Cube corner array

Figure 22.6. Typical cube-corner array retroreflector. An image of the camera can be seen at the center...

The rock-salt structure is a common ionic structure that takes its name from the mineral form of sodium chloride. In it, the Cl- ions lie at the corners and in the centers of the faces of a cube, forming a face-centered cube (Fig. 5.39). This arrangement is like an expanded ccp arrangement the expansion keeps the anions out of contact with one another, thereby reducing their repulsion, and opens up holes that are big enough to accommodate the Na+ ions. These ions fit into the octahedral holes between the Cl ions. There is one octahedral hole for each anion in the close-packed array, and so all the octahedral holes are occupied. If we look carefully at the structure, we can see that each cation is surrounded by six anions and each anion is surrounded by six cations. The pattern repeats over and over, with each ion surrounded by six other ions of the opposite charge (Fig. 5.40). A crystal of sodium chloride is a three-dimensional array of a vast number of these little cubes. 

The crystal structures of many organolithium compounds have been determined.44 Phenyllithium has been crystallized as an ether solvate. The structure is tetrameric with lithium and carbon atoms at alternating corners of a highly distorted cube. The lithium atoms form a tetrahedron and the carbons are associated with the faces of the tetrahedron. Each carbon is 2.33 A from the three neighboring lithium atoms and an ether molecule is coordinated to each lithium atom. Figures 7.2a and b show, respectively, the Li-C cluster and the complete array of atoms, except for hydrogen 45 Section 6.2 of Part A provides additional information on the structure of organolithium compounds. 

To sec how this occurs, let us consider the simplest interesting case, that of cesium chloride. The structure of CsCl is shown in Fig. 2-1,a. The chlorine atoms, represented by open circles, appear on the corners of a cube, and this cubic array is repeated throughout the entire crystal. At the center of each cube is a cesium atom (at the body-center position in the cube). Cesium chloride is very polar, so the occupied orbitals lie almost entirely upon the chlorine atoms. As a first approximation we can say that the cesium atom has given up a valence electron to... 

Praseodymium dioxide crystallizes in the fluorite-type structure (space group Fm3m) with four praseodymium atoms and eight oxygen atoms per unit cell. This structure may be visualized easily as an infinite array of coordination cubes (each consisting of a Pr atom at the center with eight O atoms at the corners) stacked so that all cube edges are shared. 

In addition to the CsCl structure, 8-8 coordination, and the NaCl structure, 6-6 coordination, there are two structures having 4-4 coordination, the cubic ZnS (zinc blende) structure and the hexagonal ZnS (wurzite) structure (Fig. 27.9a and b). Note that the zinc blende structure is an fee array of sulfide ions. There is a tetrahedrally coordinated hole at each corner of the cube the zinc ions occupy four of the eight tetrahedral holes. In wurzite, the sulfide ions form an hep array, and the zinc ions occupy half of the tetrahedral holes (Fig. 27.9c). 

Plateau. From the edges and corners of the square are surfaces which terminate on the twelve edges of the cube. They are not all planar. The only planar surfaces are those from the vertices of the square to the edges of the framework that are perpendicular to the square . The plane of the square is always parallel to one of the faces of the cube. It can be made to jump from one plane to another by either blowing onto it or by shaking the frame. There are thus three minimum surfaces with the same area. It will be recalled that in the case of the two dimensional problem, with the square array of points, the central line could occur in two positions, parallel to either side of the square. 

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