Average electron momenta in many-electron atoms

In many-electron atoms, the average electron momentum p represents the mean momentum of a single electron when all the electron motions are averaged. If any two electrons are considered simultaneously, however, the average momentum p splits into two different momenta, low momentum p_< and high momentum p_>. For the 102 atoms He through Lr in their ground states, the momenta p_< and p_> are systematically examined at the Hartree–Fock limit level. It is also shown that the sum p_>+p_< and the difference p_>–p_< of the two momenta constitute upper and lower bounds to the electron-pair relative momentum p₁₂=|p₁–p₂| and to the electron-pair center-of-mass momentum P=|p₁+p₂|/2. The tightness of the bounds is discussed for the 102 atoms.     

Approximate upper bounds to the momentum expectation value ratios 〈p 2〉/〈p −1〉 and 〈p〉/〈p −1〉 in atoms

Within an isoelectronic series of atoms, reasonably tight upper bounds on the ratios of the momentum expectation values ;p ²/;p ^–1 and p/p ^–1 respectively have been derived for the first time by using the Dresher's inequality.     

Critical discussion of simple adsorption methods used to evaluate the micropore size distribution

The well-known simple adsorption methods used to evaluate the micropore size distribution from low pressure adsorption isotherms were examined by employing model isotherms for slit-like graphite micropores obtained from nonlocal density functional theory. It was shown that in the range of pore sizes from about 0.4 to 0.9 nm, the Horvath Kawazoe (HK) method satisfactorily reproduces the shape of the micropore size distribution, but the pore sizes are underestimated. In the case of micropores wider than 0.9 nm, the method fails as the formation of the monolayer on the pore walls produces a peak corresponding to 0.6 nm micropores on the HK pore size distribution. Therefore, the HK method indicates the presence of microporosity even for nonporous samples. The Dubinin-Astakhov adsorption isotherms were also examined and it was shown that their application to represent local adsorption isotherms for homogeneous pores is questionable. However, the adsorption potential distributions seem to be promising for micropore analysis.Nomenclature A Adsorption potential kJ/mol - C ₁ Constant in Eq. 3 and 4 kJ * nm/mol - C ₂ Constant in Eq. 3 and 4 nm³ - C ₃ Constant in Eq. 3 and 4 nm⁹ - C ₄ Constant in Eq. 3 and 4 - d Adsorbate molecule diameter nm - d _A Adsorbent atom diameter nm - G Change in the Gibbs free energy kJ/mol - J Pore size distribution cm³/(g*nm) - R The universal gas constant = 8.31431 J/(mol * K) - T Absolute temperature K - V Amount adsorbed expressed in cm³ of liquid adsorbate per 1 g of the adsorbent = 0.0015468 * amount adsorbed expressed in cm³ STP/g cm³/g - x Pore width nm - X Differential adsorption potential distribution cm³ * mol/(g*kJ) - Constant defined as nm - p Pressure Pa - p ₀ Saturated pressure = 760 torr = 101325 Pa Pa - P _c Condensation pressure Pa - Degree of pore filling - S _BET BET specific surface area m²/g - S _ex External surface area obtained fromt-plot method m²/g - V _mi Micropore volume obtained fromt-plot method cm³/g - V ₁ Total pore volume cm³/g - E Characteristic energy in the Dubinin-Astakhov equation kJ/mol - n Exponent in the Dubinin-Astakhov equation      

Zur Totalsynthese von Human-Sekretin

Summary The synthesis of the heptacosapeptide amide with the primary structure of Human-secretin is described. For this purpose 7 fragments were designed, i.e. H-Gly-Leu-Val-NH₂ 25–27b,Z-Arg(Z ₂)-Leu-Leu-Gln-OH 21–24,Z-Arg(Z ₂)-Leu-Gln-OH 18–20,Z-Arg(Z ₂)-Glu(OtBu)-Gly-Ala-OH 14–17,Z-Arg(Z ₂)-Leu-OH 12–13,Z-Thr(tBu)-Ser(tBu)-Glu(OtBu)-Leu-Ser(tBu)-OH 7–11,Adoc-His(Adoc)-Ser(tBu)-Asp(OtBu)-Gly-Thr(tBu)-Phe-OH 1–6 these fragments were consequently assembled to the overall protected total sequence using the Wünsch/Weygand-method with dicyclohexylcarbodiimide. After deprotection by exposure to trifluoroacetic acid in presence of 1,2-ethanedithiol and water as scavenger, the isolated crude product was purified by column chromatography on CM-Sepharose, fast flow. This synthetized Human-secretin showed the full biological activity in comparison to Porcine-secretin.

Herrn Prof. Dr. E. Bayer zum 65. Geburtstag gewidmet.     

Two-electron atomic wave functions which satisfy proportionality relations between one-and two-electron moments

Based on momentum- and position-space analyses of the moment operators for two-electron atoms, it is shown that there exists a family of two-electron wave functions which satisfy a proportionality relation, r/ ₁ ^v /r ₁₂ ^v =p/ ₁ ^v /p ₁₂ ^v =2^–v/2, between the one and two-electron moments in position and momentum spaces, where v is an arbitrary number for which the moments are well-defined.     

Excited state wave functions

Wave functions and energies were calculated for the 2s, 3p ₀, and 4d ₀ states of the hydrogen atom using the Messmer and Rayleigh-Ritz variational methods with minimization of the second eigenvalue. The wave functions were linear expansions of Gaussian functions and both linear and exponential parameters were varied. Except for the two term expansions, calculated values of the energies and expectation values, r ^–1, r and r ² were within two percent of the true values for both methods.     

Upper Bound to the Expectation Value of the Squared Hamiltonian

An upper bound to the expectation value of the squared Hamiltonian H ² is derived which relies on replacing products of certain operators with products of the matrix representations of said operators to reduce the computational demands of H ². An example is given which shows the strength of the bound and an application with the Temple lower bound is shown.     

Comparison of the crystal structures of Co2(X 2O7)·2H2O,X=P and As

Summary Crystals of Co₂(X ₂O₇)·2H₂O,X=P/As were synthesized under hydrothermal conditions. Their crystal structures were determined by single crystal X-ray diffraction:a=6.334(1)/6.531(2),b=13.997(2)/14.206(4),c=7.637(1)/7.615(2)Å, =94.77(2)/94.74(2)°, space group P2₁/n,R=0.032/0.046,R _w=0.028/0.034 for 2423/2042 reflections and 131/119 variables. Within the twoXO₄ tetrahedra connected via a common corner to anX ₂O₇ group the average P-O bond lengths are approximately equal (1.540 and 1.543 Å), but As-O differs significantly (1.685 and 1.696 Å). A comparison with the isotypic Mn and Mg pyrophosphates shows a correlation between the ratio Me-O/X-O and the angle O-X-O.

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Vergleich der Kristallstrukturen von Co₂(X ₂O₇)·2H₂O,X=P und As

Zusammenfassung Kristalle von Co₂(X ₂O₇)·2H₂O,X=P/As wurden unter Hydrothermalbedingungen synthetisiert. Ihre Kristallstrukturen wurden mittels Röntgenbeugung an Einkristallen bestimmt:a=6.334(1)/6.531(2),b=13.997(2)/14.206(4),c=7.637(1)/7.615(2) Å, =94.77(2)/97.74(2)°, Raumgruppe P2₁/n,R=0.032/0.046,R _w=0.028/0.034 für 2423/2042 Reflexe und 131/119 Variable. In den beiden über eine gemeinsame Ecke zuX ₂O₇-Gruppen verknüpftenXO₄-Tetraedern sind die mittleren P-O-Abstände ungefähr gleich (1.540 und 1.543 Å), hingegen differiert As-O signifikant (1.685 und 1.696 Å). Ein Vergleich mit den isotypen Mn- und Mg-Pyrophosphaten zeigt eine Korrelation zwischen dem Quotienten Me-O/X-O und dem WinkelX-O-X.

     

Microwave Spectrum and Dipole Moment of 1,3‐dioxolane in the Hindered‐Pseudorotation States v = 0, 1, 2, and 3

The microwave spectrum of 1,3dioxolane (C₃H₆O₂) in the ground and first three excited states of hindered pseudorotation was studied. The transitions corresponding to the _b, _c, and _a components of the dipole moment were identified. The spectrum was analyzed using numerical diagonalization of the effective rotational Hamiltonian for four interacting states of hindered pseudorotation. The rotational constants, centrifugal distortion constants, the constants of interaction between general rotation and hindered pseudorotation, and the distances between the quasidegenerate vibrational levels ₀₁ = 64840.5, ₁₂ = 122231.7 and ₂₃ = 119732.7 MHz are determined. From the Stark effect of microwave transitions, the dipole moment components (in Debye units) in the hinderedpseudorotation states v = 0, 1, 2, and 3 are determined: 0|_b|0 = 1|_b|1 = 1.22, 2|_b|2 = 1.20, 3|_b|3 = 1.21, 0|_c|1 = 0.77, 2|_c3 = 0.66, and 1|_a|2 = 0.19.     

Investigations on microstructure, composition and properties of PECVD TiNx-coatings

Nearly stoichiometric TiN_x-coatings have been deposited on different substrates using a gaseous reaction mixture of TiCl₄, N₂, H₂ and Ar in a pulsed d.c. plasma discharge. The influence of substrate temperature, plasma power density, argon partial pressure and type of substrate on chlorine content, texture and microstructure of the coatings has been investigated keeping constant the other parameters of the plasma enhanced chemical vapor deposition (PECVD) process. Microstructure has been characterized by scanning electron microscopy (SEM) fractographs of the coatings and by determination of texture. The chlorine content quantitatively determined from energy-dispersive X-ray spectra (EDX) using a chlorine containing mineral as standard decreases on an increase of substrate temperature or plasma power density. Texture changes from 200 to 111 and random and microstructure changes from columnar growth to granular for decreasing substrate temperature as well as decreasing plasma power density. Argon partial pressure does not affect the microstructure but the texture. The properties of the coatings are independent of type of substrate for higher plasma power densities. Oxygen present at the surface of the substrate stimulates the development of a texture at low plasma power densities.     

Critical behavior and interfacial tension of mixtures of propylene glycol and ethylene glycol oligomers

This investigation presents an analysis of the critical behavior of mixtures of oligomers of propylene glycol, PG₁₇, and ethylene glycol, EG_n, withn=3, 4, 5, 6.4, 8.7, 12.1 and 22.1. The critical coordinates, _c andT _c were determined from the phase diagrams. The critical compositions compare very well with the Huggins-Flory predictions. The interaction parameter _n is around one for EG₃, EG₄ and EG₅ and it increases up to two for the higher oligomers. The break in the interaction parameter also corresponds to a minimum in the critical temperature. The phase diagrams and the interfacial tension were used to get the critical exponents and , respectively. The data were analysed with two approaches. First, from the temperature dependence of the length of the tie-lines and of the interfacial tension up to the upper critical solution temperature, UCST. Second, with the data at 30°C using the critical temperature of the systems as the variable. The first method led to =0.39±0.05 in good agreement with the result of the second method, =0.37±0.04. The exponents for the interfacial tension, , determined with the first method for PG₁₇ with EG_6.4, EG_8.7 and EG_12.1 are =1.66±0.11, 1.46±0.25 and 1.73±0.18, respectively. The second method led to =1.17±0.14. The critical exponents are compared to mean field and ising-3D predictions.     

Upper bounds to atomic electron densities in position and momentum spaces

Modified functions r ^–(r) and p ^–(p) of the spherically averaged electron densities (r) in position space and (p) in momentum space are found to be convex (i.e., the second derivatives are nonnegative everywhere) for all the 103 ground-state atoms from hydrogen (atomic number Z=1) to lawrencium (Z=103), if the parameters are chosen to be 0.6 and 1.4. The convex property of r ^–(r) and p ^–(p) is used to derive upper bounds to the density functions (r) and (p) in terms of their radial moments r ^s and p ^s or frequency moments ^t and ^t . In most cases, the present bounds are shown to be more general and more accurate than those reported in the literature.     

Crystal structure, morphology and composition of magnetron sputtered tungsten carbide films

Summary It is shown that small variations of the deposition parameters during magnetron sputtering of tungsten carbide thin films may result in drastic changes of film properties. An increasing working gas pressure for example lowers stress and hardness values. Simultaneously, the texture of the WC_1–x cristallites turns from 200 preferential orientation to 111, whereas the composition of the films does not change. In reactive sputtering with a tungsten target there is a narrow range from 2 to 3% C₂H₂ gas admixture to the working gas where the films are stochiometric (WC) and hard, and grain size and morphology are similar to that of non-reactively sputtered films. The generation of different crystallite structures and orientations in the range of 0–3% C₂H₂ admixtures are used to produce a multiphase thin film with extremely low crack propagation.     

Coordination of Heterovalent Iron Atoms in SrCo1 – yFeyO3 – zSolid Solutions

Mössbauer spectroscopy was used to study hyperfine interactions on ⁵⁷Fe nuclei of SrCo_{1 – y} Fe _y O_{3 – z} solid solutions (0.2 y 0.8). The ⁵⁷Fe spectra measured in the paramagnetic temperature range look like a superposition of two quadrupole doublets whose parameters correspond to high-spin Fe⁴⁺cations ( = 0.1 mm/s; = 0.4 mm/s) in the anion surrounding with coordination number 5 (tetragonal pyramid) and to Fe³⁺cations ( = 0.3 mm/s; = 0.4 mm/s) in the distorted octahedral environment. The relative number and pattern of distribution of heterovalent cations (Co⁴⁺, Co³⁺, Fe⁴⁺, and Fe³⁺) in the B-sublattice of perovskites were determined. The values of the electronic exchange constants in the solid solutions obtained through Mössbauer spectroscopy were compared with those obtained from thermodynamic calculations. The oxygen penetration in perovskites was found to depend on their composition and structure.     

Fonctions autocohérentes et intégrales radiales pour les ions de la série du fer

The radial integrals 3d¦r ^k ¦3d, k=–3, –1, 2, 4 and 4p¦r ^k ¦3d, k= 1, 3 for first-row transition-metal ions have been computed from analytical self-consistent field wave functions. The expressions 4p¦r ^k ¦3d allow to compute the oscillator strengths of dipolar electric transitions for an trapped in a crystalline matrix iron group ion. Les intégrales 3d¦r ^k ¦3d, k=–3, –1, 2, 4 et 4p¦r ^k ¦3d, k=1, 3, relatives aux ions de la première série de transition, sont calculées à l'aide de fonctions radiales _3d et _4p , autocohérentes. Les expressions 4p¦r ^k ¦3d permettent d'évaluer les forces d'oscillateur de transitions dipolaires électriques relatives à un ion du groupe du fer engagé dans une matrice cristalline.     

Shear-induced deformation of polystyrene coils in dilute solution from small angle neutron scattering 2. Variation of shear gradient,molecular mass and solvent viscosity

The technique of small angle neutron scattering (SANS) has been used to study the conformation of polystyrene chains in dilute solution under a constant shear gradient. The experiments reveal a distinct anisotropy of the molecular dimensions with regard to the directions parallel and perpendicular to the flow direction on the 2D-multidetector. The deformation ratio of the single polymer chain (R ²/R _iso ² )–1 as a function of the reduced shear gradient=([] · · M _w G)/RT shows a transition from the ideal ²-behaviour for dynamic infinitely flexible coils found at small gradients, to a behaviour with smaller increase at larger. These results are qualitatively consistent with the theory of Cerf for a polymer with finite internal viscosity in a shear gradient. At low(<1), a better agreement with the model of a free-draining coil (Rouse behaviour) than with the Zimm model is observed.     

Influence of hydrogen on surface conductivity of polycrystalline zinc oxide

The effect of hydrogen adsorption on the surface conductivity of polycrystalline zinc oxide has been examined. The conductivity changes during adsorption obey the Zeldovich-Roginsky equation.

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Vibrational relaxation by collision in polyatomic molecules

A model of a harmonic oscillator with friction is used to discuss the conversion of translational energy to vibrational by collision of an atom with a polyatomic molecule. It is shown that adiabatic conversion implies that E ² may substantially exceed the value calculated, neglecting the interaction of the bond with the rest of the molecule.     

Sedimentation equilibrium of suspensions of colloidal particles at finite concentrations

Equilibrium concentration profiles of non-dilute colloidal suspensions are calculated by means of the Carnahan-Starling expression for the osmotic compressibility of hard sphere liquids. The profiles depend on the average volume fraction of the suspension, , and on the field interaction parameter, ₀ (reciprocal of the Péclet number at infinite dilution). Profiles are computed for values of and ₀ typical of those encountered in sedimentation field-flow fractionation experiments. It is found that, in most cases, the volume fraction at the depletion wall is negligibly small and that the volume fraction at the accumulation wall ₀, depends on the ratio <>₀/₀ only. An inflexion point is found in the concentration profile if ₀ is larger than 0.13 whatever the value of ₀.     

Zur Kristallographie der Gleitverformung von Wolfram-Einkristallen im Zugversuch

Zusammenfassung Mittels einer speziellen Methode wurden spannungsfreie Wolfram-Einkristall-Zugproben verschiedener Orientierung im Elektronenstrahl-Zonenschmelzofen nach dem floating-zone-Verfahren hergestellt und nachfolgend auf einer Instron-Universalprüfmaschine im Zugversuch bei etwa 2,4%/Min. Dehnungsgeschwindigkeit verformt. Die erhaltenen Spannungs-Dehnungs-Diagramme zeigen eine starke Abhängigkeit des mechanischen Verhaltens der Einkristalle von der jeweiligen Kristallorientierung. Da die beobachteten Gleitspuren an der Oberfläche der Kristalle ausnahmslos als zu {110}-Ebenen gehörend indiziert werden konnten, wurde versucht, für die wirksamen {110}111-Gleitsysteme das kritische Schubspannungsgesetz anzuwenden. Auf Grund der auftretenden Diskrepanz zwischen den zu erwartenden und den tatsächlich gemessenen Spannungswerten bei der Proportionalitätsgrenze wird eine Interpretation des orientierungsabhängigen Abgleitverhaltens bei Wolfram gegeben.

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The crystallography of tungsten single crystal slip deformation in the tensile test

Strain-free tungsten single crystal tensile test specimens of various orientations were grown in an electron beam zone melting furnace using the floating zone method. The specimens were deformed under tension at a stretching rate of approx. 2.4%/min in an Instron Universal Testing Machine. Stress-strain curves show a strong dependence of the mechanical behaviour of the single crystals upon crystal orientation. As the observed slip traces on the surface of the crystals could only be indexed as belonging to {110} slip planes, the critical resolved shear stress law was applied to the active {110} 111 slip systems. In view of the inconsistencies of the measured proportional-limit stresses with the expected values for the different orientations an interpretation of the orientation-dependent slip mechanism for tungsten is proposed.

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Mit 9 Abbildungen