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. 2018 Jul 24;8:11166. doi: 10.1038/s41598-018-29501-8

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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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The ZFC (blue) and FC (red) magnetisation curves for magnetite particles with a mode radius of 5 nm and a spread of volumes (a) σ = 0.015 and (b) σ = 0.15, in an applied field 10 Oe (796 A/m). The solid curves give the results of using our Eqs (13 and 14). Dashed lines show the results of using Eq. (6) and the corresponding FC equation, given in refs^10,11. The black dots show kinetic Monte Carlo results.