Fractional Crystallization of Mixed Crystals.--With the help of the diagrams already given it will be possible to predict what will be the result of the fractional crystallization of a fused mixture of two substances which can form mixed crystals. Suppose, for example, a fused mixture of the composition _x_ (Fig. 53) is cooled down; then, as we have already seen, when the temperature has fallen to _a_, mixed crystals of composition, _b_, are deposited. If the temperature is allowed to fall {189} to _x'_, and the solid then separated from the liquid, the mixed crystals so obtained will have the composition represented by e. If, now, the mixed crystals _e_ are completely fused and the fused mass allowed to cool, separation of solid will occur when the temperature has fallen to the point _f_. The mixed crystals which are deposited have now the composition represented by _g_, i.e. _they are richer in B than the original mixed crystals_. By repeating this process, the composition of the successive crops of mixed crystals which are obtained approximates more and more to that of the pure component B, while, on the other hand, the composition of the liquid phase produced tends to that of pure A. By a systematic and methodical repetition of the process of fractional crystallization, therefore, a _practically_ complete separation of the components can be effected; a perfect separation is theoretically impossible. From this it will be readily understood that in the case of substances the freezing point of which passes through a maximum, fractional crystallization will ultimately lead to mixed crystals having the composition of the maximum point, while the liquid phase will more and more assume the composition of either pure A or pure B, according as the initial composition was on the A side or the B side of the maximum point. In those cases, however, where the curves exhibit a minimum, the solid phase which separates out will ultimately be one of the pure components, while a liquid phase will finally be obtained which has the composition of the minimum point. II.--THE TWO COMPONENTS DO NOT FORM A CONTINUOUS SERIES OF MIXED CRYSTALS. This case corresponds to that of the partial miscibility of liquids. The solid component A can "dissolve" the component B until the concentration of the latter in the mixed crystal has reached a certain value. Addition of a further amount of B will not alter the composition of the mixed crystal, but there will be formed a second solid phase consisting {190} of a solution of A in B. At this point the four phases, mixed crystals containing excess of A, mixed crystals containing excess of B, liquid solution, vapour, can coexist; this will therefore be an invariant point. The temperature-concentration curves will therefore no longer be continuous, but will exhibit a break or discontinuity at the point at which the invariant system is formed. (_a_) _The freezing-point curve exhibits a transition point_ (Curve I., Fig. 54).