The length of time during which the temperature remains constant at the point c, depends, of course, on the eutectic solution. If, therefore, we take equal amounts of solution having a different initial composition, the period of constant temperature in the cooling curve will evidently be greatest in the case of the solution having the composition of the eutectic point; and the period will become less and less as we increase the amount of one of the components. The relationship between initial composition of solution and the duration of constant temperature at the eutectic point is represented by the curve a′c′b′ (Fig. 77). When a compound possessing a definite melting point is formed, it behaves as a pure substance. If, therefore, the initial composition of the
solution is the same as that of the compound, no eutectic solution will be obtained; and therefore no line of constant temperature, such as cd (Fig. 76). In such a case, if we represent graphically the relation between the initial composition of the solution and the duration of constant temperature, a diagram is obtained such as shown in Fig. 78. The two maxima on the time-composition curve represent eutectic points, and the minima, a′, b′, e′, pure substances. The position of e′ gives the composition of the compound. When a series of compounds is formed, then for each compound a minimum is found on the time-composition curve.
If the compound formed has no definite melting point, the diagram obtained is like that shown in Fig. 79. If we start with a solution, the composition of which is represented by a point between d and b, then, on cooling, b will separate out first, and the temperature will fall until the point d is reached. The temperature then remains constant until the component b, which has separated out, is converted into the compound. After this the temperature again falls, until it again remains constant at the eutectic point c. In the case of the first halt, the period of constant temperature is greatest when the initial composition of the solution is the same as that of the compound; and it becomes shorter and shorter with
increase in the amount of either component. In this way we obtain the time-composition curve b′e″d′, of which the maximum point e″ gives the composition of the compound.
On the other hand, the period of constant temperature for the eutectic point c is greatest in the case of solutions having the same initial composition as that corresponding with the eutectic point; and it decreases the more the initial composition approaches that of the pure component a or the component e. In this way we obtain the time-composition curve a′c′e′. Here also the point e′ represents the composition of the compound. We see, therefore, that from the graphic representation of the freezing-point curve, and from the duration of the temperature-arrests on the cooling curve, for solutions of different initial composition, it is possible, without having recourse to analysis, to decide what solid phases are formed, and what is their composition.
Formation of Minerals.—Important and interesting as is the application of the Phase Rule to the study of alloys, its application to the study of the conditions regulating the formation of minerals is no less so; and although we do not propose to consider different cases in detail here, still attention must be drawn to certain points connected with this interesting subject.
In the first place, it will be evident from what has already been said, that that mineral which first crystallizes out from a molten magma is not necessarily the one with the highest melting point. The composition of the fused mass must be taken into account. When the system consists of two components which do not form a compound, one or other of these will separate out in a pure state, according as the composition of the molten mass lies on one or other side of the eutectic composition; and the separation of the one component will continue until the composition of the eutectic point is reached. Further cooling will then lead to the simultaneous separation of the two components.
If, however, the two components form a stable compound (e.g. orthoclase, from a fused mixture of silica and potassium aluminate), then the freezing-point curve will resemble that