3.2 Crystal Lattices
One of the consequences of the way in which we have defined the unit cell is that the corners of the cell have absolutely identical chemical and structural environments (in addition, in some crystals there may be locations other than at the corners of the unit cell whihc also have identical environments). It is useful to imagine a hypothetical crystal made up of numerous unit cells stacked along the three repeat direction, x, y and z, with the corners of each individual cell marked by a point. These points together with any other points in the crystal with identical environments are termed lattice points:
The array of lattice points is termed the crystal lattice, while a plane passing through three non-colinear lattice points in known as a lattice plane.
This notion of a crystal lattice provides a wonderful insight into many of the fundamental properties of crystals such as shape and symmetry. For example a crystal growing free of interference will tend to develop faces parallel to lattice planes, and in particular lattice planes with the greatest density of lattice points. The concept of the crystal lattice therefore provides us with a very useful way of understanding the seemingly infinite variety of crystal shapes found in nature. In order to make full use of the lattice concept we will need to (stretch the neurons in order to) develop some technique enabling the systematic description of the orientation of lattice planes and rows.