On getting to know the work of Frank-Kasper and the gap

Key References: “Complex alloy structures regarded as sphere packings. Analysis and classification of representative structures.“

Within this website: https://81018.com/biased/#Aristotle

Introduction: Early in our explorations with our newly minted tetrahedrons and octahedrons (1999), we observed the tetrahedral gap even before we discovering its role within intellectual history. The work of Frank-Kasper was among our early introductions to the scholarly explanation of tetrahedral gaps.

Another was The Cambridge Energy Landscape Database, Cluster Structure, with Jonathan Doye. If the link to the Cluster Structure opens an error message, “Not secure,” go to our image of their page! Also, there had been an interesting study of the gap out of Bangalore, but those pages are no longer supported.

  1. https://en.wikipedia.org/wiki/Frederick Charles Frank Also: https://www.nature.com/articles/30622
  2. Frank, F. C.; Kasper, J. S. (1958-03-10). “Complex alloy structures regarded as sphere packings. I. Definitions and basic principles”. Acta Crystallographica. International Union of Crystallography (IUCr). 11 (3): 184–190. doi:10.1107/s0365110x58000487. ISSN 0365-110X.
  3. Frank, F. C.; Kasper, J. S. (1959-07-10). “Complex alloy structures regarded as sphere packings. II. Analysis and classification of representative structures”. Acta Crystallographica. International Union of Crystallography (IUCr). 12 (7): 483–499. doi:10.1107/s0365110x59001499. ISSN 0365-110X.
  4. https://en.wikipedia.org/wiki/Frank%E2%80%93Kasper_phases
  5. Su, Z., Hsu, CH., Gong, Z. et al. Identification of a Frank–Kasper Z phase from shape amphiphile self-assembly. Nat. Chem. 11, 899–905 (2019). https://doi.org/10.1038/s41557-019-0330-x
  6. Reddy, A., Grason, G.M. A cornerstone of complex crystals. Nat. Chem. 11, 865–867 (2019). https://doi.org/10.1038/s41557-019-0333-7
  7. Liu, XY., Yan, XY., Liu, Y. et al. Self-assembled soft alloy with Frank–Kasper phases beyond metals. Nat. Mater. (2024). https://doi.org/10.1038/s41563-023-01796-7
  8. BURTON, W., CABRERA, N. & FRANK, F. Role of Dislocations in Crystal Growth. Nature 163, 398–399 (1949). https://doi.org/10.1038/163398a0.
  9. Liquid crystals. On the theory of liquid crystals F. C. Frank, Faraday Soc., 1958, 25, 19 DOI: 10.1039/DF9582500019  https://doi.org/10.1039/DF9582500019

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