By Allen Alper (Eds.)
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Additional info for Phase Diagrams. Materials Science and Technology
The A positions in Fig. 12a represent one layer of a close-packed structure. Each A a t o m touches six other A atoms arranged in a hexagon. Atoms in the adjacent layer occupy the Β or C positions, but not both. Three Β atoms contact each A atom in the layer below. An infinite n u m b e r of stacking sequences are possible in close-packed structures but only three are at all c o m m o n : hexagonal close packed (ABABAB · · ·), cubic close packed (ABCABC · · ·), and "double" hexagonal close packed (ABACABAC · · · ) .
1. APPLICATION OF PAULING'S RULES : TOPAZ Topaz is a handsome gem mineral with chemical composition A l 2 S i 0 4 F 2 . Using the first and second rules it is possible to predict the coordination of all four ions in the structure. First the radius ratios are calculated to predict probable coordination numbers for the cations. Since the radii of F " and O 2 " are about equal, the ratios are independent of the nature of the anion. Ratios calculated from the radii give the expected result that S i 4 + is four coordinated, while A l 3 + is a borderline case with both four or six coordination possible.
The contribution of nearest neighbor cation-anions to the C o u l o m b energy tends to stabilize the struc ture, and is usually the largest term in the summation. Referring to Fig. 10a where the cation is large, the c a t i o n - a n i o n distance is as small as possible. This helps minimize the C o u l o m b energy. But the energy also depends on the number of near neighbors. If the cation is sufficiently large, more anions can be fitted a r o u n d the cation, without increasing the c a t i o n - a n i o n distance.