Twinned individuals

In general, a low-temperature polymorph has lower symmetry than a high-temperature polymorph. So, in the phase transformation from high- to low-temperature polymorph, the low-temperature polymorph can have two orientations, which leads to twin formation. This is called the transformation twin. To minimize the interface energy between twinned individuals through transfer-... 

HREM is particularly suitable for determining the nature and extent of twinning in faujasite crystals which are prone (8) to twinning by reflection across 111 planes as shown in Fig. 2. Multiple twinning (not necessarily on the same member of the family of 111 planes) is common and in Fig. 3 we show a crystal ( 110] zone-axis orientation) exhibiting the consequences of simultaneous twinning on (111) and (111) planes. In such a situation two further twin planes inclined to 010 are theoretically possible (i.e. (111) and (111)), but these twinned individual would be projected along a <1JM > type zone-axis. 

Table 12a. Classification of diffraction patterns for N = 3K+L. For the correspondence between the relative rotations of twinned individuals and the twin laws see Table 11 (after Nespolo 1999). 

A different interpretation of alite has been given by Fundal (1982), who stated that alite crystals are twinned individuals of a lower symmetry which imitate a higher symmetry (a mimetic relationship). The monoclinic form of alite was said to have an index of refraction of 1.72 and a birefringence of approximately 0.0050. Tri clinic alite was reported to be polysynthetically twinned in a fused clinker and have a birefringence of 0.0020. Alite birefringence, however, exhibits two average val ues in Fundal s Table 1 (1982) 0.0043 (monoclinic) and... 

Polysynthetic twins may be of the spiral or of the alternate type, or a mixture of both. When the thickness of each twin individual reduces to 10 A, they degenerate into the various polymorphs. 

The effect of concentration of cationic (cetylpyridinium chloride, CPC), anionic (sodium dodecylsulfate, SDS) and nonionic (Twin-80) surfactants as well as effect of pH value on the characteristics of TLC separ ation has been investigated. The best separ ation of three components has been achieved with 210 M CPC and LIO M Twin-80 solutions, at pH 7 (phosphate buffer). Individual solution of SDS didn t provide effective separation of caffeine, theophylline, theobromine, the rate of separ ation was low. The separ ation factor and rate of separ ation was increase by adding of modifiers - alcohol 1- propanol (6 % vol.) or 1-butanol (0.1 % vol.) in SDS solution. The optimal concentration of SDS is 210 M. 

The most versatile arrangement, from an operations point of view, is individual transfer valves, one for the twin coolers and one for the twin filters. The use of one valve for both the filter and cooler results in a loss in flexibility, as the cooler maintenance interval is usually somewhat longer term than a filter changeout. Should one cooler be out of service, and the filter that is paired with the operating cooler be fouled, the compressor will have to shutdown. Each user will have to review the extra cost oi a second valve against the operation limit. 

The individual cubic crystals sometimes grow at equal rates, filling the spaces between them. Each assumes the shape of a trigonal pyramid, with the outer edges 5% longer than the radial edges. The multiple twin then has the macroscopic appearance of an icosahedron. 

For the smaller particles which Include only a few tens or hundreds of atoms, any twinning or faulting reduces the range of ordering to the extent that the pattern can not be Interpreted In the same way as a pattern from an extended crystal. The Individual single-crystal regions may contain only two or three atomic planes. Interpretation can be made only by calculation of patterns from postulated models for the configurations of atoms (22). 

I The occurrence of MDD shows a familial pattern because first-degree relatives of MDD patients are about three times more likely to develop MDD compared with first-degree relatives of normal control individuals. Adoption studies and twin studies reveal that the familial aggregation of MDD is due to genetic influences.5... 

Definition An intergrowth of two or more macroscopic individuals of the same crystal species is a twin, if the orientation relations between the individuals conform to crystallographic laws. The individuals are called twin partners, twin components or twin domains. 

The occurrence of twinned crystals is a widespread phenomenon. They may consist of individuals that can be depicted macroscopically as in the case of the dovetail twins of gypsum, where the two components are mirror-inverted (Fig. 18.8). There may also be numerous alternating components which sometimes cause a streaky appearance of the crystals (polysynthetic twin). One of the twin components is converted to the other by some symmetry operation (twinning operation), for example by a reflection in the case of the dovetail twins. Another example is the Dauphine twins of quartz which are intercon-verted by a twofold rotation axis (Fig. 18.8). Threefold or fourfold axes can also occur as symmetry elements between the components the domains then have three or four orientations. The twinning operation is not a symmetry operation of the space group of the structure, but it must be compatible with the given structural facts. 

---