Unit cells trigonal

Fig. 35. (continued)—(b) Antiparallel packing arrangement of two double helices, drawn in open and filled bonds, in the trigonal unit-cell projected along the c-axis. 

Fig. 37. (continued)—(b) An axial view projected along the r-axis shows the packing arrangement of three welan double helices in the trigonal unit cell. The helix drawn in solid bonds is antiparallel to the remaining helices (open bonds). Note that calcium ions are positioned between the helices and each water molecule (large open circle) shown here is connected to all three surrounding helices. The interstitial space is occupied by several other ordered water molecules (not shown). 

This polymer crystallizes in three polymorphs. The threefold helical structure packs in a trigonal unit-cell with a = 14.3 A (1.43 nm) and c = 28.7 A (2.87 nm). The 8-fold helical structure occurs in a tetragonal unit-cell with a = 13.8 A (1.38 nm) and c = 78.2 A (7.82 nm). Axial periodicity in both cases is similar [h = 9.6 A (960 pm) and 9.8 A (980 pm), respectively], but the helix twist-angle is different (120 and 45°, respectively). Distribution of the charged side-groups in these helices was discussed. An orthorhombic form, with a twofold helical structure, has a repeat of 18.6 A (1.86 nm). 

Similar frustration has been evidenced for the crystal structure of isotactic poly(2-vinylpyridine)150 161 (Figure 2.28). Also in this case three independent threefold helices are included in the trigonal unit cell and the frustration is related to a different azimuthal orientation of the chains due to the different interactions between the chains.160 Two chains (chains A in Figure 2.28) maximize their interactions at the expense of the third one (chain B). 

The gummy polysaccharide from the conn sacs of Watsonia pijra-midata crystallizes in a trigonal unit-cell, the base-plane dimensions of which depend on the relative humidity (r. h.). At 76% r.h., the dimensions are a = b = 1.40 mn, and, for the dry form, a = h = 1.34 nm. A 3(-0.495) helical conformation was proposed. The richness of the X-ray pattern led to the conclusion that the substitution is highly regular in the crystalline regions. 

Calcium and strontium salts of hyaluronic acid, at relative humidities of 66-92%, crystallize in a trigonal unit-cell, with a = b — 2.093 nm and c = 2.83 nm. On drying, the base-plane dimensions reduce to a = b = 1.832 nm, with c = 2.847 nm. Seven water molecules per disaccharide residue exist in the wet form, and two in the dry form. The adjacent chains are antiparallel, and the space group is P3212. The three disaccharide units in the 3(- 0.94) helix are nonequi-... 

The sodium salt form, at 92% r.h., crystallizes in a trigonal unit-cell, with a = b = 1.45 nra and c = 2.88 nm, with a 3(— 0.96) conformation of the chain. On conversion of the sodium form into the calcium form, the unit cell converts to the orthorhombic, with a = 0.745 nm, b = 1.781 nm, and c = 1.964 nm. The chain is a 2(0.982) helix, with the disaccharide repeat-unit. Two antiparallel chains are contained in the unit cell, along with— 30 water molecules. The space group is P2,2,21. 

Brucite, Mg(OH)2, has a structure very similar to that of Cdl2. The trigonal unit cell contains one molecule, D d, P3ml, aQ = 3.142, and cQ = 4.766 A. Figure 5.59 shows the layers. Hydrogen atoms are on the outside of the POP sandwiches. Mg2+ ions are only at C positions, but alternate O layers are vacant. 

MnF4, known since 1928, has now been obtained in single crystals,740 which have a trigonal unit cell, but the structure has not yet been reported. The ultramarine blue solid is very hygroscopic, loses F2 slowly at normal temperatures and hydrolyses instantly in contact with water. 

Table 2. Trigonal Unit Cells for the Rhombohedral (R3) LiMF(i Salts of the Second and Third Transition Series ...

Instead of a rhombohedrally-centered trigonal unit cell shown in Figure 1.26, below. 

Figure Al. Evolution of the unitcell parameters of lead phos-phate with pressure, redrawn from Angel and Bismayer (1999). The trigonal unit-cell parameters of the high-pressure phase have been transformed to the monoclinic setting through Equation (A3). The lines are the Mumaghan EoS (Table A2) fitted to the trigonal unit-cell parameters and transformed to the monoclinic cell setting.

Table A2. Parameters of the Mumaghan EoS fitted to the trigonal unit-cell data..

Table A3. Calculated trigonal unit-cell parameters for lead phosphate.

Figure A2. The relationship between the trigonal unit-cell (darker shading) and the monoclinic unit-cell (paler shading) projected down the trigonal c-axis.

For calculation of the spontaneous strain components, a Cartesian co-ordinate system must be defined. For convenience we choose the reference system of Guimares (1979) with i parallel to the trigonal c-axis,y parallel to the trigonal 6-axis, and k parallel to the [210] direction in the trigonal unit-cell (Fig. A2). From Equations (43)-(48) of Carpenter et al. (1988), we can now write down the expressions for the spontaneous strain components in terms of the observed monoclinic unit-cell parameters (here without subscript) and the extrapolated trigonal unit-cell parameters transformed into the monoclinic setting (here subscripted with o to indicate their use as the reference state) ... 

Eig. 1. (a) A trigonal unit cell of the zeolite chabazite, consisting of 36 atoms. This unit cell is also chosen as the supercell, (b) A perspective view down a channel of chabazite 54 unit cells are displayed. 

The expected composition. WN, was observed as a brown coating on W filaments [320, 321, 322], A composition near WN, (trigonal unit cell) has been observed in the electron microscope in the thinnest regions of nitrided films, but the derived structure contains three notably short N N distances of 1.71 A with eight corresponding W N ones of 2.91 3.03 A [323], The suggested structure is reminiscent of that of fluorite, but we do not feel that this compound is very w ell established. 

CH2—CHj-bond, makingphenylene mobility and disorder likely. The crystal structure of the fully ordered a-polymorph is monoclinic (C 2/m) with parallel packing of the phenylenes, while the p -structure is known to have statistical defects in a much enlarged trigonal unit cell (P3) but the detailed nature of the defects is still in dispute >. The ultimately must, in addition have CH2—CH2—... 

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