From the above discussion it should not be presumed that crystals
always develop with perfect geometric symmetry. As a matter of fact
such is seldom the case because, due to variations of conditions or
interference of surrounding crystals in liquids (ordinary or molten), a
crystal usually grows more rapidly (by building out faces) in certain
directions than in others. Under such conditions actual crystals are
said to become distorted because they are not geometrically perfect.
Whether geometrically perfect or not, all crystals respond to the law
of constancy of interfacial angles which means that on all crystals of
the same substances the angles between similar (corresponding) faces
are always equal. This is one of the most fundamental and remarkable
laws of minerals. That it must be true follows from the fact that the
crystal faces merely outwardly express in definite form the definite
internal structure or arrangement of particles which have built up the
crystal. In other words, the real structural symmetry of a crystal
never varies no matter how much its geometric symmetry may vary.
The practical application of the law of constancy of interfacial
angles lies in the fact that in many cases a mineral may actually be
identified merely by measuring the interfacial angles of its crystal
form.
The relative lengths of the crystallographic axes is a very important
feature of all crystals except those of the isometric system in which
the axes are always of equal length so that the ratio is 1:1:1. In
all the other systems, however, at least one axis differs in length
from the others and, since the amount of difference is absolutely
characteristic of each substance, the axial ratio of a crystal, when
carefully determined by measurement of the angles between the different
faces, affords a never-failing method of determining the mineral
for all systems except the isometric. By way of illustration, the
tetragonal crystal of the mineral zircon, with only one axis different
in length, shows the very definite axial ratio 1:1:0.64, while the
orthorhombic crystal of sulphur, with all three axes of different
lengths, has an axial ratio 0.813:1:1.903. These ratios of course
always hold true no matter what the size or particular outward form of
the crystal.
As might be expected from the above discussion of the remarkable
structure of crystals, experience has proved that the relative lengths
of all intercepts (or distances from the center) of all faces upon
any crystal can be expressed by whole numbers, definite fractions, or
infinity. It necessarily follows that the ratios between the intercepts
of the faces of any face on a crystal to those of any other face on
the same crystal may always be expressed by rational numbers, and this
is known as the law of definite mathematical ratio. It is a remarkable
fact that very small whole numbers or fractions, or infinity or zero,
will always express the intercepts of any crystal face.