Electron Diffraction of Face Centred Cubic (fcc) Lattices
- Practical Electron Microscopy and Database -
- An Online Book -

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Table 3560a shows the extinctions (also called forbidden spots) in the diffraction patterns of the crystals with space group Fd-3m such as diamond (C), silicon (Si), germanium (Ge), and tin (Sn) elements as a result of the destructive interference between the two interpenetrating face centred cubic (fcc) lattices displaced by a vector (1/4, 1/4, 1/4). Figure 3560 shows the diffraction pattern of a silicon (Si) crystal in [110] zone axis. The reflections marked in black are extinct in the single scattering approximation when the crystal is very thin, while the ones marked in green exist in the patterns of both thin and thick crystals. When the crystal become thicker, the multiple scattering occurs and thus these reflections can gain intensity and become visible because of more successive scatterings (even though they are probably weak if the sample is still relatively thin), for instance, electrons are indirectly scattered into the (002) reflection because of multiple scattering through the (1 -1 1) and (-1 1 1) scattering vectors. The red arrows represents the multiple scattering paths for forming the visible (002) reflection.

Table 3560a. Conditions of forbidden and allowed reflections (h k l) of common crystal structures
Bravais Lattice Forbidden reflections Allowed reflections Example Compounds
fcc h, k, l are mixed odd and even; or, all even and h + k + l ≠ 4n (Or defined by h + k + l = 4n + 2) As fcc, but if all even and h + k + l ≠ 4n, then absent (n is integer)
Si, Ge, Sn - diamond cubic

Figure 3560. Diffraction pattern of a Si crystal in [110] zone axis
orientation. The spot sizes represent the intensities.

Table 3560b. 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

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