Spin-lattice relaxation in cuprate superconductors

This presentation gives a personal review of nuclear magnetic resonance (NMR) and nuclear quadrupole resonance (NQR) spin-lattice relaxation studies in cuprate superconductors mainly dealing with the YBa₂Cu₄O₈ compound with many examples from the Zürich laboratory. The studies were performed in both the normal and the superconducting state with various NMR isotopes (e.g.,¹⁷O,^63,65Cu,^135,137Ba). The relatively broad signals were mostly obtained by a phase-alternating add-subtract spin-echo technique. We will discuss the general behavior of spin-lattice relaxation in the normal state and the calculation of the dynamic spin including an approach (on the basis of thet-J model) to calculate the relaxation for plane copper, oxygen, and yttrium. An application of the Luttingerliquid model to the relaxation of chain copper in YBa₂Cu₃O₇ and YBa₂Cu₄O₈ is also given. We then will deal with characteristic features of the YBa₂Cu₄O₈ structure: the spin gap, an electronic crossover in the normal state, the single-spin fluid model, and the d-wave pairing.     

Satelliten; Singuläre Erweiterungen und Derivationen

This paper is divided in two parts. In chapter one we generalize the concept of satellite for abelian categories, substituting Ext by an arbitrary functor E:A ^op×BEns. A very close relation to Kan functor extensions turns out. In chapter two we give a comprehensive formulation of the wellknown cohomology theories for groups and algebras-with the recently used modification in taking the group of derivations as the lowest cohomology group- starting with a categorical definition of the concept of singular extension. There is a zeroth chapter with a construction on functors, needed in both parts, and a third with examples.

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Gekürzte Fassung der Dissertation des Autors zur Erlangung des Doktorgrades der Mathematisch-Naturwissenschaftlichen Fakultät der Universität Hamburg.     

Recurrence of Ancestral Lines and Offspring Trees in Time Stationary Branching Populations

For time stationary Galton- Watson-branching populations on a general type space, the structure of the “individually positive recurrent part” of the system is described: its building blocks consist of finitely many “clans” with positive recurrent trunks. Conditions are given when this nubsystem is void, and when it equals the full system. In addition, positive recurrence on the clan level is characterized. Whereas individual positive recurrence turns out to be a symmetric concept with respect to forward and backward time direction (i. e., with respect to anceatral lines and offspring trees), with individual null recurrence this symmetry can fail even in the absence of branching, i.e., for independently migrating particle systems (Example 13.1). For discrete type spaces a classification of types as to the various individual recurrence concepts (positive, null, forward and backward in time) is proposed and illustrated by a couple of results and examples. For finite type spaces conditiom on the branching dynamics and its mean matrix for the existence of nontrivial equilibria are given.     

On the Law of The Iterated Logarithm for Rapidly Increasing Subsequences

The usual law of the iterated logarithm states that the partial sums S_n of independent and identically distributed random variables can be normalized by the sequence a_n = √nlog log n, such that limsup_n→∞ S_n/a_n = √2 a.s. As has been pointed out by Gut (1986) the law fails if one considers the limsup along subsequences which increase faster than exponentially. In particular, for very rapidly increasing subsequences {n_k≥1} one has limsup_k→∞ S_nk/a_nk = 0 a.s. In these cases the normalizing constants a_nk have to be replaced by √nk log k to obtain a non-trivial limiting behaviour: limsup_k→∞ S_nk/ √nk log k = √2 a.s. We will present an intelligible argument for this structural change and apply it to related results.     

Preparation of Cr2O3-Al2O3 Solid Solutions by Reactive Magnetron Sputtering

 (Al,Cr)₂O₃ layers were deposited on cemented carbide insert tips at a substrate temperature of 500 °C by means of reactive magnetron sputtering. An Al target was sputtered in RF mode and a Cr target in DC mode simultaneously in an oxygen/argon plasma. The influence of the Al and Cr sputter power and of the oxygen partial pressure on composition and structure of the (Al,Cr)₂O₃ layers as well as on the binding states of their components were investigated. Special attention was paid to the interpretation of the O ls and O-KLL fine structure and peak shifts. For the binary phases γ-Al₂O₃ and Cr₂O₃, a good agreement with literature values was observed in each case. In case of the ternary phases a continuous shift of the energetic position of the O1s peak, the O-KL₂₃L₂₃ transition and the modified Auger parameter α ′ of oxygen between the two binary phases γ-Al₂O₃ and Cr₂O₃ could be detected, indicating a wide range of solid solubility between Al₂O₃ and Cr₂O₃. As revealed by grazing incidence X-ray diffraction, the crystallinity of the ternary phases is less pronounced as compared to the binaries and increases with increasing oxygen flow rate.     

Noise power spectra and recovery rates obtained with different nebulizer systems in ICP atomic emission spectrometric analyses in the case of different types of salts and salt contents

The features of different nebulizer systems (cross-flow-, Meinhard- and GMK-system) in the ICP atomic emission spectrometric analyses of solutions with different contents of different salts were evaluated. As basis for the comparison of the nebulizer systems the recovery rates and noise power spectra were used. Both showed that the GMK-system could be used for the widest diversity of salts (sodium chloride, ammonium sulfate and sodium tetraborate) and concentration range (0–10% (m/v)) followed by the cross-flow-system and the Meinhard-system in ICP-OES using a 1 kW argon ICP. Of all nebulizer systems the nebulizer according to Meinhard has the lowest performance for the salts investigated. The noise power spectra of all nebulizer systems are dominated by interference noise from the sample introduction system. This noise increases with the salt concentration of the solution and the GMK-system shows the lowest increase, followed by the cross-flow- and Meinhard-system. Received: 11 October 1999 / Revised: 5 January 2000 / Accepted: 14 January 2000     

Determination of amines used in the oil and gas industry (upstream section) by ion chromatography

During production and purification of crude oil and natural gas several different amines are used as chemicals or operating materials, e.g. film forming long chain amines as corrosion inhibitors, steam volatile amines for pH correction and corrosion protection, alkanolamines as absorbents in sour gas treatment plants, etc. For analytical checks, e.g. determination of corrosion inhibitor concentration in produced media, classical chemical methods are used predominantly, because most of them can be performed in small field laboratories. Some amines, especially the small molecular aliphatic and heterocyclic amines can also be determined by ion chromatography. In our laboratory two types of separation columns (IonPac CS10 and CS12A) were available for ion chromatographic separation. The analysis of the amines in low-salt-containing water, soft water or steam condensate can be performed without problems. The presence of alkali and/or alkaline earth ions in the sample can lead to coelution with these ions, to poor peak resolution or enhanced analysis times, depending on the chromatographic conditions. This work shows some examples of ion chromatography applications for the determination of low-mo1ecular-mass ethanolamines, morpholine and piperazine and discusses the possible interferences and troubles caused by alkali and alkaline earth ions in the matrix.     

Boride-based nano-laminates with MAX-phase-like behaviour

MAX-phases being usually composed of transition metals, group A elements and carbon/nitrogen are considered interesting materials for many applications because of their tremendous bulk modulus, “reversible” plasticity, and machinability. This is mainly due to their unique kind of bonding comprising covalent, ionic as well as metallic bonds providing “easy” planes of rupture and deformability due to the layered crystal structures.In transition metal boride systems, similar types of bonding are available. In particular the W₂B₅-structure type and its stacking variations allow the synthesis of strongly layered crystal structures exhibiting unique delamination phenomena.The paper presents ab initio calculations showing the similarities of bonding between the ternary carbides and the corresponding ternary or quaternary borides. Formation of boride-based nano-laminates from auxiliary liquid phases, from the melt as well as during sintering and precipitation from supersaturated solid solutions will be discussed by means of SEM and TEM studies. The role of impurities weakening the interlayer bonding will be addressed in particular. The pronounced cleavage parallel to the basal plane gives rise for crack deflection and pull-out mechanisms if the laminates are dispersed in brittle matrices such as boron carbide, silicon carbide or other transition metal borides.     

Silver ion dynamics in the Ag5Te2Cl-polymorphs revealed by solid state NMR lineshape and two- and three-time correlation spectroscopies

The relation between structure and ion dynamics in the three polymorphs of Ag(5)Te(2)Cl has been investigated using (109)Ag, (125)Te, and (35)Cl NMR spectroscopies. Specifically, the influence of the structural phase transitions observed near 240 K (P2(1)/c<-->P2(1)/n) and near 332 K (P2(1)/n<-->I4/mcm) upon silver ion mobilities has been studied by temperature dependent (109)Ag NMR lineshapes and spin-lattice relaxation times. While the superionic high temperature phase alpha-Ag(5)Te(2)Cl is characterized by a molten cationic sublattice, fast ion dynamics in the medium-temperature phase beta-Ag(5)Te(2)Cl occurs in spatially restricted regions comprising all the crystallographically distinct silver sites. Temperature dependent magic-angle-spinning linewidths yield an activation energy of 0.38 eV, consistent with 0.44 eV measured from dc electric conductivities. For the low-temperature gamma-modification, results of two- and three-time (109)Ag correlation spectroscopies provide a detailed insight into the nature of the silver ionic hopping motion. Temperature dependent jump rates measured by two-time correlation functions yield an activation energy E(a)= 0.48 eV. (109)Ag NMR three-time correlation functions indicate that the non-exponential relaxation behavior of the silver ions can be attributed to a broad distribution of jump rates rather than correlated forward-backward jumps. Nevertheless, all the silver ions are mobile down to temperatures of about 185 K.