The self-consistent response of the electron density of a crystal copper film to an external electrostatic field

The response of the electrons of an fcc copper (001) film to an external electrostatic field is calculated. In order to determine the distribution of the screening charge, the equations of the electron density-functional theory are solved self-consistently by an original method. The position of the “image plane,” which is involved in a correct asymptotic expression for the exchange-correlation potential in the vacuum region, is first determined when performing a quantum-mechanical calculation for an anisotropic crystal film. The nonlinear electron response is characterized by the evolution of the “center of gravity” of the induced charge, which is also investigated. The calculations take into account the crystal structure of the film, and the results differ essentially from the predictions of the “jelly” model.     

Photorefractive properties of Cr-doped Sr0.61Ba0.39Nb2O6 related to crystal purity and doping concentration

The purity and the concentrations of the constituents Sr, Ba, Nb and Cr were determined in single crystals of chromium-doped Sr_0.61Ba_0.39Nb₂O₆ (SBN) by instrumental neutron activation analysis (INAA) and X-ray fluorescence analysis (XRF). Experiments with different Cr concentrations C_Cr reveal constant Sr and Ba concentrations as well as a decreasing Nb concentration with an increasing C_Cr. Therefore, Cr is incorporated at Nb lattice sites. The distribution coefficient of Cr is 1.2 between 100 and about 7000 ppm Cr and 1 above. From measurements of the holographic two-beam coupling gain Γ for different C_Cr, we deduced response times for the buildup of holographic gratings. The saturation value of Γ depends in a nonlinear manner on C_Cr and reaches its maximum at about 6000 ppm Cr. The inverse photorefractive response time of the grating erasure depends linearly on the erasure intensity for all doping concentrations. Thus a one-center model can be assumed for the charge transport in SBN:Cr. Received: 8 December 2000 / Revised version: 23 January 2001 / Published online: 21 March 2001     

A Phosphinine-Derived 1-Phospha-7-Bora-Norbornadiene: Frustrated Lewis Pair Type Activation of Triple Bonds

Salt metathesis of 1-methyl-2,4,6-triphenylphosphacyclohexadienyl lithium and chlorobis(pentafluorophenyl)borane affords a 1-phospha-7-bora-norbornadiene derivative 2 . The C≡N triple bonds of nitriles insert into the P−B bond of 2 with concomitant C−B bond cleavage, whereas the C≡C bonds of phenylacetylenes react with 2 to form λ⁴-phosphabarrelenes. Even though 2 must formally be regarded as a classical Lewis adduct, the C≡N and C≡C activation processes observed (and the mild conditions under which they occur) are reminiscent of the reactivity of frustrated Lewis pairs. Indeed, NMR and computational studies give insight into the mechanism of the reactions and reveal the labile nature of the phosphorus–boron bond in 2 , which is also suggested by detailed NMR spectroscopic studies on this compound. Nitrile insertion is thus preceded by ring opening of the bicycle of 2 through P−B bond splitting with a low energy barrier. By contrast, the reaction with alkynes involves formation of a reactive zwitterionic methylphosphininium borate intermediate, which readily undergoes alkyne 1,4-addition.     

Non-commutative generalization of integrable quadratic ODE systems

Letters in Mathematical Physics - We find all homogeneous quadratic systems of ODEs with two dependent variables that have polynomial first integrals and satisfy the Kowalevski–Lyapunov test....     

Tandem Use of Optical Sensing and Machine Learning for the Determination of Absolute Configuration,Enantiomeric and Diastereomeric Ratios,and Concentration of Chiral Samples

We have developed an optical method for accurate concentration, er, and dr analysis of amino alcohols based on a simple mix‐and‐measure workflow that is fully adaptable to multiwell plate technology and microscale analysis. The conversion of the four aminoindanol stereoisomers with salicylaldehyde to the corresponding Schiff base allows analysis of the dr based on a change in the UV maximum at 420 nm that is very different for the homo‐ and heterochiral diastereomers and of the concentration of the sample using a hypsochromic shift of another absorption band around 340 nm that is independent of the analyte stereochemistry. Subsequent in situ formation of Cu^II assemblies in the absence and presence of base enables quantification of the er values for each diastereomeric pair by CD analysis. Applying a linear programming method and a parameter sweep algorithm, we determined the concentration and relative amounts of each of the four stereoisomers in 20 samples of vastly different stereoisomeric compositions with an averaged absolute percent error of 1.7 %.     

Piezoelectric transducer vibrations in a one-dimensional approximation

Summary The theory of piezoelectric transducer vibrations, which may be treated as onedimensional, is developed in detail for thin discs vibrating in a pure thickness extensional mode. An effort has been made to obtain relations of general validity, which include losses, and which are in a simple explicit form convenient for practical calculations. The behaviour of transducers is discussed with special attention to their characteristics at the two fundamental frequencies, the so-called parallel and series resonances. Several peculiarities occur when transducers are coupled to media with considerably different acoustic impedances. These peculiarities are discussed and illustrated by numerical results for quartz and PZT 4 piezoelectric discs radiating into water, air and liquid hydrogen. The application of the theory to different types of vibrations is briefly illustrated for thin bars vibrating longitudinally. Short discussions are included on compound transducer systems, and on the properties of thin discs as receivers.     

Kripke, Putnam and the introduction of natural kind terms

In this paper, I will outline some of the important points made by Kripke and Putnam on the meaning of natural kind terms. Their notion of the baptism of natural kinds- the process by which kind terms are initially introduced into the language — is of special concern here. I argue that their accounts leave some ambiguities that suggest a baptism of objects and kinds that is free of additional theoretical commitments. Both authors suggest that we name the stuff and then let the scientists tell us what properties it really has, and hence what the real meaning is. I contend that such a barren baptism, taken at face value, cannot succeed in the semantic roles it has been assigned and that softening the stance on baptism suggests a more subtle and complex relation between reference and theoretical commitment than has emerged thus far.     

GaN/LiNbO3 (0 0 0 1) interface formation calculated from first-principles

The stable adsorption sites for both Ga and N ions on the ideal and on the reconstructed LiNbO₃ (0 0 0 1) surface are determined by means of first-principle total energy calculations. A single N layer is found to be more strongly bound to the substrate than a single Ga layer. The adsorption of a GaN monolayer on the polar substrate within different orientations is then modeled. On the basis of our results, we propose a microscopic model for the GaN/LiNbO₃ interface. The GaN and LiNbO₃ (0 0 0 1) planes are parallel, but rotated by 30° each other, with in-plane epitaxial relationship [1 0 0]_GaN‖ [1 1  0]_LiNbO3. In this way the (0 0 0 1) plane lattice mismatch between GaN and LiNbO₃ is minimal and equal to 6.9% of the GaN lattice constant. The adsorbed GaN and the underlying LiNbO₃ substrate have parallel c-axes.