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. 2018 Mar 22;8:5038. doi: 10.1038/s41598-018-21406-w

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© The Author(s) 2018

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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Experimental and model results for various dimensional property parameters of ThO₂ as a function of temperature. (A) Shows the volumetric thermal expansion coefficient as a function of temperature; (B) the theoretical density as a function of temperature; (C) lattice parameter as a function of temperature and (D) thermal expansion vs. temperature. The model results have been compared to available experimental data⁴ and the recommended correlation²². The dashed black lines show only the lattice contribution to thermal expansion, while the solid black lines represent the combined contributions of lattice and defects.