Techn. Hochsch., Diss., 2000--Aachen.

Techn. Hochsch., Diss., 2002--Aachen.

Techn. University, Diss., 2004--Berlin.

In praktischen Aufgabenstellungen können zur Modellierung zufälliger Einflüsse, welche sich durch schwache Abhängigkeiten auszeichnen, schwach korrelierte zufällige Funktionen genutzt werden. Die nähere Untersuchung von Funktionalen schwach korrelierter zufälliger Funktionen ist durch die Gestalt der Lösungen von praktischen Fragestellungen motiviert. Die stochastischen Charakteristiken dieser Lösungen lassen sich im Allgemeinen nicht exakt bestimmen, so dass auf Approximationsverfahren zurückgegriffen werden muss. Diese stehen im Mittelpunkt der Dissertation. Zu Beginn werden Entwicklungen von Momenten und Kumulanten der betrachteten linearen Integralfunktionale schwach korrelierter Prozesse nach der Korrelationslänge des Prozesses hergeleitet und eine Vermutung über die exakte Darstellung der Kumulanten formuliert. Für Integralfunktionale von schwach korrelierten Simulationsprozessen, welche aus der Interpolation von Moving-Average-Prozessen entstehen, werden die definierten Charakteristiken hergeleitet. Außerdem steht die Approximation der unbekannten Dichtefunktion im Fokus der Arbeit. Es werden verschiedene Zugänge genutzt. Eine alternative Herleitung zur bereits in der Literatur untersuchten Gram-Charlier-Entwicklung wird in Form der Edgeworth-Entwicklung angegeben. Des Weiteren werden die Sattelpunkt-Approximation und die Maximum-Entropie-Methode untersucht und anhand von Simulationsergebnissen für Integralfunktionale von Simulationsprozessen miteinander verglichen. / In engineering applications stochastic influences which are characterized by weak dependencies can be modelled, among others, by weakly correlated random functions. The solutions of such problems shape up as integral functionals of weakly correlated random functions which motivates more detailed investigations. In general the exact calculation of stochastic characteristics of such integral functionals is impossible so that we have to be content with approximation methods this thesis focuses on. At the beginning expansions of moments and cumulants of linear integral functionals of weakly correlated random processes with respect to the correlation length are considered and an explicit formula of cumulants is conjectured. For integral functionals of weakly correlated random simulation processes, defined as interpolations of moving average processes, the required expansion coefficients are derived. Furthermore the approximation of the unknown probability density is requested. In the thesis there are different approaches used. First we state an alternative way to achieve the already known Gram Charlier approximation by means of Edgeworth expansion. Then we study two further methods, namely the saddlepoint approximation and the maximum entropy method and compare them on the basis of simulation results for integral functionals of simulation processes.

Techn. Universiẗat, Diss., 2007--Darmstadt.

In praktischen Aufgabenstellungen können zur Modellierung zufälliger Einflüsse, welche sich durch schwache Abhängigkeiten auszeichnen, schwach korrelierte zufällige Funktionen genutzt werden. Die nähere Untersuchung von Funktionalen schwach korrelierter zufälliger Funktionen ist durch die Gestalt der Lösungen von praktischen Fragestellungen motiviert. Die stochastischen Charakteristiken dieser Lösungen lassen sich im Allgemeinen nicht exakt bestimmen, so dass auf Approximationsverfahren zurückgegriffen werden muss. Diese stehen im Mittelpunkt der Dissertation. Zu Beginn werden Entwicklungen von Momenten und Kumulanten der betrachteten linearen Integralfunktionale schwach korrelierter Prozesse nach der Korrelationslänge des Prozesses hergeleitet und eine Vermutung über die exakte Darstellung der Kumulanten formuliert. Für Integralfunktionale von schwach korrelierten Simulationsprozessen, welche aus der Interpolation von Moving-Average-Prozessen entstehen, werden die definierten Charakteristiken hergeleitet. Außerdem steht die Approximation der unbekannten Dichtefunktion im Fokus der Arbeit. Es werden verschiedene Zugänge genutzt. Eine alternative Herleitung zur bereits in der Literatur untersuchten Gram-Charlier-Entwicklung wird in Form der Edgeworth-Entwicklung angegeben. Des Weiteren werden die Sattelpunkt-Approximation und die Maximum-Entropie-Methode untersucht und anhand von Simulationsergebnissen für Integralfunktionale von Simulationsprozessen miteinander verglichen. / In engineering applications stochastic influences which are characterized by weak dependencies can be modelled, among others, by weakly correlated random functions. The solutions of such problems shape up as integral functionals of weakly correlated random functions which motivates more detailed investigations. In general the exact calculation of stochastic characteristics of such integral functionals is impossible so that we have to be content with approximation methods this thesis focuses on. At the beginning expansions of moments and cumulants of linear integral functionals of weakly correlated random processes with respect to the correlation length are considered and an explicit formula of cumulants is conjectured. For integral functionals of weakly correlated random simulation processes, defined as interpolations of moving average processes, the required expansion coefficients are derived. Furthermore the approximation of the unknown probability density is requested. In the thesis there are different approaches used. First we state an alternative way to achieve the already known Gram Charlier approximation by means of Edgeworth expansion. Then we study two further methods, namely the saddlepoint approximation and the maximum entropy method and compare them on the basis of simulation results for integral functionals of simulation processes.

In this thesis the superconducting and magnetic phases of LiOH(Fe,Co)(Se,S), CuFeAs/CuFeSb, and LaFeP_1-xAs_xO - belonging to the 11, 111 and 1111 structural classes of iron-based arsenides and chalcogenides - are investigated by means of 57Fe Mössbauer spectroscopy and muon spin rotation/relaxation (μSR). Of major importance in this study is the application of high magnetic fields in Mössbauer spectroscopy to distinguish and characterize ferro- (FM) and antiferromagnetic (AFM) order. A user-friendly Mössbauer data analysis program was developed to provide suitable model functions not only for high field spectra, but relaxation spectra or parameter distributions in general. In LaFeP_1-xAs_xO the reconstruction of the Fermi surface is described by the vanishing of the Γ hole pocket with decreasing x. The continuous change of the orbital character and the covalency of the d-electrons is shown by Mössbauer spectroscopy. A novel antiferromagnetic phase with small magnetic moments of ~ 0.1 μ_B state is characterized. The superconducting order parameter is proven to continuously change from a nodal to a fully gapped s-wave like Fermi surface in the superconducting regime as a function of x, partially investigated on (O,F) substituted samples. LiOHFeSe is one of the novel intercalated FeSe compounds, showing strongly increased T_C = 43 K mainly due to increased interlayer spacing and resulting two-dimensionality of the Fermi surface. The primary interest of the samples of this thesis is the simultaneously observed ferromagnetism and superconductivity. The local probe techniques prove that superconducting sample volume gets replaced by ferromagnetic volume. Ferromagnetism arises from magnetic order with T_C = 10 K of secondary iron in the interlayer. The tendency of this system to show (Li,Fe) disorder is preserved upon (Se,S) substitution. However, superconductivity gets suppressed. The results of Mössbauer spectroscopy indicate that the systems tends to a secondary structural phase, where the local iron environment observed in pure FeS is absent. Moreover, two interlayer positions of the iron are identified. The absence of enhanced superconducting T_C in LiOHFeS thus is related to a structural instability. Also, in CuFeAs the role of secondary iron at the Cu position turns out to be decisive for the observed magnetic behaviour. As in LiOHFeSe, it orders ferromagnetically at T_C ~ 11 K and superimposes with the magnetic instability of the main iron site. It is shown that a small charge doping of 0.1e/Fe, which is expected from (Cu,Fe) disorder, is sufficient to switch the system between a paramagnetic and an AFM ground state. Both magnetic orders are indistinguishable, because the magnetic order parameters are strongly coupled. This coupling was observed in the structurally identical CuFeSb, where the magnetic order parameters of both iron sites scale perfectly. The magnetically unstable CuFeAs and the ferromagnetic CuFeSb can be classified according to the theory of As height driven magnetism, predicting a change from paramagnetism to AFM and finally FM with increasing As height.

In this thesis the superconducting and magnetic phases of LiOH(Fe,Co)(Se,S), CuFeAs/CuFeSb, and LaFeP_1-xAs_xO - belonging to the 11, 111 and 1111 structural classes of iron-based arsenides and chalcogenides - are investigated by means of 57Fe Mössbauer spectroscopy and muon spin rotation/relaxation (μSR). Of major importance in this study is the application of high magnetic fields in Mössbauer spectroscopy to distinguish and characterize ferro- (FM) and antiferromagnetic (AFM) order. A user-friendly Mössbauer data analysis program was developed to provide suitable model functions not only for high field spectra, but relaxation spectra or parameter distributions in general. In LaFeP_1-xAs_xO the reconstruction of the Fermi surface is described by the vanishing of the Γ hole pocket with decreasing x. The continuous change of the orbital character and the covalency of the d-electrons is shown by Mössbauer spectroscopy. A novel antiferromagnetic phase with small magnetic moments of ~ 0.1 μ_B state is characterized. The superconducting order parameter is proven to continuously change from a nodal to a fully gapped s-wave like Fermi surface in the superconducting regime as a function of x, partially investigated on (O,F) substituted samples. LiOHFeSe is one of the novel intercalated FeSe compounds, showing strongly increased T_C = 43 K mainly due to increased interlayer spacing and resulting two-dimensionality of the Fermi surface. The primary interest of the samples of this thesis is the simultaneously observed ferromagnetism and superconductivity. The local probe techniques prove that superconducting sample volume gets replaced by ferromagnetic volume. Ferromagnetism arises from magnetic order with T_C = 10 K of secondary iron in the interlayer. The tendency of this system to show (Li,Fe) disorder is preserved upon (Se,S) substitution. However, superconductivity gets suppressed. The results of Mössbauer spectroscopy indicate that the systems tends to a secondary structural phase, where the local iron environment observed in pure FeS is absent. Moreover, two interlayer positions of the iron are identified. The absence of enhanced superconducting T_C in LiOHFeS thus is related to a structural instability. Also, in CuFeAs the role of secondary iron at the Cu position turns out to be decisive for the observed magnetic behaviour. As in LiOHFeSe, it orders ferromagnetically at T_C ~ 11 K and superimposes with the magnetic instability of the main iron site. It is shown that a small charge doping of 0.1e/Fe, which is expected from (Cu,Fe) disorder, is sufficient to switch the system between a paramagnetic and an AFM ground state. Both magnetic orders are indistinguishable, because the magnetic order parameters are strongly coupled. This coupling was observed in the structurally identical CuFeSb, where the magnetic order parameters of both iron sites scale perfectly. The magnetically unstable CuFeAs and the ferromagnetic CuFeSb can be classified according to the theory of As height driven magnetism, predicting a change from paramagnetism to AFM and finally FM with increasing As height.:1 Acronyms and Symbols 2 Introduction 3 Iron-based arsenides and chalcogenides 3.1 Structural properties 3.2 Electronic properties 3.2.1 Magnetism 3.2.2 Superconductivity 3.2.3 Nematic phase 3.3 Investigated samples 4 Moessfit - a free Mössbauer fitting program 4.1 Aspects of program design 4.2 Errors 4.2.1 Uncorrelated 4.2.2 Hesse 4.2.3 MonteCarlo 4.2.4 Minos 4.3 Fitting algorithm 4.4 Maximum entropy method (MEM) 4.5 Kolmogorov-Smirnov confidence 5 Mössbauer spectroscopy 5.1 Mössbauer effect 5.2 Relativistic Doppler effect 5.3 Full static Hamiltonian 5.3.1 Quadrupole interaction 5.3.2 Isomer shift. 5.3.3 Zeeman splitting 5.3.4 Combined interaction 5.3.5 Transition probabilities 5.3.6 The magic angle 5.4 Transmission integral 5.4.1 Absorption area 5.4.2 Ideal thickness 5.4.3 Line width and line shape 5.4.4 Levelling 5.5 Applied field measurements of powder samples 5.5.1 Paramagnet, axial symmetric EFG in transverse field geometry 6 5.5.2 Uniaxial antiferromagnet, axial symmetric EFG in transverse field geometry 6 5.5.3 Paramagnet, axial symmetric EFG in longitudinal field geometry 6 5.5.4 Uniaxial ferromagnet, axial symmetric EFG in transverse field geometry 6 5.5.5 Polarised photons 5.5.6 Total absorption cross section 5.5.7 Polarised sources 5.6 Blume line shape model 6 μSR 6.1 Muon decay and detection 6.2 Magnetic order and dynamic relaxation 6.2.1 Magnetic order 6.2.2 Time dependent field distributions 6.2.3 Aspects of μSR in iron-based arsenides and chalcogenides 6.2.4 Weak transverse field (WTF) 6.3 Superconductivity - transverse field (TF) experiments 7 Intercalated FeSe 7.1 Bulk properties: XRD, susceptibility, resistivity 7.2 Structural characterization 7.3 LiOHFeSe - Mössbauer spectroscopy 7.3.1 Applied transverse field 7.4 LiOHFeSe - μSR 7.4.1 Zero field (ZF) 7.4.2 Pinning experiment 7.4.3 Transverse field (TF) 7.5 Mössbauer investigation of LiOHFe_1-yCo_ySe_1-xS_x. 7.6 Discussion 8 LaFeO(As,P) 8.1 Preliminary measurements and electronic structure calculations 8.2 Mössbauer spectroscopy 8.3 μSR 8.3.1 Magnetic characterization 8.3.2 Spin dynamics 8.3.3 Superconductivity 8.4 Discussion 9 CuFeAs and CuFeSb 9.1 Preliminary results of CuFeAs and CuFeSb 9.2 CuFeAs: Mössbauer spectroscopy 9.2.1 Zero field (ZF) 9.2.2 Longitudinal field (LF) 9.2.3 Transverse field (TF) 9.3 CuFeAs: μSR 9.3.1 Zero field (ZF) 9.3.2 Weak transverse field (WTF) 9.4 Further investigations on CuFeAs 9.4.1 Neutron scattering 9.4.2 Theoretical calculation 9.4.3 Local element analysis with EDX/WDX 9.5 CuFeSb: Mössbauer spectroscopy 9.5.1 Zero Field (ZF) 9.5.2 Transverse field (TF) 9.6 Discussion 10 Conclusion 11 Appendix 11.1 Derivation of the quadrupole interaction and isomer shift 11.2 Matrix form of the static nuclear Hamiltonian 11.3 Mössbauer line intensities 11.4 Blume line shape model 11.4.1 Special case: two states with diagonal Hamiltonians 11.5 Moessfit models 11.5.1 FeSe_1-xS_x(Li_1-zFe_zOH) ZF, standard 11.5.2 FeSe_1-xS_x(Li_1-zFe_zOH) ZF, 4 fractions 11.5.3 FeSe_1-xS_x(Li_1-zFe_zOH) Pinning 11.5.4 FeSe_1-xS_x(Li_1-zFe_zOH) TF 11.5.5 FeSe_1-xS_x(Li_1-zFe_zOH) CS-Vzz-MEM 11.5.6 LaFeP_1-xAs_x+ ferrocene, ZF 11.5.7 LaFeP_1-xAs_x+ ferrocene, LF 11.5.8 LaFeP_1-xAs_x+ iron foil, ZF 11.5.9 LaFeAsO ZF 11.5.10 LaFeAsO TF 11.5.11 CuFeAs + ferrocen, ZF 11.5.12 CuFeAs + ferrocen, ZF, high statistics 11.5.13 CuFeAs + ferrocen, LF 11.5.14 CuFeAs + ferrocen, TF 11.5.15 CuFeSb ZF 11.5.16 CuFeSb TF

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