New upper bounds for the magnetization in ferromagnetic one-component systems

A collection of upper bounds on the magnetization in ferromagnetic one-component spin systems is derived from generalizations of the mean-field approximation. In particular, it contains sequences of bounds that converge to the true magnetization. The spin systems in question satisfy the GHS-inequality.Institut für Theoretische Physik, Universität Zürich, Zürich, Switzerland     

Super Riemann surfaces: Uniformization and Teichmüller theory

Teichmüller theory for super Riemann surfaces is rigorously developed using the supermanifold theory of Rogers. In the case of trivial topology in the soul directions, relevant for superstring applications, the following results are proven. The super Teichmüller space is a complex super-orbifold whose body is the ordinary Teichmüller space of the associated Riemann surfaces with spin structure. For genusg>1 it has 3g-3 complex even and 2g-2 complex odd dimensions. The super modular group which reduces super Teichmüller space to super moduli space is the ordinary modular group; there are no new discrete modular transformations in the odd directions. The boundary of super Teichmüller space contains not only super Riemann surfaces with pinched bodies, but Rogers supermanifolds having nontrivial topology in the odd dimensions as well. We also prove the uniformization theorem for super Riemann surfaces and discuss their representation by discrete supergroups of Fuchsian and Schottky type and by Beltrami differentials. Finally we present partial results for the more difficult problem of classifying super Riemann surfaces of arbitrary topology.Enrico Fermi Fellow. Research supported by the NSF (PHY 83-01221) and DOE (DE-AC02-82-ER-40073).     

Preparation and investigation of magnetic properties of wüstite nanoparticles

In this work wüstite nanoparticles have been prepared via high-energy ball milling, using high-purity hematite (Fe₂O₃) and iron (Fe) powders as the starting materials. In order to get a single-phase wüstite different mole ratios of (Fe/Fe₂O₃) were milled, using a planetary mill. X-ray diffraction studies of the as-milled powders show that a single-phase wüstite was formed for a mole ratio of 0.6. Lattice parameter of the wüstite was obtained from XRD data, by which a value of 0.072 was obtained for x in Fe_1−xO. A mean crystallite size of 13±1 nm was calculated for the single-phase wüstite, using Scherrer's formula. The morphology of the powders was also checked by TEM. Variations of pressure and temperature in the vial were recorded with respect to the milling time, using a GTM unit. Hysteresis loops of the as-milled powders at 5 K and room temperature have been obtained by SQUID and by VSM systems, respectively. The loops show non-zero coercivity, in contrast to the bulk wüstite. The observed magnetizations can be explained by a model based on the spinel-type defect clusters in non-stoichiometry wüstite.     

Synchronization of chaotic fractional-order systems via active sliding mode controller

In this paper, we propose a controller based on active sliding mode theory to synchronize chaotic fractional-order systems in master-slave structure. Master and slave systems may be identical or different. Based on stability theorems in the fractional calculus, analysis of stability is performed for the proposed method. Finally, three numerical simulations (synchronizing fractional-order Lü-Lü systems, synchronizing fractional order Chen-Chen systems and synchronizing fractional-order Lü-Chen systems) are presented to show the effectiveness of the proposed controller. The simulations are implemented using two different numerical methods to solve the fractional differential equations.     

Magnetic properties of mechanochemically prepared iron-wüstite (Fe-FeyO) nanocomposites

In this work, iron-wüstite (Fe-Fe_yO) nanocomposites have been prepared via high-energy ball milling (HEBM), using high-purity hematite (α-Fe₂O₃) and iron (Fe) powders as the raw materials with different Fe/Fe₂O₃ mole ratios (MR)=0.6, 0.9, 1.0, 2.3, 4.9 and 13.6. X-ray diffraction studies of the as-milled powders show that a single-phase wüstite was formed for the lowest mole ratio (MR=0.6) and mixtures with MRs higher than 0.6 result in iron-wüstite nanocomposites, except for MR=13.6 that is dominantly a pure iron phase. The mean crystallite sizes of the iron and wüstite in the nanocomposites have been calculated by Scherrer's formula, which were 9±1 and 7±1 nm, respectively. Using the formula a=3.856+0.478y, for Fe_yO, where “a” is the lattice parameter of wüstite, it is possible to estimate the value of “y” for different nanocomposites and a composition of Fe_0.93O was estimated for the wüstite single phase (MR=0.6). In addition, a gradual decrease in “y” from 0.87 to 0.83 was obtained by increasing MR values from 0.9 to 4.9, respectively. The room-temperature Mössbauer spectrum of the single-phase wüstite shows considerable asymmetry due to two overlapping quadrupole doublets. For higher MRs, room-temperature Mössbauer spectra exhibit sextets, which confirm the existence of iron in the samples. The Mössbauer spectrum of the sample with the highest mole ratio (MR=13.6) shows only a sextet related to α-Fe without any detection of wüstite, which is in agreement with the XRD results. The nanosized prepared wüstite shows ferrimagnetic like behavior, which was interpreted according to spinel-like defect clusters. The M_s values obtained from VSM measurements and those calculated based on the Mössbauer data and chemical reaction are in good agreement. By increasing MR from 0.6 to 2.3, the coercivity (H_c) increases sharply to its maximum value at about MR=2.3, for which the value of Fe content is 45% and then drops off. This behavior is discussed based on α-Fe contents in the nanocomposites and percolation threshold.     

Das elektrische und optische Verhalten der Kristalle von NaCl mit Calcium. I

Zusammenfassung Die in dieser Arbeit enthaltenen Ergebnisse betreffend die auf verschiedene Weise zubereiteten Kristalle von NaCl mit Calciumzusatz sind im Abschnitt 3.1 unter den Punkten a) bis e) und im Abschnitt 3.2 unter den Punkten a) bis d) zusammengefaßt. Im Abschnitt 4 wurden vier Möglichkeiten für die Erklärung des unterschiedlichen Verhaltens der Kristalle von NaCl-Ca gezüchtet aus der Schmelze bzw. aus der Lösung diskutiert. Als am wahrscheinlichsten erscheint die unter d) angeführte Möglichkeit, daß nämlich das optische und elektrische Verhalten dieser Kristalle vorwiegend durch die Hydrolyseprodukte beeinflußt wird.

---

The paper gives the results of measuring the dielectric losses and thermally stimulated electron emission and luminescence in NaCl crystals doped with calcium. The crystals were prepared both from the melt and from the solution. The influence of annealing either in air or in dry hydrogen chloride was studied of them. A summary of the results is given at the end of the paper.

---

---

Die Verfasser danken den Diplomchemikern M. Lébl und I. Velická-Kunzlová für ihre Hilfe bei der Zubereitung der Proben und K. Listoová für die sorgfältige Durchführung der Versuche und für die Hilfe bei deren Auswertung.     

Scanning probe microscopy on superconductors: Achievements and challenges

A dislocation dynamical model of the reaction-diffusion type is used to describe the spatio-temporal dynamics of Lüders band propagation in polycrystals. The diffusive nature of dislocation glide is traced back to the random crystallographic orientation of the active slip systems. The role of pile-ups in dislocation multiplication is accounted for by a dynamical generalization of the Hall-Petch law. It is argued that Lüders bands in polycrystals are related to a bistable dynamics of mobile dislocations. Further results obtained cover the dependences on material parameters and deformation conditions of (1) the occurrence, (2) the strain, propagation velocity and width of Lüders bands, and (3) the upper and lower yield stresses. These results are in good agreement with experimental findings.     

Zur Frage der Pb(II)-Komplexe in Gemischten KCl-KBr-Kristallen

The absorption and fluorescent spectra of mixed KCl-KBr crystals with lead admixtures were measured. A comparison with the absorption of analogical mixed solutions showed that the displacement of the absorption band of lead towards longer wave-lengths with increasing content of bromide is caused by the creation of mixed complexes. The latter are also responsible for the fluorescence of the crystals.

---

---

Die Verfasser danken herzlich Herrn Dr. A. Bohun für die wertvollen Diskussionen. Sie danken ferner Frau K. Dolealová für die Durchführung der Absorptionsmessungen der Kristalle und Frau M. Kubovská für die Züchtung der Kristalle.     

On the sympletic geometry of the super Teichmüller space

The geometry of the Teichmüller space of the super Riemann surfaces is examined. The Weil-Petersson Kähler form is calculated in terms of the super coordinate functions which provide local coordinates for the super Teichmüller space. It is shown that the Kähler form on the super Teichmüller space is closed.Work partially supported by Grant-in-Aid for Scientific Research of the Ministry of Education, Science and Culture No. 02302020Work partially supported by Grant-in-Aid for Scientific Research of the Ministry of Educations, Science and Culture No. 02740145     

Die Abhängigkeit der Koerzitivkraft von der plastischen Deformation

In der vorliegenden, Abhandlung werden die Ergebnisse der Messungen der Abhängigkeit der Koerzitivkraft von der plastischen Deformation für Eisen, Nickel einige deren magnetisch weiche Legierungen und weiter für Mumetall und Molybdänpermalloy angeführt. Bei einigen der angeführten Werkstoffe wurden interessante Anomalien im Verlauf der Abhängigkeit von H_c von der plastischen Deformation gefunden. Es wird ein wesentlich niedrigerer Wert von H_c für Nickel angeführt, als gewöhnlich angegeben wird, und eine Begründung für diesen Unterschied angeführt.     

Real-space renormalization for arbitrary single-site potential

A simple real-space renormalization in the spirit of Niemeier-van Leeuwen is used to study the critical behavior of a ⁴-model in two and three dimensions. The block spins are defined such that the single-site potential is unchanged under the transformation. Both a first order cumulant approximation and a mean-field truncation are used. For a widely varying double-well potential only a small dependence of the critical exponents upon the detailed structure of the potential is found in agreement with the universality principle. The (nonuniversal) critical temperature is in good agreement with computer simulations. The method can easily be generalized to arbitrary single-site potentials.Work performed at the Institut für Festkörperforschung, Kernforschungsanlage Jülich, D-5170 Jülich, Fed. Rep. Germany     

Zu den Formeln für das reflektierte und von einer dünnen Metallschicht durchgelassene Licht

Zusammenfassung Der Verfasser hat bewiesen, dass die in der praktischen Optik sehr oft verwendeten Formeln für die Reflexion und die Lichtdurchlässigkeit einer dünnen Schicht nur als Sonderfälle allgemeiner Formeln zu betrachten sind. Darum ist die Verallgemeinerung, die der Verfasser seinerzeit für die Reflexion des Lichtes an zwei und mehreren Schichten und Försterling für die Reflexion des Lichtes an einer dünnen Metallschicht durchgeführt haben, unzulässig. Die genaue Ableitung dieser Formeln muss von den allgemeineren Formeln ausgehen. In dieser Abhandlung ist die Ableitung der genauen Formeln für die Reflexion und für die Lichtdurchlässigkeit einer dünnen Metallschicht angeführt.     

Analysis of thermodynamic identities for materials under extreme compression

Some basic relationships for materials under extreme compression are analyzed with the help of the calculus of indeterminates. The analysis presented here provides an understanding of the origin of identities and constraints at infinite pressure which are satisfied by all physically acceptable equations of state. These identities involve the bulk modulus and its pressure derivatives, the Grüneisen parameter and its volume derivatives, the thermal expansivity, and the Anderson-Grüneisen parameter. The identity for the third-order Grüneisen parameter in terms of the pressure derivatives of the bulk modulus at extreme compression is valid even if the free-volume parameter changes with pressure.     

Die Messung des Verlaufs der Elektronenkonzentration in den laufenden Schichten in Neon

Zusammenfassung In der Arbeit wurde die Messung der Änderung der Elektronenkonzentration in den laufenden Schichten in Ne nach der in [4] vorgeschlagenen Methode vorgenommen. Die Meßergebnisse zeigen, daß sich die Methode zum Studium der laufenden Schichten im Bereiche niedriger Drücke und kleiner Entladungsströme eignet.

---

The concentration of electrons in moving striations in Ne was measured by the resonance high-frequency method proposed in [4]. The results of measurement show that the method is suitable for studying moving striations in the region of low pressures and small discharge currents.

---

---

Abschließend dankt der Verfasser Herrn Prof. V. Kunzl für die Unterstützung seiner Arbeit, den Kollegen J. Studnika und V. Veselý für die Hilfeleistung bei den Versuchen und M. Novák für seine wertvollen Hinweise.     

Equilibrium distribution function of a relativistic dilute perfect gas

An alternative to the Jüttner distribution has been recently proposed by several authors. The literature on the topic is reviewed critically. It is found that the Jüttner distribution is correct and that the alternative distribution contradicts quantum field theory, statistical physics and continuum mechanics.     

Development and applications of polarized electron spectroscopy to solids and surfaces

Recent milestones in the development of spin-polarized electron spectroscopy, along with trends in current applications to magnetic solids and surfaces, are reviewed. Emphasis is placed on the work performed in the Jülich-Cologne area since 1978 as it was originally promoted also by Bernd Mühlschlegel.Dedicated to B. Mühlschlegel on the occasion of the 60th birthday     

Characterization and uniqueness of distinguished self-adjoint extensions of Dirac operators

Distinguished self-adjoint extensions of Dirac operators are characterized by Nenciu and constructed by means of cut-off potentials by Wüst. In this paper it is shown that the existence and a more explicit characterization of Nenciu's self-adjoint extensions can be obtained as a consequence from results of the cut-off method, that these extensions are the same as the extensions constructed with cut-off potentials and that they are unique in some sense.On leave from Universität Zürich, Schöneberggasse 9, CH-8001 Zürich. Supported by Swiss National Science FoundationOn leave from Technische Universität Berlin, Straße des 17. Juni 135, D-1000 Berlin     

Über den Einbau von Nickel in die Alkalichloride

By means of the method of P. Brauer the energy of built in Ni⁺⁺-ions in the crystals of LiCl, NaCl and KCl was calculated. The results let understand the differences in the content of nickel in the mentioned crystals.

---

---

Der Verfasser dankt herzlich Herrn Dr. K. Polák für die wertvollen Diskussionen und Bemerkungen zu dieser Arbeit, Frl. Dipl.-Ing. H. Svobodová für die Durchführung der numerischen Berechnungen und Herrn Dr. K. Funk für die Beistellung der Analysenergebnisse.     

Development in time-differential in-beam Mössbauer spectroscopy

An overview of results on static and dynamic properties of single Fe atoms implanted into Si, Ge and ZnS as investigated with in-beam Mössbauer spectroscopy (IBMS) is given. The potential and limitations of the method are discussed.This work was supported in part by Gesellschaft für Schwerionenphysik Darmstadt and Bundesministerium für Forschung und Technologie, Bonn.     

Die kovariante phänomenologische Quantentheorie des elektromagnetischen Feldes im Dielektrikum

Zusammenfassung In der vorliegenden Arbeit wird eine neue Formulierung der Quanten-theorie des makroskopischen elektromagnetischen Feldes im Dielektrikum gebracht, die zu den Lorentz-Transformationen kovariant ist. Auf Grund der kovarianten Coulombschen Eichung werden die Feldgleichungen abge-leitet und Vertauschungsrelationen für das verallgemeinerte Trans-versalfeld aufgestellt. Es werden zwei Definitionen für den Gesamt-impuls und die Gesamtenergie (30)und (37)angeführt. Für den Fall, dass der Energie-Impuls-Tensor divergenzfrei ist, führen beide Definitionen zu den gleichen Eigenwerten des Impulses und der Energie, die im Falle des Strahlungstensors mit den in der Arbeit [2]abgeleiteten Werten und im Falle des Minkowskischen Tensors mit den in der Arbeit [1]abgelei-teten Werten tibereinstimmen. Für den Abrahamschen Tensor führt die Definition (37)zu den gleichen Ergebnissen wie für den Strahlungs-tensor. Schliesslich wird der Übergang von unserer phänomenologischen Theorie zur Schwingerschen Quantenelektrodynamik des Feldes im Va-kuum besprochen.