Crystal axis rotation

As witli tlie nematic phase, a chiral version of tlie smectic C phase has been observed and is denoted SniC. In tliis phase, tlie director rotates around tlie cone generated by tlie tilt angle [9,32]. This phase is helielectric, i.e. tlie spontaneous polarization induced by dipolar ordering (transverse to tlie molecular long axis) rotates around a helix. However, if tlie helix is unwound by external forces such as surface interactions, or electric fields or by compensating tlie pitch in a mixture, so tliat it becomes infinite, tlie phase becomes ferroelectric. This is tlie basis of ferroelectric liquid crystal displays (section C2.2.4.4). If tliere is an alternation in polarization direction between layers tlie phase can be ferrielectric or antiferroelectric. A smectic A phase foniied by chiral molecules is sometimes denoted SiiiA, altliough, due to the untilted symmetry of tlie phase, it is not itself chiral. This notation is strictly incorrect because tlie asterisk should be used to indicate the chirality of tlie phase and not tliat of tlie constituent molecules. 

Step 3. The computer collects about 45 frames of data. The crystal is rotated about the vertical axis for 0.3 degree for each frame. Usually the crystal is exposed to x-rays for about 5 seconds for each frame. The computer finds the centers of many reflections (typically 25 to several hundred) and determines indices for these reflections. It then determines the unit cell parameters and the orientation of the unit cells with respect to the diffractometer. 

SHG has been used to study electrode surface symmetry and order using an approach known as SH rotational anisotropy. A single-crystal electrode is rotated about its surface normal and the modulation of the SH intensity is measured as the angle (9) between the plane of incidence and a given crystal axis or direction. Figure 27.34 shows in situ SHG results for an Au(ll 1) electrode in 0.1 M NaC104 + 0.002 M NaBr, using a p-polarized beam. The results indicate the presence of two distinct onefold... 

Fig. 27a-c. Electron spin echo envelope modulation of Co(acacen), temperature 4K. a) Nuclear modulation pattern of Co(acacen) diluted into a Ni(acacen) 1/2 H20 single crystal. Crystal setting rotation axis I,

Fourier transform of the nuclear modulation pattern (From R. de Beer1 4)) c) Stick spectrum ENDOR frequencies (AmN = 1, 2) calculated from the hfs and quadruple tensors in Ref. 59 dashed lines ms = - 1/2, full lines ms = 1/2... 

Turning to the low temperature transition of the homopolymer of PHBA at 350 °C, it is generally accepted that the phase below this temperature is orthorhombic and converts to an approximate pseudohexagonal phase with a packing closely related to the orthorhombic phase (see Fig. 6) [27-29]. The fact that a number of the diffraction maxima retain the sharp definition at room temperature pattern combined with the streaking of the 006 line suggests both vertical and horizontal displacements of the chains [29]. As mentioned earlier, Yoon et al. has opted to describe the new phase as a smectic E whereas we prefer to interpret this new phase as a one dimensional plastic crystal where rotational freedom is permitted around the chain axis. This particular question is really a matter of semantics since both interpretations are correct. Perhaps the more important issue is which of these terminologies provides a more descriptive picture as to the nature of the molecular motions of the polymer above the 350 °C transition. As will be seen shortly in the case of the aromatic copolyesters, similar motions can be identified well below the crystal-nematic transition. 

If the crystal is rotated round its b axis (Fig. 89) the equatorial spots are reflections from hOl planes. The values for these spots are found as before by measuring the distance from the origin to each point of the (non-rectangular) hOl net plane (Fig. 88). Note that the indexing of equatorial reflections in this case cannot be done by a log d chart, since there are three variables, a, c, and / the reciprocal lattice method is essential. Once the indices for the equatorial reflections have been found, those of the reflections on upper and lower layer lines follow at once, since all reciprocal lattice points having the same h and l indices (such a set as 201, 211, 221, 231, and so on) are at the same distance from the axis of rotation and thus form row lines. 

Rotation round the a oj c axis of a monoclmic crystal (Fig. 90) results in a different type of photograph the spots fall on layer lines, as always when a crystal is rotated about, a principal axis, but not on row lines. Consider first the equatorial spots on a photograph obtained by rotating the crystal round the c axis these are from hied planes. The zero (hk0) level of the reciprocal la ttice is a rectangular array of points, from which... 

If a triclinic crystal is rotated round any axis of the real cell (Fig. 93), the photograph exhibits layer lines (since the various levels of the reciprocal lattice are normal to the axis of rotation), but not row lines, since none of the points on upper or lower levels are at the same distance from the axis of rotation as corresponding points on the zero level. The indices for points on the zero level are found in the same way as for photographs of monoclinic crystals rotated round the 6 axis for the zero level of a triclinic crystal rotated round c, a net with elements a, 6, and y is constructed (Fig. 94), and distances of points from the origin are measured. The other levels, projected on to the equator, are displaced with regard to the zero level in a direction which does not lie along an equatorial reciprocal axis the simplest way of measuring values is, as before, to use the zero level network,... 

When a crystal is rotated about an axis and inverted about the central point and at that point repeats itself, it is said to have an rnrit of rotary inversion. It is a twofold axis of rotary inversion if the geometrical figure is rolaled 180° and then inverted. Additionally, there are threefold, fourfold, and sixfold axes of rotary inversion possible. 

Of particular value to the study of single crystal electrodes in solution are experiments which measure the variation in SH response as the surface is rotated azimuthally about the surface normal (Fig. 4.2). In this experiment the incoming beam has a fixed polarization and the outgoing SH beam is monitored for the two different polarizations, s and p. The modulation in the SH intensity as the angle between the plane of incidence and a crystal axis or direction is changed is referred to... 

One possible such mechanism for fixing a pattern is to have a phase transition. For example, if the pattern is in terms of a distribution of large molecules on the outer membrane surface, as in the Fucus-like models discussed here, then a membrane phase transition from a more liquid-like to a more crystal-like state of the membrane could essentially immobilize the membrane bound species and freeze in the pattern. In fact several hours after fertilization in Fucus the lability (rotatability) of the polar axis significantly decreases. Indeed this freezing of the Fucus patterning is not easily explained in terms of a Turing mechanism since the rotational symmetry of the Fucus egg, as discussed previously, implies that the electrical polarity is not stable (or more precisely is marginally stable) to polar axis rotation. 

One-dimensional images of toluic acid were obtained with a stationary sample. For two-dimensional images, the 4-bromobenzoic acid crystal was rotated about an axis orthogonal to the gradient direction in constant increments of either 3° or 6° over a range of 180° to collect sets of 60 or 30 one-dimensional projections, respectively. The two-dimensional images were calculated with the filtered back-projection reconstruction algorithm (36). 

Low-symmetry crystal classes are typical for organic compounds. Densest packing of the layers may be achieved either by translation at an arbitrary angle formed with the layer plane, or by inversion, glide plane, or by screw-axis rotation. In rare cases closest packing may also be achieved by twofold rotation. 

Even though some plasma membranes, such as nerve myelin membranes, contain a high concentration of lipids that form gel phase bilayers, the presence of cholesterol keeps these membranes in a fluid phase. However, interaction with the rigid cholesterol ring affects hydrocarbon chains of lipids in the liquid crystal phase (L ) and leads to formation of a new phase, the liquid ordered (Lq) phase (27). The phase is well characterized by a variety of physical methods and does not exist in pure lipids or their mixtures. In the liquid ordered phase, the long axis rotation and lateral diffusion rates are similar to the La phase, but the acyl chains are predominantly in an all-trans conformation and, hence, the order parameters are similar to the Lp phase (see Table 1). Recently, the cholesterol-rich Lq phase has been strongly associated with microdomains in live cells—the so-called lipid rafts. ... 

Figure H.4. The crystals are manipulated by scooping them up with a small loop of nylon that is glued to the end of a pin. Surface tension firom the liquid will hold the crystal in the loop, but the crystal can also be held by using a loop that is smaller in size than the crystal of interest. This technique will work particularly well with fragile crystals, thin plates for example, that would normally fall apart in a capillary mount. Once the crystal is frozen, it is placed on an axis in line of both an X-ray source and a stream of nitrogen set to about 100,000to keep the crystal frozen. The crystal is rotated in increments during the data collection procedure to collect a full data set (typically one or two degrees per frame, depending on the resolution limits, mosaicity of the crystal, unit cell lengths, etc.).

---