are produced in tremendously large quantities today by the chemical industry. The compounds are also particularly attractive to foreign states and terrorists seeking an inexpensive mass-destruction capability. Along with contemporary warfare agents, therefore, the US Army evaluates protective equipment used by warfighters and domestic emergency responders against the compounds, and requires their certification at > or = 95 carbon atom % before use. We have investigated the (13)C spin-lattice relaxation behavior of the compounds to develop a quantitative NMR method for characterizing chemical lots supplied to the Army. Behavior was assessed at 75 and 126 MHz for temperatures between 5 and 15 degrees C to hold the compounds in their liquid states, dramatically improving detection sensitivity. T(1) values for cyanogen chloride and phosgene were somewhat comparable, ranging between 20 and 31 s. Hydrogen cyanide values were significantly shorter at 10-18 s, most likely because of a (1)H--(13)C dipolar contribution to relaxation not possible for the other compounds. The T(1) measurements were used to derive relaxation delays for collecting the quantitative (13)C data sets. At 126 MHz, only a single data acquisition with a cryogenic probehead gave a signal-to-noise ratio exceeding that necessary for certifying the compounds at > or = 95 carbon atom % and 99% confidence. Data acquired at 75 MHz with a conventional probehead, however, required > or = 5 acquisitions to reach this certifying signal-to-noise ratio for phosgene, and >/= 12 acquisitions were required for the other compounds under these same conditions. In terms of accuracy and execution time, the NMR method rivals typical chromatographic methods.