Hard cubes, close packing

Cubed compound, in PVC siding manufacture, 25 685 Cube lattice, 8 114t Cubic boron nitride, 1 8 4 654 grinding wheels, 1 21 hardness in various scales, l 3t physical properties of, 4 653t Cubic close-packed (CCP) structure, of spinel ferrites, 11 60 Cubic ferrites, 11 55-57 Cubic geometry, for metal coordination numbers, 7 574, 575t. See also Cubic structure Cubic symmetry Cubic silsesquioxanes (CSS), 13 539 Cubic structure, of ferroelectric crystals, 11 94-95, 96 Cubic symmetry, 8 114t Cubitron sol-gel abrasives, 1 7 Cucurbituril inclusion compounds,... 

If we have N hard spheres (of radius rs) forming a close-packed polyhedron, another sphere (of smaller radius rc) can fit neatly into the central hole of the polyhedron if the radius ratio has a well-defined value (see also 3.8.1.1). The ideal radius ratio (rc/rs) for a perfect fit is 0.225.. (in a regular tetrahedron, CN 4), 0.414.. (regular octahedron CN 6), 0.528.. (Archimedean trigonal prism CN 6), 0.645... (Archimedean square antiprism CN 8), 0.732.. (cube CN 8), 0.902... (regular icosahedron CN 12), 1 (cuboctahedron and twinned cuboctahedron CN 12). 

The CsCl structure corresponds to a body-centered cubic (bcc) cell, but the atom at the center is different from those at the comers. It is not truly close packed because there is more empty space for hard spheres for bcc compared to ccp and hep structures under similar conditions. Metals with a bcc structure are expected to be less dense than those with ccp or hep structures. In Section 4.3.3, we see that in many cases metals with bcc structures have comparable, or even greater, density than those with ccp or hep structures under similar conditions. Metal atoms are not hard spheres. Figure B.9a shows eight CsCl cells. This large cell can be considered as an fee cell with the dark spheres in P sites (comers and centers of faces) and light spheres in O sites (center of the cube and centers of centers of edges). Here, the CP atoms fill P and O sites... 

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