# Binary Systems

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## Binary Systems

physicochemical systems consisting of two independent components. Of particular practical importance are the condensed binary systems, which do not contain gases or vapors. Phase diagrams and composition-property diagrams of such systems are represented in a plane by plotting the composition *x* (expressed in percentages by weight or in atom- or mole-percentages of one of the components) along the abscissa and the phase transformation temperatures *T* (of the beginning and end of crystallization, polymorphic transformations, and other transitions) or the numerical values of measurable properties of binary systems (density, hardness, electrical conductivity, and other properties) along the ordinate. Only the simplest isobaric (at 1 atm pressure) phase diagrams, involving only liquid phases *L* and solid phases *S*, are discussed in this article.

If mutual solubility of components *A* and *B* in the liquid and solid state is nonexistent, the phase diagram (Figure 1) is represented by two horizontal straight lines drawn through points T_{A}and T_{B}, which correspond to the melting points of A and *B*. Above T_{B} the system consists of two liquid phases L_{A} and L_{B}; between T_{B} and T_{A}, of L_{A} and crystals of *B*; and below T_{A} , of a mixture of *A* and *B* crystals. If the mutual solubility of components *A* and *B* in the liquid state is not limited but mutual solubility is nonexistent in the solid state, then upon cooling, two solid phases, crystals of *A* and *B*, precipitate from a single liquid phase *L* (Figure 2). The liquidus curves (geometric loci of the temperatures of the beginning of crystallization) T_{A}*E**E* and T_{B}*E**E* intersect at the eutectic point *E*. The liquid, the composition of which corresponds to point *E*, solidifies at a constant temperature to give a mixture of fine crystals of *A* and *B*. From liquids having the compositions between *A* and *E*, crystals of *A* start to precipitate out on cooling, with the resulting increase in the content of *B* in the liquid. When its composition corresponds to point *E*, the process is terminated by the crystallization of the eutectic. In the same way, the solidification of liquids having compositions between *B* and *E* starts with the precipitation of the crystals of *B* and terminates by the crystallization of the eutectic. The straight line *FG* drawn through point *E* is called the solidus curve (geometric locus of the temperatures at the end of crystallization). Solidified binary systems of this type consist of two-phase mixtures of the crystals *A + B*. The isotherms of the properties of such mixtures approximate the straight line *∊ _{A} ∊_{R}* (Figure 2).

If the components *A* and *B* possess unlimited mutual solubility in the liquid as well as in the solid state, then on cooling, only a single crystalline phase precipitates out of a single liquid phase *L*, namely, the solid solution 5 (Figure 3). The phase diagram of this binary system may be without a maximum and a minimum (Figure 3, I), with a maximum (Figure 3, II), or with a minimum (Figure 3, III). The isotherms of the properties have the form of continuous curves with their convex side turned upward (Figure 3, IV) or downward (Figure 3, V).

If the mutual solubility of *A* and *B* is not limited in the liquid state but limited in the solid state, then any eutectic formed consists of a mixture of two solid solutions *ɑ* and β (Figure 4), in which case the limiting concentrations of the solid solutions correspond to points *F* and *G* at the eutectic temperature and to points *M* and *N* at room temperature. The composition-property isotherms (corresponding to temperature t) consists of three branches ∊_{A}*m*_{1},*n*_{1},∊_{B} and ∊_{A}m_{2}∊_{B} the points m_{1}, m_{2} and n_{1}, n_{2} correspond to the limiting concentrations of the solid solutions *ɑ* and *β* temperature *t*.

When from the liquid *L* there crystallizes only a single chemical compound *C*, which melts without decomposition, and when solid solutions are nonexistent, the liquidus curve exhibits a rational maximum *M* or a singular point *D*, which corresponds to the composition of compound C, and two eutectic points *E*_{1} and *E*_{2}, which correspond to the eutectics formed by *C* with *A* and *B*, respectively (Figure 5). The isotherms of properties have the form of two straight

lines intersecting at the ordinate value of compound *C*. More complex phase diagrams are discussed in the references listed below.

### REFERENCES

Kurnakov, N. S.*Izbr. trudy*, vols. 1–3. Moscow, 1960–63.

Vol, A. E.

*Stroenie i svoistva dvoinykh metallicheskikh sistem*, vols. 1–2. Moscow, 1959–62.

Hansen, M., and K. Anderko.

*Struktury dvoinykh splavov*. Moscow, 1962. (Translated from English.)

S. A. POGODIN