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. 2017 Nov 3;8:1300. doi: 10.1038/s41467-017-01360-3

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© The Author(s) 2017

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. 4 — The optimized crystal structures and phonon dispersion of the low frequency modes of tetragonal MAPbI₃. a Side view, b top view. c Phonon dispersion spectra and the corresponding projected density of states. The two yellow zones are the Pb–I stretch vibrations, which are centered around 8 and 12 meV, respectively. The green zone is the acoustic phonon mode with maximum frequency around 2.5 meV. Details of the calculations are given in Supplementary Note 9