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. 2017 Nov 15;7:15629. doi: 10.1038/s41598-017-15771-1

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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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(a) Projection of the volume of (e/a)-constant stability criteria from five-component Al-Cu-Fe-Cr-Ni space to the ternary Al-Cu-Fe diagram. The planes represent the amount of Ni (alone), Cr (alone), or Ni + Cr in a 3:1 ratio needed in order to have a stable icosahedral quasicrystal. The color shows the atomic fraction of Cr + Ni (Based on ternplot by C. Sandrock). (b) The location of experimental and predicted icosahedral quasicrystals in the Al-Cu-Fe-Cr-Ni system, projected onto the Al-Cu-Fe ternary. Features shown include (e/a)-constant for ternary Al-Cu-Fe (thick dark blue), (e/a)-constant for the atomic fractions of Cr and Ni in this study (thin blue), various cluster lines, Al₆₃Cu₂₄Fe₁₃ icosahedrite (dark blue circle), new compositions from this study (diamonds), new compositions from Asimow et al. (2016) (triangles), the 4-cluster hyperplane solution (red square), and the estimated stability region for five-component quasicrystals given by (e/a) and size constraints (contoured surface, colors indicate atomic fraction of Cr + Ni).