The above may be illustrated by considering the equilibrium between rhombic and monoclinic sulphur. The former, which is deposited from solutions, is transformed into monoclinic sulphur at about 96°, but with great care it is possible to overheat it and even to fuse it (at 113.5°) without effecting the transformation. Monoclinic sulphur, obtained by crystallizing fused sulphur, melts at 119.5°, and admits of undercooling even to ordinary temperatures, but contact with a fragment of the rhombic modification spontaneously brings about the transformation. From Reicher’s determinations, the exact transition point is 95.6°; it rises with increasing pressure about 0.05° for one atmosphere; the density of the rhombic form is greater than that of the monoclinic. The equilibria of these modifications may be readily represented on a pressure-temperature diagram. If OT, OP (fig. 6), be the axes of temperature and pressure, and A corresponds to the transition point (95.6°) of rhombic sulphur, we may follow out the line AB which shows the elevation of the transition point with increasing pressure. The overheating curve of rhombic sulphur extends along the curve AC, where C is the melting-point of monoclinic sulphur. The line BC, representing the equilibrium between monoclinic and liquid sulphur, is thermodynamically calculable; the point B is found to correspond to 131° and 400 atmospheres. From B the curve of equilibrium (BD) between rhombic and liquid sulphur proceeds; and from C (along CE) the curve of equilibrium between liquid sulphur and sulphur vapour. Of especial interest is the curve BD: along this line liquid and rhombic sulphur are in equilibrium, which means that at above 131° and 400 atmospheres the rhombic (and not the monoclinic) variety would separate from liquid sulphur.
Mercuric iodide also exhibits dimorphism. When precipitated from solutions it forms red tetragonal crystals, which, on careful heating, give a yellow rhombic form, also obtained by crystallization from the fused substance, or by sublimation. The transition point is 126.3° (W. Schwarz, Zeit. f. Kryst. 25, p. 613), but both modifications may exist in metastable forms at higher and lower temperatures respectively; the rhombic form may be cooled down to ordinary temperature without changing, the transformation, however, being readily induced by a trace of the red modification, or by friction. The density and specific heat of the tetragonal form are greater than those of the yellow.
Hexachlorethane is trimorphous, forming rhombic, triclinic and cubic crystals; the successive changes occur at about 44° and 71°, and are attended by a decrease in density.
Tetramorphism is exhibited by ammonium nitrate. According to O. Lehmann it melts at 168° (or at a slightly lower temperature in its water of crystallization) and on cooling forms optically isotropic crystals; at 125.6° the mass becomes doubly refracting, and from a solution rhombohedral (optically uniaxial) crystals are deposited; by further cooling acicular rhombic crystals are produced at 82.8°, and at 32.4° other rhombic forms are obtained, identical with the product obtained by crystallizing at ordinary temperatures. The reverse series of transformations occurs when this final modification is heated. M. Bellati and R. Romanese (Zeit. f. Kryst. 14, p. 78) determined the densities and specific heats of these modifications. The first and third transformations (reckoned in order with increasing temperature of the transition point) are attended by an increase in volume, the second with a contraction; the solubility follows the same direction, increasing up to 82.8°, then diminishing up to 125.6°, and then increasing from this temperature upwards.
The physical conditions under which polymorphous modifications are prepared control the form which the substance assumes. We have already seen that temperature and pressure exercise considerable influence in this direction. In the case of separation from solutions, either by crystallization or by precipitation by double decomposition, the temperature, the concentration of the solution, and the presence of other ions may modify the form obtained. In the case of sodium dihydrogen phosphate, NaH2PO4·H2O, a stable rhombic form is obtained from warm solutions, while a different, unstable, rhombic form is obtained from cold solutions. Calcium carbonate separates as hexagonal calcite from cold solutions (below 30°), and as rhombic aragonite from solutions at higher temperatures; lead and strontium carbonates, however, induce the separation of aragonite at lower temperatures. From supersaturated solutions the form unstable at the temperature of the experiment is, as a rule, separated, especially on the introduction of a crystal of the unstable form; and, in some cases, similar inoculation of the fused substance is attended by the same result. Different modifications may separate and exist side by side at one and the same time from a solution; e.g. telluric acid forms cubic and monoclinic crystals from a hot nitric acid solution, and ammonium fluosilicate gives cubic and hexagonal forms from aqueous solutions between 6° and 13°.
A comparison of the transformation of polymorphs leads to a twofold classification: (1) polymorphs directly convertible in a reversible manner—termed “enantiotropic” by O. Lehmann and (2) polymorphs in which the transformation proceeds in one direction only—termed “monotropic.” In the first class are included sulphur and ammonium nitrate; monotropy is exhibited by aragonite and calcite.
It is doubtful indeed whether any general conclusions can yet be drawn as to the relations between crystal structure and scalar properties and the relative stability of polymorphs. As a general rule the modification stable at higher temperatures possesses a lower density; but this is by no means always the case, since the converse is true for antimonious and arsenious oxides, silver iodide and some other substances. Attempts to connect a change of symmetry with stability show equally a lack of generality. It is remarkable that a great many polymorphous substances assume more symmetrical forms at higher temperatures, and a possible explanation of the increase in density of such compounds as silver iodide, &c., may be sought for in the theory that the formation of a more symmetrical configuration would involve a drawing together of the molecules, and consequently an increase in density. The insufficiency of this argument, however, is shown by the data for arsenious and antimonious oxides, and also for the polymorphs of calcium carbonate, the more symmetrical polymorphs having a lower density.
Morphotropy.—Many instances have been recorded where substitution has effected a deformation in one particular direction, the crystals of homologous compounds often exhibiting the same angles between faces situated in certain zones. The observations of Slavik (Zeit. f. Kryst., 1902, 36, p. 268) on ammonium and the quaternary ammonium iodides, of J.A. Le Bel and A. Ries (Zeit. f. Kryst., 1902, 1904, et seq.) on the substituted ammonium chlorplatinates, and of G. Mez (ibid., 1901, 35, p. 242) on substituted ureas, illustrate this point.
Ammonium iodide assumes cubic forms with perfect cubic cleavage; tetramethyl ammonium iodide is tetragonal with perfect cleavages parallel to {100} and {001}—a difference due to the lengthening of the a axes; tetraethyl ammonium iodide also assumes tetragonal forms, but does not exhibit the cleavage of the tetramethyl compound; while tetrapropyl ammonium iodide crystallizes in rhombic form. The equivalent volumes and topic parameters are tabulated:
| NH4I. | NMe4I. | NEt4I. | NPr4I. | |
| V | 57.51 | 108.70 | 162.91 | 235.95 |
| χ | 3.860 | 5.319 | 6.648 | 6.093 |
| ψ | 3.860 | 5.319 | 6.648 | 7.851 |
| ω | 3.860 | 3.842 | 3.686 | 4.933 |