High quality epitaxial thin films oflead magnesium niobate -lead titanate (PMN0.35PT) were deposited on MgAh04 substrates in the (001) direction with a lattice mismatch of less than 2%. Characterization by transmission electron microscopy and xray diffraction, has revealed high quality single crystal epitaxial thin films oriented in the (001) direction with a tetragonal unit cell. Capacitance measurements were completed by interdigital dielectrometry and using Finite Element Modeling the dielectric constant for the thin film yielded values ranging from 561 -799 at lk:Hz and 518-746 at 100kHz when the temperature was varied from 273-473K. Additionally, the dielectric maximum has been shifted to higher temperature and the frequency dispersion of the dielectric constant appears to be minimized. Piezoresponse microscopy and transmission electron microscopy was completed on both single and multilayer heterostructures. Transmission electron microscopy shows that the single layer samples show excellent morphology with single crystal epitaxial growth in the (001) direction. In addition piezoresponse microscopy and TEM have elucidated the difficulty in producing high quality films of PMN-0.35PT with a BaNb0.5Ti0.503 bottom electrode. The tendency for columnar growth of BaNb0.5Ti0.503 establishes an environment for polycrystalline growth drastically reducing the probability of single crystal growth in subsequent layers. Finally, piezoresponse microscopy allowed the observation of self polarization in PMN-0.35PT within the polycrystalline films which is in agreement with observations of previous researchers. / Thesis / Master of Applied Science (MASc)