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. 2018 Apr 20;8:6308. doi: 10.1038/s41598-018-24205-5

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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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Constrained formation rate of spherical carbonate concretions. Relationship between effective diffusion coefficient (D; cm²/s) and growth rate of reaction front (V; cm/s) shows the narrow range of formation conditions of spherical concretions. Taking an effective diffusion coefficient for HCO₃⁻ of 10⁻⁶ cm²/s, which is a mean value for similar kinds of clayey marine sediments together with the observed variation in reaction front thickness in small (mean values L1 to L3) to gigantic concretions (estimated values L4 to L6) shows that the growth rates of the spherical concretions was between 10⁻⁵ and 10⁻⁷ cm/s and that the concretions formed very rapidly early in diagenesis.