In the following thesis, Bi1/2Na1/2TiO3-100xBaTiO3 (BNT-100xBT for x =0.0 36, 0.058, 0.063, 0.088) single crystals are presented with different compositions on the rhombohedral and tetragonal side of the phase diagram as well as along the morphotropic phase boundary (MPB) have been investigated. In the majority of the current literature only data for <001> oriented crystals with compositions near to the MPB exist. For a full understanding of the polarization and strain mechanism in single crystals, it is necessary to investigate the behavior in different orientations. In order to close this gap, BNT-100xBT single crystals samples cut in <001>, <110> and <111> have been investigated in this thesis. The anisotropy of the piezoelectric and dielectric properties have been illuminated by the measurement of polarization and strain hysteresis as well as by the permittivity and piezoelectric coefficients as a function of temperature. The study of poling curves on virgin samples prior to permittivity measurements revealed a field-induced transition from a non-ergodic relaxor state to a ferroelectric state with long-range order below TF-R. Unpoled BNT-100xBT single crystals, however, still show isotropic behavior in their permittivity. By poling along different directions, different domain structures are induced that can be noticed directly in the anisotropy in the magnitude in permittivity. Though the permittivity becomes orientation dependent, the transition temperatures TF-R remains orientation independent within the measurement accuracy (with one exception, the <110>-oriented sample in BNT-6.3BT). As observed in polycrystalline ceramics with similar compositions, the transition temperature TF-R does not always match with the depolarization temperature Td. The depolarization behavior in all samples depends on the orientation as well as on the composition. In BNT-3.6BT, Td depends on the orientation and unequal to TF-R. While for the <001>-orientation Td is smaller than TF-R in agreement with the observation in polycrystalline ceramics, in the <111>-oriented sample Td exceeds TF-R. It can be inferred that although the long-range order has already decayed, the macroscopic polarization is preserved. This indicates that BNT-3.6BT acts as a non-ergodic relaxor in the <111>-direction. In BNT-5.8BT and BNT-6.3BT, the Td and TF-R are for each sample orientation approximately equal. The enhanced dependence of the Td on the crystal orientation in the compositions with low BT content can be explained by the different stabilities of the poling induced ferroelectric domain configurations. It is reasonable to assume an external field induces a complicated domain structure in a certain direction, i.e. <110>, which is less stable with temperature and therefore decays at temperatures which are up to 30 °C smaller than the decay temperatures of the other domain structures that were formed in other poling directions. The more energetically favorable and therefore stable a domain state is, the higher is the decay temperature. Near the MPB for BNT-5.8BT and BNT6.3BT a multistep depolarization process that is caused by the MPB character has been observed in thermally stimulated depolarization current measurements. It is possible to induce tetragonal as well as rhombohedral structure elements which are not equally stable and therefore decay from these ferroelectric phases into PNRs at different temperatures. The results of the ferroelectric and piezoelectric large signal measurements at room temperature do not provide any indication for polarization rotation being the mechanism for the observed high reversible strain such as was determined to be the case for similar lead-based relaxor systems. Nevertheless, an irreversible polarization rotation especially in the poling cycle from BNT-5.8BT in the <001> oriented sample cannot be explicitly excluded. The results can be explained based on the assumption that BNT-3.6BT is rhombohedral, BNT-5.8BT consists from rhombohedral and tetragonal phase structure elements and BNT-8.8BT is primarily tetragonal, even though it is possible to induce rhombohedral phase structure with electric field applied along specific orientations. Furthermore, bipolar polarization hysteresis at different temperatures has been investigated. The nature of the switching process is different for each of the different compositions. In rhombohedral systems, the polarization reversal at elevated temperatures involves intermediate PNR states, but near the MPB different rhombohedral and tetragonal ferreoelectric phases are created. Unusually high strains have been measured in these compositions near the MPB along the <001> directions for temperatures close to the depolarization temperature. For example, in BNT-5.8BT, strains of 0.72 % under a field from 3 kV/mm have been measured. This results in a d33* corresponding to 2400 pm/V. This high strain may be explained not only by polarization rotation but also by a combination of polarization extension and a transition between non-polar relaxor phase and electric field-induced polar ferroelectric phase.