Topological atom packing

The A15 crystal structure is a complex, cubic structure derived from the b.c.c. lattice (A2) with 8 atoms per unit cell (Pearson, 1958). It is a typical example of the topologically close-packed (tcp) structures which result from the stacking of polyhe-dra of various shapes to accommodate atoms of different sizes (Sinha, 1973 Watson and Bennet, 1984 Gladyshevskii and Bodak, 1994). These tcp structures allow a closer packing of atoms of different sizes than the geometrically close-packed f.c.c. (Al) and h.c.p. (A3) structures. The A15 structure may be regarded as the basis of the family of tcp structures since the other... 

Laves phases have what is known as a topological close-packed (TCP) structure which is often undesirable because they can act as stress risers that initiate cracks because of their hardness and morphology and because they tie up atoms needed for the more desirable coherent y phases that are involved in precipitation hardening of alloys. 

Fig. 46. Characteristics of the packing arrangement in unhydrated 1 imidazole with a separate schematics emphasizing the central loop topology lu) (H-bonds are indicated as broken lines backbone H atoms are omitted O atoms dotted N atoms hatched the hatched segments in the schematic drawing signify the imidazole rings)...

Eutactical means topologically equivalent to a close packing of Hg, however, with significantly greater interatomic distances than expected for neutral Hg atoms. 

Sites of type (e) are occupied between all successive pairs of layers in a-Al2 03 and related structures to which we refer shortly, while occupation of sites (e ) between all successive pairs of layers gives the h.c.p. MX3 structure of trifluorides such as Rhp3. In this structure each MXg octahedron is linked to six others through shared vertices (X atoms) there is no c.c.p. structure of the same topological type, for in the Re03 structure the 0 atoms occupy only three-quarters of the positions of cubic closest packing (see MSIC, p. 61). 

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