Moire patterns

Electrochemical methods for the determination of diffusion coefficients are not as popular as nonelectrochemical methods. Compared to the number of references wi th N M R data, the number of diffusion coefficients determined by electrochemical methods is insignificant 

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Figure 7.4 (A) STM image (240 x 125)2 of two rotational domains of the Moire pattern formed at Pt(l 11) by CO at 1 bar at room temperature. (B) High-resolution image of the CO overlayer at 1 bar. (C) The ( /l9 x /T9) R23.40—13CO structure the unit cell is shown the dark circles represent CO molecules adsorbed in nearly atop sites. (Reproduced from Ref. 9).

Figure 3.32 Measurement of liquid film thickness by Moire fringes (a) experimental setup and (ft) Moire pattern with liquid films of varying thicknesses. (From Kheshgi and Scriven, 1983. Copyright 1983 by Elsevier Science Ltd., Kidlington, UK. Reprinted with permission.)...

Fig. 12. STM image (10 x 10 nm2) of a densely-packed Pb monolayer on Ag(lll), showing the individual Pb atoms as well as the Moire pattern due to the lattice misfit between monolayer and substrate. Deposition from 0.5 M NaC104 + 0.1 M Na2HCit+ 1 mM Pb (N03)2 at -0.44 V vs. SCE [48],...

Superionic conducting glass systems, 12 586 Superior vena cava, 5 80 Super iron cells, 3 431t Superlattice(s), 13 499, 19 166 via MOCVD, 22 158-160 Superleaks, 17 354 Super Lewis acids, 12 191 Superluminscent LEDs, 22 176 Supermilling acid dyes, 26 396 Super milling dyes, 9 184, 185 Super-moire pattern, 17 428 Supermolecular organization, of polyamide fibers, 19 740... 

FIG. 27. A comparison between the in-plane dimensions, determined by SXS and STM, of the electrocompressive Pb upd adlayer formed on Ag(lll). The open circles are the STM data and the solid line is a least-mean-square fit to the data, while the dotted line is derived from SXS measurements (k = A/a when A is the period of the Moire pattern while a is the lattice spacing of the overlayer). (From Ref. 343.)... 

Oster, G. The Science of Moire Patterns. Barrington, N.J. Edmund Scientific Co., 1964. 

The moire of two cross sections of the hyperboloids represents the difference of two interference patterns. If the two cross sections are identical but one is displaced, the moire fringes also represent the loci of constant resolution in the displacement direction. If one focal point is fixed, and the other one is displaced, the resulting moire pattern forms a new set of hyperboloids whose foci are the two positions of the displaced focal point. This new pattern is independent of the position of the fixed focal point (a rotation of one of the original spherical wavefronts of Fig. 5 produces no moire effect). Therefore hologram interference fringes are independent of the position of the point source of the fixed reference beam. 

The so-called Moire patterns are created by superimposing infinite planar patterns. The resulting pattern is a new two-dimensional network. The simplest cases are illustrated in Figure 8-38. Consider first two identical systems of lines on transparent paper being superimposed. The starting and resulting systems have a period of A and d,... 

Figure 8-38. Moire patterns from the superposition of two patterns at increasing angles. Top two line systems Bottom two circle systems [54].

Moires patterns occur in the most diverse natural phenomena and often occure in artistic creations as well [55], They can be treated by fairly simple mathematics [56],... 

Note the similarity to heterodyne beat and to one- and two-dimensional moire patterns... 

Fig. 34. SFG spectra of CO adsorbed on Pt(l 1 1) at 300 K at submonolayer coverages (a), and in the pressure range from 1 to 500 mbar (b) (112,151). Spectra recorded at pressures > 1 mbar were corrected for absorption by gas-phase CO. On-top CO was the only species detected (Ti Sa laser system) adapted from (151) with permission. Copyright (2002) American Chemical Society, (c) High-resolution STM image (55 x 51 A ) of the Moire pattern formed by CO on Pt(l 11) at 1 bar (only one rotational domain shown). An illustration of the (. 19 x 19)R23.4°-13CO structure is included (unit cell marked by the solid line) adapted from Kruse Vestergaard et al (393) with permission. Copyright (2002) American Physical Society.

Figure 6.6. Facing page. Optical analogues showing the formation of a moire pattern, (a) Superposition of two gratings of unequal spacing (b) superposition of two identical gratings with a small relative rotation. The effects of an edge dislocation in one of the gratings are shown in (c) and (d).

Thus, one-dimensional parallel and rotational moire fringes can be clearly distinguished because they are always normal and parallel to g, respectively. Whether a one-dimensional or two-dimensional moire pattern is produced depends on the number of doubly diffracted beams that pass through the objective aperture. It is clear from Figure 6.5 that moire fringes will also be produced in dark-held images. 

Optical analogues of one-dimensional parallel and rotational moire patterns in two perfect crystals are shown in Figures 6.6(a, b). 

Because the moire patterns observed by TEM are, in effect, magnihed images of the reflecting planes, crystal defects in either of the overlapping crystals become visible see Figure 6.6(c,d). However, this technique has not been widely used for imaging crystal defects in minerals. 

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