Frank-Kasper phases structures

WoWj/2 the body-centred cubic structure of W (1 atom in 0, 0, 0 and 1 atom in A, A, /) corresponds to a sequence of type 1 and type 4 square nets at the heights 0 and A, respectively. Note, however, that for a fall description of the structure, either in the hexagonal or the tetragonal case, the inter-layer distance must be taken into account not only in terms of the fractional coordinates (that is, the c/a axial ratio must be considered). For more complex polygonal nets, their symbolic representation and use in the description, for instance, of the Frank-Kasper phases, see Frank and Kasper (1958) and Pearson (1972). 

Crystal approximants. Several crystalline phases contain more or less closely packed atomic assemblies (polyhedra, clusters) which have been considered fundamental constituents of several quasicrystals, metal glasses and liquids. Such crystalline phases (crystal approximants), as reported in the previous paragraph, are often observed in the same (or similar) systems, as those corresponding to the formation of quasicrystals and under similar preparation conditions. Crystalline phases closely related to the quasicrystals (containing similar building blocks) have generally complex structures as approximants to the ico-quasicrystals we may, for instance, mention the Frank-Kasper phases (previously described in 3.9.3.1). 

In addition to the Frank-Kasper phases, other structures may be considered in which the same four types of coordination polyhedra prevail although some regularity is lost. A few notes about these phases are reported in 3.9.3.2. 

An important contribution to the structure analysis of intermetallic phases in terms of the coordination polyhedra has been carried out by Frank and Kasper (1958). They described several structure types (Frank-Kasper structures) as the result of the interpenetration of a group of polyhedra, which give rise to a distorted tetrahedral close-packing of the atoms. Samson (1967, 1969) developed the analysis of the structural principles of intermetallic phases having giant unit cells (Samson phases). These structures have been described as arrangements of fused polyhedra rather than the full interpenetrating polyhedra. 

Fig. 3 Quasicrystalline structures observed in BCP SA. (a) TEM image of a 2D 12-fold quasicrystal derived from a star block copolymer (the inset shows its EFT pattern), (b) Transcribed tiling pattern (reprinted with permission from [34] Copyright 2010 American Physics Society), (c) TEM image and (d, e) unit cell of the Frank-Kasper sigma phase obtained from tetra-BCP SA (c-e reprinted with permission from [33] Copyright 2010 AAAS)...

---