Phase transition

“ The procedure will then consist in assuming a definite excess of energy, of entropy, and of the masses of the various components, each per unit surface, at the interface, the potential of each component being of necessity, in equilibrium, the same as it is in the adjacent masses. The interfacial transition layer thus provides in a sense a new surface-phase coexistent with those on each side of it, and having its own characteristic equation. ”

“ At temperatures and pressures represented by any point in the field I., solid only can exist as a stable phase. Since we have here one component in only one phase, the system is bivariant, and at any given temperature, therefore, ice can exist under a series of pressures ”

“ A knowledge of its variability is, therefore, of essential importance in studying the condition and behaviour of a system, and it is the great merit of the Phase Rule that the state of a system is defined entirely by the relation existing between the number of the components and the phases present, no account being taken of the molecular complexity of the participating substances, nor any assumption made with regard to the constitution of matter. It is, further, as we see, quite immaterial whether we are dealing with "physical" or "chemical" equilibrium ”

“ If the temperature is changed, the system will undergo alteration in such a way that one of the phases will disappear, and a univariant system will result; if heat be added, ice will melt, and we shall have left water and vapour; if heat be abstracted, water will freeze, and we shall have left ice and vapour; if, when the temperature is altered, the pressure is kept constant, then we shall ultimately obtain only one phase (see Chap. IV.) .
The triple point is not only the point of intersection of the vaporization and sublimation curves, but it is also the end-point of the fusion curve. ”

“ The systems which we now proceed to study are characterized by the fact that the different phases have no longer all the same chemical composition, and cannot, therefore, according to definition, be considered as one-component systems. ”

“ The Phase Rule.—When the material system contains only a single phase, the number of independent variations, in addition to change of temperature and pressure, that can spontaneously occur in its constitution is thus one less than the number of its independent constituents. But where several phases coexist in contact in the same system, the number of possible independent variations may be much smaller. The present independent variables μ1, ..., μn are specially appropriate in this problem, because each of them has the same value in all the phases. ”

“ A system consisting of n components can exist in n + 2 phases only when the temperature, pressure, and concentration have fixed and definite values; if there are n components in n + 1 phases, equilibrium can exist while one of the factors varies, and if there are only n phases, two of the varying factors may be arbitrarily fixed. ”

“ Thus, for example, if a liquid solution of two components, A and B, having the composition represented by the point x (Fig. 50) , is allowed to cool, the system will pass along the line xx′. At the temperature of the point a, mixed crystals will be deposited, the composition of which will be that represented by b. As the temperature continues to fall, more and more solid will be deposited; and since the solid phase is relatively rich in the component B, the liquid will become relatively poorer in this. ”

“ One component in the solid state can exist in equilibrium with a ternary liquid phase under varying conditions of temperature and concentration of the components in the solution; and before the state of the system is defined, these two variables, temperature and composition of the liquid phase, must be fixed. On the other hand, the curves formed by the intersection of these planes represent univariant systems; at a given temperature two solid phases can exist in equilibrium with a ternary solution, only when the latter has a definite composition. ”

“ In discussing the equilibria in systems containing a solid solution, it is of essential importance to remember that a solid solution constitutes only one phase, a phase of varying composition, as in the case of liquid solutions. ”

“ Or, if a mass consists of two coexistent phases, one of which is a critical phase having two independently variable components, and either the temperature or the pressure of the mass is maintained constant, it will not be possible by mechanical or thermal means, or by changing the quantities of the components, to cause the critical phase to change into a pair of coexistent phases, so as to give three coexistent phases in the whole mass. ”

“ When the number of phases exceeds the number of components by unity, the system is capable of a single variation of phase. The pressure and all the potentials may be regarded as functions of the temperature. The determination of these functions depends upon the elimination of the proper quantities from the fundamental equations in , etc. ”

“ 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. ”

“ Since a phase cannot vary continuously without variations of the temperature or the potentials, it follows from these conditions that the phase at any point in a fluid system which has the same independently variable components throughout, and is in equilibrium under the influence of gravity, must be one of a certain number of phases which are completely determined by the phase at any given point and the difference of level of the two points considered. ”

“ One component in two phases, however, constitutes a univariant system, and we can therefore see that calcium chloride hexahydrate in contact with solution of the same composition will constitute a univariant system. The temperature of equilibrium will, however, vary with the pressure ”

“ While an ethereal particle is performing a complete oscillation, a series of others, to which it has communicated its motion, are also performing oscillations in various phases—the adjacent particle being a little behind the first, the next a little behind the second, and so on, until, in the file of particles, we come to one which is in the same phase of its oscillation as the first one. ”

“ These theories have proved of incalculable value in elucidating electrical and radiation phenomena.
Another discovery of Gibbs, made in 1876, has also had brilliant results. It is known as the Phase Law. The homogeneous substances into which a material system is divided is called a phase. Carbonate of lime, lime, and carbonic acid gas are the three phases of a system which comprises Iceland spar partially dissociated into lime and carbonic acid gas. ”

“ We will now consider the conditions of stability in respect to continuous changes of phase, or, as it may also be called, stability in respect to adjacent phases. We may use the same general test as before, except that the expression (133) is to be applied only to phases which differ infinitely little from the phase of which the stability is in question. In this case the component substances to be considered will be limited to the independently variable components of the fluid, and the constants etc., must have the values of the potentials for these components in the given fluid. ”

“ Mention must, however, be made of certain systems which contain no liquid phase, and in which only solids and gases are in equilibrium. Since, in all cases, there can be but one gas phase, four solid phases will be necessary in order to form an invariant system. When only three solid phases are present, the system is univariant; and when only two solid phases coexist with gas, it is bivariant. If, however, we make the restriction that the gas pressure is constant, we diminish the variability by one. ”

“ The phase rule asserts that a homogeneous substance having n components is capable of only n + 1 independent phases, while a heterogeneous system of r coexistent phases, each of which has n independently variable components, is capable of degrees of freedom or variations in phase, of which not more than can coexist at the same pressure and temperature. ”

“ If the components are completely miscible in the solid state, they will also be completely miscible in the liquid state, and there can therefore be only one liquid phase. The system can at no point become invariant, because there can never be more than three phases present. When, therefore, the two components form a continuous series of mixed crystals, the equilibrium curve must also be continuous. ”

“ A system, now, which in itself is stable, and which becomes instable only in contact with a particular phase, is said to be metastable, and the region throughout which this condition exists is called the metastable region. ”

“ We may call such bodies as differ in composition or state different phases of the matter considered, regarding all bodies which differ only in quantity and form as different examples of the same phase. Phases which can exist together, the dividing surfaces being plane, in an equilibrium which does not depend upon passive resistances to change, we shall call coexistent. ”