The Phase Rule and Its Applications. Alexander Findlay
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).
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 which transformation of one form into the other takes place on passing 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 pass through the triple point for rhombic sulphur—monoclinic sulphur—liquid sulphur, and on passing 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, 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.
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).
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 analogous 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 analogy, for the conditions under which ordinary white tin passes into the grey modification are, in many ways, quite analogous to those under which a substance passes 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 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