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By Riseborough P.S.

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16 The Perovskite Structure The perovskite structure, as exemplified by BaT iO3 , is cubic at high temperatures but becomes slightly tetragonal on cooling below a ferro-electric transition temperature. The cubic structure has the space group P m3m. The structure is composed of the T i atoms positioned on the simple cubic lattice sites (0, 0, 0), and the Ba atoms positioned at the body center sites ( 21 , 12 , 12 ). e. at (0, 0, 21 ), (0, 12 , 0) and ( 12 , 0, 0). An alternate representation of the unit cell is found by centering the lattice on the Ba ions, by translating the origin via 12 (1, 1, 1).

In particular, Carbon, Silicon and Germanium can crystallize in the diamond structure. The great strength of diamond is a consequence of the three-dimensional network of strong covalent bonds. 34. 2 Exercise 3 Find the angles between the tetrahedral bonds of diamond. 3 Graphite Structure Graphite is the stable form of carbon. Graphite has a hexagonal unit cell and has the space group P 63 /mmc. The primitive lattice vectors may be represented by √ a1 = 3 a eˆx √ 3 3 a eˆx + a eˆy a2 = 2 2 a3 = c eˆz (35) where a is the length of the side of the hexagon.

Linus Pauling has produced a set of empirical rules which determine the coordination numbers in terms of the ionic radii of the ions. ), there are three types of holes between the close packed spheres and each type of hole has a different size. It is assumed that the cations fit into one set of holes. c. unit cell is surrounded by an octahedron and, therefore, has a coordination number of 6. There are also tetrahedral holes with coordination number 4. c. cube, and the vertices of the tetrahedra are located at the corner and the three neighboring face centers.

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