Figure 18.4

In Fig 18.4 the plane containing the atoms intersects the x axis at a. This plane does not intersect with the y and z axes at all. We may rephrase this by saying that the intersections with y and z axis at y = and z = . The x, y and z intersections are at ( a, , ). Taking the reciprocals of these, we get ( 1/a, 0, 0 ) and since a, b and c are characteristics of the crystal, we can simply refer to it as (100)

These are the Miller indices of this plane. Using the same procedure verify that the Miller indices of the other planes in the figure (18.4) are (110), (111). In a simple cubic lattice, the (100) plane is identical to the (1/2, 0 0 )plane, because it has exactly the same density and the relative positions of atoms / ions. Therefore all planes parallel to the (100) planes may be referred to as the (100) planes. In a "body centered" cubic lattice such as the CsCl lattice, the (100) planes containing the Cl^- ions would be different from the (200) planes containing the Cs⁺ ions. Now that we can label all these planes accurately, let us see how the distance between the planes can be determined using Bragg's law.