Some important structure types (from: Basic Solid State Chemistry, by Anthony R. West)
1.17 Some important structure types
a) Rock salt (NaCl), zinc blende or sphalerite (ZnS), fluorite (CaF2), antifluorite (Na2O)
These structures are considered together because they all have ccp/fcc anions and differ only in the positions of the cations. In Fig. 1.20 are shown the anions in a fcc unit cell with all possible O, T+ and T- sites for the cations. The different structures are generated as fol1ows: Rock salt: O occupied; T+ and T- empty Zinc blende: T+ (or T-) occupied; O, T- (or T+) empty Antifluorite: T+, T- occupied; O empty Unit cel1s are shown in Fig. 1.24, in oblique projection (a-c) and as projections on the ab face of the unit cel1 in (d-f). Bach is described in more detail later. A general rule regarding coordination numbers is that in any structure of formula AxXy,the coordination numbers of A and X must be in the ratio of y: x. In both rock salt and zinc blende, x = y and therefore, in each, anions and cations have the same coordination number. In antifluorite, of formula A2X, the coordination numbers of cation and anion must be in the ratio of 1:2. Since the cations occupy tetrahedral sites, the anioncoordination number must be eight. In order to see this, it is convenient to redefine the origin of the unit cell to coincide with a cation rather than an anion. This is done by displacing the unit cell along a body diagonal by one quarter of the length of the diagonal. The cation at X in Fig. 1.24(c), with coordinates ¼ ¼ ¼, may be chosen as the new origin of the unit cell. The co- ordinates of all atoms in the new cell are given by subtracting ¼ ¼ ¼ from their coordinates in the old cell, as in the following table.
a) Rock salt (NaCl), zinc blende or sphalerite (ZnS), fluorite (CaF2), antifluorite (Na2O)
These structures are considered together because they all have ccp/fcc anions and differ only in the positions of the cations. In Fig. 1.20 are shown the anions in a fcc unit cell with all possible O, T+ and T- sites for the cations. The different structures are generated as fol1ows: Rock salt: O occupied; T+ and T- empty Zinc blende: T+ (or T-) occupied; O, T- (or T+) empty Antifluorite: T+, T- occupied; O empty Unit cel1s are shown in Fig. 1.24, in oblique projection (a-c) and as projections on the ab face of the unit cel1 in (d-f). Bach is described in more detail later. A general rule regarding coordination numbers is that in any structure of formula AxXy,the coordination numbers of A and X must be in the ratio of y: x. In both rock salt and zinc blende, x = y and therefore, in each, anions and cations have the same coordination number. In antifluorite, of formula A2X, the coordination numbers of cation and anion must be in the ratio of 1:2. Since the cations occupy tetrahedral sites, the anioncoordination number must be eight. In order to see this, it is convenient to redefine the origin of the unit cell to coincide with a cation rather than an anion. This is done by displacing the unit cell along a body diagonal by one quarter of the length of the diagonal. The cation at X in Fig. 1.24(c), with coordinates ¼ ¼ ¼, may be chosen as the new origin of the unit cell. The co- ordinates of all atoms in the new cell are given by subtracting ¼ ¼ ¼ from their coordinates in the old cell, as in the following table.
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