Alternative unit cells

The rhombohedral primitive lattice is often described in terms of a hexagonal lattice, but the lattice points can also be indexed in terms of a cubic face-centred lattice in the unique case in which the rhombohedral angle ar is exactly equal to 60°, (also see Section 4.5). 

As in two-dimensions, a lattice with a three-dimensional unit cell derived from regular pentagons, such as an icosahedron, cannot be constructed. 

Crystal system Lattice symbol Lattice parameters 

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Carbon, ring oxygen replacement by, 141-143 2-Carboxy-5-(2-hydroxymethyl)-4-methylthiazole, synthesis and transformations, 284-286 Carrageenans, 366-368,418-419 Cellotetraose hemihydrate, 331 Cellulose, 326, 329-332 alternate unit cells, 329-330 derivatives, 332... 

Crystallographic data for the material tabulated here has been deposited with the CCDC as supplementary publication CCDC-136762 CSD WISVOJ. For the manganese-molybdenum cluster the checkers also obtained a second crystalline modification with an alternative unit cell, namely, Ri, a = ll. ilS (5) A, c = 44.25 (2) A, V = 11570 (5) A, featuring a different packing arrangement of the cluster units. 

Fig. 4. A piano pattern. Lower part divided into identical unit cells such as ABCD. Alternative unit cells EFQH and T.JKL are also outlined.

Crystal family Standard unit cell choice Alternative unit cell choice... 

FIG. 1.4. (a) Alternative unit cells of layer structure of AS2O3. (b) Projection of unit cell of a... 

This procedure, although simple in principle, requires skill and ingenuity. It is now carried out automatically by computers, which can test large numbers of alternative unit cells in minimal time. 

Cesium chloride consists of interpenetrating simple cubic lattices of Cs and Q ions.The figure shows a unit cell with Cr ions at the corners of the unit cell and a Cs ion at the center. (A space-filling model is on the left a model with ions shrunk in size to emphasize the structure is on the right.) An alternative unit cell would have Cs ions at the corners with a Cl ion at the center. 

Sodium chloride has a face-centered cubic lattice. W The unit cell shown here (as a space-filling model) has Cl ions at the corners and at the centers of the faces of the cube.The Cl ions are much larger than Na" ions, so the Cl ions are nearly touching and have approximately a cubic close-packed structure the Na" ions are in cavities in this structure. (6) The alternative unit cell shown here has Na ions at the comers and the centers of the faces of the unit cell. 

Figure 28.1 shows the unit cell of the sodium chloride lattice with the sodium ions at the corners of the unit cell. An alternate unit cell could be taken by locating chloride ions at the corners of the unit cell. This unit cell is a cube with sides equal to 5.63 X 10 ° m. It contains four sodium ions a one-eighth share of each of eight sodium ions at the corners of the unit cell and a one-half share of each of six sodium ions in the faces. There are four chloride ions a one-fourth share of each of the twelve ions at the centers of the edges, plus the chloride ion at the center of the cell. 

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