Most chemical elements and compounds are capable of assuming the
crystalline condition. Crystallization may take place when solid matter
separates from solution (e.g. sugar, salt, alum), from a fused mass
(e.g. sulphur, bismuth, felspar), or from a vapour (e.g. iodine,
camphor, haematite; in the last case by the interaction of ferric
chloride and steam). Crystalline growth may also take place in solid
amorphous matter, for example, in the devitrification of glass, and the
slow change in metals when subjected to alternating stresses. Beautiful
crystals of many substances may be obtained in the laboratory by one or
other of these methods, but the most perfectly developed and largest
crystals are those of mineral substances found in nature, where
crystallization has continued during long periods of time. For this
reason the physical science of crystallography has developed side by
side with that of mineralogy. Really, however, there is just the same
connexion between crystallography and chemistry as between
crystallography and mineralogy, but only in recent years has the
importance of determining the crystallographic properties of
artificially prepared compounds been recognized.
_History._--The word "crystal" is from the Gr. [Greek: krystallos],
meaning clear ice (Lat. _crystallum_), a name which was also applied to
the clear transparent quartz ("rock-crystal") from the Alps, under the
belief that it had been formed from water by intense cold. It was not
until about the 17th century that the word was extended to other bodies,
either those found in nature or obtained by the evaporation of a saline
solution, which resembled rock-crystal in being bounded by plane
surfaces, and often also in their clearness and transparency.
The first important step in the study of crystals was made by Nicolaus
Steno, the famous Danish physician, afterwards bishop of Titiopolis, who
in his treatise _De solido intra solidum naturaliter contento_
(Florence, 1669; English translation, 1671) gave the results of his
observations on crystals of quartz. He found that although the faces of
different crystals vary considerably in shape and relative size, yet the
angles between similar pairs of faces are always the same. He further
pointed out that the crystals must have grown in a liquid by the
addition of layers of material upon the faces of a nucleus, this nucleus
having the form of a regular six-sided prism terminated at each end by a
six-sided pyramid. The thickness of the layers, though the same over
each face, was not necessarily the same on different faces, but depended
on the position of the faces with respect to the surrounding liquid;
hence the faces of the crystal, though variable in shape and size,
remained parallel to those of the nucleus, and the angles between them
constant. Robert Hooke in his _Micrographia_ (London, 1665) had
previously noticed the regularity of the minute quartz crystals found
lining the cavities of flints, and had suggested that they were built up
of spheroids. About the same time the double refraction and perfect
rhomboidal cleavage of crystals of calcite or Iceland-spar were studied
by Erasmus Bartholinus (_Experimenta crystalli Islandici
disdiaclastici_, Copenhagen, 1669) and Christiaan Huygens (_Traite de la
lumiere_, Leiden, 1690); the latter supposed, as did Hooke, that the
crystals were built up of spheroids. In 1695 Anton van Leeuwenhoek
observed under the microscope that different forms of crystals grow from
the solutions of different salts. Andreas Libavius had indeed much
earlier, in 1597, pointed out that the salts present in mineral waters
could be ascertained by an examination of the shapes of the crystals
left on evaporation of the water; and Domenico Guglielmini (_Riflessioni
filosofiche dedotte dalle figure de' sali_, Padova, 1706) asserted that
the crystals of each salt had a shape of their own with the plane angles
of the faces always the same.
The earliest treatise on crystallography is the _Prodromus
Crystallographiae_ of M. A. Cappeller, published at Lucerne in 1723.
Crystals were mentioned in works on mineralogy and chemistry; for
instance, C. Linnaeus in his _Systema Naturae_ (1735) described some
forty common forms of crystals amongst minerals. It was not, however,
until the end of the 18th century that any real advances were made, and
the French crystallographers Rome de l'Isle and the abbe Hauy are
rightly considered as the founders of the science. J. B. L. de Rome de
l'Isle (_Essai de cristallographie_, Paris, 1772; _Cristallographie, ou
description des formes propres a tous les corps du regne mineral_,
Paris, 1783) made the important discovery that the various shapes of
crystals of the same natural or artificial substance are all intimately
related to each other; and further, by measuring the angles between the
faces of crystals with the goniometer (q.v.), he established the
fundamental principle that these angles are always the same for the same
kind of substance and are characteristic of it. Replacing by single
planes or groups of planes all the similar edges or solid angles of a
figure called the "primitive form" he derived other related forms. Six
kinds of primitive forms were distinguished, namely, the cube, the
regular octahedron, the regular tetrahedron, a rhombohedron, an
octahedron with a rhombic base, and a double six-sided pyramid. Only in
the last three can there be any variation in the angles: for example,
the primitive octahedron of alum, nitre and sugar were determined by
Rome de l'Isle to have angles of 110 deg., 120 deg. and 100 deg.
respectively. Rene Just Hauy in his _Essai d'une theorie sur la
structure des crystaux_ (Paris, 1784; see also his Treatises on
Mineralogy and Crystallography, 1801, 1822) supported and extended these
views, but took for his primitive forms the figures obtained by
splitting crystals in their directions of easy fracture of "cleavage,"
which are aways the same in the same kind of substance. Thus he found
that all crystals of calcite, whatever their external form (see, for
example, figs. 1-6 in the article CALCITE), could be reduced by cleavage
to a rhombohedron with interfacial angles of 75 deg. Further, by
stacking together a number of small rhombohedra of uniform size he was
able, as had been previously done by J. G. Gahn in 1773, to reconstruct
the various forms of calcite crystals. Fig. 1 shows a scalenohedron
([Greek: skalenos], uneven) built up in this manner of rhombohedra; and
fig. 2 a regular octahedron built up of cubic elements, such as are
given by the cleavage of galena and rock-salt.
[Illustration: FIG. 1.--Scalenohedron built up of Rhombohedra.]
[Illustration: FIG. 2.--Octahedron built up of Cubes.]
The external surfaces of such a structure, with their step-like
arrangement, correspond to the plane faces of the crystal, and the
bricks may be considered so small as not to be separately visible. By
making the steps one, two or three bricks in width and one, two or three
bricks in height the various secondary faces on the crystal are related
to the primitive form or "cleavage nucleus" by a law of whole numbers,
and the angles between them can be arrived at by mathematical
calculation. By measuring with the goniometer the inclinations of the
secondary faces to those of the primitive form Hauy found that the
secondary forms are always related to the primitive form on crystals of
numerous substances in the manner indicated, and that the width and the
height of a step are always in a simple ratio, rarely exceeding that of
1 : 6. This laid the foundation of the important "law of rational
indices" of the faces of crystals.
The German crystallographer C. S. Weiss (_De indagando formarum
crystallinarum charactere geometrico principali dissertatio_, Leipzig,
1809; _Ubersichtliche Darstellung der verschiedenen naturlichen
Abtheilungen der Krystallisations-Systeme_, Denkschrift der Berliner
Akad. der Wissensch., 1814-1815) attacked the problem of crystalline
form from a purely geometrical point of view, without reference to
primitive forms or any theory of structure. The faces of crystals were
considered by their intercepts on co-ordinate axes, which were drawn
joining the opposite corners of certain forms; and in this way the
various primitive forms of Hauy were grouped into four classes,
corresponding to the four systems described below under the names cubic,
tetragonal, hexagonal and orthorhombic. The same result was arrived at
independently by F. Mohs, who further, in 1822, asserted the existence
of two additional systems with oblique axes. These two systems (the
monoclinic and anorthic) were, however, considered by Weiss to be only
hemihedral or tetartohedral modifications of the orthorhombic system,
and they were not definitely established until 1835, when the optical
characters of the crystals were found to be distinct. A system of
notation to express the relation of each face of a crystal to the
co-ordinate axes of reference was devised by Weiss, and other notations
were proposed by F. Mohs, A. Levy (1825), C. F. Naumann (1826), and W.
H. Miller (_Treatise on Crystallography_, Cambridge, 1839). For
simplicity and utility in calculation the Millerian notation, which was
first suggested by W. Whewell in 1825, surpasses all others and is now
generally adopted, though those of Levy and Naumann are still in use.
Although the peculiar optical properties of Iceland-spar had been much
studied ever since 1669, it was not until much later that any connexion
was traced between the optical characters of crystals and their external
form. In 1818 Sir David Brewster found that crystals could be divided
optically into three classes, viz. isotropic, uniaxial and biaxial, and
that these classes corresponded with Weiss's four systems (crystals
belonging to the cubic system being isotropic, those of the tetragonal
and hexagonal being uniaxial, and the orthorhombic being biaxial).
Optically biaxial crystals were afterwards shown by J. F. W. Herschel
and F. E. Neumann in 1822 and 1835 to be of three kinds, corresponding
with the orthorhombic, monoclinic and anorthic systems. It was,
however, noticed by Brewster himself that there are many apparent
exceptions, and the "optical anomalies" of crystals have been the
subject of much study. The intimate relations existing between various
other physical properties of crystals and their external form have
subsequently been gradually traced.
The symmetry of crystals, though recognized by Rome de l'Isle and Hauy,
in that they replaced all similar edges and corners of their primitive
forms by similar secondary planes, was not made use of in defining the
six systems of crystallization, which depended solely on the lengths and
inclinations of the axes of reference. It was, however, necessary to
recognize that in each system there are certain forms which are only
partially symmetrical, and these were described as hemihedral and
tetartohedral forms (i.e. [Greek: hemi-], half-faced, and [Greek:
tetartos], quarter-faced forms).
As a consequence of Hauy's law of rational intercepts, or, as it is more
often called, the law of rational indices, it was proved by J. F. C.
Hessel in 1830 that thirty-two types of symmetry are possible in
crystals. Hessel's work remained overlooked for sixty years, but the
same important result was independently arrived at by the same method by
A. Gadolin in 1867. At the present day, crystals are considered as
belonging to one or other of thirty-two classes, corresponding with
these thirty-two types of symmetry, and are grouped in six systems. More
recently, theories of crystal structure have attracted attention, and
have been studied as purely geometrical problems of the homogeneous
partitioning of space.
The historical development of the subject is treated more fully in the
article CRYSTALLOGRAPHY in the 9th edition of this work. Reference may
also be made to C. M. Marx, _Geschichte der Crystallkunde_ (Karlsruhe
and Baden, 1825); W. Whewell, _History of the Inductive Sciences_,
vol. iii. (3rd ed., London, 1857); F. von Kobell, _Geschichte der
Mineralogie von 1650-1860_ (Munchen, 1864); L. Fletcher, _An
Introduction to the Study of Minerals_ (British Museum Guide-Book); L.
Fletcher, _Recent Progress in Mineralogy and Crystallography_
[1832-1894] (Brit. Assoc. Rep., 1894).