The emergence of ferroelectric and antiferroelectric properties in the semiconductor industry's most prominent high-k dielectrics, HfO₂ and ZrO₂, is leading to technology developments unanticipated a decade ago. Yet the failure to clearly distinguish ferroelectric from antiferroelectric behavior is impeding progress. Band-excitation piezoresponse force microscopy and molecular dynamics are used to elucidate the nanoscale electric field-induced phase transitions present in ZrO₂-based antiferroelectrics. Antiferroelectric ZrO₂ is clearly distinguished from a closely resembling pinched La-doped HfO₂ ferroelectric. Crystalline grains in the range of 3 – 20 nm are imaged independently undergoing reversible electric field induced phase transitions. The electrically accessible nanoscale phase transitions discovered in this study open up an unprecedented paradigm for the development of new nanoelectronic devices.