HEXAGONAL PYRAMIDAL CLASS (Hemimorphic-tetartohedral.) No other element is here associated with the hexad axis, which is uniterminal. The pyramids all consist of six faces at one end of the crystal, and prisms are all hexagonal prisms ; perpendicular to the hexad axis are the pedions.
Lithium potassium sulphate, strontium antimonyl dextro-tartrate, and lead-anti monyl dextro-tartrate are examples of this type of symmetry. The mineral nepheline is placed in this class because of the ab sence of symmetry in the etched figures on the prism faces (fig. 92).
(g ) Regular Grouping of Crystals Crystals of the same kind when occur ring together may sometimes be grouped in parallel position and so give rise to special structures, of which the dendritic (from 8EV8pov, a tree) or branch-like aggregations of native copper or of magnetite and the fibrous structures of many minerals furnish examples. Sometimes, owing to changes in the surround ing conditions, the crystal may continue its growth with a different external form or colour, e.g., sceptre-quartz. ' Regular intergrowths of crystals of totally different substances such as staurolite with kyanite, rutile with haematite, blonde with chalcopyrite, calcite with sodium nitrate, are not uncommon. In these cases certain planes and edges of the two crystals are parallel. (See O. Mugge, "Die regelmassigen Verwachsungen von Min eralien verschiedener Art," Neues Jahrbuch fur Mineralogie, 1903, vol. xvi. pp., But by far the most important kind of regular conjunction of crystals is that known as "twinning." Here two crystals or individuals of the same kind have grown together in a certain symmetrical manner, such that one portion of the twin may be brought into the position of the other by reflection across a plane or by rotation about an axis. The plane of reflection is called the twin-plane, and is parallel to one of the faces, or to a possible face, of the crystal: the axis of rotation, called the twin-axis, is parallel to one of the edges or perpendicular to a face of the crystal.
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 { I oo } , 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 18o° about the normal to the same plane. Such a crystal (fig. 81) is therefore described as being twinned on the plane { An octahedron (fig. 83) twinned on an octahedral face {III} 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 rota tion through 180° about the triad axis of symmetry which is perpendicular to this face. This kind of twinning is especially fre quent 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 "inter penetration 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 { I I II.
Since in many cases twinned crystals may be explained by therotation of one portion through two right angles, R. J. Hairy introduced the term "hemitrope" (half turn) ; the word "macle" had been earlier used by Rome 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 recog nized 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, Sec. 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 hemi morphite) 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, etc.) be longing 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 Only rarely do actual crystals present the symmetrical appearance shown in the fig ures given above, in which similar faces are all represented as of equal size. It fre quently happens that the crystal is so placed with respect to the liquid in which it grows that there will be a more rapid de position of material on one part than on another ; for instance, if the crystal be at tached to some other solid it cannot grow in that direction. Only when a crystal is freely suspended in the mother-liquid and material for growth is supplied at the same rate on all sides does an equably developed form result.
Two misshapen or distorted octahedra are represented in figs. 85 and 86; the f or mer is elongated in the direction of one of the edges of the octahedron, and the latter is flattened parallel to one pair of faces.
It will be noticed in these figures that the edges in which the faces intersect have the same directions as be fore, though here there are additional edges not present in fig. 3. The angles (70° 32' or 109° 28') between the faces also remain the same; and the faces have the same inclinations to the axes and planes of symmetry as in the equably developed form. Al though from a geometrical point of view these figures are no longer symmetrical with respect to the axes and planes of sym metry, yet crystallographically they are just as symmetrical as the ideally developed form, and, however much their irregularity of development, they still are regular (cubic) octahedra of crystallography. A remarkable case of irregular development is presented by the mineral cuprite, which is often found as well developed cubes; but in the variety known as chalcotrichite it occurs as a matted aggregate of delicate hairs, each of which is an individual crystal enormously elongated in the direction of an edge of the cube.
The symmetry of actual crystals is sometimes so obscured by irregularities of growth that it can only be determined by measure ment of the angles. An extreme case, where several of the planes have not been developed at all, is illustrated in fig. 87, which shows the actual shape of a crystal of zircon from Ceylon; the ideally developed form (fig. 88) is placed at the side for com parison, and the parallelism of the edges between corresponding faces will be noticed. This crystal is a combination of five simple forms, viz., two tetragonal prisms (a and m), two tetragonal bipyramids (e and p), and one ditetragonal bipyramid (x, with 16 faces).
The actual form, or "habit," of crystals may vary widely in different crystals of the same substance, these differences de- , pending largely on the conditions under which the growth has taken place. The material may have crystallized from a fused mass or from a solution ; and in the latter case the solvent may be of different kinds and contain other substances in solution, or the temperature may vary. Calcite (q.v.) affords a good ex ample of a substance crystallizing in widely different habits, but all crystals are referable to the same type of symmetry and may be reduced to the same fundamental form.
When crystals are aggregated together, and so interfere with each other's growth, special structures and external shapes often result, which are sometimes characteristic of certain substances, especially amongst minerals.
Incipient crystals, the development of which has been arrested owing to unfavourable conditions of growth, are known as crystallites (q.v.). They are met with in imperfectly crystallized substances and in glassy rocks (obsidian and pitchstone), or may be obtained artificially from a solution of sulphur in carbon di sulphide rendered viscous by the addition of Canada-balsam. To the various forms H. Vogelsang gave, in 1875, the names "globulites," "margarites," "longulites," etc. At a more advanced stage of growth these bodies react on polarized light, thus pos sessing the internal structure of true crystals; they are then called "microlites." These have the form of minute rods, needles or hairs, and are aggregated into feathery and spherulitic forms or skeletal crystals. They are common constituents of microcrystal line igneous rocks, and often occur as inclusions in larger crystals of other substances.
Inclusions of foreign matter, accidentally caught up during growth, are frequently present in crystals. Inclusions of other minerals are specially frequent and conspicuous in crystals of quartz, and crystals of calcite may contain as much as 6o% of included sand. Cavities, either with rounded boundaries or with the same shape ("negative crystals") as the surrounding crystal, are often to be seen; they may be empty or enclose a liquid with a movable bubble of gas.
The faces of crystals are rarely perfectly plane and smooth, but are usually striated, studded with small angular elevations, pitted or cavernous, and sometimes curved or twisted. These irregularities, however, conform with the symmetry of the crystal, and much may be learnt by their study. The parallel grooves or furrows, called "striae," are the result of oscillatory combination between adjacent faces, narrow strips of first one face and then another being alternately developed. Sometimes the striae on crystal-faces are due to repeated lamellar twinning, as in the plagioclase felspars. The directions of the striations are very characteristic features of many crystals : e.g., the faces of the hexagonal prism of quartz are always striated hori zontally, whilst in beryl they are striated vertically. Cubes of pyrites (fig. 89) are striated parallel to one edge, the striae on adjacent faces being at right angles, and due to oscillatory combination of the cube and the pentagonal dodecahedron (compare fig. 36) ; whilst cubes of blende (fig. 9o) are striated parallel to one diag onal of each face, i.e., parallel to the tetra hedron faces. (Compare fig. 31.) These striated cubes thus possess different de grees of symmetry and belong to differ ent symmetry-classes. Oscillatory com bination of faces gives rise also to curved surfaces. Crystals with twisted surfaces (see DOLOMITE) are, however, built up of smaller crystals arranged in nearly parallel position. Sometimes a face is entirely replaced by small faces of other forms, giving rise to a drusy surface; an example of this is shown by some octahedral crystals of fluorspar (fig. 2) which are built up of minute cubes.
The faces of crystals are sometimes partly or completely re placed by smooth bright surfaces inclined at only a few minutes of arc from the true position of the face; such surfaces are called "vicinal faces," and their indices can be expressed only by very high numbers. In apparently perfectly developed crystals of alum the octahedral face, with the simple indices { III} is usually replaced by faces of very low triakis-octahedra, with indices such as { 2 51.2 51.2 50 } ; the angles measured on such crystals will therefore deviate slightly from the true octahedral angle. Vicinal faces of this character are formed during the growth of crystals, and have been studied by H. A. Miers (Phil. Trans., 1903, Ser. A. vol. 202). Other faces with high indices, viz., "prerosion faces" and the minute faces forming the sides of etched figures (see below), as well as rounded edges and other surface irregularities, may, however, result from the corrosion of a crystal subsequent to its growth. The pitted and cavernous faces of artificially grown crystals of sodium chloride and of bismuth are, on the other hand, a result of rapid growth, more material being supplied at the edges and corners of the crystal than at the centres of the faces.
The internal structure of crystals has, since 1912, been worked out by the application of X-rays, and is now such an extensive and specialized subject that a separate article is devoted to it. (See X-RAYS, NATURE OF : X-Rays and Crystal Structure.)