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.

[Ill.u.s.tration: FIG. 5.]

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 {35} 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 pa.s.sing 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 and monoclinic sulphur respectively. If the vapour phase is absent and the system maintained under a constant pressure, _e.g._ {36} atmospheric pressure, there will also be a definite temperature at which the two solid forms are in equilibrium, and on pa.s.sing through which complete and reversible transformation of one form into the other occurs.

This temperature, which refers to equilibrium in absence of the vapour phase, is known as the _transition temperature_ or _inversion temperature_.

Were we dependent on measurements of pressure and temperature, the determination of the transition point might be a matter of great difficulty. When we consider, however, that the other physical properties of the solid phases, _e.g._ the density, undergo an abrupt change on pa.s.sing through the transition point, owing to the transformation of one form into the other, then any method by which this abrupt change in the physical properties can be detected may be employed for determining the transition point. A considerable number of such methods have been devised, and a description of the most important of these is given in the Appendix.

In the case of sulphur, the transition point of rhombic into monoclinic sulphur was found by Reicher[51] to lie at 95.5. Below this temperature the octahedral, above it the monoclinic, is the stable form.

Condensed Systems.--We have already seen that in the change of the melting point of water with the pressure, a very great increase of the latter was necessary in order to produce a comparatively small change in the temperature of equilibrium. This is a characteristic of all systems from which the vapour phase is absent, and which are composed only of solid and liquid phases. Such systems are called _condensed systems_,[52] and in determining the temperature of equilibrium of such systems, practically the same point will be obtained whether the measurements are carried out under atmospheric pressure or under the pressure of the vapour of the solid or liquid phases. The transition point, therefore, as determined in open vessels at atmospheric pressure, will differ only by a very slight amount from the triple point, or point at which the two solid or liquid phases are in equilibrium under the pressure of their vapour. {37} The determination of the transition point is thereby greatly simplified.

Suspended Transformation.--In many respects the transition point of two solid phases is a.n.a.logous to the melting point of a solid, or point at which the solid pa.s.ses into a liquid. In both cases the change of phase is a.s.sociated with a definite temperature and pressure in such a way that below the point the one phase, above the point the other phase, is stable.

The transition point, however, differs in so far from a point of fusion, that while it is possible to supercool a liquid, no definite case is known where the solid has been heated above the triple point without pa.s.sing into the liquid state. Transformation, therefore, is suspended only on one side of the melting point. In the case of two solid phases, however, the transition point can be overstepped in both directions, so that each phase can be obtained in the metastable condition. In the case of supercooled water, further, we saw that the introduction of the stable, solid phase caused the speedy transformation of the metastable to the stable condition of equilibrium; but in the case of two solid phases the change from the metastable to the stable modification may occur with great slowness, even in presence of the stable form. This tardiness with which the stable condition of equilibrium is reached greatly increases in many cases the difficulty of accurately determining the transition point. The phenomena of suspended transformation will, however, receive a fuller discussion later (p. 68).

Transition Curve--Rhombic and Monoclinic Sulphur.--Just as we found the melting point of ice to vary with the pressure, so also do we find that change of pressure causes an alteration in the transition point. In the case of the transition point of rhombic into monoclinic sulphur, increase of pressure by 1 atm. raises the transition point by 0.04-0.05.[53] The transition curve, or curve representing the change of the transition point with pressure, will therefore slope to the right away from the pressure axis. This is curve OC (Fig. 5).

{38}

Triple Point--Monoclinic Sulphur, Liquid, and Vapour. Melting Point of Monoclinic Sulphur.--Above 95.5, monoclinic sulphur is, as we have seen, the stable form. On being heated to 120, under atmospheric pressure, it melts. This temperature is, therefore, the point of equilibrium between monoclinic sulphur and liquid sulphur under atmospheric pressure. Since we are dealing with a condensed system, this temperature may be regarded as very nearly that at which the solid and liquid are in equilibrium with their vapour, _i.e._ the triple point, solid (monoclinic)--liquid--vapour.

This point is represented in the diagram by B.

Triple Point--Rhombic and Monoclinic Sulphur and Liquid.--In contrast with that of ice, the fusion point of monoclinic sulphur is _raised_ by increase of pressure, and the fusion curve, therefore, slopes to the right. The transition curve of rhombic and monoclinic sulphur, as we have seen, also slopes to the right, and more so than the fusion curve of monoclinic sulphur. There will, therefore, be a certain pressure and temperature at which the two curves will cut. This point lies at 151, and a pressure of 1320 kilogm. per sq. cm., or about 1288 atm.[54] It, therefore, forms another triple point, the existence of which had been predicted by Roozeboom,[55] at which rhombic and monoclinic sulphur are in equilibrium with liquid sulphur. It is represented in our diagram by the point C.

_Beyond this point monoclinic sulphur ceases to exist in a stable condition._ At temperatures and pressures above this triple point, rhombic sulphur will be the stable modification, and this fact is of mineralogical interest, because it explains the occurrence in nature of well-formed rhombic crystals. Under ordinary conditions, prismatic sulphur separates out on cooling fused sulphur, but at temperatures above 151 and under pressures greater than 1288 atm., the rhombic form would be produced.[56]

Triple Point--Rhombic Sulphur, Liquid, and Vapour. Metastable Triple Point.--On account of the slowness with {39} which transformation of one form into the other takes place on pa.s.sing the transition point, it has been found possible to heat rhombic sulphur up to its melting point (114.5). At this temperature, not only is rhombic sulphur in a metastable condition, but the liquid is also metastable, its vapour pressure being greater than that of solid monoclinic sulphur. This point is represented in our diagram by the point b.

From the relative positions of the metastable melting point of rhombic sulphur and the stable melting point of monoclinic sulphur at 120, we see that, of the two forms, the metastable form has the lower melting point.

This, of course, is valid only for the relative stability in the neighbourhood of the melting point; for we have already learned that at lower temperatures rhombic sulphur is the stable, monoclinic sulphur the metastable (or unstable) form.

Fusion Curve of Rhombic Sulphur.--Like any other melting point, that of rhombic sulphur will be displaced by increase of pressure; increase of pressure raises the melting point, and we can therefore obtain a metastable fusion curve representing the conditions under which rhombic sulphur is in equilibrium with liquid sulphur. This metastable fusion curve must pa.s.s through the triple point for rhombic sulphur--monoclinic sulphur--liquid sulphur, and on pa.s.sing this point it becomes a stable fusion curve. The continuation of this curve, therefore, above 151 forms the stable fusion curve of rhombic sulphur (curve CD).

These curves have been investigated at high pressures by Tammann, and the results are represented according to scale in Fig. 6,[57] _a_ being the curve for monoclinic sulphur and liquid; _b_, that for rhombic sulphur and liquid; and _c_, that for rhombic and monoclinic sulphur.

Bivariant Systems.--Just as in the case of the diagram of states of water, the areas in Fig. 5 represent the conditions for the stable existence of the single phases: rhombic sulphur in the area to the left of AOCD; monoclinic sulphur in the area OBC; liquid sulphur in the area EBCD; sulphur vapour below the curves AOBE. As can be seen from the diagram, {40} the existence of monoclinic sulphur is limited on all sides, its area being bounded by the curves OB, OC, BC. At any point outside this area, monoclinic sulphur can exist only in a metastable condition.

[Ill.u.s.tration: FIG. 6.]

Other crystalline forms of sulphur have been obtained,[58] so that the existence of other systems of the one-component sulphur besides those already described is possible. Reference will be made to these later (p. 51).

{41}

C. _Tin._

Another substance capable of existing in more than one crystalline form, is the metal tin, and although the general behaviour, so far as studied, is a.n.a.logous to that of sulphur, a short account of the two varieties of tin may be given here, not only on account of their metallurgical interest, but also on account of the importance which the phenomena possess for the employment of this metal in everyday life.

After a winter of extreme severity in Russia (1867-1868), the somewhat unpleasant discovery was made that a number of blocks of tin, which had been stored in the Customs House at St. Petersburg, had undergone disintegration and crumbled to a grey powder.[59] That tin undergoes change on exposure to extreme cold was known, however, before that time, even as far back as the time of Aristotle, who spoke of the tin as "melting."[60]

Ludicrous as that term may now appear, Aristotle nevertheless unconsciously employed a strikingly accurate a.n.a.logy, for the conditions under which ordinary white tin pa.s.ses into the grey modification are, in many ways, quite a.n.a.logous to those under which a substance pa.s.ses from the solid to the liquid state. The knowledge of this was, however, beyond the wisdom of the Greek philosopher.

For many years there existed considerable confusion both as to the conditions under which the transformation of white tin into its allotropic modification occurs, and to the reason of the change. Under the guidance of the Phase Rule, however, the confusion which obtained has been cleared away, and the "mysterious" behaviour of tin brought into accord with other phenomena of transformation.[61]

Transition Point.--Just as in the case of sulphur, so also in the case of tin, there is a transition point above which the {42} one form, ordinary white tin, and below which the other form, grey tin, is the stable variety.

In the case of this metal, the transition point was found by Cohen and van Eyk, who employed both the dilatometric and the electrical methods (Appendix) to be 20. Below this temperature, grey tin is the stable form.

But, as we have seen in the case of sulphur, the change of the metastable into the stable solid phase occurs with considerable slowness, and this behaviour is found also in the case of tin. Were it not so, we should not be able to use this metal for the many purposes to which it is applied in everyday life; for, with the exception of a comparatively small number of days in the year, the temperature of our climate is below 20, and _white tin is, therefore, at the ordinary temperature, in a metastable condition_.

The change, however, into the stable form at the ordinary temperature, although slow, nevertheless takes place, as is shown by the partial or entire conversion of articles of tin which have lain buried for several hundreds of years.

On lowering the temperature, the velocity with which the transformation of the tin occurs is increased, and Cohen and van Eyk found that the temperature of maximum velocity is about -50. Contact with the stable form will, of course, facilitate the transformation.

The change of white tin into grey takes place also with increased velocity in presence of a solution of tin ammonium chloride (pink salt), which is able to dissolve small quant.i.ties of tin. In presence of such a solution also, it was found that the temperature at which the velocity of transformation was greatest was raised to 0. At this temperature, white tin in contact with a solution of tin ammonium chloride, and the grey modification, undergoes transformation to an appreciable extent in the course of a few days.

Fig. 7 is a photograph of a piece of white tin undergoing transformation into the grey variety.[62] The bright surface of the tin becomes covered with a number of warty ma.s.ses, formed of the less dense grey form, and the number and size of these continue to grow until the whole of the white tin has pa.s.sed {43} into a grey powder. On account of the appearance which is here seen, this transformation of tin has been called by Cohen the "tin plague."

[Ill.u.s.tration: FIG. 7.]

{44}

Enantiotropy and Monotropy.--In the case of sulphur and tin, we have met with two substances existing in polymorphic forms, and we have also learned that these forms exhibit a definite transition point at which their relative stability is reversed. Each form, therefore, possesses a definite range of stable existence, and is capable of undergoing transformation into the other, at temperatures above or below that of the transition point.

Another cla.s.s of dimorphous substances is, however, met with as, for instance, in the case of the well-known compounds iodine monochloride and benzophenone. Each crystalline form has its own melting point, the dimorphous forms of iodine monochloride melting at 13.9 and 27.2,[63] and those of benzophenone at 26 and 48.[64] This cla.s.s of substance differs from that which we have already studied (_e.g._ sulphur and tin), in that at all temperatures up to the melting point, only one of the forms is stable, the other being metastable. There is, therefore, no transition point, and transformation of the crystalline forms can be observed _only in one direction_. These two cla.s.ses of phenomena are distinguished by the names _enantiotropy_ and _monotropy_; enantiotropic substances being such that the change of one form into the other is a reversible process (_e.g._ rhombic sulphur into monoclinic, and monoclinic sulphur into rhombic), and monotropic substances, those in which the transformation of the crystalline forms is irreversible.

[Ill.u.s.tration: FIG. 8.]

[Ill.u.s.tration: FIG. 9.]

These differences in the behaviour can be explained very well in many cases by supposing that in the case of enantiotropic substances the transition point lies below the melting point, while in the case of monotropic substances, it lies above the melting point.[65] These conditions would be represented by the Figs. 8 and 9.

In these two figures, O_{3} is the transition point, O_{1} and O_{2} the melting points of the metastable and stable forms {45} respectively. From Fig. 9 we see that the crystalline form I. at all temperatures up to its melting point is metastable with respect to the form II. In such cases the transition point could be reached only at higher pressures.

Although, as already stated, this explanation suffices for many cases, it does not prove that in all cases of monotropy the transition point is above the melting point of the two forms. It is also quite possible that the transition point may lie below the melting points;[66] in this case we have what is known as _pseudomonotropy_. It is possible that graphite and diamond,[67] perhaps also the two forms of phosphorus, stand in the relation of pseudomonotropy (_v._ p. 49).

The disposition of the curves in Figs. 8 and 9 also explains the phenomenon sometimes met with, especially in organic chemistry, that the substance first melts, then solidifies, and remelts at a higher temperature. On again determining the melting point after re-solidification, only the higher melting point is obtained.

The explanation of such a behaviour is, that if the determination of the melting point is carried out rapidly, the point O_{1}, the melting point of the metastable solid form, may be realized. At this temperature, however, the liquid is metastable with respect to the stable solid form, and if the temperature is {46} not allowed to rise above the melting point of the latter, the liquid may solidify. The stable solid modification thus obtained will melt only at a higher temperature.

D. _Phosphorus._

An interesting case of a monotropic dimorphous substance is found in phosphorus, which occurs in two crystalline forms; white phosphorus belonging to the regular system, and red phosphorus belonging to the hexagonal system. From determinations of the vapour pressures of liquid white phosphorus, and of solid red phosphorus,[68] it was found that the vapour pressure of red phosphorus was considerably lower than that of liquid white phosphorus at the same temperature, the values obtained being given in the following table.