Volume 23, Issue 5

Mit Hilfe informationstheoretischer Argumente wird der Anfangszustand zur Zeit t 0 bei der Ableitung kinetischer Gleichungen eliminiert, indem man ihn auf Grund der JAYNESschen Methode aus der vorausgesetzten Kenntnis des Zustandes zur Zeit t bestimmt. Damit kann eine abgeschlossene allgemeine Bewegungsgleichung der Form iñ 1,t = Tni, t erhalten werden.

Ausgehend von einer allgemeinen Bewegungsgleichung für die Einteilchenverteilungsfunktion aus der vorangegangenen Arbeit werden durch Partialsummation und den Grenzübergang τ → ∞ kinetische Gleichungen für verdünnte Gase und für Plasmen in Debye-Hückel-Näherung abgeleitet.

Die von verschiedenen Autoren bei der Ableitung von kinetischen Gleichungen festgestellten Schwierigkeiten in Form von Säkularitäten und Divergenzen können durch geeignete Partialsummationen überwunden werden. Damit ist die Anwendung der Störungstheorie in der klassischen Statistik gerechtfertigt. Aus dem Auftreten von Divergenzen wurden in der Literatur verschiedene physikalische Schlußfolgerungen (logarithmische Dichteabhängigkeit der Transportkoeffizienten, Ungültigkeit der Bogoljubovschen Synchronisationsannahme) gezogen. Das ist nicht gerechtfertigt, da sich die Schwierigkeiten streng überwinden lassen.

We consider a gas consisting of particles (molecules) with spin 1/2 and vanishing electrical charge. We assume the existence of spin-dependent two-body-potentials of interaction between these particles. Our aim is to establish conditions for the appearance of ferromagnetism in such systems. Calculations are done for a modified Lennard-Jones-type two-body-potential. The sum-over states is expanded with respect to cluster-integrals which are approximately calculated up to the fourth order. Cluster of higher order seem to give only uniportant contributions to the conditions mentioned. The conditions for ferrmagnetism are fulfilled, if the density of the gas is higher and the temperature lower than some critical values. The dependence of magnetization on temperature is given and some considerations regarding the equation of state are made. It is supposed that liquids of the same composition and interaction will also show ferromagnetism. The results seem to hold also for potentials which are not of the Lennard-Jones-type, but have the appropriate spin-dependence.

The kernel of the linearized integral equation for the order parameter Δ (r) was shown] by DE GENNES to be the solution of a diffusion equation in the case of a very impure superconductor. On the basis of the method of the correlation function originating from DE GENNES and further developed by LÜDERS, boundary conditions to the diffusion equation are derived for surfaces and for interfaces between different conductors. In the case of good electrical contact, our results are identical with those given by DE GENNES.

Aus dem Verhältnis von Nernst-Koeffizient zu Hall-Beweglichkeit ist es möglich, unter gewissen Voraussetzungen eine direkte Aussage über die Art der Ladungsträgerstreuung zu erhalten. Es werden die Einflüsse von Entartung und Anisotropie diskutiert und das Ergebnis mit Messungen an Kristallen der Halbleiterlegierung Bi 2 Te 2,7 Se 0,3 verglichen.

The electrical conductivity and density of pure molten thallium sulphate and the conductivity of TlMeSO 4 , where Me = Li, Na, K, Rb, or Cs, have been measured between 700 and 1150 °C. We have also measured the densities of four equimolar sulphate mixtures and their pure components. The excess volumes were less than 0.5%. The deviations from ideality for the conductivities and their Arrhenius activation energies have been compared with other sulphate systems. The electrical conductivity of a pure univalent sulphate depends both on the radius of the cation and on its mass. In mixtures, there are large negative excess conductivities and positive excess activation energies, when we have cations of different sizes.

The interdiffusion coefficients (D) of Na + , Ag + , K + , Rb* and Τl + in pure f. c. c. Li 2 SO 4 have been measured between 590 and 820 °C. D and the Arrhenius’ activation energies decrease in the same order as the ionic radii increase. D is a function both of the masses and the radii of the impurity cations. The results show that the Na + and Ag* ions mainly diffuse in the sulphate lattice with the same mechanism as the lithium ions, while the larger ions are mobile in defects in the lattice. The Li*, Na + and Ag* ions are probably diffusing between octahedral positions.

The thermal conductivity and the thermal diffusivity of the three alkali nitrates LiNO 3 , RbNO 3 and CsNO 3 have been measured over a temperature range between 50° and 100 °C above their melting points. Any temperature dependence of the thermal conductivity cannot be established for any of the investigated liquids but the results indicate that it must be less than 10 -3 °C -1 . The experimental results are compared with the conductivities which can be calculated with already excisting theories. A somewhat modified theoretical approach is suggested for estimating the thermal conductivity, where no adjustable parameters are being used. The experimental and theoretical values at the melting points agree within about 10 percent.

Es wird eine Methode zur Aufzeichnung der zeitlichen Entwicklung der Phasengrenze festflüssig während der Erstarrung von Metallen mit Hilfe kurzer, periodischer Ultraschallimpulse beschrieben. Die damit ermittelten Erstarrungsprofile stimmen in wesentlich höherem Maße mit den theoretisch geforderten überein als die nach dem üblichen Verfahren, dem Dekantieren, erzielten. In diesem Zusammenhang werden die Fehlereinflüsse beim Dekantieren kurz diskutiert.

Proton resonance shifts of molecules adsorbed on the surface of silicagels are investigated. In order to explain these shifts which are in the direction to higher fields (compared with the resonances of free liquids) the influence of paramagnetic impurities in the silicagel surface, the different diamagnetic volume susceptibilities, as well as the influence of the relaxation process and of bonding effects are discussed. It is pointed out that the observed resonance shifts are mainly caused by bonding effects in our case. An inhomogeneous broadening of the resonance lines (by a factor F up to 12), found by comparison with spinecho experiments, is shown to be correlated with the shifts. Using this fact the dependence of the factor F on the surface coverage can be explained qualitatively.

From the triatomic molecule SO 2 with 18 valency electrons we generated the mononegative radical ion with the aid of electrolytic techniques. In this way we could vary the radical concentration over a wide range and could also study the influence of counter ions and solvent molecules. The semi-empirical LCAO-MO theory of WALSH was used to calculate the g-factor shift. UV spectroscopic data of SO 2 and Hückel-MO-calculations of the spin density distribution of the unpaired electron in the antibonding MO of SO 2 - resulted in Δg theor = (3.9 ± 0.6) x 10 -3 which agrees rather well with Δg exp = (3.414 ± 0.003) x 10 -3 . The quoted error of the theoretical value refers to approximations, which have to be introduced in addition to the approximations of the LCAO-MO theory of WALSH. The HMO spin density distribution compares nicely with the distribution calculated from anisotropic hfs constants of SO 2 - in a KCl single crystal which have been measured recently by SCHNEIDER et al. Higher concentrations of SO 2 molecules resulted in another EPR line with Δg exp = 4.6 x 10 -3 which we attribute to the solvated radical ion (SO 2 ) x SO 2 - . From the temperature dependance of the concentration ratio of the radical species in we determined W = - 6.9 kcal mol -1 , x = 2, and K(0 °C) = 8.0 x 10 -5 mol 2 lit -2 .

The Coriolis Coupling constants of GeCl 4 and SnCl 4 are obtained from the contours of the ν 4 bands and used to determine the force fields. From consideration of these and that previously reported for SiCl 4 it is shown that even relatively inaccurate Coriolis constants can yield better force fields and Bastiansen-Morino shrinkage effects than experimental mean amplitudes of vibration; but that for SnCl 4 , because of significant differences between usually valid approximate force fields and the Coriolis constant fixed one, a wrong value of the constant may have been obtained. It is also shown that the force field obtained from Vol’kenshtein’s theory of absolute Raman intensities is not very good for GeCl 4 and wildly inaccurate for SnCl 4 .

The IR-spectrum of gypsum (CaSO 4 ·2 H 2 O) in the frequency range from 10 000 to 1200 cm -1 has been investigated with polarized light at room temperature. Between 3700 and 1200 cm -1 , the measurements confirm the data of HASS and SUTHERLAND and as well as those of SCHAAK derived from IR and reflection measurements. The IR-spectrum shows a great number of bands, most of which can be assigned to combination and fundamental vibrations in terms of normal vibrations of the water molecules and the sulfate ions. The influence of the lattice vibrations is briefly discussed. The existence of hydrogen bonds between the water molecules and the sulfate ions gives rise to combinations of fundamental vibrations of both complexes.

Messungen des Dichroismus von Anthracen-d 2 (9,10) im polarisierten Licht, der Vergleich mit der bekannten Zuordnung des IR-Schwingungsspektrums von Anthracen und der Vergleich mit den gerechneten nichtebenen Schwingungen von Anthracen-d 2 (9,10) ermöglichen eine erste Deutung des IR-Spektrums.

The lifetimes of certain states in the First Positive System of N 2 (B 3 Π g → A 3 Σu + ) and the Asundi-Bands of CO (a′ 3 Σ → a 3 Π) have been measured as a function of pressure after excitation in a pulsed rf discharge. The fluorescence of the investigated CO-system shows exponential decay in contrast to the First Positive System of N 2 that throughout has two decay constants. The pressure dependence of the lifetimes has been investigated in the range of 10 -2 to 1 torr. This allows to calculate quenching cross-sections of the excited states.

A method is described to determine the velocity dependence of scattering processes from timeof-flight measurements with crossed molecular beams. Scattering of a potassium atomic beam by short pulses of a carbon dioxide molecular beam generates attenuation pulses in the intensity of the potassium beam. The time-of-flight broadening of these attenuation pulses is measured employing signal averaging to improve the signal-to-noise ratio from 1 to 100. The experimental results are in accordance with computed time-of-flight distributions based on the additionally measured velocity distributions and geometries of the two molecular beams, and using the known velocity dependence of the K-CO 2 scattering cross section.

When an electric current is passed through a rare-gas alkali plasma the electron temperature rises above the gas temperature. This effect was investigated in a streaming argon-potassium plasma at atmospheric pressure and a gas temperature of 2000 °K. The applicability of the line reversal method to the measurement of the electron temperature has been investigated. General conditions under which the electron temperature equals the line reversal temperature have been derived. In the case studied, the plasma had to be optically thick for the resonance radiation used. The electron temperature was measured with this method as a function of the current density. The results were compared with the values calculated from the theory and with the values calculated from the also measured conductivities. For electron temperatures above 2400 °K all three give the same results.

It has been suggested 1 that counting photons scattered from a single-mode laser beam passing through a plasma, may be used for determining correlations in the plasma. Higher-order moments of the distribution of photon counts are related to an ensemble average of higher-order products of the electric field. Hence, this method yields also information about higher-order correlations of the electron density fluctuations, in contrast with the measurement of the scattering cross section which depends only on second-order correlations. In this paper, the connection between the statistics of photon counts and the properties of electron density fluctuations is discussed in detail, concentrating on the first and second moment of the photon count distribution. The incident wave is assumed to be plane and ideally monochromatic. For stable plasmas in a steady state, the results are written in terms of the distribution functions of the electron and ion velocities. Weakly turbulent unstable plasmas in the phase of exponential growth are also considered, using as a characteristic parameter the spectrum of the electric micro-field.

The practicability of a method using two wires as transmission line for microwaves as a diagnostic method on a shock tube was investigated. The energy distribution around the wires was calculated which showed a high spatial resolution independent of the frequency for this method. The wires cause bow shocks because the flow is hypersonic which should be taken into account. The geometrical dimensions happen to be the same as those in a probe method used by HOBSON, hence the disadvantages are comparable.

The Kubo formula for the shear viscosity of a Debye-Hückel plasma is evaluated by an extension of ERNST’S method. In the main the result can be shown to be equivalent to the result derived by BRAUN from the LENARD-BALESCU equation with the CHAPMAN-ENSKOG method. Moreover a correction of BRAUN’S result can be given as caused by the particle interaction.

A fully 3-dimensional plasma consisting of up to 96 charged particles is simulated in a computer. The plasma is confined to a sphere (or cube) with specularly reflecting walls. The forces are computed using a predictor corrector method with variable time steps. From initial configurations randomly chosen the evolution of the plasma is followed numerically. Distribution functions and moments with respect to various phase variables are obtained as time averages: the distribution of velocity, kinetic and potential energy, of the electric microfield, the micropotential as measured at a neutral point of reference (usually the center of the system) , the mean square electric field, the microfield correlation function and the particle relaxation times. As the sphere used in the experiments has dimensions only slightly larger than the Debye sphere, collective phenomena and those due to major density fluctuations cannot be expected. Despite these limitations the mean electric field is found to be high by approx. 10% compared to the Holtsmark field. Furthermore other comparisons to existing theories with respect to the variables already mentioned are carried out.