pressure of supercooled water is greater than that of ice at the same temperature.
From the relative positions of the curves OB and OA (Fig. 4) we see that at all temperatures above 0°, the (metastable) sublimation curve of ice, if it could be obtained, would be higher than the vaporization curve of water. This shows, therefore, that at 0° a "break" must occur in the curve of states, and that in the neighbourhood of this break the curve above that point must ascend less rapidly than the curve below the break. Since, however, the differences in the vapour pressures of supercooled water and of ice are very small, the change in the direction of the vapour-pressure curve on passing from ice to water was at first not observed, and Regnault regarded the sublimation curve as passing continuously into the vaporization curve. The existence of a break was, however, shown by James Thomson[41] and by Kirchhoff[42] to be demanded by thermo-dynamical considerations, and the prediction of theory was afterwards realized experimentally by Ramsay and Young in their determinations of the vapour pressure of water and ice, as well as in the case of other substances.[43]
From what has just been said, we can readily understand why ice and water cannot exist in equilibrium below 0°. For, suppose we have ice and water in the same closed space, but not in contact with one another, then since the vapour pressure of the supercooled water is higher than that of ice, the vapour of the former must be supersaturated in contact with the latter; vapour must, therefore, condense on the ice; and in this way there will be a slow distillation from the water to the ice, until at last all the water will have disappeared, and only ice and vapour remain.[44]
Other Systems of the Substance Water.—We have thus far discussed only those systems which are constituted by the three phases—ice, water, and water vapour. It has, however, been recently found that at a low temperature and under a high pressure ordinary ice can pass into two other crystalline varieties, called by Tammann[45] ice II. and ice III., ordinary ice being ice I. According to the Phase Rule, now, since each of these solid forms constitutes a separate phase (p. 9), it will be possible to have the following (and more) systems of water, in addition to those already studied, viz. water, ice I., ice II.; water, ice I., ice III.; water, ice II., ice III., forming invariant systems and existing in equilibrium only at a definite triple point; further, water, ice II.; water, ice III.; ice I., ice II.; ice I., ice III.; ice II., ice III., forming univariant systems, existing, therefore, at definite corresponding values of temperature and pressure; and lastly, the bivariant systems, ice II. and ice III. Several of these systems have been investigated by Tammann. The triple point for water, ice I., ice III., lies at -22°, and a pressure of 2200 kilogms. per sq. cm. (2130 atm.), as indicated in Fig. 2, p. 27.[46] In contrast with the behaviour of ordinary ice, the temperature of equilibrium in the case of water—ice II., and water—ice III., is raised by increase of pressure.
B. Sulphur.
Polymorphism.—Reference has just been made to the fact that ice can exist not only in the ordinary form, but in at least two other crystalline varieties. This phenomenon, the existence of a substance in two or more different crystalline forms, is called polymorphism. Polymorphism was first observed by Mitscherlich[47] in the case of sodium phosphate, and later in the case of sulphur. To these two cases others were soon added, at first of inorganic, and later of organic substances, so that polymorphism is now recognized as of very frequent occurrence indeed.[48] These various forms of a substance differ not only in crystalline shape, but also in melting point, specific gravity, and other physical properties. In the liquid state, however, the differences do not exist.
According to our definition of phases (p. 9), each of these polymorphic forms constitutes a separate phase of the particular substance. As is readily apparent, the number of possible systems formed of one component may be considerably increased when that component is capable of existing in different crystalline forms. We have, therefore, to inquire what are the conditions under which different polymorphic forms can coexist, either alone or in presence of the liquid and vapour phase. For the purpose of illustrating the general behaviour of such systems, we shall study the systems formed by the different crystalline forms of sulphur, tin, and benzophenone.
Sulphur exists in two well-known crystalline forms—rhombic, or octahedral, and monoclinic, or prismatic sulphur. Of these, the former melts at 114.5°; the latter at 120°.[49] Further, at the ordinary temperature, rhombic sulphur can exist unchanged, whereas, on being heated to temperatures somewhat below the melting point, it passes into the prismatic variety. On the other hand, at temperatures above 96°, prismatic sulphur can remain unchanged, whereas at the ordinary temperature it passes slowly into the rhombic form.
If, now, we examine the case of sulphur with the help of the Phase Rule, we see that the following systems are theoretically possible:—
I. Bivariant Systems: One component in one phase.
(a) Rhombic sulphur.
(b) Monoclinic sulphur.
(c) Sulphur vapour.
(d) Liquid sulphur.
II. Univariant Systems: One component in two phases.
(a) Rhombic sulphur and vapour.
(b) Monoclinic sulphur and vapour.
(c) Rhombic sulphur and liquid.
(d) Monoclinic sulphur and liquid.
(e) Rhombic and monoclinic sulphur.
(f) Liquid and vapour.
III. Invariant Systems: One component in three phases.
(a) Rhombic and monoclinic sulphur and vapour.
(b) Rhombic sulphur, liquid and vapour.
(c) Monoclinic sulphur, liquid and vapour.
(d) Rhombic and monoclinic sulphur and liquid.
Triple Point—Rhombic and Monoclinic Sulphur and Vapour. Transition Point.—In the case of ice, water and vapour, we saw that at the triple point the vapour pressures of ice and water are equal; below this point, ice is stable; above this point, water is stable. We saw, further, that below 0° the vapour pressure of the stable system is lower than that of the metastable, and therefore that at the triple point there is a break in the vapour pressure curve of such a kind that above the triple point the vapour-pressure curve ascends more slowly than below it. Now, although the vapour pressure of solid sulphur has not been determined, we can nevertheless consider that it does possess a certain, even if very small, vapour pressure,[50] and that at the temperature at which the vapour pressures of rhombic and monoclinic sulphur become equal, we can have these two solid forms existing in equilibrium with the vapour. Below that point only one form, that with the lower vapour pressure, will be stable; above that point only the other form will be stable. On passing through the triple point, therefore, there will be a change of the one form into the other. This point is represented in our diagram (Fig. 5) by the point O, the two curves AO and OB representing diagrammatically the vapour pressures of rhombic
