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, Traité de cristallographie, Cristallographie physique (Paris, 1884); C. Soret, Éléments 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.)