Practical Electron Microscopy and Database

For hcp crystals, the (0 0 0 l) reflections, e.g. for the case with 164 (P-3m1) space group, are forbidden when l is odd. However, those reflection positions often show diffraction intensity, which is probably caused by chemical order on the basal planes, or by double or multiple diffraction (scattering).

Figure 3034 shows a [110] L1₀ (P4/mmm)-FePt crystal, consisting of a (111) twin in fct (face centered tetragonal) phase structure. The reflections connected by the solid and dashed lines originate from twin and matrix, respectively. The extra weak reflections marked by the white arrowheads in Figure 3036 (a) are from chemical ordering in the L1₀-FePt structure. The twin plane is parallel to (1 -1 -1) or (-1 1 -1)_t, where the subscript “t” represents the twin reflection. The c-axes of the twin and matrix are on the same plane and form a mirror symmetry relative to the (1 -1 -1) or (-1 1 -1)_t twin plane.

If chemical ordering exists in a crystalline phase, e.g. quasicrystals, then HAADF imaging due to Z-contrast can be an effective technique to analyze such structures.

[1] Z. R. Dai, Shouheng Sun, and Z. L. Wang, Phase Transformation, Coalescence, and Twinning of Monodisperse FePt Nanocrystals, NANO LETTERS, 1 (8), 443-447, 2001.