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Are in contact along the cube edge, which is of length √ 2rA and the body diagonal, along which the atoms A and X√are in contact, is of length 2 3rA . 732rA . As well as being of different relative sizes, there are different numbers, or proportions, of these interstitial sites. For both the octahedral sites in ccp, and the cubic sites in the simple cubic structure, the proportion is one interstitial site to one (large) atom or ion, but for the tetrahedral interstitial sites in ccp the proportion is two sites to one atom.
5) and also relate the polymorphous forms of many organic compounds—the structures only differing in the way in which the molecules are packed together under the inﬂuence of the weak van der Waals forces. 2 Tetrahedral and octahedral structures—silicon carbide and alumina B4 (2H) Wurtzite B3 (3C) Zinc blende c = 15 √2 a √3 c=6 √2 a √3 c=4 √2 a √3 c=3 c=2 √2 a √3 √2 a √3 Consider, for example, the crystal structures which consist of close-packed or nearly close-packed layers of large atoms or ions with the smaller atoms or ions occupying some or all of the tetrahedral interstitial sites.
Typical minerals are melilite, Ca2 Mg(Si2 O7), or hemimorphite, Zn4 (OH)H2 O(Si2 O7 ). (c) Three or more tetrahedra linked together to form rings, each tetrahedron sharing two oxygen anions (cyclosilicates): the Si:O ratio is Sin O3n , where n is the number of tetrahedra in the ring. A typical mineral is beryl, with a ring of six tetrahedra, Be3Al2 (Si6 O18 ). (d) Many tetrahedra linked together to form single chains (inosilicates): each tetrahedron shares two oxygen anions, as in the ring structures above, and which therefore give rise to the same Si:O ratio.