(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-antimonyl dextro-tartrate are examples of this type of symmetry.
The mineral nepheline is placed in this class because of the absence
of symmetry in the etched figures on the prism faces (fig. 92).
(g) _Regular Grouping of Crystals._
Crystals of the same kind when occurring together may sometimes be
grouped in parallel position and so give rise to special structures, of
which the dendritic (from [Greek: dendrou], 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
surrounding 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 cyanite, rutile with haematite, blende 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 Mineralien verschiedener
Art," _Neues Jahrbuch fur Mineralogie_, 1903, vol. xvi. pp. 335-475).
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.
[Illustration: FIG. 81.--Twinned Crystal of Gypsum.]
[Illustration: 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 deg. 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 deg. 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 deg. about a triad axis, or by reflection
across the octahedral plane which is perpendicular to this axis; the
twin-plane is therefore (111).
[Illustration: FIG. 83.--Spinel-twin.]
[Illustration: 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. Hauy introduced the term
"hemitrope" (from the Gr. [Greek: hemi]-, half, and [Greek: tropos], a
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 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._
Only rarely do actual crystals present the symmetrical appearance shown
in the figures given above, in which similar faces are all represented
as of equal size. It frequently happens that the crystal is so placed
with respect to the liquid in which it grows that there will be a more
rapid deposition of material on one part than on another; for instance,
if the crystal be attached 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.
[Illustration: FIG. 85.]
[Illustration: FIG. 86.