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. 2020 Oct 29;11:5461. doi: 10.1038/s41467-020-19168-z

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© The Author(s) 2020

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. 7 — We report a GAP-MD simulation of the liquid–liquid-phase transition (LLPT) in phosphorus, described by compressing a system of 1984 atoms from 0.3 to 1.5 GPa over 100 ps (10⁵ timesteps), with the temperature set to 2000 K. a Consecutive snapshots from the trajectory, with coordination numbers, N, indicated by colour coding. b Evolution of density and atomic connectivity through the LLPT. The former, shown in the upper panel, starting with a low-density, compressible molecular liquid, increases rapidly between about 0.7 and 0.8 GPa, and then reaches much higher densities for the less compressible network liquid. The fraction of 3-coordinated atoms is unity in ideal P₄, but strongly lowered because of the LLPT; the network liquid contains much higher- and some lower-coordinated environments (cf. panel a). The count of three-membered rings can similarly be taken as an indicator for the presence of molecular P₄ units: in the ideal molecular liquid, only P₄ tetrahedra are found (each having four faces, and hence four three-membered rings, one per atom); in the network liquid, three-membered rings are still present, but their count is reduced to about a fifth, making way for larger rings consistent with a covalently bonded network.