the following table is given a list of the most important polymorphous substances, and the temperatures of the transition point.[109]
| Substance. | Transition temperature. |
| Ammonium nitrate— | |
β-rhombic  |
35° |
|
α-rhombic |
83° |
|
Rhombohedral |
125° |
| Mercuric iodide | 126° |
| Potassium nitrate | 129° |
| Silver iodide | 145° |
| Silver nitrate | 160° |
| Sulphur | 95.5° |
| Tetrabrommethane | 46.8° |
| Thallium nitrate— | |
|
Rhombic |
80° |
|
Rhombohedral |
142.5° |
| Thallium picrate | 46° |
| Tin | 20° |
Sublimation and Vaporization Curves.—We have already seen, in the case of ice and liquid water, that the vapour pressure increases as the temperature rises, the increase of pressure per degree being greater the higher the temperature. The sublimation and vaporization curves, therefore, are not straight lines, but are bent, the convex side of the curve being towards the temperature axis in the ordinary pt-diagram.
In the case of sulphur and of tin, we assumed vapour to be given off by the solid substance, although the pressure of the vapour has not hitherto been measured. The assumption, however, is entirely justified, not only on theoretical grounds, but also because the existence of a vapour pressure has been observed in the case of many solid substances at temperatures much below the melting point,[110] and in some cases, e.g. camphor,[111] the vapour pressure is considerable.
As the result of a large number of determinations, it has been found that all vapour pressure curves have the same general form alluded to above. Attempts have also been made to obtain a general expression for the quantitative changes in the vapour pressure with change of temperature, but without success. Nevertheless, the qualitative changes, or the general direction of the curves, can be predicted by means of the theorem of Le Chatelier.
As we have already learned (p. 16), the Phase Rule takes no account of the molecular complexity of the substances participating in an equilibrium. A dissociating substance, therefore, in contact with its vaporous products of dissociation (e.g. ammonium chloride in contact with ammonia and hydrogen chloride), will likewise constitute a univariant system of one component, provided the composition of the vapour phase as a whole is the same as that of the solid or liquid phase (p. 13). For all such substances, therefore, the conditions of equilibrium will be represented by a curve of the same general form as the vapour pressure curve of a non-dissociating substance.[112] The same behaviour is also found in the case of substances which polymerize on passing into the solid or liquid state (e.g. red phosphorus). Where such changes in the molecular state occur, however, the time required for equilibrium to be established is, as a rule, greater than when the molecular state is the same in both phases.
From an examination of Figs. 13 and 14, it will be easy to predict the effect of change of pressure and temperature on the univariant systems S-V or L-V. If the volume is kept constant, addition of heat will cause an increase of pressure, the system S-V moving along the curve AO until at the triple point the liquid phase is formed, and the system L-V moving along the curve OB; so long as two phases are present, the condition of the system must be represented by these two curves. Conversely, withdrawal of heat will cause condensation of vapour, and therefore diminution of pressure; the system will therefore move along the vaporization or sublimation curve to lower temperatures and pressures, so long as the system remains univariant.
If transference of heat to or from the system is prevented, increase of volume (diminution of pressure) will cause the system L-V to pass along the curve BO; liquid will pass into vapour and the temperature will fall.[113] At O solid may appear, and the temperature of the system will then remain constant until the liquid phase has disappeared (p. 57); the system will then follow the curve OA until the solid phase disappears, and we are ultimately left with vapour. On the other hand, diminution of volume (increase of pressure) will cause condensation of vapour, and the system S-V will pass along the curve AO to higher temperatures and pressures; at O the solid will melt, and the system will ultimately pass to the curve OB or to OC (p. 57).
Addition or withdrawal of heat at constant pressure, and increase or diminution of the pressure at constant temperature, will cause the system to pass along lines parallel to the temperature and the pressure axis respectively; the working out of these changes may be left to the reader, guided by what has been said on pp. 60 and 61.
The sublimation curve of all substances, so far as yet found, has its upper limit at the melting point (triple point), although the possibility of the existence of a superheated solid is not excluded. The lower limit is, theoretically at least, at the absolute zero, provided no new phase, e.g. a different crystalline modification, is formed. If the sublimation pressure of a substance is greater than the atmospheric pressure at any temperature below the point of fusion, then the substance will sublime without melting when heated in an open vessel; and fusion will be possible only at a pressure higher than the atmospheric. This is found, for example, in the case of red phosphorus (p. 47). If, however, the sublimation pressure of a substance at its triple point S-L-V is less than one atmosphere, then the substance will melt when heated in an open vessel.
In the case of the vaporization curve, the upper limit lies at the critical point where the liquid ceases to exist;[114] the lower limit is determined by the range of the metastable state of the supercooled liquid.
The interpolation and extrapolation of vapour-pressure curves is rendered very easy by means of a relationship which Ramsay and Young[115] found to exist between the vapour-pressure curves of different substances. It was observed that in the case of closely related substances, the ratio of the absolute temperatures corresponding to equal vapour pressures is constant, i.e.
