Generalized binary phase diagram

Phase diagrams are the roadmaps from which the number of phases, their compositions, and their fractions can determined as a function of temperature. In general, binary-phase diagrams can be characterized as exhibiting complete or partial solid solubility between the end members. In case of the latter, they will contain one or both of the following reactions depending on the species present. The first is the eutectic reaction is which a liquid becomes saturated with respect to the end members such that at the eutectic temperature two solids precipitate out of the liquid simultaneously. The second reaction is known as the peritectic reaction in which a solid dissociates into a liquid and a second solid of a different composition at the peritectic temperature. The eutectic and peritectic transformations also have their solid state analogues, which are called eutectoid and peritectoid reactions, respectively. 

Fig. 38. Isothermal sections at 25°C of (a) intra-lanthanide and (b) intra-actinide generalized binary phase diagrams, showing equilibrium phase boundaries [with estimated hysteresis for (a)] as full hnes (Benedict et al. 1986). The broken line in (a) indicates the interpolated boundary for the volume collapse transition of the lanthanides. The atomic radius of Ce at room temperature as a function of pressure is shown in (c) (Franceschi and Olcese 1969), with the Kondo-volume collapse transition at about 7 kbar. This transition can be traced to negative pressures by alloying (Lawrence et al. 1984), as seen in (d) via the temperature dependence of the resistance.

W. G. Moffat, Handbook of Binary Phase Diagrams, General Electric Co., Schenectady, N.Y., 1976. 

The general thermodynamic treatment of binary systems which involve the incorporation of an electroactive species into a solid alloy electrode under the assumption of complete equilibrium was presented by Weppner and Huggins [19-21], Under these conditions the Gibbs Phase Rule specifies that the electrochemical potential varies with composition in the single-phase regions of a binary phase diagram, and is composition-independent in two-phase regions if the temperature and total pressure are kept constant. 

Figure 2.13. Building blocks of binary phase diagrams examples of three-phase (invariant) reactions. In the upper part the general appearance, inside a phase diagram, of the two types of invariant equilibria is presented, that is, the so-called 1 st class (or eutectic type) and the 2nd class (or peritectic type) equilibria. In the lower part the various invariant equilibria formed by selected binary alloys for well-defined values of temperature and composition are listed. In the Hf-Ru diagram, for instance, three 1 st class equilibria may be observed, 1 (pHf) — (aHf) + HfRu (eutectoid, three solid phases involved), 2 L — (3Hf + HfRu (eutectic), 3 L —> HfRu + (Ru) (eutectic).

An-An alloys. A summary ofthe phase diagrams for adjacent actinide metals is shown in the connected binary phase diagrams of Fig. 5.11. The structure of this diagram resembles that reported in Fig. 5.10 for the lanthanides notice, however, that such a sequence of interconnected diagrams could be used as a generalized diagram in a more limited way only, possibly for the heavier actinides from americium onward. 

M4 K.C. Mills High Temp.-High Press., 4 (1972) 371 -377. M5 G. W. Moffat The Handbook of Binary Phase Diagrams, General Electric Company, Schenectady, New York, 1978. Nbl NBS Tables ... 

The determination of was examined by first considering the liquid solution behavior and then the solid mixture properties. The liquid phase properties are typically determined by using a solution model to interpolate between the binary limits. In general, the use of only the binary phase diagrams in the data base for model parameter estimation does not give good values for the ternary liquid mixture properties. The solid solution behavior is normally determined from an analysis of the pseudo-binary phase diagram. Extrapolation of the solid solution behavior determined in this manner to lower values of temperature should be undertaken with caution. 

A phase diagram of a one-component system can be plotted readily in two dimensions, with the pressure and the temperature as coordinates. If we connect the outer lines in Fig. 7.1 mutually, then we could identify a pulped tetrahedron in the figure. However, this model is not sufficient even in a binary system, as besides temperature and pressure the composition emerges as an additional variable. Mostly, common binary phase diagrams are an isobaric section of a general three-dimensional phase diagram with the mole fraction as third variable. However, the mole fractions may be different in the various coexistent phases. In the sense of intensive variables, instead of the mole fraction, the chemical potential ii is the logical pendant to temperature T and pressure p. 

---