Practical Electron Microscopy and Database

Figure 3001a shows 4mm net symmetry in ZOLZ [001] zone-axis of cubic Zr₄₁Ti₁₄Cu_12.5Ni₁₀Be_22.5 with space group Fm-3m.

Figure 3001b shows the CBED pattern of β-pyrochlore oxide superconductor KOs₂O₆ along the [001] zone axis. [2] The square array with small dark disks near the center is zero-order Laue zone (ZOLZ) and the surrounding circle formed by the highly contrasted disks is first-order Laue zone (FOLZ). The magnified image of the inset presents a four-fold rotational symmetry along the c* axis and two mirror symmetries m_a and m_b, indicating that the whole pattern (WP) has 4mm symmetry.

Figure 3001b. CBED pattern taken from a KOs₂O₆ crystal along [001] zone axis. [2]

4mm1_R is the only possible diffraction group symmetry with a 4mm whole pattern symmetry for the cubic <100>, <010> and <001> zone axes. In this case, the only crystal point group which permits a 4mm1_R diffraction group symmetry is m-3m.

Note that the projection-diffraction symmetry can never be lower than the whole-pattern symmetry since the whole-pattern symmetry reflects the symmetry of the full three-dimensional (3-D) crystal.

[1] Q. Wei, N. Wanderka, P. Schubert-Bischoff, and M-P. Macht, S. Friedrich, Crystallization phases of the Zr41Ti14Cu12.5Ni10Be22.5 alloy after slow solidification, J. Mater. Res., 15 (8) 1729, (2000).
[2] Jun-Ichi Yamaura, Zenji Hiroi, Kenji Tsuda, Koichi Izawa, Yasuo Ohishi, Satoshi Tsutsui, Re-examination of the crystal structure of the β-pyrochlore oxide superconductor KOs2O6 by X-ray and convergent-beam electron diffraction analyses, Solid State Communications 149 (2009) 31-34.