Visualizing Chain Correlations and Their Evolution Across a Ferroelectric Phase Transition in BaTiO₃

The nature of certain structural phase transitions is frequently categorized as displacive or order-disorder type. Either of them is typically thought to describe a majority of known ferroelectric phase transition [1]. Although BaTiO₃ is a classical ferroelectric, its ferroelectric (FE)-paraelectric (PE) phase transition challenges the purely displacive or order-disorder cases. The displacive model is attributed by the softening of a transverse optical mode caused by relative displacement of Ti and neighboring oxygen within the octahedron [2-3]. However, the diffuse line observed in both FE and PE phases [4-5] suggests the necessary introduction of order-disorder model, which assumes the occupation of Ti on symmetry-equivalent sites along &lt;111&gt; direction, with a chain-like correlated Ti off-center shift [6-8]. Unlike the well-accepted soft mode in displacive case, the chain correlations is primarily evidenced by the investigation of diffuse line in reciprocal space [4, 5, 8]. However, the real-space behavior of the chain correlations and their evolution across phase transition remain elusive.<br/><br/>Here, we directly track the chain correlations of BaTiO₃ across the FE-PE phase transition using in situ scanning transmission electron microscopy (in situ STEM) and give atomic evidence of the order-disorder case. We visualize the famous chain-correlated &lt;111&gt; Ti off-center shift in both the FE and PE phase of BaTiO₃ and reveal their link to diffuse lines observed in reciprocal space. By quantitatively tracking the chain correlations across FE-PE transition, we demonstrate the order-disorder case is governed by a competition between local ferroelectric correlation and thermal fluctuation. Notably, an inverse enhancement of correlation across the <i>Tc</i> is observed. Our visualization and tracking of chain correlations in BaTiO₃ emphasize the role of order-disorder case on describing the FE-PE transition of BaTiO₃.<br/><br/>References:<br/>1. M. E. Lines, et al., <i>Principles and Applications of Ferroelectric and Related Materials</i> 1979<br/>2. G. Shirane, et al., <i>Physical Review Letters</i> 19, 234 (1967)<br/>3. H. Vogt, et al., <i>Physical Review B</i> 26, 5904 (1982)<br/>4. S. Ravy, et al., <i>Physical Review Letters</i> 99, 118601 (2007)<br/>5. M. Pasciak, et al., <i>Physical Review Letters</i> 120, 167601 (2018)<br/>6. B. Zalar, et al., <i>Physical Review Letters</i> 90, 037601 (2003).<br/>7. J. Hlinka, et al., <i>Physical Review Letters</i> 101, 167402 (2008)<br/>8. M. S. Senn, et al., <i>Physical Review Letters</i> 116, 207602 (2016)