Local Structure and Polarization in Relaxor and Ferroelectric Tetragonal Tungsten Bronzes Measured by 4D STEM

Classical and relaxors ferroelectrics are critical for many modern technologies, notably as functional materials in transducer and capacitor applications. Prominent, commercially used materials in these categories are lead-based, which is undesirable due to lead’s toxicity. In the search for lead-free alternatives, tetragonal tungsten bronze (TTB) oxides have been examined due to their flexible chemistry and wide range of properties, including relaxor and classical ferroelectric behavior.^[1] TTBs commonly exhibit commensurately or incommensurately modulated superlattices, and an empirical link has been established between superlattice type and ferroelectric order.^[2] The modulation includes tilting within the oxygen-octahedral network and related cation displacements. Several studies have attempted to characterize the structure by various methods, though these have been inconclusive to due various inherent technique limitations.^[3,4] An Ama2 unit cell was proposed as a commensurate approximation of the incommensurate modulation.^[5] This model implies the presence, locally, of one of two possible orientations of the modulation. In this work, we seek to provide more detailed information regarding the structure and origin of ferroelectric properties in TTBs using scanning transmission electron microscopy (STEM).<br/><br/>Current state-of-the-art in STEM, including aberration correction and advanced pixelated detectors, allows precise atomic-scale characterization of materials. In this work, we use 4D STEM (a technique in which a complete electron diffraction pattern is collected for each probe position) to analyze the structural modulation and polarization of two TTB compositions: Ba₄Nd₂Nb₄Ti₆O₃₀, a commensurately modulated classical ferroelectric, and Ba₅Sm₁Sn₃Nb₇O₃₀, an incommensurately modulated relaxor. We perform two types of experiments at different length scales. The first 4D STEM experiments, nano-beam electron diffraction (NBED), allow us to measure the local modulation orientation and polarization at nanometer-scale resolution over approximately 1 m² fields of view from a single dataset. We design custom virtual detectors informed by electron diffraction simulations of the Ama2 cell. To identify the local modulation orientation, we use a virtual detector sensitive to the corresponding superlattice reflections; and for measuring local polarization, we calculate the normalized difference signal between the and disk pairs. The resulting images map these key structural signatures (modulation orientation and polarization) over the scanned region. Next, we study the structure of the materials at atomic resolution using phase contrast imaging from a second set of 4D STEM experiments. We analyze the images using our recently developed vector pair correlation function method ^[6] to quantify the ordering of atomic displacements on the anion and cation sublattices, determining the correlation length of the modulation and polar distortions on a sublattice-specific basis. By applying 4D STEM characterization to TTBs we relate structural information from both nanometer and atomic length scales to the materials’ functional, macroscopic properties.<br/><br/>[1] V. V. Shvartsman, D. C. Lupascu, <i>J. Am. Ceram. Soc.</i> <b>2012</b>, <i>95</i>, 1.<br/>[2] X. Zhu, M. Fu, M. C. Stennet, P. M. Vilarinho, I. Levin, C. A. Randall, J. Gardner, F. D. Morrison, I. M. Reaney, <i>Chem. Mater.</i> <b>2015</b>, <i>27</i>, 3250.<br/>[3] T. Woike, V. Petricek, M. Dused, N. K. Hansen, P. Fertey, C. Lecomte, A. Arakcheeva, G. Chapuis, M. Imlau, R. Pankrath, <i>Acta Crystallogr. Sect. B</i> <b>2003</b>, <i>59</i>, 28.<br/>[4] L. A. Bursill, J. L. Peng, <i>Acta Cryst</i> <b>1987</b>, <i>43</i>, 49.<br/>[5] I. Levin, V. Krayzman, G. Cibin, M. G. Tucker, M. Eremenko, K. Chapman, R. L. Paul, <i>Sci. Rep.</i> <b>2017</b>, <i>7</i>, DOI 10.1038/s41598-017-15937-x.<br/>[6] S. D. Funni, Z. J. Yang, M. J. Cabral, C. Ophus, X. M. Chen, E. C. Dickey, <i>APL Mater.</i> <b>2021</b>, <i>9</i>, 091110.