Hexagonally modulated layer

Hexagonal modulated layers Hexagonal perforated layers Perforated layers... 

The existence of a second class of complex phases, the modulated and perforated layer structures, has largely been explored by Bates and co-workers (Forster et al. 1994 Hamley et al. 1993, 1994 Khandpur et al. 1995 Schulz et al. 1996), who used SANS and TEM to investigate shear oriented structures. The thermally-induced phase transition from the lam to the hex phase in polyolefin diblocks was studied in detail by Hamley et al. (1993, 1994) using SANS, TEM and rheology. Intermediate hexagonal modulated lamellar (HML) and hexagonal perforated layer (HPL) structures were observed on heating PEP-PEE, PE-PEP and PE-PEE diblocks, where PEP is poly(ethylene-propylene), PEE is... 

A more complex example may be represented by TaSe2 its modification called 2H-TaSe2 is hexagonal (space group P6 mmc, with two formula units in the unit cell). This layered compound shows a displacive 2D modulation (defined by two vectors) its symmetry may be therefore described in terms of a supergroup in a 5D superspace (Janner and Janssen 1980). A general point is therefore denoted by the 5 parameters x,y,z, t, u, and a position vector by the five components xa + yb + zc + td + ue of the superspace, with a, b, c basis in the position space and d and e in the internal subspace . 

Phase 1 has a two-layer unit cell for the hydroxide component. In the (100) projection (in which the structural calculations were performed) the two idealised hydroxide layers (F in Fig. 5) have a relative rotation of 22° (98°), so that they may be related by an a-glide plane parallel to [010] of the sulphide component and perpendicular to the layers, or by a two-fold axis parallel to [010] of the sulphide component. The ortho-hexagonal subcells of the idealised hydroxide layers can be defined as mutually rotated by 98°, and they will be rotated by 41° and 139° from the component unit cell of the sulphide layers. Thus, the two hydroxide layers have the same orientation to the sulphide component (and to the common modulation), but the cell geometry assumed by Organova et al. makes them non-equivalent (Table 3). The published diffraction pattern suggests that the structure is of the SC type (or perhaps SI), modulated in the b direction. The close relationship with the tochilinites is apparent from the mutual orientation of the adjacent hydroxide and sulphide layers the deviation from that in tochilinites is only 4°. However, in tochilinites successive hydroxide layers are parallel. 

Both layers contain Pb and Bi atoms, and syntheses from these metals and sulphur suggest that the minor elements present in the natural material (Fe and Sb) are not essential for the formation of the structures. The sulphur atoms peripheral to the pseudo-hexagonal layers again complement the half-octahedral coordination of Pb and Bi in the surfaces of the T layers, the total coordination of which varies between deformed octahedral and bi-capped trigonal prismatic (which are also commonly observed in simpler Pb -I- Bi sulphosalt structures). Both sets of layers are sinusoidally modulated in phase with the periodic variation of coordination the period being slightly more than 5 T subcells (Fig. 18). 

Also in bulk block copolymers microphase-separate into ordered liquid crystalline phases. A variety of phase morphologies such as lamellae (LAM), hexagonally ordered cylinders (HEX), arrays of spherical microdomains (BCC, FCC), modulated (MLAM) and perforated layers (FLAM), ordered bicontinuous structures such as the gyroid, as well as the related inverse structures have been documented. The morphology mainly depends on the relative block length. If, for instance, both blocks are of identical length, lamellar structures are preferred. 

Micas are layer silicates (phyllosilicates) whose structure is based either on a brucite-like trioctahedral sheet [Mg(OH)2 which in micas becomes Mg304(0H)2] or a gibbsite-like dioctahedral sheet [Al(OH)3 which in micas becomes Al204(0H)2]. This module is sandwiched between a pair of oppositely oriented tetrahedral sheets. The latter sheet consists of Si(Al)-tetrahedra which share three of their four oxygen apices to form a two-dimensional hexagonal net (Fig. 1). In micas, the association of these two types of sheet produces an M layer, which is often referred as the 2 1 or TOT layer. 

Nd dhcp basal plane moment modulated along fr, and parallel to fcj on hexagonal sites B and C layers antiferromagnetically coupled = 19.2 K Cubic sites order at 7.8 K, as in high temp, phase but moments modulated with different periodicity along bi and pointing 30° to b, l9 2 1.84... 

Figure 1 Common morphologies of microphase-separated block copolymers body-centered cubic packed spheres (BCC), hexagonally ordered cylinders (HEX), g)Toid (Ia3d), hexagonaUy perforated layers (HPLs), modulated lamellae (MLAM), lamellae (LAM), cylindrical micelles (CYL), and spherical micelles (MIC). (Reproduced from Ref. 2. Wiley-VCH, 1998.)...

One of the remarkable phenomena in nematic liquid crystals is the appearance of modulated structures under the action of an electric field [1-3]. These structures are characterized by the periodic distortion of the nematic director field in a certain preferred direction, and could be optically visualized as regular patterns of black and white stripes (domains) arranged perpendicular to the distortion plane. If the direction of distortion is degenerate in the layer plane, domains form a rectangular, hexagonal, or some other type of lattice, which could periodically transform to each other, i.e., oscillating domain patterns appear. 

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