Many of the physical properties of crystals vary with the direction in
the material, but are the same in certain directions; these directions
obeying the same laws of symmetry as do the faces on the exterior of the
crystal. The symmetry of the internal structure of crystals is thus the
same as the symmetry of their external form.
(a) _Elasticity and Cohesion._
The elastic constants of crystals are determined by similar methods to
those employed with amorphous substances, only the bars and plates
experimented upon must be cut from the crystal with known orientations.
The "elasticity surface" expressing the coefficients in various
directions within the crystal has a configuration symmetrical with
respect to the same planes and axes of symmetry as the crystal itself.
In calcite, for instance, the figure has roughly the shape of a rounded
rhombohedron with depressed faces and is symmetrical about three
vertical planes. In the case of homogeneous elastic deformation,
produced by pressure on all sides, the effect on the crystal is the same
as that due to changes of temperature; and the surfaces expressing the
compression coefficients in different directions have the same higher
degree of symmetry, being either a sphere, spheroid or ellipsoid. When
strained beyond the limits of elasticity, crystalline matter may suffer
permanent deformation in one or other of two ways, or may be broken
along cleavage surfaces or with an irregular fracture. In the case of
plastic deformation, e.g. in a crystal of ice, the crystalline particles
are displaced but without any change in their orientation. Crystals of
some substances (e.g. para-azoxyanisol) have such a high degree of
plasticity that they are deformed even by their surface tension, and the
crystals take the form of drops of doubly refracting liquid which are
known as "liquid crystals." (See O. Lehmann, _Flussige Kristalle_,
Leipzig, 1904; F. R. Schenck, _Kristallinische Flussigkeiten und
flussige Krystalle_, Leipzig, 1905.)
[Illustration: FIG. 91.--Glide-plane of Calcite.]
In the second, and more usual kind of permanent deformation without
fracture, the particles glide along certain planes into a new (twinned)
position of equilibrium. If a knife blade be pressed into the edge of a
cleavage rhombohedron of calcite (at b, fig. 91) the portion abcde of
the crystal will take up the position a'b'cde. The obtuse solid angle at
a becomes acute (a'), whilst the acute angle at b becomes obtuse (b');
and the new surface a'ce is as bright and smooth as before. This result
has been effected by the particles in successive layers gliding or
rotating over each other, without separation, along planes parallel to
cde. This plane, which truncates the edge of the rhombohedron and has
the indices (110), is called a "glide-plane." The new portion is in
twinned position with respect to the rest of the crystal, being a
reflection of it across the plane cde, which is therefore a plane of
twinning. This secondary twinning is often to be observed as a repeated
lamination in the grains of calcite composing a crystalline limestone,
or marble, which has been subjected to earth movements. Planes of
gliding have been observed in many minerals (pyroxene, corundum, &c.)
and their crystals may often be readily broken along these directions,
which are thus "planes of parting" or "pseudo-cleavage." The
characteristic transverse striae, invariably present on the cleavage
surfaces of stibnite and cyanite are due to secondary twinning along
glide-planes, and have resulted from the bending of the crystals.
One of the most important characters of crystals is that of "cleavage";
there being certain plane directions across which the cohesion is a
minimum, and along which the crystal may be readily split or cleaved.
These directions are always parallel to a possible face on the crystal
and usually one prominently developed and with simple indices, it being
a face in which the crystal molecules are most closely packed. The
directions of cleavage are symmetrically repeated according to the
degree of symmetry possessed by the crystal. Thus in the cubic system,
crystals of salt and galena cleave in three directions parallel to the
faces of the cube {100}, diamond and fluorspar cleave in four directions
parallel to the octahedral faces {111}, and blende in six directions
parallel to the faces of the rhombic dodecahedron {110}. In crystals of
other systems there will be only a single direction of cleavage if this
is parallel to the faces of a pinacoid; e.g. the basal pinacoid in
tetragonal (as in apophyllite) and hexagonal crystals; or parallel (as
in gypsum) or perpendicular (as in mica and cane-sugar) to the plane of
symmetry in monoclinic crystals. Calcite cleaves in three directions
parallel to the faces of the primitive rhombohedron. Barytes, which
crystallizes in the orthorhombic system, has two sets of cleavages, viz.
a single cleavage parallel to the basal pinacoid {001} and also two
directions parallel to the faces of the prism {110}. In all of the
examples just quoted the cleavage is described as perfect, since
cleavage flakes with very smooth and bright surfaces may be readily
detached from the crystals. Different substances, however, vary widely
in their character of cleavage; in some it can only be described as good
or distinct, whilst in others, e.g. quartz and alum, there is little or
no tendency to split along certain directions and the surfaces of
fracture are very uneven. Cleavage is therefore a character of
considerable determinative value, especially for the purpose of
distinguishing different minerals.
Another result of the presence in crystals of directions of minimum
cohesion are the "percussion figures," which are produced on a
crystal-face when this is struck with a sharp point. A percussion figure
consists of linear cracks radiating from the point of impact, which in
their number and orientation agree with the symmetry of the face. Thus
on a cube face of a crystal of salt the rays of the percussion figure
are parallel to the diagonals of the face, whilst on an octahedral face
a three-rayed star is developed. By pressing a blunt point into a
crystal face a somewhat similar figure, known as a "pressure figure," is
produced. Percussion and pressure figures are readily developed in
cleavage sheets of mica (q.v.).
Closely allied to cohesion is the character of "hardness," which is
often defined, and measured by, the resistance which a crystal face
offers to scratching. That hardness is a character depending largely on
crystalline structure is well illustrated by the two crystalline
modifications of carbon: graphite is one of the softest of minerals,
whilst diamond is the hardest of all. The hardness of crystals of
different substances thus varies widely, and with minerals it is a
character of considerable determinative value; for this purpose a scale
of hardness is employed (see MINERALOGY). Various attempts have been
made with the view of obtaining accurate determinations of degrees of
hardness, but with varying results; an instrument used for this purpose
is called a sclerometer (from [Greek: skleros], hard). It may, however,
be readily demonstrated that the degree of hardness on a crystal face
varies with the direction, and that a curve expressing these relations
possesses the same geometrical symmetry as the face itself. The mineral
cyanite is remarkable in having widely different degrees of hardness on
different faces of its crystals and in different directions on the same
face.
Another result of the differences of cohesion in different directions is
that crystals are corroded, or acted upon by chemical solvents, at
different rates in different directions. This is strikingly shown when a
sphere cut from a crystal, say of calcite or quartz, is immersed in
acid; after some time the resulting form is bounded by surfaces
approximating to crystal faces, and has the same symmetry as that of the
crystal from which the sphere was cut. When a crystal bounded by faces
is immersed in a solvent the edges and corners become rounded and
"prerosion faces" developed in their place; the faces become marked all
over with minute pits or shallow depressions, and as these are extended
by further solution they give place to small elevations on the corroded
face. The sides of the pits and elevations are bounded by small faces
which have the character of vicinal faces. These markings are known as
"etched figures" or "corrosion figures," and they are extremely
important aids in determining the symmetry of crystals. Etched figures
are sometimes beautifully developed on the faces of natural crystals,
e.g. of diamond, and they may be readily produced artificially with
suitable solvents.
[Illustration: FIG. 92.--Nepheline.]
[Illustration: FIG. 93.--Calcite.]
[Illustration: FIG. 94.--Beryl.