The actual form, or "habit," of crystals may vary widely in different
crystals of the same substance, these differences depending 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 example 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 disulphide rendered viscous by the
addition of Canada-balsam. To the various forms H. Vogelsang gave, in
1875, the names "globulites," "margarites" (from [Greek: margarites], a
pearl), "longulites," &c. At a more advanced stage of growth these
bodies react on polarized light, thus possessing 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
microcrystalline 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 60% 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 horizontally,
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.
90) are striated parallel to one diagonal of each face, i.e. parallel to
the tetrahedron faces (compare fig. 31). These striated cubes thus
possess different degrees of symmetry and belong to different
symmetry-classes. Oscillatory combination 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.
[Illustration: FIG. 89.--Striated Cube of Pyrites.]
[Illustration: FIG. 90.--Striated Cube of Blende.]
The faces of crystals are sometimes partly or completely replaced 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 (111), is usually replaced by faces of very low
triakis-octahedra, with indices such as (251.251.250); 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.
(i) _Theories of Crystal Structure._
The ultimate aim of crystallographic research is to determine the
internal structure of crystals from both physical and chemical data. The
problem is essentially twofold: in the first place it is necessary to
formulate a theory as to the disposition of the molecules, which
conforms with the observed types of symmetry--this is really a
mathematical problem; in the second place, it is necessary to determine
the orientation of the atoms (or groups of atoms) composing the
molecules with regard to the crystal axes--this involves a knowledge of
the atomic structure of the molecule. As appendages to the second part
of our problem, there have to be considered: (1) the possibility of the
existence of the same substance in two or more distinct crystalline
forms--polymorphism, and (2) the relations between the chemical
structure of compounds which affect nearly identical or related crystal
habits--isomorphism and morphotropy. Here we shall discuss the modern
theory of crystal structure; the relations between chemical composition
and crystallographical form are discussed in Part III. of this article;
reference should also be made to the article CHEMISTRY: _Physical_.
Hauy.
The earliest theory of crystal structure of any moment is that of Hauy,
in which, as explained above, he conceived a crystal as composed of
elements bounded by the cleavage planes of the crystal, the elements
being arranged contiguously and along parallel lines. There is, however,
no reason to suppose that matter is continuous throughout a crystalline
body; in fact, it has been shown that space does separate the molecules,
and we may therefore replace the contiguous elements of Hauy by
particles equidistantly distributed along parallel lines; by this
artifice we retain the reticulated or net-like structure, but avoid the
continuity of matter which characterizes Hauy's theory; the permanence
of crystal form being due to equilibrium between the intermolecular (and
interatomic) forces. The crystal is thus conjectured as a
"space-lattice," composed of three sets of parallel planes which enclose
parallelopipeda, at the corners of which are placed the constituent
molecules (or groups of molecules) of the crystal.
Frankenheim; Bravais.
The geometrical theory of crystal structure (i.e. the determination of
the varieties of crystal symmetry) is thus reduced to the mathematical
problem: "in how many ways can space be partitioned?" M. L. Frankenheim,
in 1835, determined this number as fifteen, but A. Bravais, in 1850,
proved the identity of two of Frankenheim's forms, and showed how the
remaining fourteen coalesced by pairs, so that really these forms only
corresponded to seven distinct systems and fourteen classes of crystal
symmetry. These systems, however, only represented holohedral forms,
leaving the hemihedral and tetartohedral classes to be explained.
Bravais attempted an explanation by attributing differences in the
symmetry of the crystal elements, or, what comes to the same thing, he
assumed the crystals to exhibit polar differences along any member of
the lattice; for instance, assume the particles to be (say) pear-shaped,
then the sharp ends point in one direction, the blunt ends in the
opposite direction.
Sohncke.
A different view was adopted by L. Sohncke in 1879, who, by developing
certain considerations published by Camille Jordan in 1869 on the
possible types of regular repetition in space of identical parts, showed
that the lattice-structure of Bravais was unnecessary, it being
sufficient that each molecule of an indefinitely extended crystal,
represented by its "point" (or centre of gravity), was identically
situated with respect to the molecules surrounding it. The problem then
resolves itself into the determination of the number of "point-systems"
possible; Sohncke derived sixty-five such arrangements, which may also
be obtained from the fourteen space-lattices of Bravais, by
interpenetrating any one space-lattice with one or more identical
lattices, with the condition that the resulting structure should conform
with the homogeneity characteristic of crystals. But the sixty-five
arrangements derived by Sohncke, of which Bravais' lattices are
particular cases, did not complete the solution, for certain of the
known types of crystal symmetry still remained unrepresented. These
missing forms are characterized as being enantiomorphs consequently,
with the introduction of this principle of repetition over a plane, i.e.
mirror images. E. S. Fedorov (1890), A. Schoenflies (1891), and W.
Barlow (1894), independently and by different methods, showed how
Sohncke's theory of regular point-systems explained the whole thirty-two
classes of crystal symmetry, 230 distinct types of crystal structure
falling into these classes.
By considering the atoms instead of the centres of gravity of the
molecules, Sohncke (_Zeits. Kryst. Min._, 1888, 14, p. 431) has
generalized his theory, and propounded the structure of a crystal in the
following terms: "A crystal consists of a finite number of
interpenetrating regular point-systems, which all possess like and
like-directed coincidence movements. Each separate point-system is
occupied by similar material particles, but these may be different for
the different interpenetrating partial systems which form the complex
system." Or we may quote the words of P. von Groth (_British Assoc.
Rep._, 1904): "A crystal--considered as indefinitely extended--consists
of n interpenetrating regular point-systems, each of which is formed of
similar atoms; each of these point-systems is built up from a number of
interpenetrating space-lattices, each of the latter being formed from
similar atoms occupying parallel positions. All the space-lattices of
the combined system are geometrically identical, or are characterized by
the same elementary parallelopipedon."
A complete resume, with references to the literature, will be found in
"Report on the Development of the Geometrical Theories of Crystal
Structure, 1666-1901" (_British Assoc. Rep._, 1901).