In order to develop high performance materials with improved properties it is necessary to characterize the material down to the atomic level. Atom probe tomography is a strong method which meets this requirement. Within this thesis preparation methods, which allow the reproducible and artifact-free production of atom probe tips out of the intermetallic titanium aluminide alloy TNM were developed. Initially, the chemical composition of the constituent phases was determined by atom probe tomography on electrolytic polished tips which were subsequently sharpened by a focussed ion beam. Specific heat treatments were conducted in order to adjust the volume fraction and particle size of the ordered ωo phase. Complementary characterization methods such as scanning electron microscopy and transmission electron microscopy (TEM) were applied for a basic characterization of these. For atom probe tomography analyses of the βo- and the ωo phase, a site-specific sample preparation by focussed ion beam was applied. For the choice of the preparation method and the substrate of the atom probe tip the applicability of transmission kikuchi diffraction for phase identification prior the atom probe tomography had to be considered. Molybdenum TEM grids as a substrate material offer the possibility of transmission kikuchi diffraction and efficient measurements, the preparation of these grids was also a part of this thesis. By application of this preparation process the chemical composition of the βo and ωo phase was evaluated and, moreover, a characterization of the βo/ωo-interface was conducted.