and tetragonal crystal don’t allowed face-centered, side-centered lattice and he

Question

and tetragonal crystal don’t allowed face-centered, side-centered lattice and hexagonal,trigonal and tricilinic crystal don’t allowed body,face and side-centered lattice monoclinic crystal don’t allowed body,face-centered lattice 3 Crystal Structures and Crystal Chemistry Table 1.1 The seven crystal systems Crystal system Unit cell shapeb Essential symmetry Allowed lattices Cubic Tetragonal Orthorhombic Hexagonal Trigonal (a) Trigonal (b) Monoclinic' Triclinic Four threefold axes One fourfold axis Three twofold axes or mirror planes P, F, I, A (B or C) One sixfold axis One threefold axis One threefold axis One twofold axis or mirror plane P, F, I a b * c, ?-F- 90° b * c, ?-F-: 90°, ?-120° a b * c, ?-?-' 900-Y-120° a amb c,-?-y490 a b * c, ?--ys: 90°, ? 96 90° P, C one Two settings of the monoclinic cell are used in the literature, the most commonly used one given here, with b as the unique axis and the other with c defined as the unique axis: a * b * c, ? ?-900-Y 90° The symbol means 'not necessarily equal to'. Sometimes, crystals possess pseudo-symmetry. For example, a unit cell may be geometrically cubic but not possess the essential symmetry elements for cubic symmetry: the true symmetry is then lower, perhaps tetragonal.

Explanation / Answer

Since it is chemistry question, the best way to answer this questions is to answer a general question why there are only 14 types of Bravais lattices? It is a fully geometrical concept, the periodicity of the crystalline materials involves the basic repetition of a basic unit called unit cell. In 3-D space the cell can be defined by three non-coplanar vectors called fundamental translations. There are only 14 unique ways to choose non-equivalent basis vectors in 3D space and these basis vectors generates 14 unique lattice types. Moreover, many barvais lattice can be expressed by other simple lattices. E.g. fcc cubic lattice can be expressed as trigonal /R lattice.

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