Lattice symbols

SYSTEM IN SYSTEM LATTICE SYMBOLS AXES AND ANGLES... 

The factors given in both 2.2.4. and Table 2-1 arise due to the unit-cell axes, intercepts and angles involved for a given crystal lattice structure. Also given are the lattice symbols which are generally used. The axes and angles given for each system are the restrictions on the unit cell to make... 

According to Hahn (2002), mS and oS are the standard setting independent symbols for the centred monoclinic and the one-face-centred orthorhombic Bravais lattices. Symbols between parentheses oC, oA, etc. represent alternative settings of these Bravais lattices. 

Fig. 1.3 The fourteen Bravais lattice unit cells and associated lattice symbols.

Crystal system Lattice symbols Relation between cell edges and angles Characteristic symmetry... 

Seven systems Axes and angles 14 Bravais Lattices Lattice symbols... 

Crystal system Lattice symbol Structure symbol ... 

System Axial lengths and angles Bravais lattice Lattice symbol... 

In addition to different types of crystal system there are also different types of lattice within those crystal systems, which correspond to specific arrangements of the atoms/ions within them. As discussed earlier, the two-dimensional system with the simplest sort of lattice which contains only one lattice point, is termed primitive. Similarly, for each three-dimensional crystal system there is always a primitive unit cell which consists of atoms located at the comers of the particular parallelepiped (i.e. a solid figure with faces which are parallelograms). For example. Figure 1.5 shows primitive lattices (symbol P) for both tetragonal and hexagonal systems. 

Crystal system (Lattice type) Lattice symbol Lattice parameters... 

Pearson. The symbols give, successively, the crystal system, the Bravais lattice symbol, and the number of atoms per unit cell. The notation is summarized in... 

The nomenclature committee of the American Society for Testing Materials (1957) proposed a nomenclature which expresses the chemical formula followed by the number of atoms per unit cell and the Bravais lattice symbol. This notation was later developed by Schubert (1964) and by Pearson (1967). This symbology may be used for classification purposes and might help to find out if a particular structure type had been determined before, but it does not contain information on the geometry of the structure. 

Lattice system Bravais lattices symbol Hermann-Mauguin Properties... 

System and lattice symbol Point group Hermann-Mauguin symbol Short Full Plane group number Symmetry elements additional to discrete tranlations... 

Figure 4.15 The plane groups of the square and hexagonal lattices (symbols as given in the lower right of Figure 4.14).

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