Liquidus surface

Let us now consider two real ternary systems to illustrate the complexity of ternary phase diagrams in some detail. While the first is a system in which the solid state situation is rather simple and attention is primarily given to the liquidus surfaces, the solid state is the focus of the second example. 

The shape, the slope, of the liquidus line (or liquidus surface) is obviously an important point which has to be considered. 

Figure 7.12 shows the liquidus surface of a ternary system with complete miscibility at solid state between components 1-2 and complete immiscibility at solid state between components 1-3 and 2-3. Note also that components 1 and 2 form a lens-shaped two-phase field, indicating ideality in the various aggregation states (Roozeboom type I). 

Let us now treat compositional relations in the ternary system Di-An-Ab. Figure 7.14A shows the projection of the liquidus surface of the system onto the compositional plane the locations of cotectic line E -E" and of the isotherms are based on the experiments of Bowen (1913), Osborn and Tait (1952), and Schairer and Yoder (1960). 

Figure 10.86 Calculated liquidus surface of the five-component oxide system with fixed values of 20.4wt%Al2O3 and 8.2 wt%MgO.

We wish here to obtain the thermodynamic equations defining the liquidus surface of a solid solution, (At BB)2, ). It is assumed that the A and atoms occupy the sites of one sublattice of the structure and the C atoms the sites of a second sublattice. For the specific systems considered here Sb and play the role of C in the general formula above. It is also assumed that the composition variable is confined to values near unity so that the site fractions of atomic point defects is always small compared to unity. This apparently is the case for the solid solutions in the two systems considered. Then it can be shown theoretically (Brebrick, 1979), as well as experimentally for (Hgj CdJ2-yTe)l(s) (Schwartz et al, 1981 Tung et al., 1981b), that the sum of the chemical potentials of A and C and that of and C in the solid are independent of the composition variable y ... 

Equations (A5) and (A6) describe the interspecies equilibrium in the liquid phase for some composition xlt x2. If this liquid is on the liquidus surface of Ax BuC(s), then the liquidus equations given by Eqs. (12) and (13) must also be satisfied. Using the general relation between relative chemical potential and activity coefficient given by Eq. (60), the liquidus equations are... 

Fig. 38. Liquidus surface in the Hg-Cd-Te system on the Hg-Cd-rich side of the HgTe-CdTe pseudobinary section. The liquidus temperature in degrees Celsius is plotted against the atom fraction of for fixed values of z that are shown along the right vertical axis. The composition of the liquid phase is written as (Hg , Cdz),Te, y. Experimental points shown as symbols. The single diamond point is for = 0.09. Arrows below each liquidus lines indicate where the atom fractions of Cd and are equal.

The calculated liquidus isotherms for the Hg-Cd-Te system in Fig. 28 show that the liquidus temperature is not always a maximum in the HgTe-CdTe pseudobinary section. Figure 38 shows the liquidus surface between this pseudobinary and the Hg-Cd axis in more detail for comparison with ten experimental ternary liquidus points obtained by Szofran and Lehoczky... 

Fig. 39. Liquidus surface as in Fig. 38 but showing the crossing of the iiquidus lines for high z values.

Fig. 41. The partial pressure of mercury in atmospheres plotted against 103 times the reciprocal absolute temperature for a traverse across the liquidus surface such that the atom fractions Cd and are always equal. The number near each circle give the atom fraction of mercury in the liquid phase at the pressure and temperature specified by the circle. 

Finally, Table XIII gives a tabulation of liquid composition, liquidus temperature, x value of the coexisting solid, and mercury pressure at the liquidus temperature. The table is arranged in sections for different z values in the liquidus composition (Hg, CdJyTe, r Since the calculated liquidus surface for -rich compositions and high temperatures is given only for z values up to 0.5 in Fig. 27, entries with less than j are also included for the high z values. 

A two dimensional representation of the ternary liquidus surface on the base composition triangle. 

These lines are called liquidus isotherms. The intersections of adjoining liquidus surfaces like ae, be and ce are called the boundary curves. When a liquid whose composition lies in the region surrounded by Aceh is cooled, the first crystalline phase that appears is A, and hence A is called the primary phase and the region Aceh is the primary field of A. In this field, solid A is the last solid to disappear when any composition within this field is heated. Similarly,B and C are primary phases in their respective primary fields, Baec and Caeb. 

Consider first the Al-Fe-Ni system. Generally, the equilibrium phase diagram is known to be helpful in analysing the process of intermetallic layer formation. Projection of the liquidus surface on the concentration triangle and distribution of the phase fields in the solid state for Al-rich Al-Fe-Ni alloys are shown in Fig. 5.15. 

Figure 2.3 (a) Isometric projection (solid diagram) for a hypothetical ternary system (b) isotherm (horizontal section) (c) binary-phase subset (d) liquidus surface. 

Figure 11.11. An isothermal horizontal section (a), a vertical section, or isopleth (h), and the liquidus surface from the isometric projection of Figure 11.10.

The liquidus surface would run from the liquidus on the copper-tin diagram to that on the copper-lead and tin-lead diagrams. In Figure 9,... 

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