That the general and physical characters of a chemical substance are
profoundly modified by crystalline structure is strikingly illustrated
by the two crystalline modifications of the element carbon--namely,
diamond and graphite. The former crystallizes in the cubic system,
possesses four directions of perfect cleavage, is extremely hard and
transparent, is a non-conductor of heat and electricity, and has a
specific gravity of 3.5; whilst graphite crystallizes in the hexagonal
system, cleaves in a single direction, is very soft and opaque, is a
good conductor of heat and electricity, and has a specific gravity of
2.2. Such substances, which are identical in chemical composition, but
different in crystalline form and consequently in their physical
properties, are said to be "dimorphous." Numerous examples of dimorphous
substances are known; for instance, calcium carbonate occurs in nature
either as calcite or as aragonite, the former being rhombohedral and the
latter orthorhombic; mercuric iodide crystallizes from solution as red
tetragonal crystals, and by sublimation as yellow orthorhombic crystals.
Some substances crystallize in three different modifications, and these
are said to be "trimorphous"; for example, titanium dioxide is met with
as the minerals rutile, anatase and brookite (q.v.). In general, or in
cases where more than three crystalline modifications are known (e.g. in
sulphur no less than six have been described), the term "polymorphism"
is applied.
On the other hand, substances which are chemically quite distinct may
exhibit similarity of crystalline form. For example, the minerals
iodyrite (AgI), greenockite (CdS), and zincite (ZnO) are practically
identical in crystalline form; calcite (CaCO3) and sodium nitrate
(NaNO3); celestite (SrSO)4 and marcasite (FeS2); epidote and azurite;
and many others, some of which are no doubt only accidental
coincidences. Such substances are said to be "homoeomorphous" (Gr.
[Greek: homoios], like, and [Greek: morphe], form).
Similarity of crystalline form in substances which are chemically
related is frequently met with and is a relation of much importance:
such substances are described as being "isomorphous." Amongst minerals
there are many examples of isomorphous groups, e.g. the rhombohedral
carbonates, garnet (q.v.), plagioclase (q.v.); and amongst crystals of
artificially prepared salts isomorphism is equally common, e.g. the
sulphates and selenates of potassium, rubidium and caesium. The
rhombohedral carbonates have the general formula R"CO3, where R"
represents calcium, magnesium, iron, manganese, zinc, cobalt or lead,
and the different minerals (calcite, ankerite, magnesite, chalybite,
rhodochrosite and calamine (q.v.)) of the group are not only similar in
crystalline form, cleavage, optical and other characters, but the angles
between corresponding faces do not differ by more than 1 deg. or 2 deg.
Further, equivalent amounts of the different chemical elements
represented by R" are mutually replaceable, and two or more of these
elements may be present together in the same crystal, which is then
spoken of as a "mixed crystal" or isomorphous mixture.
In another isomorphous series of carbonates with the same general
formula R"CO3, where R" represents calcium, strontium, barium, lead or
zinc, the crystals are orthorhombic in form, and are thus dimorphous
with those of the previous group (e.g. calcite and aragonite, the other
members being only represented by isomorphous replacements). Such a
relation is known as "isodimorphism." An even better example of this is
presented by the arsenic and antimony trioxides, each of which occurs as
two distinct minerals:--
As2O3, Arsenolite (cubic); Claudetite (monoclinic).
Sb2O3, Senarmontite (cubic); Valentinite (orthorhombic).
Claudetite and valentinite though crystallizing in different systems
have the same cleavages and very nearly the same angles, and are
strictly isomorphous.
Substances which form isodimorphous groups also frequently crystallize
as double salts. For instance, amongst the carbonates quoted above are
the minerals dolomite (CaMg(CO3)2) and barytocalcite (CaBa(CO3)2).
Crystals of barytocalcite (q.v.) are monoclinic; and those of dolomite
(q.v.), though closely related to calcite in angles and cleavage,
possess a different degree of symmetry, and the specific gravity is not
such as would result by a simple isomorphous mixture of the two
carbonates. A similar case is presented by artificial crystals of silver
nitrate and potassium nitrate. Somewhat analogous to double salts are
the molecular compounds formed by the introduction of "water of
crystallization," "alcohol of crystallization," &c. Thus sodium sulphate
may crystallize alone or with either seven or ten molecules of water,
giving rise to three crystallographically distinct substances.
A relation of another kind is the alteration in crystalline form
resulting from the replacement in the chemical molecule of one or more
atoms by atoms or radicles of a different kind. This is known as a
"morphotropic" relation (Gr. [Greek: morphe], form, [Greek: tropos],
habit). Thus when some of the hydrogen atoms of benzene are replaced by
(OH) and (NO2) groups the orthorhombic system of crystallization remains
the same as before, and the crystallographic axis a is not much
affected, but the axis c varies considerably:--
a : b : c
Benzene, C6H6 0.891 : 1 : 0.799
Resorcin, C6H4(OH)2 0.910 : 1 : 0.540
Picric acid, C6H2(OH)(NO2)3 0.937 : 1 : 0.974
A striking example of morphotropy is shown by the humite (q.v.) group of
minerals: successive additions of the group Mg2SiO4 to the molecule
produce successive increases in the length of the vertical
crystallographic axis.
In some instances the replacement of one atom by another produces little
or no influence on the crystalline form; this happens in complex
molecules of high molecular weight, the "mass effect" of which has a
controlling influence on the isomorphism. An example of this is seen in
the replacement of sodium or potassium by lead in the alunite (q.v.)
group of minerals, or again in such a complex mineral as tourmaline,
which, though varying widely in chemical composition, exhibits no
variation in crystalline form.
For the purpose of comparing the crystalline forms of isomorphous and
morphotropic substances it is usual to quote the angles or the axial
ratios of the crystal, as in the table of benzene derivatives quoted
above. A more accurate comparison is, however, given by the "topic
axes," which are calculated from the axial ratios and the molecular
volume; they express the relative distances apart of the crystal
molecules in the axial directions.
The two isomerides of substances, such as tartaric acid, which in
solution rotate the plane of polarized light either to the right or to
the left, crystallize in related but enantiomorphous forms.
REFERENCES.--An introduction to crystallography is given in most
text-books of mineralogy, e.g. those of H. A. Miers and of E. S. Dana
(see MINERALOGY). The standard work treating of the subject generally
is that of P. Groth, _Physikalische Kristallographie_ (4th ed.,
Leipzig, 1905). A condensed summary is given by A. J. Moses, _The
Characters of Crystals_ (New York, 1899).
For geometrical crystallography, dealing exclusively with the external
form of crystals, reference may be made to N. Story-Maskelyne,
_Crystallography, a Treatise on the Morphology of Crystals_ (Oxford,
1895) and W. J. Lewis, _A Treatise on Crystallography_ (Cambridge,
1899). Theories of crystal structure are discussed by L. Sohncke,
_Entwickelung einer Theorie der Krystallstruktur_ (Leipzig, 1879); A.
Schoenflies, _Krystallsysteme und Krystallstructur_ (Leipzig, 1891);
and H. Hilton, _Mathematical Crystallography and the Theory of Groups
of Movements_ (Oxford, 1903).
The physical properties of crystals are treated by T. Liebisch,
_Physikalische Krystallographie_ (Leipzig, 1891), and in a more
elementary form in his _Grundriss der physikalischen Krystallographie_
(Leipzig, 1896); E. Mallard, _Traite de cristallographie,
Cristallographie physique_ (Paris, 1884); C. Soret, _Elements de
cristallographie physique_ (Geneva and Paris, 1893).
For an account of the relations between crystalline form and chemical
composition, see A. Arzruni, _Physikalische Chemie der Krystalle_
(Braunschweig, 1893); A. Fock, _An Introduction to Chemical
Crystallography_, translated by W. J. Pope (Oxford, 1895); P. Groth,
_An Introduction to Chemical Crystallography_, translated by H.
Marshall (London, 1906); A. E. H. Tutton, _Crystalline Structure and
Chemical Constitution_, 1910. Descriptive works giving the
crystallographic constants of different substances are C. F.
Rammelsberg, _Handbuch der krystallographisch-physikalischen Chemie_
(Leipzig, 1881-1882); P. Groth, _Chemische Krystallographie_ (Leipzig,
1906); and of minerals the treatises of J. D. Dana and C. Hintze.
(L. J. S.)