A. The Ternary Eutectic Point.—In passing to the consideration of those ternary systems in which one or more solid phases can exist together with one liquid phase, we shall first discuss not the solubility curves, as in the case of two-component systems, but the simpler relationships met with at the freezing point. That is, we shall first of all examine the freezing point curves of ternary systems.
Since it is necessary to take into account not only the changing composition of the liquid phase, but also the variation of the temperature, we shall employ the right prism for the graphic representation of the systems, as shown in Fig. 95. A, B, and C in this figure, therefore, denote the melting points of the pure components. If we start with the component A at its melting point, and add B, which is capable of dissolving in liquid A, the freezing point of A will be lowered; and, similarly, the freezing point of B by addition of A. In this way we get the freezing point curve Ak1B for the binary system; k1; being an eutectic point. This curve will of course lie in the plane formed by one face of the prism. In a similar manner we obtain the freezing point curves Ak2C and Bk3C. These curves give the composition of the binary liquid phases in equilibrium
with one of the pure components, or at the eutectic points, with a mixture of two solid components. If, now, to the system represented say by the point k1, a small quantity of the third component, C, is added, the temperature at which the two solid phases A and B can exist in equilibrium with the liquid phase is lowered; and this depression of the eutectic point is all the greater the larger the addition of C. In this way we obtain the curve k1K, which slopes inwards and downwards, and indicates the varying composition of the ternary liquid phase with which a mixture of solid A and B are in equilibrium. Similarly, the curves k2K and k3K are the corresponding eutectic curves for A and C, and B and C in equilibrium with ternary solutions. At the point K, the three solid components are in equilibrium with the liquid phase; and this point, therefore, represents the lowest temperature attainable with the three components given. Each of the ternary eutectic curves, as they may be called, is produced by the intersection of two surfaces, while at the ternary eutectic point, three surfaces, viz. Ak1Kk2, Bk1Kk3, and Ck1Kk3 intersect. Any point on one of these surfaces represents a ternary solution in equilibrium with only one component in the solid state; the lines or curves of intersection of these represent equilibria with two solid phases, while at the point K, the ternary eutectic point, there are three solid phases in equilibrium with a liquid and a vapour phase. The surfaces just mentioned represent bivariant systems. 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. Lastly, the ternary eutectic point, K, represents an invariant system; three solid phases can exist in equilibrium with a ternary solution, only when the latter has one fixed composition and when the temperature has a definite value. This eutectic point, therefore,
has a perfectly definite position, depending only on the nature of the three components.
Instead of employing the prism, the change in the composition of the ternary solutions can also be indicated by means of the projections of the curves k1K, k2K, and k3K on the base of the prism, the particular temperature being written beside the different eutectic points and curves. This is shown in Fig. 96.
The numbers which are given in this diagram refer to the eutectic points for the system bismuth—lead—tin, the data for which are as follows:—[[331]]
| Melting point of pure metal. | Percentage composition of binary eutectic mixture. | Temperature of binary eutectic point. | ||
| Bi | Pb | Sn | ||
| Bismuth, 268° | 55 | 45 | — | Bi—Pb, 127° |
| Lead, 325° | 58 | — | 42 | Bi—Sn, 133° |
| Tin, 232° | — | 37 | 63 | Pb—Sn, 182° |
| Percentage composition of ternary eutectic mixture. | Temperature of ternary eutectic point. | ||
| Bi | Pb | Sn | |
| 52 | 32 | 16 | 96° |