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 <111> 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.

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 <111> 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 Tc 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.

References:
1. M. E. Lines, et al., Principles and Applications of Ferroelectric and Related Materials 1979
2. G. Shirane, et al., Physical Review Letters 19, 234 (1967)
3. H. Vogt, et al., Physical Review B 26, 5904 (1982)
4. S. Ravy, et al., Physical Review Letters 99, 118601 (2007)
5. M. Pasciak, et al., Physical Review Letters 120, 167601 (2018)
6. B. Zalar, et al., Physical Review Letters 90, 037601 (2003).
7. J. Hlinka, et al., Physical Review Letters 101, 167402 (2008)
8. M. S. Senn, et al., Physical Review Letters 116, 207602 (2016)