Volume 31, Issue 12

Recently a reciprocity theorem has been derived from the transport-relaxation equations for a simple system, consisting of one medium (Ref. 1 ). With a composite system, consisting of two immiscible media in contact, a plausible generalized reciprocity scheme, here called universal reciprocity postulate, is suggested now. It leads to an equivalent reciprocity requirement at the inter-face between both media and thus decisively restricts - in form of provable Onsager relations - the possible constitutive laws connecting the thermodynamical forces and fluxes at the interface. For the formulation of these ideas, some mathematical tools are developed in advance. Finally, heat conduction is treated, as the most simple example, first in the direct way, then according to the more sophisticated mathematical tools.

A metric theory of gravitation is suggested which reduces to Einstein's theory in the case of vanishing matter. If matter is present, in the Lagrangian formulation of the theory the principle of minimal coupling is given up by directly linking the matter variables to the curvature tensor. The theory contains a free parameter of dimension length. It is considered not to be a universal constant but a length characteristic for the mass of the material system described. Results diverging from those of General Relativity are to be expected for regions with high curvature i. e. especially for gravitational collapse and dense phases of the cosmos. An exact, static and spherically symmetric solution with constant matter density is discussed; it indicates that, possibly, gravitational collapse is avoided.

Although the equation of motion, recently proposed for the classical radiating electron, is of non-local character in proper time, the Newtonian initial data (position and velocity) are sufficient to guarantee existence and uniqueness of the solutions. The corresponding existence proof is accomplished by the Picard-Lindelöf method of successive approximations. This method indicates the possibility of a perturbation expansion of the exact solution in terms of the non-locality parameter. Such a perturbation expansion does not seem to be possible in the Lorentz-Dirac theory.

The extrema of the position-dependent spontaneous magnetization in a periodically layered two-dimensional Ising model are calculated exactly. Their asymptotic behaviour for infinite width of the surrounding homogeneous sublayer is given. The perturbations caused by the neighbouring sublayers on this extremum in a very thick sublayer are shown to be decoupled. Thus the asymptotic decay of the magnetization far from a single layer-shaped inhomogeneity can be inferred from the quoted asymptotics of an extremum, and it is found to be d -3/2 exp (-d/ξ₁˂ where d is the distance to the inhomogeneity and ξ₁˂ the correlation length in the underlying homogeneous lattice. The connection of this decay law to the asymptotic decay of correlations is dicussed.

The inverse operator technique used for the treatment of magnetic field influence on transport processes in polyatomic gases is extended to the case where the spherical approximation for the relaxation coefficient of [W] p [J] q polarizations cannot be used. The general procedure is outlined and subsequently illustrated for the magnetic field influence on the heat conductivity.

A new approach to the calculation of a teratomic recombination rate constant k(T) has been dem-onstrated. An expression for k(T) has been obtained in the eikonal approximation. The numerical calculation has been carried out for the Rb*-Xe system. Good agreement in the order of magnitude between the present results and the experimental data of Carrington et al. has been obtained.

It is shown that the well-known "4/3-problem" of the old Abraham-Lorentz model for the extended electron is still present in Rohrlich's redefinition of the electromagnetic four-momentum, if the latter is applied to an accelerated electron. The notorious factor 4/3 emerges now in connection with the Schott term. Since this term is an indispensable constituent of the Lorentz-Dirac equation of motion for the radiating electron, this equation appears to be not completely reliable.

The flow alignment in the isotropic and nematic phases of a liquid crystal is studied theoretically with special emphasis on temperatures close to the transition temperature. The point of departure is a nonlinear, inhomogeneous relaxation equation for the alignment tensor which is applicable to both phases. The stationary solutions of this equation are analysed. In addition to some well-known results which are recovered as limiting cases for small velocity gradients, it is found that a sufficiently large velocity gradient can induce a transition into an ordered phase if the temperature is between the transition temperature for equilibrium conditions and a somewhat larger critical temperature. In the nematic phase, a weak dependence of the flow alignment angle on the magnitude of the velocity gradient is obtained. The relaxation towards a steady state is also considered.

For a medium whose anisotropy is caused by a physical quantity expressed by an axial vector, e. g. an ambient magnetic field, the viscosity tensor has 8 independent components and is consequently decomposed in 8 terms. One term, multiplied with the bulk viscosity, connects the traces of the viscous pressure tensor and the velocity gradient, while traces and tracefree parts of these two tensors are coupled by two other terms, whose coefficients are required to be equal by Onsager's symmetry relations. The remaining 5 terms are represented by generalized Hess-Waldmann projectors. The corresponding 5 viscosity coefficients are related to those introduced by Braginskii, de Groot-Mazur, and Hess-Waldmann.

We show analytically that the nonlinear coupling of a large amplitude electromagnetic wave with finite amplitude ion fluctuations leads to filamentation. The latter consists of striations of the electromagnetic radiation trapped in depressions of the plasma density. The filamentation is found to be either standing or moving normal to the direction of the incoming radiation. Criteria for the existence of localized filaments are obtained. Small amplitude results are discussed.

LEED intensity spectra of the clean (00 and ⅕ 0 beams) and cesium covered (½ 0 beam) Pt(100) surface at normal or nearly normal incidence are compared with a double diffraction approach developed for the scattering process. A second order scattering approach is always restricted to cases where strong attenuation or weak scattering of the propagating electrons can be assumed. The comparison shows that many (but not all) intensity features of Pt(100) can be attributed to first and second order scattering processes only. Some of the maxima are likely to represent resonances. For proper assignment an effective inner potential is chosen that accounts for slowly varying dynamical effects as well as distortions of the crystal. The approach reveals only interpretations rather than predictions. However, it needs nearly no computational effort.

Oriented single crystalline samples of Ih-ice have been investigated by light scattering. The lade of observable phonon directional dispersion effects shows that ferroelectric domains with dimensions of the order of light wave lengths as stated earlier in the literature, do not exist. The depolarization ratio of the phonons originating from O-H stretching vibrations is found to be independent of the wave vector direction. This demonstrates clearly that the proton distribution is statistical.

The NMR lines of 109 Ag have been investigated in solutions of several silver salts in acetonitrile, propionitrile, pyridine, and ethylenediamine, and also in aqueous solutions of Na 2 S 2 O 3 and ethyl-amine. In these solvents the Ag + -ions form one or several complexes. In any case a single NMR line was to be detected, i. e. a rapid chemical exchange between different complexes in a sample may be assumed. The concentration dependence of the chemical shifts was determined with high accuracy for these solutions. From these results the chemical shift data of some defined complexes were derived. The chemical shifts of mixtures of AgCl and AgBr and also of AgCl and Agl dissolved in 70% aqueous solution of ethylamine are linear functions of the anions mole fraction. In two samples of AgNO 3 dissolved in organic solvents, the ratio υ( 109 Ag)/υ( 107 Ag) = 1.149 640 (1) was measured in good agreement with the value from silver salts in aqueous solutions; i. e. no primary isotopic effect was to be detected within these limits of error (0.9 ppm).

The Poisson ratio υ of a polycrystalline aggregate was calculated for both the face-centered cubic and the body-centered cubic cases. A general two-body central-force interatomatic potential was used. Deviations of υ from 0.25 were verified. A lower value of υ is predicted for the f.c.c. case than for the b.c.c. case. Observed values of υ for twenty-three cubic elements are discussed in terms of the predicted values. Effects of including volume-dependent electron-energy terms in the inter-atomic potential are discussed.

The dielectric loss of ten polar molecules in dilute solutions has been measured in the 0.3 GHz to 300 GHz range. Besides the Debye-absorption of the polar molecules, in all solvents, i.e. heptane, cyclohexane, mesitylene and decalin there could be separated an additional part of dielectric loss in the range of mm-waves. This absorption has been approximated by a Debye-curve to gain the step of dispersion and the time-constant. The dielectric loss of the unpolar solvents themselves, which is due to collision induced dipole moments, has also been investigated. The results are discussed and compared with the FIR-absorption of the polar molecules.

Linear Wave Coupling to a Plasma of Enhanced Electron Temperature at the Lower Hybrid Resonance Radio frequency waves in the range of the lower hybrid resonance are coupled to a plasma of enhanced electron temperature (≈ 10 6 K) and reduced collision frequency (≈ 7 · 10 5 s -1 ). The experiment demonstrates the persistance of resonance behavior even under this conditions. Radial eigenmodes are dominant, but exhibit - as compared to linear theoretical models - additional damping with an effective collision frequency in the order of 3 · 10 7 s-1 . For the conditions considered this effect is attributable to Landau damping.

The Influence of Mirror Configurations Near the Lower Hybrid. Resonance Hydrogen plasmas in magnetic mirror configurations are generated by microwaves and inductively coupled to a weak rf-source. In contrast to previous investigations the rf-frequency is varied; resonant behaviour near the lower hybrid frequency is found, attributable to radial eigenmodes. The influence of various mirror ratios and consequently varying axial density gradients on the position of the modes is studied. Shifts of the coupling coil are found to be of minor importance, since the resonant behaviour is dominated by oscillations of the whole plasma body.

Nonlinear Wave Coupling to a Plasma of Enhanced Electron Temperature In continuation of former investigations radio waves of different amplitude in the domain of lower hybrid resonance were coupled to a plasma of enhanced electron temperature. Under linear conditions no dependence of resonance behaviour on the wave amplitude was observed. Exceeding a treshhold maximum of absorption and electron density decreased significantly; both observations may be explained by onset of nonlinear and parametric effects. Increasing the amplitude the discharge only could be maintained by increasing the neutral gas pressure. In the power range of 15 to 20 kW electron density grew rapidly at resonance.

Analysis of Binary Compound Thin Films with the Electron Microprobe Two methods for the quantitative analysis of binary compound thin films by electron micro-probe have been developed and applied on some compounds with A 15-structure. Appropriate calibration curves for these compounds are given and compared with results of three theoretical or semiempirical methods showing fairly good agreement.

The influence of different representations of the dispersion dependence ε (i ξ) on calculating van der Waals interactions from Lifshitz theory is studied. It is shown that with satisfactory accuracy ε (i ξ) can be described by means of Krupp's empirical formula [ε (i ξ) -1]/[ε (i ξ) +1] = a · exp(-b ξ). Making use of that formula a simple expression for the Hamaker function A (h, T) is obtained. Numerical calculations are carried out, the results being compared with those of other authors and with experimental data.

A complete vibrational analysis is performed for the 53 atomic PMo 12 O 40 model of T d symmetry. The symmetry coordinates are classified into those of (a) ligand vibrations, (b) framework-ligand couplings, (c) framework vibrations, and (d) interligand vibrations. Simple valence force fields are estimated, and the influence of inclusion of redundancies on the calculated frequencies and symmetry force constants is investigated. Comments are made on calculated symmetry force constant values up to 345 mdyne/Å. Vibrational frequencies are calculated for the Mo 3 O 7 and Mo 3 O 13 units and for the PMo 12 O 40 3- complex ion. For the latter compound the calculated values are compared with experimental data from infrared and Raman spectra.

A general formula is derived for the potential energy of an ion in an ionic solution using all assumptions of the Debye-Hückel theory except the assumption of constant permittivity. For the solvent the spatial correlation of polarization fluctuations is taken into account. The potential energy of an ion in it's ionic atmosphere is calculated for different models of the spatial correlation of polarization fluctuations and the corresponding excess free energy and activity coefficient of an ion is evaluated. It is concluded that the Debye-Hückel theory using a constant value of e should only be valid for electrolyte concentrations lower than 10 -7 mol · dm -3 . The paper intends to show the consequences of dropping the assumption of constant permittivity and so encourage further efforts towards a more exact treatment of the problem.

The electric conductivities, densities and activation energies of RbC 2 H 3 O 2 and CsC 2 H 3 O 2 pure salts and (Na, Rb) C 2 H 3 O 2 and (Na, Cs) C 2 H 3 O 2 molten mixtures are reported. Deviations from addivity for the V m , Λ e and E Λ values are explained. The results for X 2 H 3 O 2 where X=Na, K, Rb, Cs and for (Na, X) C 2 H 3 O 2 , where X = K, Rb, Cs are discussed.

The utility of a conventional microwave spectrometer in determining the relative disposition of a CO 2 -laser line and a molecular transition and ultimately the exact frequency of an infrared transition, is demonstrated by making use of three non-linear spectroscopic effects, high frequency Stark effect, IR-MW double resonance and IR-MW double photon transitions. New situations are encountered in the production of the double photon transitions and the observation of the high frequency Stark effect. From a combination of the double photon transitions with double resonance signals produced in single d. c. Stark components it was concluded that the R (2) transition of the υ 1 band of the linear molecule FCN lies 104 ± 15 MHz lower in frequency than the R(20), 9.4 μm CO 2 -laser line i.e. R(2) transition = 1079.58711 ± 0.0005 cm -1 .

The ESR spectra of 4-oxyl-benzyl-phosphonium-bromide radicals show a temperature dependence of the methylene protons and the phosphorus nucleus coupling constants which is explained by a hindered rotation of the phenoxyl ring of the radicals. Furthermore compounds with different phosphor substituents exhibit the phenomenon of a two jump process. This effect is described by an isomerisation of two symmetric radical conformations. Activation energies for this process are found to be around 7 kcal/Mol. The conformation of the radicals can be discussed as staggered ethane analogues. A lower limit value for the hyperconjugation Bᴾ -parameter is proposed.

For temperatures above the Néel-point it is shown that there are severe deviations from pure paramagnetism in the ESR-behaviour of stoechiometric MnO. The experimental results in the temperature range between 130 K and 480 K are interpreted by a model of local order. The excitation energy necessary to decouple the antiferromagnetic bonding is computed to be about ΔE= 250 ± 15 cm -1 . For a temperature of T=T N +10 we derive that according to this theory 73% of all spins in MnO still remain in antiparallel order. Further calculations show that the bonding is compatible with an isotropic exchange interaction of next nearest neighbours having a coupling constant of J 2 = 3.42 K. Finally, an interesting aspect is discussed connecting the formation of antiferromagnetic clusters and the absorption behaviour of MnO in the far infrared.

Several rotational transitions in the ground vibrational state of 35 ClF 5 and 37 ClF 5 have been measured. From the frequency data the following constants have been derived: B 0 ( 35 ClF 5 ) = 3550.272(4) MHz; B 0 ( 37 ClF 5 ) = 3545.885 (4) MHz; D J = 0.76(9) kHz; D JK = -0.67 (15) kHz; e Q q( 35 ClF 5 ) = 43.93(8) MHz; e Q q( 37 ClF 5 ) = 34.63(6) MHz; μ = 0.536(10) D. The bond angle F ax -Cl-F eq is estimated at 86.5(1.0)°.

The diamagnetic susceptibilities, refractive indices and densities were measured as a function of temperature for three 4,4'-disubstituted benzoic acid-phenylester compounds. The polarizabilities were calculated using the Vuks formula and Neugebauer's relations. The orientational order parameters obtained from the magnetic and from the optical data as a function of temperature, in the absence of single crystal data, were compared.

In this paper equilibrium models for the calculation of the excess Gibbs free energy of binary liquid mixtures are developed, the component A of which undergoes chain-forming self-association whilst the component B acts as an 'inert' solvent. It is shown that the extension of the well-known chain-association model of Mecke and Kempter, in which the probability of chain prolongation is assumed to be independent of chain length, is unable to establish satisfactory results because it does not exhibit sufficient unsymmetry. Reduction of the probability of chain growth with in-creasing chain length leads to an improved model with the geometric series replaced by the exponential series. This model, in which only two parameters are used, i. e. the equilibrium constants K for mutual solvation of A and B, and ρ for self-association of A, allows fitting of isothermal experimental G E /R T literature data on cycloalkanol-cycloalkane, alkanol-alkane, and NMF -CCl 4 systems within the limits of experimental error. Compared with the two-parameter Wilson equation which gives equally small standard deviations, our equilibrium model has the advantage of allowing passage from G E to H E data and of being applicable to liquid-liquid equilibria.

A special method of preparation of cholesteric liquid crystals is reported, which is useful for the investigation of cholesteric structures with very small pitches. This freeze-etching method makes it possible to observe pitches with scanning electron microscopy without influencing the structure by solvent molecules.

Different types of chaotic flow are possible in the 3-dimensional state spaces of two simple non-linear differential equations. The first equation consists of a 2-variable, double-focus subsystem complemented by a linearly coupled third variable. It produces at least three types of chaos: Lorenzian chaos, "sandwich" chaos, and "horseshoe" chaos. Two figure 8-shaped chaotic regimes of the latter type are possible simultaneously, running through each other like 2 links of a chain. In the second equation, a transition between two different types of horseshoe chaos (spiral chaos and screw chaos) is possible. While sandwich chaos allows for a genuine strange attractor, the same has not yet been demonstrated for horseshoe chaos. Unlike the situation in the analogous 1-dimensional case, an emergent period-3 solution is not necessarily stable in the horseshoe. Since chaos is a "super-oscillation" (emergent with the third dimension), the existence of "super-chaos" is postulated for the nect level. A six-minute, super-8 sound film, demonstrating the different behavioral modes and their bifurcations in the 2 equations, has been prepared. Chaos sounds as musical as a snore.

Ultrasound absorption has been measured in binary mixtures of phenol with carbontetrachloride and cyclohexane covering the complete concentration range at 20, 30, 40, and 50 °C. Absorption maxima in dilute phenolic solutions are interpreted as arising from cyclic association of phenol to trimers or tetramers.

Ultrasound absorption has been measured in pure trifluoroacetic acid and its approximately equimolar mixture with acetic acid (51.5 mole% of acetic acid) at 20, 30, 40, and 50 °C and atmospheric pressure over the frequency range 3 - 57 MHz. The absorption curve of trifluoroacetic acid could be flitted by a single relaxation step (relaxation frequency 3.5 - 11 MHz, low frequency absorption about one tenth of that of acetic acid), whereas the equimolar mixture followed a two step relaxation curve (lower relaxation frequency 1.5 - 3 MHz, absorption correspondingly higher than in pure trifluoroacetic acid, higher relaxation frequency 12.5 - 39 MHz, absorption about 3% of the low frequency absorption).

The stability of some heterocyclic compounds derived from the condensation of succinic and glutaric anhydrides with aliphatic diamines is compared using calculated values for the total energies. Further, some results derived from the electronic population analysis and the available experimental data are used to give information about the corresponding electronic structure. The CNDO/2 and INDO methods have been used for the calculations.

Rotation spectra of 1.2,4-thiadiazole have been studied for naturally occurring 34 S-, 13 C-and 15 N-species of the normal and the 5-d 1 form, and the 12 sets of moments of inertia have been used to determine the substitution structure in the two principal axes systems. Agreement within less than 0.0005 Å and 0.02° for distances and angles, respectively, between the two independent sets of structure parameters was obtained through the use of the rotation of axes under substitution in combination with the first and second moment conditions. The averaged bond lengths (in Å) and angles (in degrees) are: S(1) - N(2) : 1.6490 C(5)S(1)N(2) : 92.75 N(2) - C(3) : 1.3166 S(1)N(2)C(3) : 107.09 C(3) - N(4) : 1.3663 N(2)C(3)N(4) : 120.12 N(4) - C(5) : 1.3133 C(3)N(4)C(5) : 107.74 C(5) - S(1) : 1.7071 N(4)C(5)S(1) : 112.30 C(5) - H(5) : 1.0785 S(1)C(5)H(5) : 123.90 C(3) - H(3) : 1.078 N(2)C(3)H(3) : 119.94 The H(3) atom was assumed on the external bisector of N(2)C(3)N(4) at a distance of 1.078 Å from C(3). Geometric features of the four thiadiazoles are compared, and the method used in the structure calculation is discussed.

The near infrared absorption of pure ethylene in the region of the second overtone of the C-H stretching fundamentals (8200 cm -1 to 9500 cm -1 ) was measured at supercritical temperatures (T c = 9.5 °C) between 22 °C and 200 °C from 0.7 bar to 3000 bar. The density and temperature dependence of bandshape, maximum frequency and absorption intensity are reported and discussed. The bands observed within a wide range of experimental conditions are assigned to combination and overtone modes. The molar integrated intensity B̅ λ determined between the wavelength of maximum absorption and the high frequency absorption boundary was observed to be independent of pressure and temperature. This enables spectroscopic concentration determinations on ethylene in high pressure - high temperature phase equilibria and reactions.

New complexes were prepared from the reaction of vanadyl ion with malononitrile and succinonitrile. Both complexes were found to exhibit a decrease in C ≡ N streatching frequency. The reaction of vanadyl ion with malononitrile ion gives a complex in which the C ≡ N stretching frequency is increased. The increase or decrease is related to the type of bonding and to the difference in π-back bonding.

Investigation The electrical conductivity of the first eight homologous N-(4-n-alkoxybenzylidene)-4'-n-butylanilines is investigated in the isotropic, nematic and smectic phases using the electrolyte tetra-butylammonium picrate. The anisotropy ratio of the electrical conductivity shows pretransition behaviour in the nematic phases close to the transition to the smectic phases. This behaviour be-comes more distinct with increasing alkyl chain length of the liquid crystals. In the nematic phase of 40·4 an anisotropy ratio of V = 0.55 is determined at the lowest electrolyte concentration. Values of about V=0.05 were found in the smectic phases of several homologues. In the nematic phase, an increase of the electrolyte concentration effects an increase of the anisotropy ratio. This effect is systematically enhanced with increasing alkyl chain length.

Measurements of the proton spin-lattice relaxation time, T 1 , in polycrystalline NH 4 ReO 4 have shown that mechanical sample rotation in the static magnetic field reduces T 1 for proton magnetic resonance frequencies within the range 30 - 42 MHz. The rotation induced proton spin-lattice relaxation times, T 1 ′ , were measured at different Larmor frequencies, sample rotation frequencies, and temperatures. At room temperature T 1 ′ increases with increasing proton Larmor frequency. The dependence of T 1 ′ on sample rotation frequency and temperature is small. The "normal" proton T 1 times were determined as a function of temperature at 30 and 42 MHz. From these measurements an average activation energy of 2.4 kcal/mole was obtained for the NH 4 + reorientation. The "normal" spin-lattice relaxation behavior was observed to be non-exponential at 30 MHz above 200 K and at 42 MHz above 260 K and is nearly independent on temperature above 300 K.

Supersaturations for the onset of cavitation in water were determined for various gases. At ambient pressure, the threshold supersaturations (in atm) required for profuse cavitation to initiate both in bulk water and at the glass-water interface were CH 4 , 120; Ar, 160; N 2 , 190; He, 360. Exposure of the water and its containing surfaces to hydrostatic pressures up to 1100 atm prior to equilibration with gas had no detectable effect on these threshold values. This indicates that preformed gas nuclei are not significantly involved. Cavitation at the glass-water interface was investigated for CH 4 , Ar and N 2 saturations up to 570 atm. For 320 atm saturations, the threshold super-saturation was about one-half that for decompression directly to ambient pressure, and for 550 atm it was about one-third. These results indicate that the dissolved gas concentration is a critical factor limiting the spontaneous nucleation of bubbles in gas supersaturated liquids.

A three-dimensional reconstruction requires the same integral dose as a conventional two-dimensional micrograph provided that the level of significance and the resolution are identical. The necessary dose D for one of the K projections in a reconstruction series is, therefore, the integral dose divided by K.

Second virial coefficients of ground state nitrogen atoms have been calculated in the temperature range 6000 - 20000 K. The results have been obtained using experimental potentials for the states 1 ∑ g + , 3 ∑ u + 5 ∑ g + and of the nitrogen molecule and an ab initio Heitler-London potential for the 2 ∑ u + repulsive potential. Differences up to a factor of 5 are found between the present second virial coefficients and the corresponding values of Kessel'man et al.

We propose a new set of field equations within the framework of a Poincare gauge theory of gravitation. These equations couple momentum to the torsion and spin to the curvature of spacetime and encompass an Einstein-like limit.

Susceptibility and magnetic shieldings of all nuclei are calculated for water and hypofluorous acid. A finite perturbation SCF method with gauge invariant gaussian basis set is used. Results calculated with a slightly extended basis set agree well with experimental values.

It is shown that field emission of cations from adsorption layers of salts results from an ionic conductivity of the salt layers.

For an ionic melt consisting of two components and of three ion constituents, we derive the interrelation between the Soret coefficient and the initial and final values of the thermoelectric power of a thermocell containing the melt considered. We only use the general formulas of Thermodynamics of Irreversible Processes and there is no restriction with respect to the valency types of the electrolytes.

The principal force constants for ReF 6 + have been calculated using the GVFF. Mean amplitudes of vibration and bond orders are also estimated. The results are briefly discussed and some comparisons with related species are made.

The utility of the rotating platinum electrode for the study of fast reactions has been shown by evaluating the specific reaction rates of brominations of m-acetotoluidide, acetanilide and o-acetotoluidide in aqueous solution.