Frank-Kasper phase

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). 

Tetrahedrally close-packed phases, Frank-Kasper phases (cross-reference note)... 

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. 

Sir Frederick Charles Frank (1911-1998) received his Ph.D. in 1937 from Oxford University, followed by a postdoctoral position at the Kaiser Wilhelm Institut fiir Physik in Berlin. During World War II, Frank was involved with the British Chemical Defense Research Establishment, and because of his keen powers of observation and interpretation, he was later transferred to Scientific Intelligence at the British Air Ministry. In 1946, Frank joined the H. H. Wills Physics Laboratory at the University of Bristol under its director, Nevill Mott, who encouraged him to look into problems concerned with crystal growth and the plastic deformation of metallic crystals. A stream of successes followed, establishing his scientific fame, as evidenced by many eponyms the Frank-Read source, the Frank dislocation, Frank s rule, Frank-Kasper phases. His theoretical work has been the foundation of research by innumerable scientists from around the world. Frank was awarded the Order of the British Empire (OBE) Medal in 1946, elected a Fellow of the Royal Society (FRS) in 1954, and was knighted in 1977. 

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. 

Those tellurium atoms that are located in the center of the cluster molecules tend to bond to a large number of copper atoms. In some compounds, the copper atoms themselves form polyhedra, described as Frank-Kasper polyhedra [62]. In these cases, the clusters consist of interpenetrating Frank-Kasper polyhedra, which are [34b, 63] well known from a number of intermetallic phases (e.g.. Laves phases). 

Frank-Kasper phas A phase that occurs in certain complex alloys involving both icosahedra and tettahedra packed closely together. See also quasicrystal. 

Lee, S., Bluemle, M. J., and Bates, F. S. (2010). Discovery of a Frank-Kasper o phase in sphere-forming block copolymer melts. Science 330, 349-353. 

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)...

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