 | |
| Fig. 81.—Twinned Crystal of Gypsum. | Fig. 82.—Simple Crystal of Gypsum. |
In the twinned crystal of gypsum represented in fig. 81 the two portions are symmetrical with respect to a plane parallel to the ortho-pinacoid (100), i.e. a vertical plane perpendicular to the face b. Or we may consider the simple crystal (fig. 82) to be cut in half by this plane and one portion to be rotated through 180° about the normal to the same plane. Such a crystal (fig. 81) is therefore described as being twinned on the plane (100).
An octahedron (fig. 83) twinned on an octahedral face (111) has the two portions symmetrical with respect to a plane parallel to this face (the large triangular face in the figure); and either portion may be brought into the position of the other by a rotation through 180° about the triad axis of symmetry which is perpendicular to this face. This kind of twinning is especially frequent in crystals of spinel, and is consequently often referred to as the “spinel twin-law.”
In these two examples the surface of the union, or composition-plane, of the two portions is a regular surface coinciding with the twin-plane; such twins are called “juxtaposition-twins.” In other juxtaposed twins the plane of composition is, however, not necessarily the twin-plane. Another type of twin is the “interpenetration twin,” an example of which is shown in fig. 84. Here one cube may be brought into the position of the other by a rotation of 180° about a triad axis, or by reflection across the octahedral plane which is perpendicular to this axis; the twin-plane is therefore (111).
 | |
| Fig. 83.—Spinel-twin. | Fig. 84.—Interpenetrating Twinned Cubes. |
Since in many cases twinned crystals may be explained by the rotation of one portion through two right angles, R. J. Haüy introduced the term “hemitrope” (from the Gr. ἡμι-, half, and τρόπος, a turn); the word “macle” had been earlier used by Romé d’Isle. There are, however, some rare types of twins which cannot be explained by rotation about an axis, but only by reflection across a plane; these are known as “symmetric twins,” a good example of which is furnished by one of the twin-laws of chalcopyrite.
Twinned crystals may often be recognized by the presence of re-entrant angles between the faces of the two portions, as may be seen from the above figures. In some twinned crystals (e.g. quartz) there are, however, no re-entrant angles. On the other hand, two crystals accidentally grown together without any symmetrical relation between them will usually show some re-entrant angles, but this must not be taken to indicate the presence of twinning.
Twinning may be several times repeated on the same plane or on other similar planes of the crystal, giving rise to triplets, quartets and other complex groupings. When often repeated on the same plane, the twinning is said to be “polysynthetic,” and gives rise to a laminated structure in the crystal. Sometimes such a crystal (e.g. of corundum or pyroxene) may be readily broken in this direction, which is thus a “plane of parting,” often closely resembling a true cleavage in character. In calcite and some other substances this lamellar twinning may be produced artificially by pressure (see below, Sect. II. (a), Glide-plane).
Another curious result of twinning is the production of forms which apparently display a higher degree of symmetry than that actually possessed by the substance. Twins of this kind are known as “mimetic-twins or pseudo-symmetric twins.” Two hemihedral or hemimorphic crystals (e.g. of diamond or of hemimorphite) are often united in twinned position to produce a group with apparently the same degree of symmetry as the holosymmetric class of the same system. Or again, a substance crystallizing in, say, the orthorhombic system (e.g. aragonite) may, by twinning, give rise to pseudo-hexagonal forms: and pseudo-cubic forms often result by the complex twinning of crystals (e.g. stannite, phillipsite, &c.) belonging to other systems. Many of the so-called “optical anomalies” of crystals may be explained by this pseudo-symmetric twinning.
(h) Irregularities of Growth of Crystals; Character of Faces.