Growing environmental concerns, coupled with increasing regulatory restrictions, are requiring industries to develop non-lead-based compositions of ferroelectric and piezoelectric materials. These materials—now widely used in sensors, actuators, and transducers—are for the most part lead-based compounds such as Pb(Zr,Ti)O₃ (PZT). Indeed, PZT represents the dominant market share for use in these technologies. Moreover, next generation compounds, which include Pb(Mg_1/3Nb_2/3)O₃-xat%PbTiO₃ (PMN-x%PT) crystals with ultrahigh piezo-/electromechanical properties, are also Pb-based systems and thus are problematic for meeting more restrictive environmental standards. As alternative, Pb-free ferroelectrics such as NBT-derived single crystals represent viable next-generation materials for use in ferro-/piezoelectric applications. Development of these types of NBT-based crystals has made important advancements in the last decade. In fact, the performances of NBT-based materials are beginning to approach the properties of the widely used commercial PZT ceramic material. Nonetheless, additional studies are needed before it being able to compete with PMN-x%PT and PZN-x%PT crystals in next-generation applications. As a new type of piezoelectric material, much remains to be learned about Pb-free piezoelectric crystals. For instance, in addition to enhancing our understanding the nature of the piezoelectric third-rank tensor coefficients such as d₃₃ and d₁₅, a thorough knowledge of the Curie temperature, leakage current, and electromechanical properties is also essential for increasing the applications potential of these crystals. As detailed herein, multiple dopants may have to be incorporated into NBT to modify its microstructure and properties to meet these specific requirements, which may further complicate its chemical structure-property relationships. This study, therefore, was designed to investigate the heterogeneous structure of NBT-based single crystals, using x-ray diffraction, transmission electron microscopy, and neutron inelastic scattering, with the goal of investigating the mechanism coupling of morphotropic phase boundary (MPB) and the maximum property responses in A-site disordered perovskite Pb-free piezoelectric systems. Using the framework of polar nanoregions and adaptive phase theory, I sought to determine how the nanostructure of these single crystals change with temperature and composition—and how these factors impact its properties. Diffuse scattering, domain morphology, and phonon dispersions were used to investigate both the static and dynamic properties of these heterogeneous structures. / Ph. D.