Standard diffraction patterns

Abstract

Figs. 32 and 33 show standard diffraction diagrams for cubic and hexagonal crystals in certain orientations. The symmetry of these diagrams should enable crystals belonging to one of the above two systems and possibly to the tetragonal system to be recognized. Rotation of the crystal about an axis so that two or more of the standard patterns can be obtained, may enable a satisfactory identification of the diffracting medium to be made without recording the patterns. However, it is advisable not to rely completely on such judgement. Some notes on these diagrams are given:

• Cubic crystals (Fig. 32)

• The patterns in each column have the same fundamental network but different reflections occur according to the extinction rules.

• A body-centred cubic structure gives a face-centred reciprocal lattice and vice versa.

• The diamond cube is essentially the same as a face-centred cube except that reflections with ∑h ² = odd multiples of four are weak or absent. However, in this case these reflections could occur by double reflection.

• Though double reflection does not affect the other cases, it does tend to even out the intensities of spots.

• For the [111] projection, hexagonal and rectangular symmetries can be discerned.

• [123] represents the more general case for [kkl], with h ≠ k ≠ l. The diagram for such a case requires the smallest whole numbers which satisfy hu+kv+lw = o, and careful choice of the correct angle for the particular set of indices with the correct signs.