Über die Existenz invarianter Tori in Hamiltonschen Systemen, die bis auf eine endlich oft differenzierbare Störung analytisch und integrabel sind

Es wird die Existenz invarianter Tori in Hamiltonschen Systemen bewiesen, die bis auf eine 2n-mal stetig differenzierbare Störung analytisch und integrabel sind, wobei n die Anzahl der Freiheitsgrade bezeichnet. Dabei wird vorausgesetzt, dass die Stetigkeitsmodule der 2n-ten partiellen Ableitungen der Störung einer Endlichkeitsbedingung (Integralbedingung) genügen, welche die Hölderbedingung verallgemeinert. Bisher konnte die Existenz invarianter Tori nur unter der Voraussetzung bewiesen werden, dass die 2n-ten Ableitungen der Störung hölderstetig sind.

Heusler compounds for thermoelectric applications

The demands for energy is leading to social and political conflicts in the world. For example, the limited resources of fossil fuels causing a dependence on the oil conveying countries in the world, leading to political discords. One way to save energy is to increase the efficiency of a process. In the field of thermoelectricity waste heat is used to produce electricity, this leads to an improvement of the efficiency. Heusler compounds with C1b structure with the general formula XY Z (X, Y = transition metal, Z = main group element) are in focus of the present thermoelectric research. Their mechanical and thermal stability is exceptional in comparison to the commonly used thermoelectric materials. The possibility to substitute small amounts of elements from the parent compound without destructing the lattice structure allows tuning the electronic properties. This tunability also allows to avoid the use of toxic and expensive elements. The reported thermoelectric Heusler compounds exhibit high electrical conductivity and moderate values of the Seebeck coefficients, which lead to a high powerfactor. The disadvantage of Heusler compounds is their high thermal conductivity. Introducing mass disorder on the X-site lattice is one effective way to produce additional phonon scattering and with it to decrease the thermal conductivity. Another approach is to implement a nano or micro structure in the thermoelectric material. This can be achieved by phase separation, composite materials, pulverization with additional spark plasma sintering or by a complex lattice structure. In the first part of this work, the influence of element substitutions on the Zr0.5Hf0.5NiSn system was investigated, to obtain the knowledge on how to optimize the electronic properties of the Heusler compounds with C1b structure. In line with this, the change of the electronic structure was investigated and a possible mechanism is predicted. In the second part of this work, the phenomenon of phase separation was investigated. First, by applying a phase separation in the well-known system Co2MnSn and subsequently by systematic investiga- tions on the TixZryHfzNiSn. In the third part, the results from the previous parts before were used to produce and explain the best reported Heusler compound with C1b structure exhibiting a Figure of Merit of ZT= 1.2 at 830 K.