The incommensurate modulation of tetragonal tungsten bronze quantified by high resolution 4D STEM
Many members of the tetragonal tungsten bronze (TTB) family of oxides display an incommensurate periodic lattice distortion, the nature of which has been the subject of some controversy. Here we present a study of this structural modulation in the relaxor ferroelectric Ba 5 SmSn 3 Nb 7 O 30 (BSSN) by quantitative scanning transmission electron microscopy (STEM). Additionally, we characterize the modulation in BSSN by employing a fast, pixelated direct electron detector to perform high resolution phase contrast STEM imaging of the crystalline lattice. By quantitatively analyzing the images, we visualize the atomic structural correlations present in the material on both the cation and anion sublattices. This analysis reveals the incommensurate structure to have an octahedral tilting pattern and cooperative A2 site cation displacements, analogous to an Ama2 commensurate cell. Finally, we show that the modulation is composed of a structural motif with a period of 3 x $d_{1\bar{1}0}$ and modified by discommensurations, likely arise from frustrated octahedral tilting in the odd-valued periodicity.