Commensuration pattern

Very interesting studies have been made of the pattern for UPD on single crystal metal substrates [49]. A commensurate pattern is usually observed for the formation of a partial monolayer. The theory of UPD and formation of the initial monolayer is an area of active research. Of course, the phenomenon of UPD is restricted to formation of a monolayer. Once this has formed, the deposition process reverts to one of metal ion M"+ on metal M. By comparing the UPD process with anion-specific adsorption, the role of partial charge transfer in these processes is clarified. 

A myriad of minor moons and rings have the same disposition with respect to the parent planet that the asteroid belt and the inner planets have with respect to the srm. Closer examination of the orbital relationship within these groups, and also of the accumulation of the asteroids with respect to their mean orbit, demonstrate the same commensuration pattern as the planets around the srm, only on a different scale. 

Figure 19 Instantaneous (top row) and thermally averaged (bottom row) domain structures in simulations of an AB diblock copolymer assembling on a commensurate pattern of selective lines with undulatory (left column) or peristaltic (right column) roughness. Only the A-rich blocks are shown.

Figure 2. (001) projection of (a) AbTi3 and (b) AlnTi structures. A model for island-like precipitates composed of the core AlsTi3 phase and the periphery AlnTi phase is shown in (c), and (d) shows a schematic illustration of commensurate AbTia (small solid circles) and AlijTi (small open circles) diffraction patterns [14],... 

First, in the striated muscles, the cross-sectional organization of filaments is highly ordered in a hexagonal pattern commensurate with the ratio of actin to myosin filaments and the distribution of active myosin heads, S-1 segments, helically every 60 degrees around the myosin filament. In smooth muscle, with perhaps 13 actin filaments per myosin filament, many actin filaments appear to be ranked in layers around myosin filaments. It is not known how the more distant actin filaments participate in contraction. 

The simulated LEED pattern is shown in Figure 7-B. Comparison of the simulated LEED pattern with the observed LEED pattern (lower camera shutter speed) is shown in Figure 7-C. As can be seen, there is good agreement. This PYR layer structure is incommensurate that is, the mesh vectors of the layer are not exact multiples of the substrate mesh. The nearest commensurate structure would have been (2/3x/21, 79°)R30°, Figure 7-D. Although this commensurate alternative is numerically quite similar... 

Figure 7. Continued. E. Diagram of calculated LEED pattern corresponding to nearest commensurate structure, (2v/3xv/21, 79.1 )R30. Continued on next page.

A group of crystals show diffraction patterns in which two or more 3D lattices having periods commensurate or incommensurate to each other may be recognized. In other words, the crystal consists of two or more interpenetrating substructures (two or more different atom sets) with different periods at least along one direction (see Fig. 3.42). Names such as composite crystals, vernier structures, misfit-layer structures, and chimney-ladder structures have been used for this group of structures. 

Figure 4.19 Model structures of (a) incommensurate and (b) commensurate phases of K2Pb[Cu(N02)6]. The displacement pattern of Jahn-Teller active phonons is shown by arrows. In (a) the phonon mode has wave-vector k — (0.425, 0.425, 0) and in (b), wave-vector of the phonon mode is k = (, j, ). (After Yamada, 1977.)...

A crystal is not, in actual fact, a simple array of points, each of which is a pattern-unit. In the first place, an atom is not a point its electrons, which scatter the X-rays, are distributed over distances commensurable with the interatomic distances. Secondly, each pattern-unit in a crystal often consists, not of one atom, but a group of atoms. The pattern-unit is thus not a point, but has a diffuse and often irregular form. However, for the purpose of diffraction theory, as far as it is carried in this chapter, the diffuse pattern-unit may be mentally replaced by a point. It will be shown in Chapter VII that the form of the pattern-unit affects the intensities of the diffracted beams but it does not affect their positions, which depend only on the space-lattice, the fundamental arrangement of identical pattern-units. 

In CoOP above 300 K the compound exists in the Cccm space group, but with characteristic diffuse X-ray lines indicative of the Peierls modulation and no evidence of superstructure formation. Below 300 K a superstructure develops as shown by the appearance of satellite reflections on the X-ray diffraction photographs. At 280 K a phase transition to the Pccn space group occurs and associated with this are changes in the satellite pattern.78 74 Superstructure development which is commensurate with the Peierls modulation is completed about 250 K. 

Notes 1. Preparation All preparations are by equilibration of the oxide with oxygen at temperatures and oxygen pressure predetermined from experimental data. 2. The diffraction patterns all show strong face-center-cubic reflections with commensurate, weak, superstructure reflections by whatever means they are taken. 

The NMR experiment was performed on nB in C11B2O4. The spectrum in the commensurate phase is discussed. The magnetic moment at the Cu(A) site is estimated to be 0.45 /tg, which is almost 50% of the moment derived from the neutron diffraction experiment. The magnetic moment at the Cu(B) sites is absent in the commensurate phase. The asymmetric nature of the spectral pattern is not understood so far. A phenomenological understanding of the commensurate to incommensurate transition is discussed on the basis of the molecular-field approximation. More precise discussion of the commensurate phase and also of the incommensurate phase will be presented in the near future. 

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