A crystal lattice may be considered as an aggregate of a set of parallel equi-distant planes of high density of lattices points, Hence lattice planes are also called Cleavage Points.
Or a given lattice, the lattice planes can be chosen in a different number of ways, for example (a), (b), (c), and (d) as shown in the figure 1.1.4
The problem is that how to designate a plane in the crystal. Miller evolved a method to designate a plane in a crystal by three numbers (h,k,l) known as Miller indices.
Fundamental Crystallographic terms
Lattice is defined as an array of points which are imaginarily kept to represent the position of atoms in the crystal that every lattice point has got the same environment as that o the other and hence one lattice point cannot be distinguished from the other lattice point.
Space Lattice or Crystal Lattice is a three dimensional collection of points in space. The environment about any particular point is in everyway the same.
The regular pattern of points which describe the three dimensional arrangement of particles in a crystal structure is called the Crystal Lattice or Space lattice.
Basis is formed by associating with every lattice point a uint of assembly of atoms or molecules identical in composition. This unit assembly is called Basis.
The Crystal Structure is formed by the addition of a basis to every lattice point.