Band 23, Heft 4

Für alle Moleküle und Ionen des Typs XY 4 mit D 4h -Symmetrie, von denen Frequenzdaten bekannt sind, werden Kraftkonstanten, mittlere Schwingungsamplituden und Coriolis-Kopplungskonstanten berechnet. Es ergibt sich, daß die Coriolis-Kopplungskonstanten eine eindeutige Massenabhängigkeit zeigen.

Die Verteilung der Ladungsträger über den Querschnitt eines in bezug auf Elektronen und Löcher symmetrisch angenommenen, stromdurchflossenen Halbleiterdrahtes wird analytisch berechnet. Zugleich lassen sich Magnetfeld und Temperatur analytisch und graphisch ausdrücken. Dabei wurden die Rekombination der Ladungsträger, das eigene Magnetfeld des Stromes sowie die Wärmeleitung mit in Betracht gezogen. Die hier erzielte Näherung ist gerade im Fall großer Rekombinationsgeschwindigkeit und hoher Beweglichkeiten anwendbar, in dem andere analytische Lösungsmethoden nicht den Voraussetzungen entsprechen. Man bemerkt einen Anstieg der Trägerkonzentration an der Zylinderachse, dem aber die Rekombination dämpfend entgegenwirkt.

The absorption band spectrum of fluorine has been observed in the extreme vacuum ultraviolet using the Hopfield continuum as light source. The spectrum was photographied by means of a 3 m Hilger normal incidence spectrograph fitted with a differential pumping system. From a rapidly converging v′-progression of bands at 877-857 Å the dissociation energy of the F 2 -molecule in the groundstate has been established as (1.44 ± 0.07) eV. In connection with the emission band spectrum of F 2 in the visible it has been possible to determine the states of the participating transitions in the ultraviolet as well as in the visible region.

The atomic distribution curve of molten Sn was determined in the temperature range from 226 °C (supercooled melt) to 1140 °C. The interatomic distance in the first coordination sphere is 3.14 A and the corresponding coordination number is 5.8. The short range order at all temperatures is closely related to that of tetragonal white tin. At high temperatures the distribution becomes less ordered and approaches that of hard spheres. The degree of short range order does not seem to affect the electrical conductivity. The existance of a mesomeric bonding system is evidently more important for the conductivity than a periodic arrangement of the atoms.

The self-diffusion coefficients of both ions in molten zinc chloride have been measured with the porous-frit technique 1-3 . The result can be described with Arrhenius equations: where D is expressed in cm 2 s -1 , R in cal mole -1 degree -1 , and T in degrees Kelvin. A comparison is made with earlier data by BOCKRIS et al. 4 and an attempt is made to correlate the experimentally observed external transport number 5 and the corresponding calculated quantity 6,7 .

Es wird eine neue Diffusionsmethode angegeben, die darauf beruht, daß sich bei pulsierender Flüssigkeitsströmung in einem porösen oder lamellerten Diaphragma an den Poren- bzw. Lamellenwänden sehr stabile Flüssigkeitsschichten ausbilden, die, in wechselnder Richtung von sehr unterschiedlich konzentrierten Lösungen bespült, hohe Konzentrationsgradienten bei großen Austauschflächen zulassen. Bei geeigneter Anordnung kann der Stofftransport um mehrere Zehnerpotenzen gegenüber den bekannten Anordnungen gesteigert werden bei gleichzeitig sehr erheblich verminderten konvektiven Störungen.

Es wird das elektrische Potential einer Punktladung berechnet, die sich in einem Medium mit einem Gradienten der Dielektrizitätskonstanten befindet. Das Potential läßt sich mit einer Integral- oder Reihendarstellung angeben.

The dynamic fluorine polarization by the Overhauser effect has been studied at four different magnetic field values and at various temperatures in several fluorocarbon solutions. The importance of intermolecular contact couplings is very sensitively dependent on the chemical environment of the fluorine nuclei. The experimental data are interpreted in terms of the stochastic “pulse model” of molecular collisions derived in a preceding paper. The parameters of the model, such as the relative contribution of scalar couplings, the shape and the time scale of collision pulses and the correlation times of the molecular motion are given explicitly for six fluorocarbon solutions of free radicals.

In the convergent cylindrical shock wave of a Z-pinch discharge (diameter/length ratio : 44 cm per 10 cm), magnetic probe measurements have been made of the current density and the velocity of the current sheet. For discharges in Helium, Argon and Krypton at mass densities from 2.2·10 -7 to 5.5·10 -6 g/cm 3 one finds: 1. Only a small portion of the total current contracts with the shock wave. The direction of this current is maintained even when the total current reverses. 2. The gas pressure behind the shock front is a constant for each gas independent of the filling pressure. 3. At small radii the contraction is determined by the inertia of the moving plasma only. 4. With higher filling pressures a considerable part of the small contracting current flows ahead of the shock front.

The remission spectra of a number of Cu 2+ -containing oxidic solids in the region between 3500 and 25 000 cm -1 were found to show always — independent of the macroscopic lattice-symmetry — the typical three-band-structure expected for tetragonally distorted octahedra. It could be derived from the spectra of the perovskite-mixed-crystals Sr 2 (Cu χ Zni _ x Me)O 6 [Me=W 6+ , Te 6+ ] (0<χ≦1) hat these three bands have to be assigned to the transitions B 1g → A 1g , -→ B 2g and → Eg with increasing energy. A crystal field formalism is developed, which allows a quantitative treatment of the spectra in correspondence with crystallographic data. The calculated ligand-field-parameters Δ do not differ much from those of Ni 2+ and Co 2+ in the same host lattices.

Starting from bulk single crystals, tellurium has been prepared for transmission electron microscopy. The foil orientation was {101̅0} , two planes of the reciprocal lattice being projected into the electron diffraction image plane. Dislocations and small angle grain boundaries were observed and could be explained by considering glide on {101̅0} and (0001). Hints for a “rhombohedral” view of the tellurium lattice were found.

Es wird über Elektronen-Feinbereichsbeugung an Quarzeinkristallsplittern berichtet. Beobachtet wurde eine ringförmige Anordnung von Reflexen. Die auftretenden verbotenen Reflexe werden diskutiert.

Es werden die systematischen und statistischen Fehler bei der Ermittlung der Kristallitvolumina nach STEPHEN und BARNES sowie nach EBEL behandelt. Außerdem wird eine vereinfachte Variante der erstgenannten Methode, welche im Gegensatz zu dieser nur eine Aufnahme erfordert, aufgezeigt. Aus einer Gegenüberstellung der drei Verfahren ergeben sich ihre zweckmäßigen Anwendungsbereiche. Zahl und Schwärzung der Interferenzpunkte auf einem Debye-Scherrer-Kreis gestatten eine Bestimmung des mittleren Kristallitvolumens, sowie der Halbwertsbreite der Volumsverteilung der kohärent streuenden Gitterbereiche in dem vom einfallenden Röntgen-Strahlenbündel erfaßten Probenvolumen. Ein Vergleich der Verfahren sowie eine Erörterung der Fehlermöglichkeiten ist Gegenstand der folgenden Betrachtungen.

The intensity weighted mean over the nuclear quadrupole hyperfine structure multiplet of a molecular rotational transition yields, to first order, the “undisturbed” rotational transition frequency. This fact may serve to effectively separate the two interrelated problems of calculating the rotational constants of the molecule from the “undisturbed” frequencies and the nuclear quadrupole coupling parameters from the multiplet splitting patterns.

Strong interacting wave fields in a wedge-shaped crystal are separated into different plane waves when leaving the crystal and reveal points on the dispersion surface. By rotating the crystal while moving the film one obtains a photographical record of a section through the dispersion surface which may be compared with theory. An experiment with a macroscopic MgO wedge is reported. The 002 interference with excitation error nearly zero was recorded near the [I10] zone axis while rotating the crystal about the [001] axis. The diagrams are compared with dynamical 17-beam calculations. The results show that a reduction of the infinite dynamical system of equations to 17 equations is correct under these special geometrical conditions.

Die Spektren der Elektronenspinresonanz des Kupfer-Natrium-Chlorophyllins in Methanol zeigen eine Hyperfeinstruktur vom Kupferkern und eine Superhyperfeinstruktur von vier Stickstoffkernen am Porphyrinring. Bei Raumtemperatur findet man mit g 0 =2,1077, A 0 Cu =- 98 · 10 -4 und A 0 N = -14·10 -4 cm -1 ein anderes Spektrum als bei 77 °K mitg∥= 2,2033, g⟂=2,0518, A ∥ Cu = -205·10 -4 cm -1 , A ⟂ Cu ∼ - 30 · 10 -4 cm -1 , A ∥ N = -15,9 · 10 -4 cm -1 . Durch die Verknüpfung dieser Meßwerte mit den Koeffizienten für die Linearkombination der Atomeigenfunktionen, die die chemische Bindung in Kupferkomplexen beschreiben, erhält man für die dσ-Bindung α=0,91 und α′=0,51. Zur Berechnung der Linearkoeffizienten für die dπ-Bindung in der Porphyrinebene (β) und außerhalb dieser Ebene (δ) wurde aus den optischen Messungen ΔE xy und ΔΕ xy erhalten und mit diesen Werten aus den ESR-Spektren β=0,81 und δ=0,85 berechnet. Hiermit ist in Cu-Chlorophyllin die da-Bindung stark ionisch, die dπ-Bindung ebenfalls, jedoch senkrecht zur Porphyrinebene stärker ionisch als in der Porphyrinebene.

In solids containig spins I=1/2 only, the NMR-transients in solids are given approximately by formulas derived earlier 1 . They can be extended to solids with a second, but nonresonant kind of spins S using a simple substitution. The results are exact to second order in the pulse distances and include the dependences of the signal amplitudes on experimental parameters e. g. pulse lengths etc. If the phases of the modulation of two 90°-pulses differ by 0° or 90°, a calculation up to the fourth order yields approximations of the shapes of the resulting echoes 2 . It is shown that the sum of these echo amplitudes in certain cases agree with the shape of the free-induction-decay 3 after a single pulse. If the spins S fluctuate rapidly with respect to the Larmor period the echo amplitudes show a strong dependence on variations of the external Zeeman field and the temperature. The results are checked by experiments.

A system of interacting particles is treated by the methods of quantum mechanics. Among the variables the three Euler angles are introduced which give the orientation of the system as a whole in an inertial frame of reference. This allows an expansion of the Schrödinger eigenfunctions in terms of elements of irreducible representations of the rotation group. This method, originally suggested by Wigner, is extended to include particles with spin. Two and three particle systems, one particle having spin 1/2, the rest being spinless, are treated explicitly. If the two spinless particles are regarded as the core of a nucleus, the spin 1/2 particle as an extra nucleon, one can compare this “three particle nuclear model” with other nuclear models. It permits calculations of Nilsson diagrams and, compared with other models, a more straightforward adjustment of parameters to empirical data.

For the description of a three-body-system 6 coordinates are introduced which take full advantage of the symmetry properties of the system. The Schrödinger equation in these coordinates is derived. Using rotational and reflection symmetry one obtains a set of l respectively l+1 coupled differential equations containing only the 3 coordinates of the triangle formed by the 3 masses. Solutions are given for special potentials and arbitrary l. The physical meaning of the differential operators appearing in the equations becomes evident from their application to the solution functions. This leads to a rearrangement of the Hamiltonian in a very transparent form and gives a hint how to get the most effective perturbation expansion. A simple example is worked out. For systems with Coulomb interaction a modification of the method is suggested by physical considerations. The calculation of the ground state energy of the Helium atom shows the rapid convergence of the procedure.

A kinetic theory for the Brownian motion of spherical rotating particles is given starting from a generalized Fokker-Planck equation. The generalized Fokker-Planck collision operator is a sum of two ordinary Fokker-Planck differential operators in velocity and angular velocity space respectively plus a third term which provides a coupling of translational and rotational motions. This term stems from a transverse force proportional to the cross product of velocity and angular velocity of a Brownian particle. Collision brackets pertaining to the generalized Fokker-Planck operator are defined and their general properties are discussed. Application of WALDMANN'S moment method to the Fokker-Planck equation yields a set of coupled linear differential equations (transport-relaxation equations) for certain local mean values. The constitutive laws for diffusion, heat conduction by Brownian particles and spin diffusion are deduced from the transport-relaxation equations. The transport-relaxations coefficients appearing in them are given in terms of the two friction coefficients for the damping of translational and rotational motions and a third coefficient which is a measure of the transverse force. By the coupling of translational and rotational motions a diffusion flow gives rise to a correlation of linear and angular velocities.