The mixed perovskite oxides KTa1−xNbxO3, or KTN, are a model system for studying ferroelectric behavior and phase transitions under pressure. Crystals withx> 0.1 exhibit ferroelectric soft‐mode behavior and a sequence of phase transitions, while forx⩽ 0.02 a pressure‐induced ferroelectric‐to‐relaxor crossover occurs. The system also exhibits a pressure‐induced crossover from classical‐to‐quantum behavior ultimately leading to the complete suppression of the phase transition and the formation of a quantum paraelectric state. © 2004 American Institute of Physics