Role of Incommensurate Modulation in Ba₄(Sm_1–xLa_x)₂Ti₄Nb₆O₃₀ Tetragonal Tungsten Bronzes

Abstract

The role of incommensurate (IC) modulation in the evolution of the pinched polarization−electric field (P−E) hysteresis loops has been investigated and discussed based on the structure and polarization evolution in Ba 4 (Sm 1−x La x ) 2 Ti 4 Nb 6 O 30 tetragonal tungsten bronzes. The relaxor behavior in the La-rich compound is accompanied by an IC modulation structure. Introduction of smaller Sm in the system increases the driving force for the transition from an IC modulation structure to a commensurate superstructure, which coupled with the ferroelectric transition in the middle composition with x = 0.5. In the Sm-rich compounds, the IC modulation structure reappears as a metastable state to balance the structural instability caused by the too small average ionic radius of the rare-earth ion; meanwhile, the field-induced transition from the IC modulation structure to the commensurate superstructure is confirmed by selected area electron diffraction using an in situ bias technique as the structural origin for the pinched P−E loops. A phase diagram has been established by combining the ferroelectric phase transition and the modulation structure transition, and a new region with both very small A-site size (A1 + A2)/2 and A1-site tolerance factor (t A1 ) related to the ferroelectric compounds with pinched P−E loops (pinched FE) was added into the previously reported crystal-chemical framework (Chem. Mater. 2015, 27, 3250−3261). The present work expands the composition−structure−property relationships in tungsten bronze ferroelectrics by including the recently reported "pinched FE" and meanwhile extends the composition manipulation ranges from the crossover between relaxor and normal ferroelectrics to ferroelectrics with pinched P−E loops.