# Structural Diagram

## Structural Diagram

(also called equilibrium diagram or phase diagram), a graphic representation of the relations between the structural parameters of a physicochemical system (such as temperature and pressure) and its composition. In the simplest case, when the system consists of only one component, a structural diagram is a three-dimensional figure constructed along three perpendicular coordinate axes, along which the temperature *T*, the pressure *p*, and the molar volume *v* are plotted. The use of a three-dimensional structural diagram is inconvenient because of its unwieldiness; there-fore, a projection of a structural diagram onto one of the coordinate planes, usually the *p-T* plane, is used in practice.

The structural diagram of carbon dioxide, CO_{2}, is shown (not to scale) in Figure 1 as a very simple example. Any point of the structural diagram (a figurative point) depicts the state of CO_{2} at the temperature and pressure that correspond to the point. The point *O* (the triple point) corresponds to equilibrium of the three phases—solid, liquid, and gaseous CO_{2}. The three curves intersect at point *O: OA* (the volatilization curve), which corresponds to equilibrium between the solid and gaseous CO_{2}; *OC* (the evaporation curve), which corresponds to equilibrium between liquid and gaseous CO_{2}; and *OB* (the melting curve), for solid and liquid CO_{2}. The curves divide the plane of the diagram into three fields, which are the domains of the three phases: the solid phase *S*, the liquid *L*, and the gaseous *G*. The point *C* corresponds to the critical temperature of CO_{2} (31.0°C), at which the difference between the properties of liquid and gas disappears. According to the terminology of the phase rule, invariant equilibrium corresponds to *O*; monovariant equilibrium, to the points on curves *OA, OB*, and *OC*; and divariant equilibrium, to the points in the fields *S*, *L*, and G. In the case of polymorphism the structural diagram grows complicated—the number of triple points is equal to the number of polymorphous trans-formations. (*See*BINARY SYSTEMS for structural diagrams of systems with more than one component.)

The experimental construction of structural diagrams is accomplished by various methods of physicochemical analysis, thermal and X-ray spectral analysis, optical and electron microscopy, dilatometry, and the measurement of electrical resistance, hardness, and other properties. The correctness of the construction of a structural diagram is checked on the basis of the phase rule, the correspondence principle, and the continuity principle. Structural diagrams are used extensively in practice in metals science, metallurgy, and chemistry. For example, an iron-carbon structural diagram is of great importance for the heat treatment of steel.

### REFERENCES

Anosov, V. la., and S. A. Pogodin.*Osnovnye nachala fizikokhimicheskogo analiza*. Moscow-Leningrad, 1947.

Anosov, V. la.

*Kratkoe vvedenie v fiziko-khimicheskii analiz*. Moscow, 1959.

Dreving, V. P., and la. A. Kalashnikov.

*Pravilo faz s izlozheniem osnov termodinamiki*, 2nd ed. Moscow, 1964.

S. A. POGODIN