The crystal lattice a mathematical concept

We have discussed the unit cell, which has imaginary boundaries. For simplification, each unit cell in a crystal can be represented by a single point. The result is called a crystal lattice, which is an imaginary three-dimensional arrangement of points such that the view in a given direction from each point in this lattice is identical to the view in the same direction from any other lattice point. In other words, it is an array of points that 

FIGURE 2.16. The crystal structure is composed of a crystal lattice (represented by points) and a structural motif (the atomic contents of one unit cell). The convolution of these two items will giv e the entire crystal structure. 

Crystals are defined as solids with a regularly repeated internal arrangement of 

Crystals develop faces in a manner that depends on the internal structure of the crystal, the concentration of atoms on a face, and the relative rate of growth of that face. 

For diffraction purposes crystals are generally grown by a very slow precipitation from a saturated solution. The aim is to obtain a crystal about 0.1 - 0.3 mm in all dimensions. 

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