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. 2021 Jan 8;12:201. doi: 10.1038/s41467-020-20370-2

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© The Author(s) 2021

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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Fig. 5 — Low-barrier migration pathways for a vacancy and b interstitial dumbbell migration in M₃HCh. Top-left insets show M⁺ migration when viewing HM₆ octahedron from the top to down. For orthorhombic Na₃HS, there are many migration pathways, one of which is shown as a representative example (see Supplementary Fig. 15 for details). c Migration barriers for cation transport via the vacancy and interstitial dumbbell mechanism in M₃HCh as a function of the force constant k_rot with respect to the HM₆ rotational motion. d Arrhenius plots of the total conductivity values for undoped M₃HCh cold-pressed samples in the temperature range from 25 to 100 °C.