Cubic system

Abstract

In §3,4 it was pointed out that the interplanar spacings of cubic crystals depend on √N, where N = h ²+k ² + l ². All possible values of N up to 64 are given in Table 8. Diffraction with any of these indices can occur for a primitive lattice. The occurrences for the body-centred cubic (b.c.c.) and face-centred cubic (f.c.c.) lattices are denoted by ×. The values of √N given here should be sufficiently accurate for most calculations of interplanar spacings. Solution of diffraction patterns necessitates the determination and comparison of angles as well as spacings. Table 9 lists the angles between planes in cubic crystals calculated from the formula

$$\cos \phi = \frac{{{h_1}{h_2} + {k_1}{k_2} + {l_1}{l_2}}}{{\sqrt {(h_1^2 + k_1^2 + l_1^2)\sqrt {(h_2^2 + k_2^2 + l_2^2)} } }}$$

where (h ₁ k ₁ l ₁) and (h ₂ k ₂ l ₂) are the indices of the two planes and ∅ is the angle between them. The formula applies equally weli to the angle ρ between two zone axes with the same indices, since the direction of these axes will be normal to the two planes.