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Additional info for Electron Microscopy and Holography II
The random phason strain produces local disordering in the quasiperiodic arrangement of L and S in the one-dimensional quasilattice, and flipping of lattice points in the twodimensional quasilattice (Fig. 17). The random phason strain leads to a gentle function of the window from a rectangle function, and consequently results in the quick reduction of the elongation function of the Fourier transform of the window function. Consequently, the random phason strain causes the disappearance of weak spots in diffraction patterns and the appearance of diffuse scattering on the background.
The detailed interpretation of the lattice and structure images is mentioned again in the section VI. FIGURE29. (a) Electron diffraction pattem of the A1-Mn-Si icosahedral phase, (b) Fourier diffractogram of the lattice image of Figure 28a, and (c) Fourier diffractogram of the structure image of Figure 28b. QUASICRYSTALS STUDIED BY ATOMIC-SCALE OBSERVATIONS OF TEM 35 FIGURE30. HRTEMimage of an A1-Pd-Mn decagonal phase, taken with the incident beam parallel to the 10-fold symmetry axis. A structure image in a thin region of the left side and a lattice image in a thick region of the right side are observed.
Conversely, an intensity distribution of fundamental reflections appearing in Figure 25a has r scaling. Also, one can see pentagonal symmetry in the intensity distribution of Figure 25f, as indicated by small white arrows. The pentagonal symmetry results from the breakdown of Friedel's law by dynamical scattering in electron diffraction and shows that this quasicrystal has noncentral symmetry. This quasicrystal is called a fivefold, or pentagonal superstructure, because its diffraction pattern (Fig.