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. 2017 Jun 20;8:15944. doi: 10.1038/ncomms15944

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Copyright © 2017, The Author(s)

Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/

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Free-energy-like quantity versus internal energy (in meV per 5-atom cell) for (1−x)Ba(Zr_0.2Ti_0.8)O₃−x(Ba_0.7Ca_0.3)TiO₃ with x=0.50 (BCTZ-0.5) in yellow, and BaTiO₃ (BTO) in red, at their P4mm–Amm2 transition temperatures (which are 297 and 283 K, respectively). Results correspond to the use of a 18 × 18 × 18 supercell. This free-energy-like quantity is the logarithm of the normalized canonical distribution²⁸.