Untwinned crystals

Sorum [12] to a final R of 0.10. Thus, the reinvestigation of the structure of acetylcholine bromide, [C7H1602N] + Br, with X-ray diffraction intensities collected from two untwinned crystals showed that the crystals are monoclinic, and are characterized by a space group of P21/ra, with a = 10.966 (4), b = 13.729 (7), c = 7.159 (4) A, p = 108.18 (7)°, and Z = 4. The structure was refined by full-matrix least squares calculations using 1730 observed reflections, and anisotropic temperature factors for all non-hydrogen atoms. The final R was found to be 0.041. Atomic coordinates, thermal parameters, bond lengths, and angles were compared with those from a previous work on acetylcholine derivatives. 

Refinement as an obverse/reverse twin leads to a significant improvement (see Table 7.4 and the files retl-03.res andretl-03.1st) Figure 7.11 shows the final model. The structure was previously determined from an untwinned crystal (Clegg, 1982) and the quality of the twin refinement is comparable to that of the original untwiimed refinement. 

Each Bravais system has its corresponding minimum and maximum symmetry. Thus the Bravais lattice must be monoclinic (P or C) if the crystal has only one mirror plane or one twofold axis (crystal classes m or 2). However, the monoclinic unit cell will also allow the symmetry 2/m. Thus the symmetry of the contents of the unit cell (the motif) may be less than that of the empty cell. In this case we speak of merohedry. The formation of twins is relatively frequent for merohedral crystals. A twin (Fig. 2.28) is an interpenetration or aggregation of several crystals of the same species whose relative orientations follow well-defined laws. These orientations are related by symmetry operations which do not belong to the crystal class of the untwinned crystal, either by a rotation about a translation... 

The twin law (201) of type A twins in stoichiometric LaSe2 is based on the ratio a/c 2 of the monoclinic cell. The apparent unit cell has a = 8.52(1), b = 8.58(1), c = 8.52(1) A. The angles a, (3, Y very nearly approach 90° but the intensity distribution definitely indicates triclinic symmetry. The structure of this twin was refined to R = 0.05 and no structural difference was noted between LaSe2 crystals that are twinned according to (100) or (201). Untwinned crystals were... 

Polymorphism. Many crystalline polyolefins, particularly polymers of a-olefins with linear alkyl groups, can exist in several polymorphic modifications. The type of polymorph depends on crystallisa tion conditions. Isotactic PB can exist in five crystal forms form I (twinned hexagonal), form II (tetragonal), form III (orthorhombic), form P (untwinned hexagonal), and form IP (37—39). The crystal stmctures and thermal parameters of the first three forms are given in Table 3. Form II is formed when a PB resin crystallises from the melt. Over time, it is spontaneously transformed into the thermodynamically stable form I at room temperature, the transition takes about one week to complete. Forms P, IP, and III of PB are rare they can be formed when the polymer crystallises from solution at low temperature or under pressure (38). Syndiotactic PB exists in two crystalline forms, I and II (35). Form I comes into shape during crystallisation from the melt (very slow process) and form II is produced by stretching form-1 crystalline specimens (35). 

Crystal growth modifiers have been employed to improve filterabiHty and water retention of Ca(OCl)2 2H20, which typically crystallizes as fine plates. Addition of zinc dust or salts produces larger square- and diamond-shaped, untwinned dihydrate crystals (215). Coarse prismatic crystals are obtained by use of carbohydrates and carboxyHc acids and thek salts (216). 

According to the experimental results obtained on untwinned YBCO single crystals [1, 2, 3], temperature dependence of resistivity in the planes is linear, i.e. ppiane = d + 0-2T, where a and <22 are constants. On the other hand, temperature dependence of the chain resistivity in YBCO was found to follow approximately a quadratic dependence, i.e. Pchain = b +, where bi and 62 are constants [3]. T2 dependence... 

These mixed oxides have been considered as nonlinear optical materials (see Nonlinear Optical Materials). They crystallize as ordered derivatives of the cristobalite structure. As early X-ray structural studies were performed on twinned crystals grown from congment melts, their true symmetry was not firmly established. Untwinned single crystals have been produced by hydrothermal methods, and the space group has been convincingly established as 14. 

Twinning by complete merohedry (Zt = UU ) by definition produces a diffraction pattern with the same geometrical appearance as the single crystal, which in its turn may be geometrically identical to the pattern of IM twinned as Zt = 351. In contrast, for twinning by selective merohedry (Zt = UE, UE, UU E, UU E, UU EE ), the two D-type Ci correspond to have two reflections at Ij = 2(mod 6) and 4(mod 6). This is the same geometrical appearance of IM twinned as Zt = 3451. The distinction between IM twins and the 3T polytype (twinned or untwinned) requires by very careful examination of the violation of the additional reflection conditions (Nespolo et al. 2000a). 

It is very difficult indeed to grow untwinned single crystals of the 7-modifications, because always a domain stmcture develops vdien passing the transition tempera-tures33.78,86) Ncycrthciess aneutron diffraction powder experiment on 7-Cs2PbCu... 

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