Incommensurate Modulation and Competing Ferroelectric/ Antiferroelectric Modes in Tetragonal Tungsten Bronzes

The nanoscale structure of Sr0.61Ba0.39Nb2O6, a classic uniaxial relaxor ferroelectric crystallizing with the tetragonal tungsten bronze (TTB) structure and exhibiting an incommensurate modulation, has been determined by atomistic refinements using combined data from variable-temperature neutron total scattering, extended X-ray absorption fine structure, and threedimensional single-crystal diffuse scattering. We found the modulation to arise from the intergrowth of structural slabs featuring distinct types of octahedral rotations directed to minimize octahedral deformations. This modulation involves displacements of the A cations (Sr and Ba) but exerts no significant effect on the polar displacements of Nb. Our results demonstrated the coexistence of competing polar Gamma 3- and antipolar Gamma 2- modes for off-centering of Nb above the nominal ferroelectric transition temperature of 350 K. The nanoscale-correlated antipolar distortions, which exhibit their largest amplitudes at 425 K, are suppressed below the transition. We identified coupling between the polar off-centering of Nb on its two symmetrically distinct sites as a fundamental characteristic controlling the ferroelectric-to-relaxor crossover in TTBs. We then used it to propose a simple microscopic interpretation for the previously established empirical trend that links crystal-chemical parameters in these systems to their polar response.