Chemnitz, Techn. Univ., Diplomarb., 2003.

This document describes the construction of a computer-based simulation of instationary heat transfer through heat protective textiles. Especially mathematical modeling, numerical treatment and inverse determination of unknown parameters is handled in case of a fault arc test. First simulation results of different model variants are presented. / Die Arbeit beschreibt die Erstellung einer computerbasierten Simulation für instationäre thermische Vorgänge in Hitzeschutztextilien. Speziell wird dabei ein Störlichtbogentest von der mathematischen Modellbildung über die numerische Umsetzung bis hin zur inversen Bestimmung unbekannter Modellparameter betrachtet. Erste Simulationsergebnisse bei verschiedenen Modellvarianten werden dargestellt.

This document describes the construction of a computer-based simulation of instationary heat transfer through heat protective textiles. Especially mathematical modeling, numerical treatment and inverse determination of unknown parameters is handled in case of a fault arc test. First simulation results of different model variants are presented. / Die Arbeit beschreibt die Erstellung einer computerbasierten Simulation für instationäre thermische Vorgänge in Hitzeschutztextilien. Speziell wird dabei ein Störlichtbogentest von der mathematischen Modellbildung über die numerische Umsetzung bis hin zur inversen Bestimmung unbekannter Modellparameter betrachtet. Erste Simulationsergebnisse bei verschiedenen Modellvarianten werden dargestellt.

In this thesis we used ESR to investigate magnetic properties of low D vandium and copper oxides in which small quantum spins are arranged in 1D chains and 2D layers. The thesis covers five different low dimensional spin systems. They turned out to be experimental reliazation of some of the most intersiting theoritical models in the field of quantum magnetism.

This experimental work focusses on the magnetic thermal conductivity, κ_mag, of the one-dimensional two-leg spin ladder system Sr_14Cu_24O_41 and the spin chain system SrCuO_2. These two S = 1/2 antiferromagnetic Heisenberg compounds possess enormous magnetic contributions to the heat transport which in some cases exceed the phonon contributions by more than one order of magnitude. Despite of intense ongoing experimental and theoretical investigations, the underlying mechanism of the magnetic heat transport remains unclear. The study of κ_mag aims a better understanding of the basic physics which determine mobility, scattering and dissipation of the dispersing magnetic excitations. The most important tool used in this study is to selectively influence the structure and the electronic and magnetic properties of the compounds through doping. For this purpose single crystalline samples were produced using the Traveling Solvent Floating Zone technique, a crucible-free technology, which allows the growth of centimeter sized single crystals of high quality. In particular, the successful growth of large quantities of the hole-free ladders La_4Sr_10Cu_24O_41 allowed the realization of inelastic neutron scattering and, for the first time, the acquisition of the complete magnetic excitation spectrum of the spin ladder, composed not only by the triplon band, but also by the two-triplon continuum, permitting an accurate determination of the coupling constants in this system. The importance of the cyclic-exchange, previously unclear, was asserted. In order to study the scattering mechanisms of the magnetic excitations (triplons) off static defects in the two-leg ladder Sr_14Cu_24O_41, this compound was doped with tiny amounts of Zn. Occupying the Cu site in the ladders, the Zn plays the role of a non-magnetic defect, imposing an upper limit to the mean free path of the triplons. The thermal conductivity of Sr_14Cu_(14−z)Zn_zO_41, with z = 0, 0.125, 0.25, 0.5 and 0.75, shows a strong decrease of both the phononic and magnetic contributions with increasing z value. In particular, the decrease of the magnetic part indicates an increased scattering of the triplons off Zn defects. The analysis of κ_mag, using a kinetic model, allows the extraction of the triplon mean free path l_mag. This quantity was successfully correlated to the mean Zn-Zn distance along the ladders, confirming the validity of the employed kinetic model and corroborating results of previous works. In SrCuO_2, the magnetic contribution to the thermal conductivity appears as a hump-like anomaly on the high-T back of the low-T phonon peak. In order to better separate the magnetic contribution from the phononic background, small amounts of Sr were substituted by the smaller and lighter Ca, leading, on the one hand, to an increased scattering of the phonons and consequently to a suppression of the phononic thermal conductivity. On the other hand, since Ca is isovalent to Sr, no significant changes of the magnetic properties of the system are expected: a magnetic peak belonging to κ_mag should appear. Measurements of the thermal conductivity of Sr_(1−x)Ca_xCuO_2 for x = 0, 0.0125, 0.025, 0.05 and 0.1 show indeed a systematic decrease of the phonon thermal conductivity with increasing x. However, against initial expectations, no magnetic peak appears. Instead, the magnetic thermal conductivity decreases at intermediate and low temperatures with increasing doping level, indicating a strong influence of the Ca dopant on the magnetic system. Surprisingly, no changes of κ_mag occur at higher temperatures, where κ_mag remains constant for all doping levels. To explain this intriguing temperature and doping dependence of κ_mag, three scenarios are proposed. One of the scenarios is based on the phenomenon of mutual spinon and phonon heat transport, the so called spin-phonon-drag mechanism. Another scenario assumes an effective scattering of spinons off Ca defects. In a third scenario, the appearance of a gap in the doped compounds is considered. The obvious effect of the Ca dopant on the magnetic thermal conductivity motivated a more detailed investigation of the doping dependence of electronic and magnetic properties in Sr_(1−x)Ca_xCuO_2. NMR data reveal the presence of a magnetic gap for the x = 0.1 compound. The doping dependent evolution of the specific heat at low-T is consistent with this result. Furthermore, susceptibility data may be explained within a segmentation of the spin chains, which in turn can be also related to the opening of a gap. These results strongly support that the reduction of κ_mag in the Ca doped compounds is related to a smaller number of magnetic excitations participating in the heat transport due to the presence of the gap. A possible reduction of the chain length, as suggested by the susceptibility data, is also consistent with the scenario of a reduced κ_mag due to an increased scattering of magnetic excitations. In spite of these partially consistent results, there are still no clear-cut explanations for the evolution of κ_mag upon doping. In particular, it cannot be completely ruled out that a fraction of the Ca dopant goes into the chains, a point which has to be urgently clarified in order to allow a correct interpretation of the data.

Fundamental conservation laws predict a dissipationless transport behavior in one-dimensional S=1/2 spin chains. This truly ballistic heat transport suggests anomalously large life times and mean free paths of the elementary excitations of the spin chain, spinons. Despite this rigorous prediction, in any real system, the transport is dissipative, due to the interaction of spinons with defects and phonons. Nevertheless, a promising large magnetic thermal conductivity \\kappa_{mag} has been observed in a few copper-oxide systems. Characteristic for these cuprate systems is a large exchange interaction J along the spin chain. However, due to the limited number and knowledge of the systems showing a large \\kappa_{mag}, it has been difficult, to identify overarching trends. The goal of this thesis therefore is twofold. First, to test new compounds for the appearance of magnetic heat transport and second, to broaden the understanding of the known compounds by studying the influence of various kinds of impurities. In particular, three families of materials are studied. First, the thermal conductivity \\kappa(T) of the compounds TiOBr and TiOCl is investigated. Below room temperature the compounds undergo two phase transitions T_{c2} and T_{c1}. Above T_{c2} the compounds contain S=1/2 spin chains with J_{Cl}=676 K and J_{Br}=375 K respectively, formed by direct orbital overlap of the Ti-atoms. Below T_{c1} the chains dimerize to form a non-magnetic ground state. The thermal conductivity exhibits pronounced anomalies at T_{c2} and T_{c1} confirming the transitions being of second and first order respectively. Surprisingly, \\kappa(T) appears to be dominated by phonon heat conduction, since no indications of a significant magnetic contribution is found. This is in contrast to the expectation of a spin chain system. In this context possible scenarios to understand the unusual behavior of the thermal conductivity are discussed. Second, two related materials, the single chain Sr_{2}CuO_{3} and the double chain SrCuO_{2} are investigated. In high purity samples huge magnetic heat conductivities and concomitantly, extremely large spinon mean free paths of >0.5 µm for Sr_{2}CuO_{3} and >1 µm for SrCuO_{2} are observed. This demonstrates that \\kappa_{mag} is only limited by extrinsic scattering processes, which is a clear signature of ballistic transport in the underlying spin model. Additionally, various subtle modifications of the spin chain are studied. Due to the large mean free path a pristine picture of the intrinsic incidents is expected. In particular, a chemical pressure is applied to the spin chain by doping SrCuO_{2} with Ca. This has a surprisingly strong effect on \\kappa_{mag}. Furthermore, the influence of magnetic Ni and non-magnetic Mg doping is studied for SrCuO_{2}. While Ni-doping has a large impact on the magnetic thermal conductivity, Mg-doping shows no influence. In order to clarify this surprising behavior, \\kappa_{mag} is compared to measurements of the single chain compound Sr_{2}CuO_{3}. Third, the magnetic thermal conductivity of the spin chain material CaCu_{2}O_{3} doped with non-magnetic Zn impurities is studied. \\kappa_{mag} of the pure compound is linear up to room temperature, which is indicative of a T-independent scattering rate of the magnetic excitations. Both, magnitude and T-dependence of \\kappa_{mag} exhibit a very unusual doping dependence. At moderate Zn-doping the linear temperature dependence of \\kappa_{mag} is preserved and the absolute value of \\kappa_{mag} increases. A slight suppression of \\kappa_{mag} occurs only at high Zn doping, where, surprisingly, the T-dependence of \\kappa_{mag} changes from linearity to one with a higher power of T . In order to clarify this surprising behavior, the results are compared to a detailed study of the g-tensor of the impurities in the material by means of ESR experiments, which reveal a change of the impurity type with increasing Zn-content.

In this thesis we used ESR to investigate magnetic properties of low D vandium and copper oxides in which small quantum spins are arranged in 1D chains and 2D layers. The thesis covers five different low dimensional spin systems. They turned out to be experimental reliazation of some of the most intersiting theoritical models in the field of quantum magnetism.

Fundamental conservation laws predict a dissipationless transport behavior in one-dimensional S=1/2 spin chains. This truly ballistic heat transport suggests anomalously large life times and mean free paths of the elementary excitations of the spin chain, spinons. Despite this rigorous prediction, in any real system, the transport is dissipative, due to the interaction of spinons with defects and phonons. Nevertheless, a promising large magnetic thermal conductivity \\kappa_{mag} has been observed in a few copper-oxide systems. Characteristic for these cuprate systems is a large exchange interaction J along the spin chain. However, due to the limited number and knowledge of the systems showing a large \\kappa_{mag}, it has been difficult, to identify overarching trends. The goal of this thesis therefore is twofold. First, to test new compounds for the appearance of magnetic heat transport and second, to broaden the understanding of the known compounds by studying the influence of various kinds of impurities. In particular, three families of materials are studied. First, the thermal conductivity \\kappa(T) of the compounds TiOBr and TiOCl is investigated. Below room temperature the compounds undergo two phase transitions T_{c2} and T_{c1}. Above T_{c2} the compounds contain S=1/2 spin chains with J_{Cl}=676 K and J_{Br}=375 K respectively, formed by direct orbital overlap of the Ti-atoms. Below T_{c1} the chains dimerize to form a non-magnetic ground state. The thermal conductivity exhibits pronounced anomalies at T_{c2} and T_{c1} confirming the transitions being of second and first order respectively. Surprisingly, \\kappa(T) appears to be dominated by phonon heat conduction, since no indications of a significant magnetic contribution is found. This is in contrast to the expectation of a spin chain system. In this context possible scenarios to understand the unusual behavior of the thermal conductivity are discussed. Second, two related materials, the single chain Sr_{2}CuO_{3} and the double chain SrCuO_{2} are investigated. In high purity samples huge magnetic heat conductivities and concomitantly, extremely large spinon mean free paths of >0.5 µm for Sr_{2}CuO_{3} and >1 µm for SrCuO_{2} are observed. This demonstrates that \\kappa_{mag} is only limited by extrinsic scattering processes, which is a clear signature of ballistic transport in the underlying spin model. Additionally, various subtle modifications of the spin chain are studied. Due to the large mean free path a pristine picture of the intrinsic incidents is expected. In particular, a chemical pressure is applied to the spin chain by doping SrCuO_{2} with Ca. This has a surprisingly strong effect on \\kappa_{mag}. Furthermore, the influence of magnetic Ni and non-magnetic Mg doping is studied for SrCuO_{2}. While Ni-doping has a large impact on the magnetic thermal conductivity, Mg-doping shows no influence. In order to clarify this surprising behavior, \\kappa_{mag} is compared to measurements of the single chain compound Sr_{2}CuO_{3}. Third, the magnetic thermal conductivity of the spin chain material CaCu_{2}O_{3} doped with non-magnetic Zn impurities is studied. \\kappa_{mag} of the pure compound is linear up to room temperature, which is indicative of a T-independent scattering rate of the magnetic excitations. Both, magnitude and T-dependence of \\kappa_{mag} exhibit a very unusual doping dependence. At moderate Zn-doping the linear temperature dependence of \\kappa_{mag} is preserved and the absolute value of \\kappa_{mag} increases. A slight suppression of \\kappa_{mag} occurs only at high Zn doping, where, surprisingly, the T-dependence of \\kappa_{mag} changes from linearity to one with a higher power of T . In order to clarify this surprising behavior, the results are compared to a detailed study of the g-tensor of the impurities in the material by means of ESR experiments, which reveal a change of the impurity type with increasing Zn-content.

This experimental work focusses on the magnetic thermal conductivity, κ_mag, of the one-dimensional two-leg spin ladder system Sr_14Cu_24O_41 and the spin chain system SrCuO_2. These two S = 1/2 antiferromagnetic Heisenberg compounds possess enormous magnetic contributions to the heat transport which in some cases exceed the phonon contributions by more than one order of magnitude. Despite of intense ongoing experimental and theoretical investigations, the underlying mechanism of the magnetic heat transport remains unclear. The study of κ_mag aims a better understanding of the basic physics which determine mobility, scattering and dissipation of the dispersing magnetic excitations. The most important tool used in this study is to selectively influence the structure and the electronic and magnetic properties of the compounds through doping. For this purpose single crystalline samples were produced using the Traveling Solvent Floating Zone technique, a crucible-free technology, which allows the growth of centimeter sized single crystals of high quality. In particular, the successful growth of large quantities of the hole-free ladders La_4Sr_10Cu_24O_41 allowed the realization of inelastic neutron scattering and, for the first time, the acquisition of the complete magnetic excitation spectrum of the spin ladder, composed not only by the triplon band, but also by the two-triplon continuum, permitting an accurate determination of the coupling constants in this system. The importance of the cyclic-exchange, previously unclear, was asserted. In order to study the scattering mechanisms of the magnetic excitations (triplons) off static defects in the two-leg ladder Sr_14Cu_24O_41, this compound was doped with tiny amounts of Zn. Occupying the Cu site in the ladders, the Zn plays the role of a non-magnetic defect, imposing an upper limit to the mean free path of the triplons. The thermal conductivity of Sr_14Cu_(14−z)Zn_zO_41, with z = 0, 0.125, 0.25, 0.5 and 0.75, shows a strong decrease of both the phononic and magnetic contributions with increasing z value. In particular, the decrease of the magnetic part indicates an increased scattering of the triplons off Zn defects. The analysis of κ_mag, using a kinetic model, allows the extraction of the triplon mean free path l_mag. This quantity was successfully correlated to the mean Zn-Zn distance along the ladders, confirming the validity of the employed kinetic model and corroborating results of previous works. In SrCuO_2, the magnetic contribution to the thermal conductivity appears as a hump-like anomaly on the high-T back of the low-T phonon peak. In order to better separate the magnetic contribution from the phononic background, small amounts of Sr were substituted by the smaller and lighter Ca, leading, on the one hand, to an increased scattering of the phonons and consequently to a suppression of the phononic thermal conductivity. On the other hand, since Ca is isovalent to Sr, no significant changes of the magnetic properties of the system are expected: a magnetic peak belonging to κ_mag should appear. Measurements of the thermal conductivity of Sr_(1−x)Ca_xCuO_2 for x = 0, 0.0125, 0.025, 0.05 and 0.1 show indeed a systematic decrease of the phonon thermal conductivity with increasing x. However, against initial expectations, no magnetic peak appears. Instead, the magnetic thermal conductivity decreases at intermediate and low temperatures with increasing doping level, indicating a strong influence of the Ca dopant on the magnetic system. Surprisingly, no changes of κ_mag occur at higher temperatures, where κ_mag remains constant for all doping levels. To explain this intriguing temperature and doping dependence of κ_mag, three scenarios are proposed. One of the scenarios is based on the phenomenon of mutual spinon and phonon heat transport, the so called spin-phonon-drag mechanism. Another scenario assumes an effective scattering of spinons off Ca defects. In a third scenario, the appearance of a gap in the doped compounds is considered. The obvious effect of the Ca dopant on the magnetic thermal conductivity motivated a more detailed investigation of the doping dependence of electronic and magnetic properties in Sr_(1−x)Ca_xCuO_2. NMR data reveal the presence of a magnetic gap for the x = 0.1 compound. The doping dependent evolution of the specific heat at low-T is consistent with this result. Furthermore, susceptibility data may be explained within a segmentation of the spin chains, which in turn can be also related to the opening of a gap. These results strongly support that the reduction of κ_mag in the Ca doped compounds is related to a smaller number of magnetic excitations participating in the heat transport due to the presence of the gap. A possible reduction of the chain length, as suggested by the susceptibility data, is also consistent with the scenario of a reduced κ_mag due to an increased scattering of magnetic excitations. In spite of these partially consistent results, there are still no clear-cut explanations for the evolution of κ_mag upon doping. In particular, it cannot be completely ruled out that a fraction of the Ca dopant goes into the chains, a point which has to be urgently clarified in order to allow a correct interpretation of the data.

Für die Simulation technischer Bauteile mit Hilfe der Finite-Elemente-Methode (FEM) werden tensorielle Stoffgesetze benötigt, die zu einem beliebigen dreidimensionalen Verzerrungszustand und gegebenenfalls der Belastungsvorgeschichte und -geschwindigkeit des Materials die zugehörige Spannungsantwort liefern. Die Entwicklung derart komplexer Materialmodelle verläuft oftmals über Zwischenstufen, die zunächst nur Vorhersagen für den einachsigen Zug-/Druckversuch erlauben. Zur automatischen Verallgemeinerung solcher eindimensionaler Materialbeschreibungen zu vollständig dreidimensionalen Stoffgesetzen für die Finite-Elemente-Methode wird im Rahmen dieser Arbeit das Konzept repräsentativer Raumrichtungen vorgeschlagen, welches auf der Integration einachsiger Spannungszustände über eine diskrete Anzahl gleichmäßig verteilter (repräsentativer) Raumrichtungen basiert. Zur Untersuchung der grundlegenden Eigenschaften des Algorithmus wurden verschiedene inelastische tensorielle Beispielstoffgesetze herangezogen, deren eindimensionale Formulierung als Eingangsmodell für die repräsentativen Raumrichtungen dient. Hierbei zeigt sich, dass die wesentlichen Materialeigenschaften des jeweiligen uniaxialen Eingangsmodells bei der Verallgemeinerung vollständig erhalten bleiben. Weiterhin werden einige wichtige Effekte vom Konzept automatisch generiert, wie z. B. die anisotrope Entfestigung technischer Gummiwerkstoffe oder die formative Verfestigung metallischer Werkstoffe, was eine realitätsnahe Simulation dieser Materialklassen ohne zusätzlichen Arbeitsaufwand erlaubt. Das Konzept wurde zusätzlich auf Stoffgesetze angewendet, die ausschließlich in Form einer eindimensionalen Materialbeschreibung vorliegen und somit konkrete Anwendungsfällle darstellen. Darüber hinaus wurden für einige ausgewählte Stoffgesetze in repräsentativen Raumrichtungen Vergleiche mit Ergebnissen aus experimentellen Versuchen vorgenommen, wobei sich stets eine gute Übereinstimmung zwischen Experiment und Simulation ergibt. Das Konzept repräsentativer Raumrichtungen wurde in die zwei kommerziellen Finite-Elemente-Programme MSC.Marc und ABAQUS implementiert. Hiermit können Simulationen inhomogener Verzerrungs- und Spannungsverteilungen durchgeführt werden, obwohl das zugrunde liegende Stoffgesetz lediglich einachsige Spannungszustände beschreibt. In diesem Zusammenhang werden verschiedene Methoden vorgestellt, mit deren Hilfe die Effizienz einer FEM-Simulation erheblich gesteigert werden kann. Dies betrifft zum einen die Generierung einer gleichmäßigen Verteilung von repräsentativen Raumrichtungen mit Hilfe eines numerischen Algorithmus zur Simulation sich abstoßender elektrischer Punktladungen auf der Kugeloberfläche. Zum anderen besteht die Möglichkeit, die einzelnen Sätze von repräsentativen Raumrichungen in den Gaußpunkten eines finiten Elementes unterschiedlich zueinander auszurichten, was bei gleichbleibendem Rechenaufwand eine beträchtliche Erhöhung der Rechengenauigkeit erlaubt. / The simulation of technical components using the finite element method (FEM) requires tensorial constitutive models which describe the complete relation between a given three-dimensional state of strain (in some cases also the loading history and strain rate) and the corresponding state of stress. The development of such complex material models often leads to an intermediate stage that enables the prediction of uniaxial tension and compression only. The automatic generalization of those one-dimensional material descriptions to complete three-dimensional constitutive models for the finite element method can be accomplished by using the concept of representative directions which is based on the integration of uniaxial stresses over a discrete number of uniformly distributed (representative) directions in space. In order to investigate the fundamental characteristics of the algorithm several inelastic tensorial constitutive models were used, whose one-dimensional formulation serves as the input model for the use within the representative directions. In this context it becomes evident that the essential material properties of the respective uniaxial input model are completely preserved during the process of generalization. Furthermore, some important effects are produced automatically by the concept such as the anisotropic stress softening of technical rubber materials or the distortional hardening of metallic materials, which enables a realistic simulation of those material classes without spending additional effort. The concept was also applied to material models that are available in form of a one-dimensional material description only, so that these can be regarded as concrete applications. In addition, some of the material models in representative directions were compared to experimental data, whereas a good agreement between measurement and simulation can be noticed. The concept of representative directions has been implemented into the commercial finite element programs MSC.Marc and ABAQUS. This enables simulations of inhomogeneous strain and stress distributions even though the underlying material model describes uniaxial loading processes only. In this context, several methods are introduced which can be applied to increase the efficiency of a finite element simulation to a great extent. On the one hand this affects the generation of a uniform distribution of representative directions using a numerical algorithm simulating the repulsion of electric charges on the surface of a sphere. On the other hand, it is possible to adjust the sets of representative directions at the integration points of a finite element differently, which leads to an increasing computational accuracy at constant computational effort.