Bravais stmctures

If atoms, molecules, or ions of a unit cell are treated as points, the lattice stmcture of the entire crystal can be shown to be a multiplication ia three dimensions of the unit cell. Only 14 possible lattices (called Bravais lattices) can be drawn in three dimensions. These can be classified into seven groups based on their elements of symmetry. Moreover, examination of the elements of symmetry (about a point, a line, or a plane) for a crystal shows that there are 32 different combinations (classes) that can be grouped into seven systems. The correspondence of these seven systems to the seven lattice groups is shown in Table 1. 

Alloy phases will be described sfructurally using the following multiple (and somewhat redundant) nomenclature Name(s) Prototype (Pearson Symbol, Stmcture Report Symbol). As an example CuZn ( 8-Cu-Zn, /3-brass) CsCl (cP2, B2) type. (Note The Pearson symbol already contains the crystal system and Bravais lattice). Alloy phase compilations with stmctural data are available. 

In all of these stmctures the atomic positions are fixed by the space group S5munetry and it is only necessary to determine which of a small set of choices of positions best fits the data. According to the theory of space groups, all stmctures composed of identical unit cells repeated in three dimensions must conform to one of 230 groups that are formed by combining one of 14 distinct Bravais lattices with other symmetry operations. 

AU crystal stmcmres can be built up from the Bravais lattices by placing an atom or a group of atoms at each lattice point. The crystal stmcture of a simple metal and that of a complex protein may both be described in terms of the same lattice, but wha-eas the number of atoms allocated to each lattice point is often just one for a simple metallic crystal it may easily be thousands for a protein crystal. The number of atoms associated with each lattice point is called the motif, the lattice complex or the basis. The motif is a fragment of structure that is just sufficient, when repeated at each of the lattice points, to construct the whole of the crystal. A crystal structore is built up from a lattice plus a motif. 

The overall symmetry of the stmcture is related to the value of n in the series formula. In cases where n is a [(multiple of 3)-1], the stmcture has a Bravais hexagonal lattice, while if n is given by a [(multiple of 3)] or a [(multiple of 3)+1], the structure conforms to a Bravais rhombohedral lattice. 

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