The Phase Rule and Its Applications. Alexander Findlay

83.03° 200 " 82.29° 250 "

      So far as investigations have been carried out, it appears that in most cases the transition curve is practically a straight line.

      It has, however, been found in the case of Glauber's salt, that with increase of pressure the transition curve passes through a point of maximum temperature, and exhibits, therefore, a form similar to that assumed by Tammann for the fusion curve.^[124]

      Suspended Transformation. Metastable Equilibria.—Hitherto we have considered only systems in stable equilibrium. We have, however, already seen, in the case of water, that on cooling the liquid down to the triple point, solidification did not necessarily take place, although the conditions were such as to allow of its formation. Similarly, we saw that rhombic sulphur can be heated above the transition point, and monoclinic sulphur can be obtained at temperatures below the transition point, although in both cases transformation into a more stable form is possible; the system becomes metastable.

      The same reluctance to form a new phase is observed also in the phenomena of superheating of liquids, and in the "hanging" of mercury in barometers, in which case the vapour phase is not formed. In general, then, we may say that a new phase will not necessarily be formed immediately the system passes into such a condition that the existence of that phase is possible; but rather, instead of the system undergoing transformation so as to pass into the most stable condition under the existing pressure and temperature, this transformation will be "suspended" or delayed, and the system will become metastable. Only in the case of the formation of the liquid from the solid phase, in a one-component system, has this reluctance to form a new phase not been observed.

      To ensure the formation of the new phase, it is necessary to have that phase present. The presence of the solid phase will prevent the supercooling of the liquid; and the presence of the vapour phase will prevent the superheating of the liquid. However, even in the presence of the more stable phase, transformation of the metastable phase occurs with very varying velocity; in some cases so quickly as to appear almost instantaneous; while in other cases, the change takes place so slowly as to require hundreds of years for its achievement. It is this slow rate of transformation that renders the existence of metastable forms possible, when in contact with the more stable phase. Thus, for example, although calcite is the most stable form of calcium carbonate at the ordinary temperature,^[125] the less stable modification, aragonite, nevertheless exists under the ordinary conditions in an apparently very stable state.

      As to the amount of the new phase required to bring about the transformation of the metastable phase, quantitative measurements have been carried out only in the case of the initiation of crystallization in a supercooled liquid.^[126] As the result of these investigations, it was found that, in the case of superfused salol, the very small amount of 1 × 10^-7 gm. of the solid phase was sufficient to induce crystallization. Crystallization of a supercooled liquid, however, can be initiated only by a "nucleus" of the same substance in the solid state, or, as has also been found, by a nucleus of an isomorphous solid phase; it is not brought about by the presence of any chance solid.

      Velocity of Transformation.—Attention has already been drawn to the sluggishness with which reciprocal transformation of the polymorphic forms of a substance may occur. In the case of tin, for example, it was found that the white modification, although apparently possessing permanence, is in reality in a metastable state, under the ordinary conditions of temperature and pressure. This great degree of stability is due to the tardiness with which transformation into the grey form occurs.

      What was found in the case of tin, is met with also in the case of all transformations in the solid state, but the velocity of the change is less in some cases than in others, and appears to decrease with increase of the valency of the element.^[127] To this fact van't Hoff attributes the great permanence of many really unstable (or metastable) carbon compounds.

      Reference has been made to the fact that the velocity of transformation can be accelerated by various means. One of the most important of these is the employment of a liquid which has a solvent action on the solid phases. Just as we have seen that at any given temperature the less stable form has the higher vapour pressure, but that at the transition point the vapour pressure of both forms becomes identical, so also it can be proved theoretically, and be shown experimentally, that at a given temperature the solubility of the less stable form is greater than that of the more stable, but that at the transition point the solubility of the two forms becomes identical.^[128]

      If, then, the two solid phases are brought into contact with a solvent, the less stable phase will dissolve more abundantly than the more stable; the solution will therefore become supersaturated with respect to the latter, which will be deposited. A gradual change of the less stable form, therefore, takes place through the medium of the solvent. In this way the more rapid conversion of white tin into grey in presence of a solution of tin ammonium chloride (p. 42) is to be explained. Although, as a rule, solvents accelerate the transformation of one solid phase into the other, they may also have a retarding influence on the velocity of transformation, as was found by Reinders in the case of mercuric iodide.^[129]

      The velocity of inversion, also, is variously affected by different solvents, and in some cases, at least, it appears to be slower the more viscous the solvent;^[130] indeed, Kastle and Reed state that yellow crystals of mercuric iodide, which, ordinarily, change with considerable velocity into the red modification, have been preserved for more than a year under vaseline.

      Temperature, also, has a very considerable influence on the velocity of transformation. The higher the temperature, and the farther it is removed from the equilibrium point (transition point), the greater is the velocity of change. Above the transition point, these two factors act in the same direction, and the velocity of transformation will therefore go on increasing indefinitely the higher the temperature is raised. Below the transition point, however, the two factors act in opposite directions, and the more the temperature is lowered, the more is the effect of removal from the equilibrium point counteracted. A point will therefore be reached at which the velocity is a maximum. Reduction of the temperature below this point causes a rapid falling off in the velocity of change. The point of maximum velocity, however, is not definite, but may be altered by various causes. Thus, Cohen found that in the case of tin, the point of maximum velocity was altered if the metal had already undergone transformation; and also by the presence of different liquids.^[131]

      Lastly, the presence of small quantities of different substances—catalytic agents or catalyzers—has a great influence on the velocity of transformation. Thus, e.g., the conversion of white to red phosphorus is accelerated by the presence of iodine (p. 47).

      Greater attention, however, has been paid to the study of the velocity of crystallization of a supercooled liquid, the first experiments in this direction having been made by Gernez^[132] on the velocity of crystallization of phosphorus and sulphur. Since that time, the velocity of crystallization of other supercooled liquids has been investigated; such as acetic acid and phenol by Moore;^[133] supercooled water by Tumlirz;^[134] and a number of organic substances by Tammann,^[135] Friedländer and Tammann,^[136] and by Bogojawlenski.^[137]

      In measuring the velocity of crystallization, the supercooled liquids were contained in narrow glass tubes, and the time required for the crystallization to advance along a certain length of the tube was determined, the velocity being expressed in millimetres per minute. The results which have so far been obtained may be summarized as follows. For any given degree of supercooling of a substance, the velocity of crystallization is constant. As the degree of supercooling increases, the velocity of crystallization also increases, until a certain point is reached at which the velocity is a maximum, which has a definite characteristic value for each substance. This maximum velocity remains constant over