Complex alloy structures regarded as sphere packings. I. Definitions and basic principles

1958/03/10 by F. C. Frank, J. S. Kasper · 1,283 citations
Chemistry · Materials Science · Mathematics · #Alloy #Artificial intelligence #Chemistry #Class (philosophy) #Combinatorics #Computer science #Crystallography #Geometry #Materials science #Mathematics #Metallurgy #Polyhedron #Pure mathematics #Tetrahedron #Topology (electrical circuits) #X-ray Diffraction in Crystallography

paper · pdf · doi:10.1107/s0365110x58000487

published in Acta Crystallographica 11(3), 184-190 (Wiley)

openalex publication_date 1958/03/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/25

Abstract

Complex alloy structures, particularly those of transition metals, are considered as determined by the geometricnl requirements for sphere packing. A characteristic of the class of structures discussed is that tetrahedral groupings of atoms occur everywhere in the structure--alternatively stated, coordination polyhedra have only triangular faces. The topological and geometrical properties of such polyhedra are examined and rules and theorems regarding them are deduced. Justification is given for the prominence of four such polyhedra (for coordination numbers of 12, 14, 15, and 16) in actual structures. General principles regarding the combination of these polyhedra into full structures are deduced and necessary definitions are given for terms that facilitate the detailed discussion of this class of structures. (auth)

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