 181  Author
 MartaE. Escobar, EnriqueJ. Baran  Requires cookie*   Title
 Kraftkonstanten des V04 3 ~ Ions im ZirkonGitter [1]    Abstract
 Force Constants of the VOt 3 ~ Ion in the Zircon Lattice The force constants for the V04 s ~ ion present in the different rare earth orthovanadates of the zircon type have been computed using a modified valence force field and recently reported Raman data. It is shown that the V0 bond strenghtening runs parallel to the unit cell contraction. The Raman spectrum of the tetragonal modification of LaV04 is reported for the first time. Bekanntlich kristallisieren die Orthovanadate der Seltenen Erden des Typs LnV04, mit Ln = Ce bis Lu sowie ScV04 und YV04 im tetragonalen ZirkonTyp (Raumgruppe D4h und Z = 4) [2, 3]. Auch für LaV04 konnte kürzlich diese Kristallmodifikation nachgewiesen werden [4, 5] obwohl in diesem Fall die stabilere Form dem monoklinen MonazitTyp angehört [2, 3, 6]. Vor kurzem haben wir die RamanSpektren der tetragonalen Orthovanadate aufgenommen und an Hand einer "SiteSymmetrie"Analyse gedeutet [7]. Diese Reihe bot eine ausgezeichnete Gelegenheit, um den Einfluß der dreiwertigen Lanthanide auf die inneren Anionenschwingungen zu untersuchen. In erster Näherung zeigt es sich, daß die Frequenz der symmetrischen Valenzschwingung ^(Aj) mit Abnahme des Zellenvoluminas, in der Richtung vom PrV04 zum LUV04 , ansteigt [7]. Um diesen Effekt in quantitativer Weise zu erfassen und um deutlicheren Einblick in die Schwingungseigenschaften des V04 3 ~Ions in diesen Kristallgittern zu erhalten, haben wir jetzt eine Berechnung der Kraftkonstanten durchgeführt. Zu dieser Berechnung wurden das "Kopplungsstufenverfahren" von Fadini [8, 9] und die Frequenzwerte der RamanMessung [7] herangezogen. Bloß von CeV04 und ErV04 ließen sich keine guten Spektren erhalten [7], während wir die tetragonal e   
Reference
 Z. Naturforsch. 35a, 1110—1111 (1980); eingegangen am 14. August 1980   
Published
 1980   
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 ZNA198035a1110_n    Volume
 35  
183  Author
 R. Haase, H.J Jansen  Requires cookie*   Title
 Diffusion in Binary Nonelectrolyte Solutions    Abstract
 For binary liquid mixtures of nonelectrolytes, we consider the dependence of the diffusion coefficient on composition and temperature, making use of an analytical expression for the kinematic diffusion coefficient (diffusion coefficient divided by thermodynamic factor). We present recent experimental data for the ideal liquid system chlorobenzene + bromobenzene and for the nonideal liquid system water f methanol as well as literature data for other nonideal mixtures. The diffusion coefficient (interdiffusion coefficient) D of a binary liquid mixture is a function of composition and temperature while the dependence on pressure may usually be neglected. For a binary nonelectrolyte solution it is expedient to write [1] D = D* B. (1) Here D* is the kinematic diffusion coefficient and B a thermodynamic factor given by 5 = 1+ (3 In fi/d In X()T,P , (2) xj denoting the mole fraction, fi the activity coefficient (on the mole fraction scale) of component i (i= 1, 2), T the temperature, and P the pressure. We now use an exponential expression for D* (instead of that commonly applied to D) : D* = D°exp{E*/RT), (3) where D° and E* are functions of the composition and R denotes the gas constant. E* is analogous to, but not identical with, the activation energy in the exponential expression for D. We derive from (1) and (2) for an ideal mixture (/,=!): B = l, D = D* (ideal mixture). (4) Generalizing experimental results [2 — 5], referring mainly to the liquid system chlorobenzene + bromobenzene, we conclude that the following additional Reprint requests to Prof. Dr. R. Haase, Melatener Str. 107, 5100 Aachen. relation holds for ideal mixtures: D° = Dx° xx + D2° X2, E*= const (ideal mixture). (5) The constants Z)1° and D2° are the limiting values of D° for xt = 1 and x2 = 1, respectively. The Eqs. (3), (4), and (5) imply that the diffusion coefficient varies linearly with the mole fraction x2 or x1 (= lx2). For the ideal system chlorobenzene + bromobenzene, the available diffusion data [2, 3, 5] covering the whole range of compositions and the temperature range between 10 °C and 80 °C lead to the following values of the constants in (5): ZV = 148.9 10~ 5 cm 2 s" 1 , D2° = 117.810~ 5 cm 2 s" 1 , E* = 11.15 kj mol" 1 . They are only slightly different from those obtained previously [4]. For nonideal mixtures (/j 4= 1) the function D(x2) is no longer linear but usually exhibits a minimum or at least shows negative deviations from additivity. (Exceptions are rare.) An example for a case with a minimum is the liquid system water + methanol for which measurements of the diffusion coefficient have been carried out recently [5]. These experimental data (see Table 1) cover the whole range of compositions at 20 °C, 40 °C, and 60 °C. Unfortunately the activity coefficients given in the literature are not reliable enough for an evaluation of the diffusion data in the sense of the relations (1), (2), and (3).   
Reference
 Z. Naturforsch. 35a, 1116—1117 (1980); received August 22 1980   
Published
 1980   
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 ZNA198035a1116_n    Volume
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184  Author
 P. S. Grover  Requires cookie*   Title
 Annihilation of Positrons in Rare Gases — A Phenomenological Study    Abstract
 The life time, /, of positrons in rare gases under the simultaneous influence of a steady magnetic and an alternating electric field is studied. X depends on the frequency and attains a maximum when the frequency equals the cyclotron frequency. The extent of this dependence is quite sensitive to the positron atom momentum transfer rates. The annihilation of positrons in rare gases under the influence of temperature, electric fields and magnetic fields has been studied by several workers [1 — 16], as such studies provide tests of models of positronatom interaction. Here, we propose method in which a steady magnetic and on alternating electric field are applied to an atomic gas in which positrons undergo scattering and annihilation processes. The energy of the positrons is assumed to be smaller than the positronium formation threshold, so that they suffer only elastic collisions and eventually annihilate with the electrons of the atoms. In the presence of a uniform alternating electric field, E = E0 exp (i OJ t), and a magnetic field, B, the behaviour of the positrons is described by the Boltzmann equation [11, 17] : 3/(V,i) 31 dt + E V x B 3 /(V,D 3V (1) are the scattering and annihilation Here e, m and v = j V  are the positron charge, mass and velocity, respectively, and c is the velocity of light. /(V, f)dVdf specifies the number of positrons at time t with velocity V in the ranges d£ and dV. • dt)m and terms, respectively. To solve (1), we write f(V,t)=f0{v,t) + —Vfj exp(i to t) [17], where fj is a function of v and fi ' ^ /o • Using this expansion and evaluating the scattering and annihilation terms following ref.   
Reference
 Z. Naturforsch. 35a, 1118—1119 (1980); received September 8 1980   
Published
 1980   
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 ZNA198035a1118_n    Volume
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185  Author
 H. Stumpf, W. Kleih  Requires cookie*   Title
 Quantum Statistical Derivation of Rate Equations for Electronic Processes in Polar Crystals with External Electric Field    Abstract
 Applying the NakajimaZwanzig method to the von Neumann equation of a system of interacting electrons and nuclei, etc., and evaluating the PauliMaster equation according to RieckersStumpf, we obtain a system of reaction equations for electronphononphoton processes in a polar crystal. Further elaboration of these reaction equations leads to rate equations for electrons which include impurity center processes as well as conduction band processes in an external electric field. If the conduction band processes run faster than the other processes, the rate equations can be reduced to a Boltzmann equation with drift term for the conduction electrons, coupled to rate equations for impurity center electrons where the number of conduction electrons must not be conserved. Furthermore, the basic problem of electronic state formation in external fields is discussed, the corresponding interaction terms are derived and a functional for the calculation of "bound" states in external fields is given.   
Reference
 Z. Naturforsch. 35a, 1121—1135 (1980); received July 2 1980   
Published
 1980   
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 ZNA198035a1121    Volume
 35  
187  Author
 A.J P Alix, E. Rytter  Requires cookie*   Title
 Characteristic Normal Modes of Vibration and Generalized Normal Forces: Basic Properties and Relation to Fundamental Molecular Constants    Abstract
 A survey is given of the simplified formulae for energy distributions, force constants, secular equations, Coriolis coupling constants, isotopic substitutions, compliances, mean amplitudes, bond moment and polarizability parameters, interaction coordinates and restoring forces in the cases where either a completely characteristic normal mode or a generalized normal force can be assumed. The obtained results may be of use for the following main purposes: (i) computation of quantities which can be employed in the assignment of spectra, band shapes, intensities ... (ii) evaluation of fundamental molecular constants and isotopic shifts which can be approximated with good accuracy. As illustration, the equations have been applied sucessfully to twodimensional cases and to Molybdenumhexacarbonyl.   
Reference
 Z. Naturforsch. 35a, 1142—1151 (1980); received June 21 1980   
Published
 1980   
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 default:Reihe_A/35/ZNA198035a1142.pdf    Identifier
 ZNA198035a1142    Volume
 35  
188  Author
 B. Faucher, A. S. Krausz  Requires cookie*   Title
 The Kinetics of Plastic Flow    Abstract
 The plastic flow associated with the three main methods of combining deformation mechanisms is described in terms of deformation kinetics. It is shown that the determination of the deformation kinetics as the initial step in the analysis is indispensable to the establishment of the activation parameters in functional forms. To this purpose, the effects of stress and temperature on the plastic strain rate are determined for three types of combined mechanisms, and qualitative comparison with experimental results is presented.   
Reference
 Z. Naturforsch. 35a, 1152—1161 (1980); received June 26 19S0   
Published
 1980   
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 default:Reihe_A/35/ZNA198035a1152.pdf    Identifier
 ZNA198035a1152    Volume
 35  
189  Author
 A.G M Maaswinkel  Requires cookie*   Title
 Resonance Absorption of a Wavelengthshifted Probe Beam in a LaserProduced Plasma    Abstract
 The resonance absorption of a weak probe beam in a plasma, produced by 0.53 jj.m laser irradiation of planar targets at 10 14 W/cm 2 , has been investigated. The probe beam (A= 1.06 jam) could be delayed in time relative to the 0.53 jxm pulse. Thus a shift of the resonance absorption maximum towards smaller angles of incidence for increasing time delays was found. This is expected on account of the hydrodynamic expansion. The absorption of intense laser radiation in dense hot plasmas is a central problem in laser fusion experiments. Of particular interest is resonance absorption since it is independent of the intensity and wavelength of the laser, and is effective even in a collisionless plasma. Resonance absorption has been observed at a number of wavelengths: at 1.06 fxm [1—2] and 0.53 [Jim [2], and more recently   
Reference
 Z. Naturforsch. 35a, 1162—1165 (1980); received October 8 1980   
Published
 1980   
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 ZNA198035a1162    Volume
 35  
190  Author
 V. D. Sharma, Radhe Shyam  Requires cookie*   Title
 NonEquilibrium Relaxing Gas Flow Behind Three Dimensional Unsteady Curved Shock Wave    Abstract
 A shock wave is assumed to exist in a threedimensional unsteady flow of a relaxing gas. The variation of flow parameters at any point behind the shock surface is determined in terms of the shock geometry and the upstream flow conditions. The expressions for the vorticity and the curvature of a streak line at the rear of the shock surface are also determined in terms of the known quantities.   
Reference
 Z. Naturforsch. 35a, 1166—1170 (1980); received August 15 1980   
Published
 1980   
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 ZNA198035a1166    Volume
 35  
191  Author
 G. Abbate, U. Bernini, E. Ragozzino, F. Somma  Requires cookie*   Title
 Temperature Coefficient of the Refractive Index of H20 and D20 and Proposed Models of Water Structure    Abstract
 The temperature coefficient of the refractive index, (dn/dT)p, has been measured for deuterium oxide. The observed values are considered together with those previously obtained for water. The experimental data cannot be explained with the best known models of molecular polarizability, at least in the approximation generally used in these models. Therfore they are discussed on the basis of a different approximation, suggested by a wellknown structural model of liquid water. It is shown that the experimental results are very well explained, in a wide range of temperature, with the hypothesis of the existence of "structural voids".   
Reference
 Z. Naturforsch. 35a, 1171—1177 (1980); received July 28 1980   
Published
 1980   
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 ZNA198035a1171    Volume
 35  
192  Author
 Peter Lamparter, Siegfried Steeb  Requires cookie*   Title
 Structure Factors of Liquid CuPb Alloys by Neutron Diffraction    Abstract
 By means of neutron diffraction the structure factors and pair correlation functions of five CuPb alloys, Cu, and Pb in the liquid state have been determined. The nearest neighbour distances have been obtained. The marked effect of small angle scattering with the melt with critical composition (65 at % Cu) is a proof for microsegregation tendency. By comparison with a segregation model for the structure factor the short range order parameter has been derived for melts with 65 and 35 at % Cu, respectively. Experimental In the present work pure Cu, pure Pb, and five alloys with different compositions are investigated. The specimen containers were sealed quartz tubes with 10 mm inner diameter and 0.5 mm wall thickness, surrounded by a lube made from 0.1 mm thick Vanadium foil. The height of he specimens was 45 mm. The neutron diffraction experiments were performed at Kernforschungszentrum Karlsruhe (FR 2, Project 14). The heating device was a Vanadium tube furnace in a vacuum vessel heated by direct current supplied by an electronic temperature control unit. The neutron wavelength was 0.103 nm. The scattered intensity was measured in the angle region 5° 2 0 ^ 118° with 0.25° step scan width. The scan was started four hours after the sample had been heated up to the measuring temperature to assure thermal equilibrium. The average counting rate per position was 6000 counts. For some samples the complete scan was done twice. Thus it could be proofed that no structural change took place during the measuring time. For correction of the measured data the PaalmannPings method [1], and for the normalization the KroghMoe method [2] were applied to obtain the structure factors. The multiple scattering correction was done corresponding to [3]. The densities were extrapolated from data given in [4]. The compositions, the densities, and the temperatures of the samples are listed in Table 1. The neutron scattering parameters are listed in Table 2.   
Reference
 Z. Naturforsch. 35a, 1178—1181 (1980); received September G 1980   
Published
 1980   
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 ZNA198035a1178    Volume
 35  
193  Author
 J. Brickmann  Requires cookie*   Title
 Local Instabilities of Quantum Trajectories in NonLinear Dynamical Systems    Abstract
 Local instability of wave packets is related to an exponential increase of the second moments of the components A Pi 2 and A Qi 2 of the momentum and position operator as a function of the expectation values <Pj> and <(?<> • Equations of motion for zlPi 2 and AQi 2 are derived. In the quasiclassical limit, the instability criterion approaches the TodaBrumer criterion [1, 2] for classical trajectories. Local instabilities for trajectories in classical wdimensional dynamical systems can be related to the existence of an exponential timedependence of the distance d(t) = (d\, d2, ...,d2n)   
Reference
 Z. Naturforsch. 35a, 1182—1185 (1980); received August 14 1980   
Published
 1980   
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 ZNA198035a1182    Volume
 35  
194  Author
 ChaoCheng, '. Yang, Ryuzo Takagi, Isao Okada  Requires cookie*   Title
 Internal Cation Mobilities in the Molten Systems (LiNa)N03 and (NaCs)N03    Abstract
 For the molten salt systems (LiNa)N03 and (NaCs)N03, relative differences of intei'nal mobilities have been measured with the Klemm method. The internal mobilities, b, are calculated from these data and the available conductivity data. In the mixtures of the former system, &xa is always greater than In the latter system, the Chemla crossing point occurs. It is found that bu and &xa in the binary alkali nitrate systems so far investigated are well expressed, except at small molar volumes, by b = {^4/(F— F 0)} exp(— E/RT) with constant A and E, where V is the molar volume and F° a constant for bu and nearly a constant for The values of bes at equal concentrations of CSNO3 in the systems (LiCs)N03 and (NaCs)NOs are practically equal. The internal mobilities obtained are discussed in terms of free space, mutual ionic attraction and thermal agitation.   
Reference
 Z. Naturforsch. 35a, 1186—1191 (1980); received August 19 1980   
Published
 1980   
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 ZNA198035a1186    Volume
 35  
195  Author
 D. Gloyna, A. Kawski, I. Gryczyński  Requires cookie*   Title
 Einfluß von Substituenten auf die Fluoreszenzquantenausbeute bei DonatorAkzeptorsubstituierten transStilbenen    Abstract
 For 4'acceptor substituted 4dimethylaminostilbenes 1 the fluorescence quantum yield <ps increases in nheptane and toluene with decreasing acceptor interaction (i.e. with decreasing polarity in the Sistate). At the same time, the lifetimes Tf w change with q>f so that k[ n remains approximately constant. Changes in cpf for compounds 1 result from a strong change of the rate constant ktp of radiationless deactivation. This is interpreted in terms of the decreased stabilization of the Sistate occurring with the increase in the polarity of the investigated compounds in nonpolar solvents, and remains in good agreement with the calculations carried out previously.   
Reference
 Z. Naturforsch. 35a, 1192—1196 (1980); eingegangen am 18. Juli 1980   
Published
 1980   
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 ZNA198035a1192    Volume
 35  
196  Author
 A. Kawski, Z. Kojro, M. Alicka  Requires cookie*   Title
 Viskositätsund Lösungsmittelabhängigkeit der Fluoreszenzanisotropie und der Lebensdauer von pTerphenyl    Abstract
 Effect of Viscosity and Solvent upon the Fluorescence Anisotropy and Lifetime of pT er phenyl The fluorescence anisotropics (FA) r and the lifetimes of pterphenyl in different solvents have been measured, the effective volumes and the rotational relaxation times being determined. The deviation from the linear dependence of 1/r on 1/r] (»/viscosity of the solvent) may explained by the length of the pterphenyl molecule. The FA measurements were carried out by a method with an Arago compensator, a new method of the automatization of measurements being employed.   
Reference
 Z. Naturforsch. 35a, 1197—1200 (1980); eingegangen am 31. Juli 1980   
Published
 1980   
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 ZNA198035a1197    Volume
 35  
197  Author
 G. Köhler, S. Solar, N. Getoff  Requires cookie*   Title
 Thionine Fluorescence Quenching by Metal Cations    Abstract
 The mechanism of the fluorescence quenching of aqueous thionine by various metal ions (Ce 3+_ , Fe 2+ , Mn 2+ , Mg 2+ , Cs+ and Na +) was studied at pn = 2.5. The following SternVolmer constants (Ksv) were determined: XSv(Fe 2 +) == 1.13 dm 3 mol 1 , Ksw(Mn 2 +) = 0.24 dm 3 mol" 1 , Ksv(Ce 3 +) = 0.24 dm 3 mol 1 , i£sv(Cs~) — 0.03 dm 3 mol 1 . At concentrations below 1 mol.dm 3 Na2S04 and MgS04 are very weak quenchers (Ksv(Na + or Mg 2+) = 0.007), but the influence on the fluorescence yield increases considerably at higher cation concentrations. This was attributed to the formation of ground state complexes between thionine and SO4 2ions. The salt concentration affects considerably the quenching rate of Fe 2+ ions, but much less so that of the other cations. Fluorescence quenching mechanisms are discussed.   
Reference
 Z. Naturforsch. 35a, 1201—1206 (1980); received August 14 1980   
Published
 1980   
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 ZNA198035a1201    Volume
 35  
198  Author
 P. Bordewijk  Requires cookie*   Title
 The Application of the MemoryFunction Formalism to Dielectric Relaxation    Abstract
 The application of the memoryfunction formalism to dielectric relaxation is reconsidered. It is shown that the socalled Corresponding MicroMacro Correlation theorem is not valid and that for a single macroscopic dielectric relaxation time, the singlemolecule dipole correlation function may nevertheless be nonexponential. The deviations from the exponential decay for the singlemolecule dipole correlation function are due to spatially dependent orientational correlations, and can at least partly be interpreted in terms of dielectric friction. The unsureness about these correlations implies that it is simpler to determine the rotational diffusion coefficient from the collective orientation correlation time as determined from dielectric measurements than from the singlemolecule dipole correlation function as obtained from infrared spectroscopy.   
Reference
 Z. Naturforsch. 35a, 1207—1217 (1980); received July 2 1980   
Published
 1980   
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 ZNA198035a1207    Volume
 35  
199  Author
 AsitB. Rakshit  Requires cookie*   Title
 Reaction of the Ground and Metastable Excited C + and N + Ions with C2H4, CH3CI and S02 Gases at 300 K    Abstract
 Rate coefficients and product distributions were measured for the reactions of C + and X + ions with C2H4, CH3CI and SO2. The reactant ions were produced by electron impact using electron energies of 30 V and 100 V and then injected into a flow tube. The product ion distributions for these reactions depend significantly on the electron energy at which the reactant ions are formed. Reactions with CH3CI and SO2 of ions formed at 100 V yield product ion distributions with a preference for fragmentation channels. In the case of C2H4, the simple charge transfer channel is favoured at high energy. Various new product ions have been identified from these studies, some of which having not been observed previously 7 . Rate coefficients for these reactions at 30 V agree closely with the calculated values using Langevin and ADO theory.   
Reference
 Z. Naturforsch. 35a, 1218—1222 (1980); received September 24 1980   
Published
 1980   
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