By Koji Kosuge

This unified presentation of the chemistry of non-stoichiometric compounds is the 1st monograph at the topic for 2 a long time. in keeping with statistical thermodynamics and structural inorganic chemistry, with descriptions of contemporary examples and purposes, this may be worthwhile to either researchers in and undergraduates in reliable nation chemistry and physics.

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**Extra resources for Chemistry of Non-stoichiometric Compounds**

**Sample text**

This form is called rhombohedron in den ¯ 3m, ¯ and 32. 6. Parallel projections of these forms are presented in Fig. 31. 7 gives an overview of the 32 crystallographic point symmetry groups. pentagondodecahedron tristetrahedron deltoiddodecahedron tetrahedral pentagondodecahedron {111} {h1 0h3 } { h1 h2 h2 } h1 > h2 { h1 h2 h2 } h1 < h2 { h1 h2 h3 } 3 4 5 7 6 rhombic dodecahedron tetrahedron {110} 23 cube 2 Pos. 6 The forms of the cubic and icosahedral PSG. The Miller indices are only valid for cubic crystals.

2. The system of four space diagonals of the cube represents the simplest point symmetry group (abbreviated as PSG in what follows) of the combination of two polar 3-fold axes (“polar” means direction and inverse direction are not equivalent). As one can easily show with the aid of the transformation formulae or a stereographic projection, this arrangement also contains three 2-fold axes, which run parallel to the cube edges, that is, at half the angle of the larger angle between two 3-fold axes.

It turns out that each system has at most three different viewing directions. 3 The seven crystal systems. System Minimal symmetry Triclinic 1 Monoclinic Orthorhombic 2 or m = 2¯ 22 or mm = 2¯ 2¯ Trigonal (rhombohedral) 3 or 3¯ Tetragonal 4 or 4¯ Hexagonal 6 or 6¯ Cubic 23 Conditions for lattice parameters of symmetry-adapted reference system (viewing directions) ai , αi not fixed (1. arbitrary, 2. arbitrary, 3. arbitrary) α1 = α3 = 90◦ ¯ 2. arbitrary, 3. arbitrary) (1. a2 2 or 2, ◦ αi = 90 ¯ 2.