Interpenetration twins

Analytical Methods. Fluorite is readily identified by its crystal shape, usually simple cubes or interpenetrating twins, by its prominent octahedral cleavage, its relative softness, and the production of hydrogen fluoride when treated with sulfuric acid, evidenced by etching of glass. The presence of fluorite in ore specimens, or when associated with other fluorine-containing minerals, may be deterrnined by x-ray diffraction. 

Calcium Boroarsenate occurs in New Jersey as the mineral cahnite4 (see p. 14) it forms white, vitreous, tetragonal sphenoids, occurring in characteristic interpenetrating twins. The refractive index is 1-662. 

Figure 5. Surface SEM image of ZSM-5(40) showing faceted crystals with interpenetrating twins.

Fig. 2.28. Merohedral interpenetration twin of pyrite, FeSj, class m3...

Fig. 2.67 Structure of NaCl-type projected on (001) (a) and on (110) (b). It is noted that NaCl-type structure composed of interpenetrated subcells of CCP Na and Cl and the twin plane (203)oh mentioned above corresponds to the plane (113)nj,ci.

Sometimes twinned crystals appear to be interpenetrating, as in the calcium fluoride twin illustrated in Fig. 41 6. Here we may imagine (in the crystal nucleus) a common 111 sheet of atoms, the symmetry of which is trigonal the crystal on one side of it is rotated 60° with respect to the one on the other side. The twin plane is not always respected during subsequent growth one individual may encroach on the domain of the other, so that the junction surface in the final crystal is irregular. 

Figure 6.13 Effects of twinning reentrant corner (a) and particle interpenetrations (b) ( Elsevier 2003).

As in the electric discharge experiment, two sets of primary twins generally interpenetrate, which also induces a second generation of twins (Fig. 1.13a). Activated dislocations occur at a density varying between 1013 and 1014nT2. Strong interaction between dislocations is manifested in numerous triple junctions. 

Examples of twinned qnartz crystals, illnstrating (a) the lack of hemihedral facets in a completely interpenetrating crystal, and (b) the existence of oppositely handed qnartz crystals in a single twiimed stractme. (The fignre was adapted from Ref 14.)... 

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... 

Orthoclase (monocUnic) Gypsum (monocUnic) Twin axis is z- The Carlsbad twin Swallow-tail twin Interpenetrant across 010. Composition plane (100)... 

Twins occur, especially for lower molecular masses. For example, objects with six arms are common for 110 twinning in low mass polyethylene because (110) and (liO) faces are inclined at 67.5°, close to 60° (18). Moreover, laths are prone to develop with such a twin boundary along its center line (11,19) because of the accelerated growth provided by the notch at its tip, which aids molecular attachment. More exotic, three-dimensional twins are shown by a-polypropylene in quadrites (20) and by interpenetrating layers in polyethylene (21). 

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