Practical Electron Microscopy and Database

Based on the periodicity of the observed reflections in diffraction patterns or profiles, it is possible to distinguish the crystal structures. For instance, Figure 2507 shows the comparison of XRD (X-ray diffraction) results from different cubic crystal structures. Here, the three integers (h, k, and l) represent the Miller indices.

Table 2507a shows the d-ratios for cubic crystal, where d₁ and d₂ are d-spacings.

Table 2507a. d-ratio for cubic crystal

Table 2507b. Some symmetrical diffraction patterns of cubic crystals.

Zone axis	[100]	[110]	[111]
Symmetry	Square	Rectangular	Hexagonal
Aspect Ratio	1:1	1: for BCC, SC (almost hexagonal for FCC)	Equilateral

The lattice spacing of cubic structures may be given by,

         ------------------------------- [2507]

where,
          a -- The lattice constant.