The crystal field strength parameter and the maximum splitting of the 7F1 manifold of the Eu3+ ion in oxides

We examine, from both the experimental and theoretical point of view, the behavior of the maximum splitting ΔE, of the 7F1 manifold of the Eu3+ ion as a function of the so-called crystal field strength parameter, Nv, in a series of oxides. In connection with the original theory that describes the relation between ΔE and Nv, a more consistent procedure to describe this relation is presented for the cases of small total angular momentum J. Good agreement is found between theory and experiment. © 1995.

Exchange and crystal field effects in the ESR spectra of Eu(2+) in LaB(6)

Electron spin resonance of Eu(2+) (4f(7), S=7/2) in a La hexaboride (LaB(6)) single crystal shows a single anisotropic Dysonian resonance. From the observed negative g shift of the resonance, it is inferred that the Eu(2+) ions are covalent exchange coupled to the B 2p-like host conduction electrons. From the anisotropy of the spectra (linewidth and field for resonance), we found that the S ground state of Eu(2+) ions experience a cubic crystal field of a negative fourth order crystal field parameter (CFP), b(4)=-11.5(2.0) Oe, in agreement with the negative fourth order CFP, A(4), found for the non-S ground state R hexaborides. These results support covalency as the dominant contribution to the fourth order CFP for the whole R hexaboride family.

Bumps and rings in a two-dimensional neural field: splitting and rotational instabilities

In this paper we consider instabilities of localised solutions in planar neural field firing rate models of Wilson-Cowan or Amari type. Importantly we show that angular perturbations can destabilise spatially localised solutions. For a scalar model with Heaviside firing rate function we calculate symmetric one-bump and ring solutions explicitly and use an Evans function approach to predict the point of instability and the shapes of the dominant growing modes. Our predictions are shown to be in excellent agreement with direct numerical simulations. Moreover, beyond the instability our simulations demonstrate the emergence of multi-bump and labyrinthine patterns. With the addition of spike-frequency adaptation, numerical simulations of the resulting vector model show that it is possible for structures without rotational symmetry, and in particular multi-bumps, to undergo an instability to a rotating wave. We use a general argument, valid for smooth firing rate functions, to establish the conditions necessary to generate such a rotational instability. Numerical continuation of the rotating wave is used to quantify the emergent angular velocity as a bifurcation parameter is varied. Wave stability is found via the numerical evaluation of an associated eigenvalue problem.

A computer-algebraic approach to the study of the symmetry properties of molecules and clusters

This thesis work is dedicated to use the computer-algebraic approach for dealing with the group symmetries and studying the symmetry properties of molecules and clusters. The Maple package Bethe, created to extract and manipulate the group-theoretical data and to simplify some of the symmetry applications, is introduced. First of all the advantages of using Bethe to generate the group theoretical data are demonstrated. In the current version, the data of 72 frequently applied point groups can be used, together with the data for all of the corresponding double groups. The emphasize of this work is placed to the applications of this package in physics of molecules and clusters. Apart from the analysis of the spectral activity of molecules with point-group symmetry, it is demonstrated how Bethe can be used to understand the field splitting in crystals or to construct the corresponding wave functions. Several examples are worked out to display (some of) the present features of the Bethe program. While we cannot show all the details explicitly, these examples certainly demonstrate the great potential in applying computer algebraic techniques to study the symmetry properties of molecules and clusters. A special attention is placed in this thesis work on the flexibility of the Bethe package, which makes it possible to implement another applications of symmetry. This implementation is very reasonable, because some of the most complicated steps of the possible future applications are already realized within the Bethe. For instance, the vibrational coordinates in terms of the internal displacement vectors for the Wilson's method and the same coordinates in terms of cartesian displacement vectors as well as the Clebsch-Gordan coefficients for the Jahn-Teller problem are generated in the present version of the program. For the Jahn-Teller problem, moreover, use of the computer-algebraic tool seems to be even inevitable, because this problem demands an analytical access to the adiabatic potential and, therefore, can not be realized by the numerical algorithm. However, the ability of the Bethe package is not exhausted by applications, mentioned in this thesis work. There are various directions in which the Bethe program could be developed in the future. Apart from (i) studying of the magnetic properties of materials and (ii) optical transitions, interest can be pointed out for (iii) the vibronic spectroscopy, and many others. Implementation of these applications into the package can make Bethe a much more powerful tool.

Relativistic molecular calculations of superheavy molecules

Relativistic molecular calculations within the Dirac-Slater scheme have been used in a study of the electronic structure of 6d-metal superheavy hexafluorides. The theoretical results are compared with calculations and measurements of the homolog 4d- and 5d-metal hexafluorides. Large spin-orbit splitting dominates the electronic structure and even has the same order of magnitude as the crystal-field splitting for the valence electrons for the superheavy molecules. Ionization energies have been calculated using a transition state procedure.

Self-consistent relativistic molecular calculations of superheavy molecules: (_110 X)F_6

Using new relativistic molecular calculations within the Dirac-Slater scheme it is now feasible to study theoretically molecules containing superheavy elements. This opens a new era for the prediction of the physics and chemistry of superheavy elements. As an example we present the results for (_110 X) F_6, where it is shown that relativistic effects are nearly of the same order of magnitude as the crystal-field splitting.

Ligand substituents effect on 10Dq

Reaction of 5,6-dihydro-5,6-epoxy-1,10-phenanthroline (L) with Ni(ClO4)(2)center dot 6H(2)O in methanol in 3:1 M proportion at room temperature yields [NiL3](ClO4)(2)center dot 2H(2)O. The X-ray crystal structure of the cation Nil(3)(2+) has been determined. Aminolysis of the three epoxide rings in NiL32+ by 4-substituted anilines in boiling water without any Lewis acid catalyst gives a family of Ni(II) complexes with octahedral NiL62+ core. In these complexes, crystal field splitting 10Dq varies from 11601 to 15798 cm(-1) in acetonitrile. The variation in 10Dq is found to be satisfactorily linear (r(2) = 0.951) with the Hammett sigma(R) parameter of the substituent on the anilino fragment. 10Dq increases with the increase in the electron donation ability of the substituent.

The magnetic phase diagram of Gd(2)Sn(2)O(7)

Measurements of the magnetic susceptibility of the frustrated pyrochlore magnet Gd(2)Sn(2)O(7) have been performed at temperatures below T = 5 K and in magnetic fields up to H = 12 T. The phase boundaries determined from these measurements are mapped out in an H-T phase diagram. In this gadolinium compound, where the crystal-field splitting is small and the exchange and dipolar energy are comparable, the Zeeman energy overcomes these competing energies, resulting in at least four magnetic phase transitions below 1 K. These data are compared against those for Gd(2)Ti(2)O(7) and will, we hope, stimulate further studies.

Magnetic susceptibility study of Ce3+ in PbCeA (A=Te, Se, S)

The magnetic susceptibility of Pb(1-x)Ce(x)A (A=S, Se and Te) crystals with Ce3+ concentrations 0.006 <= x <= 0.036 was investigated in the temperature range from 2 K to 300 K. The magnetic susceptibility data was found to be consistent with a E-2(5/2) lowest manifold for Ce3+ ions with a crystal-field splitting Delta=E(Gamma(8))-E(Gamma(7)) of about 340 K, 440 K and 540 K for Pb1-xCexTe, Pb1-xCexSe, and Pb1-xCexS, respectively. For all the three compounds the doublet Gamma(7) lies below the Gamma(8) quadruplet which confirms the substitution of Pb2+ by Ce3+ ions in the host crystals. The observed values for the crystal-field splitting are in good agreement with the calculated ones based on the point-charge model. Moreover, the effective Lande factors were determined by X-band (similar to 9.5 GHz), electron paramagnetic measurements (EPR) to be g=1.333, 1.364, and 1.402 for Ce ions in PbA, A = S. Se and Te, respectively. The small difference with the predicted Lande factor g of 10/7 for the Gamma(7) (J=5/2) ground state was attributed to crystal-field admixture. (C) 2012 Elsevier B.V. All rights reserved.

Numerische und analytische Untersuchungen stark korrelierter fermionischer Mehrbandsysteme

In dieser Arbeit werden vier unterschiedliche, stark korrelierte, fermionische Mehrbandsysteme untersucht. Es handelt sich dabei um ein Mehrstörstellen-Anderson-Modell, zwei Hubbard-Modelle sowie ein Mehrbandsystem, wie es sich aus einer ab initio-Beschreibung für ein korreliertes Halbmetall ergibt.rnrnDie Betrachtung des Mehrstörstellen-Anderson-Modells konzentriert sich auf die Untersuchung des Einflusses der Austauschwechselwirkung und der nicht-lokalen Korrelationen zwischen zwei Störstellen in einem einfach-kubischen Gitter. Das zentrale Resultat ist die Abstandsabhängigkeit der Korrelationen der Störstellenelektronen, welche stark von der Gitterdimension und der relativen Position der Störstellen abhängen. Bemerkenswert ist hier die lange Reichweite der Korrelationen in der Diagonalrichtung des Gitters. Außerdem ergibt sich, dass eine antiferromagnetische Austauschwechselwirkung ein Singulett zwischen den Störstellenelektronen gegenüber den Kondo-Singuletts der einzelnen Störstellen favorisiert und so den Kondo-Effekt der einzelnen Störstellen behindert.rnrnEin Zweiband-Hubbard-Modell, das Jz-Modell, wird im Hinblick auf seine Mott-Phasen in Abhängigkeit von Dotierung und Kristallfeldaufspaltung auf dem Bethe-Gitter untersucht. Die Entartung der Bänder ist durch eine unterschiedliche Bandbreite aufgehoben. Wichtigstes Ergebnis sind die Phasendiagramme in Bezug auf Wechselwirkung, Gesamtfüllung und Kristallfeldparameter. Im Vergleich zu Einbandmodellen kommen im Jz-Modell sogenannte orbital-selektive Mott-Phasen hinzu, die, abhängig von Wechselwirkung, Gesamtfüllung und Kristallfeldparameter, einerseits metallischen und andererseits isolierenden Charakter haben. Ein neuer Aspekt ergibt sich durch den Kristallfeldparameter, der die ionischen Einteilchenniveaus relativ zueinander verschiebt, und für bestimmte Werte eine orbital-selektive Mott-Phase des breiten Bands ermöglicht. Im Vergleich mit analytischen Näherungslösungen und Einbandmodellen lassen sich generische Vielteilchen- und Korrelationseffekte von typischen Mehrband- und Einteilcheneffekten differenzieren.rnrnDas zweite untersuchte Hubbard-Modell beschreibt eine magneto-optische Falle mit einer endlichen Anzahl Gitterplätze, in welcher fermionische Atome platziert sind. Es wird eine z-antiferromagnetische Phase unter Berücksichtigung nicht-lokaler Vielteilchenkorrelationen erhalten, und dabei werden bekannte Ergebnisse einer effektiven Einteilchenbeschreibung verbessert.rnrnDas korrelierte Halbmetall wird im Rahmen einer Mehrbandrechnung im Hinblick auf Korrelationseffekte untersucht. Ausgangspunkt ist eine ab initio-Beschreibung durch die Dichtefunktionaltheorie (DFT), welche dann durch die Hinzunahme lokaler Korrelationen ergänzt wird. Die Vielteilcheneffekte werden an Hand einer einfachen Wechselwirkungsnäherung verdeutlicht, und für ein Wechselwirkungsmodell in sphärischer Symmetrie präzisiert. Es ergibt sich nur eine schwache Quasiteilchenrenormierung. Besonders für röntgenspektroskopische Experimente wird eine gute Übereinstimmung erzielt.rnrnDie numerischen Ergebnisse für das Jz-Modell basieren auf Quanten-Monte-Carlo-Simulationen im Rahmen der dynamischen Molekularfeldtheorie (DMFT). Für alle anderen Systeme wird ein Mehrband-Algorithmus entwickelt und implementiert, welcher explizit nicht-diagonale Mehrbandprozesse berücksichtigt.rnrn

Manifestation of Colossal Thermoelectric Power by Charge Ordered Small and Intermediate Bandwidth Manganites

Thermoelectric materials are revisited for various applications including power generation. The direct conversion of temperature differences into electric voltage and vice versa is known as thermoelectric effect. Possible applications of thermoelectric materials are in eco-friendly refrigeration, electric power generation from waste heat, infrared sensors, temperature controlled-seats and portable picnic coolers. Thermoelectric materials are also extensively researched upon as an alternative to compression based refrigeration. This utilizes the principle of Peltier cooling. The performance characteristic of a thermoelectric material, termed as figure of merit (ZT) is a function of several transport coefficients such as electrical conductivity (σ), thermal conductivity (κ) and Seebeck coefficient of the material (S). ZT is expressed asκσTZTS2=, where T is the temperature in degree absolute. A large value of Seebeck coefficient, high electrical conductivity and low thermal conductivity are necessary to realize a high performance thermoelectric material. The best known thermoelectric materials are phonon-glass electron – crystal (PGEC) system where the phonons are scattered within the unit cell by the rattling structure and electrons are scattered less as in crystals to obtain a high electrical conductivity. A survey of literature reveals that correlated semiconductors and Kondo insulators containing rare earth or transition metal ions are found to be potential thermoelectric materials. The structural magnetic and charge transport properties in manganese oxides having the general formula of RE1−xAExMnO3 (RE = rare earth, AE= Ca, Sr, Ba) are solely determined by the mixed valence (3+/4+) state of Mn ions. In strongly correlated electron systems, magnetism and charge transport properties are strongly correlated. Within the area of strongly correlated electron systems the study of manganese oxides, widely known as manganites exhibit unique magneto electric transport properties, is an active area of research.Strongly correlated systems like perovskite manganites, characterized by their narrow localized band and hoping conduction, were found to be good candidates for thermoelectric applications. Manganites represent a highly correlated electron system and exhibit a variety of phenomena such as charge, orbital and magnetic ordering, colossal magneto resistance and Jahn-Teller effect. The strong inter-dependence between the magnetic order parameters and the transport coefficients in manganites has generated much research interest in the thermoelectric properties of manganites. Here, large thermal motion or rattling of rare earth atoms with localized magnetic moments is believed to be responsible for low thermal conductivity of these compounds. The 4f levels in these compounds, lying near the Fermi energy, create large density of states at the Fermi level and hence they are likely to exhibit a fairly large value of Seebeck coefficient.

Laser induced fluorescence of BaS: Sm phosphor and energy level splitting of Sm3+ ion

Fluorescence of BaS: Sm phosphor has been studied using a pulsed Nitrogen laser (337.1 nm) as the excitation source. The spectrum consists of a broad band in the region 540–660nm superposed by the characteristic Sm3+ lines. Energy level splitting pattern of Sm3+ due to crystal field effects has been calculated and relevent field parameters are evaluated. Analysis shows that Sm3+ takes up Ba2+ substitutional sites.

Syntheses, EPR spectral studies and crystal structures of manganese(II) complexes of neutral N,N donor bidentate Schiff bases and azide/thiocyanate as coligand

Four manganese(II) complexes Mn2(paa)2(N3)4 (1), [Mn(paa)2(NCS)2] 3/2H2O (2), Mn(papea)2(NCS)2 (3), [Mn(dpka)2(NCS)2] 1/2H2O(4) of three neutral N,N donor bidentate Schiff bases were synthesized and physico- chemically characterized by means of partial elemental analyses, electronic, infrared and EPR spectral studies. Compounds 3 and 4 were obtained as single crystals suitable for X-ray diffraction. Compound 4 recrystallized as Mn(dpka)2(NCS)2. Both the compounds crystallized in the monoclinic space groups P21 for 3 and C2/c for 4. Manganese(II) is found to be in a distorted octahedral geometry in both the monomeric complexes with thiocyanate anion as a terminal ligand coordinating through the nitrogen atom. EPR spectra in DMF solutions at 77 K show hyperfine sextets with low intensity forbidden lines lying between each of the two main hyperfine lines and the zero field splitting parameters (D and E) were calculated.