X-shapes

Somatoids are often twinned on the (322) plane to give star-shaped or x-shaped twins (Eig. 4.15 a). Incorporation of low levels of Si in the structure promotes twinning with 0.04 mol mol Si, akaganeite was almost 100% twinned (Cornell, 1992). These crystals have a visibly roughened surface. Increasing citrate concentration during forced hydrolysis at 100 °C and pH 1 reduced the length of the somatoids from... 

Japanese twins of quartz have attracted interest since ancient times because they exhibit a remarkably platy V-shape, in contrast to the hexagonal prismatic morphology of coexisting single crystals. Since they grow on substrate, the V-shape was assumed to represent the upper half of an X-shape [12], which implies that the Japanese twins are penetration twins. The platy form of Japanese twins has been explained as being due to preferential growth at a re-entrant corner formed by two individuals. If the platy form is indeed simply due to the re-entrant corner effect, we should expect a variation of forms, from V-shape to fan-shape, as the effect proceeds, as shown in Fig. 10.9. If, however, it represents the upper half of an X-shape, Japanese twins should be penetration twins, not contact twins. 

If two individuals conjugate on an r or a z face, a nucleus of a Japanese twin with 1122 as the composition plane is formed. This indicates that a Japanese twin is not a penetration twin (i.e. not the upper half of an X-shape), but a contact twin (i.e. the upper half of a Y-shape). Horizontal banding in geode agate (see Section 10.9) appears through grain size variation due to gravitational sedimentation, and con-... 

The longstanding idea of superluminal motion has become subject to renewed interest, due to a number of recent discoveries and observations, as described in a survey by Recami [27]. Thus the squared mass of muon-neutrinos is found to be negative. There are further observations that can be interpreted as superluminal expansions inside quasars, in some galaxies and in galactic objects. Also, so called X-shaped waves have been observed [69] to propagate at a... 

The room-temperature photooxidation of CF3I was repeated by Heicklen,71 who was unaware of the earlier work. He used radiation mainly at 3130 A and followed the reaction by in situ infrared spectroscopy in an x-shaped Pyrex cell with quartz and NaCl windows. The sole oxidation product was CF20. Its quantum yield was the same with 1.33 or 93 torr of 02 present. Heicklen did not use reaction (3-5) in his mechanism. 

X waves constitute the most striking example of superluminal effects, because they propagate in free space over large distances. We want to stress that the existence of superluminal X-shaped waves was predicted by ER. This is, in our opinion, one of the most impressive among the (verified) ER predictions, and was just put forward as early as 1982 in a fundamental paper by Barut et al. [50]. The point is that, on the basis of ER, an (extended) tachyon is just expected... 

Figure 6. The shape of a spherical particle as its appears in (a) its rest frame, (b) in a frame moving with subluminal (but relativistic) velocity, (c) a frame moving at the light velocity (an unphysical case ), and (d) a superluminal frame. This last figure clearly shows that, according to ER, tachyons are X-shaped objects (waves). A spatial dimension has been dropped for simplicity of representation. (From Barut et al. [50].)...

There is presently no serious doubt about the actual evidence for superluminal group velocities, provided by the experiments on photon tunneling and X-shaped waves. On the contrary, it is still a subject of debates and controversies the question whether such a superluminal behavior does imply violation... 

Fig. 61 (a) Example of an X-shaped molecules and (b,c) dependence of wall thickness on the number of lateral chains, shown for the case of a square cylinder phase (b) double wall structure of T-shaped bolaamphiphiles (c) single wall cylinders formed by X-shaped molecules [330]... 

X-Shaped Polyphiles Liquid Crystalline Honeycombs with Single Molecule Walls... 

Attaching only one lateral chain to the rod-like core (T-shaped amphiphiles 181-183) gave rise to LC honeycomb phases where the cross-section of the honeycomb walls contains two rods arranged side-by-side, i.e., the honeycombs have double walls (Fig. 61a) [8]. However, attaching two lateral chains to opposite sides of the aromatic core (X-shaped polyphiles like compound 187) generates polygonal honeycombs with walls that are only one molecule thick (Fig. 61b) [319]. As a consequence of the thinner walls, effectively more space is left available for the lateral chains inside the cells. Hence, honeycombs with smaller cells could be achieved by using two short lateral chains instead of only one chain with the same total volume [330]. 

X-Shaped Tetraphiles Liquid Crystalline Multicolor Tilings... 

Fig. 63 X-shaped quaternary bolaamphiphile 189 forming hexagonal cylinder phases with models showing (a) the three-color, (b) two-color and (c) single color hexagon tiling patterns in the left bottom comer the core-shell structure of the mixed cells is illustrated dark = Rp-chains white = Rsi-chains gray = mixed cells [42]...

FIGURE 3.22 General idea of polymer membrane formation at the interface of a two-phase organic/aqueous flow in an X-shaped microchannel layout [435]. Reprinted with permission from the American Chemical Society. 

A further feature of the spectrum in Figure 9.24 is the sharp spike at the centre of each x/ -shaped transition. The reason for this is that saturation of the transition has occurred. This was discussed in Section 2.3.5.2 in the context of Lamb dips in microwave and millimetre wave spectroscopy and referred to the situation in which the two energy levels involved, m(lower) and (upper), are close together. Under these circumstances saturation occurs when... 

In Fig. 1 a conventional diagram is given for producing the X-shape junction between two nanotubes. Certain symbols for system states St and interstates transitions Bj are given in the bottom and top rows of the abscissa axis,... 

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