Four-Component Quaternary Phase Diagrams

On the line connecting the points representing the compositions of larnite (La, (3-Ca2Si04) and forsterite (Fo, Mg2Si04) the compounds merwinite (Ca3Mg[Si04]2) 

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The chemical compositions of clays are very complex, and frequently more than three components must be considered. Four-component (quaternary) phase diagrams can be represented by a tetrahedron. As an example. Figure 3.9 shows the quaternary system Ca0-Mg0-Al203-Si02 and several of its subsystems that divide the tetrahedra volume into four-component phase assemblies. 

Relatively few four-component systems have been studied in any detail. Fig. 2.24a shows diagrammatically the way in which the quaternary phase diagram for the system phosphated nonyl phenolethoxylate (PNE)-phosphated fatty alcohol ethoxylate (PFE)-n-hexane-water (Fig. 2.24b) is built up [42]. 

Quaternary systems are composed of four components with a common ion and form four ternary and six binary systems. The concentration diagram of the quaternary system can be represented by a tetrahedron. The vertical projection of every ternary system is placed on one face of the tetrahedron. The phase diagram of the quaternary system A+, B+, C +, D + // X with the formation of the congruently melting binary compound BCX3 is shown in Figure 3.39. 

The crystallization behaviour of the glasses containing MgO is more difficult to describe. Unlike ternary systems, four component phase diagrams are properly represented by a regular tetrahedron with each apex representing 100% of each component. The crystallization path is therefore in three dimensions which is sometimes difficult to visualize. The method of representation chosen to describe the observed behaviour is as planes of constant MgO content in the regions of interest to this study. Figures 2, 3, and 4 are planes of the quaternary system at 5, 10 and 15 wt% levels respectively and have been compiled from various sources... 

Fig. 62. The quaternary system cholesterol-lecithin-sodium cholate-water. The tetrahedron on the left is a representation of this four-component system. The five triangles of decreasing size at the right of the diagram schematically represent cuts taken parallel to the base of the tetrahedron (lecithin-sodium cholate-water), to which a given amount of cholesterol at different overall cholesterol concentrations (2%, 4%, 6%, 25%) has been added. Choi, cholesterol L, lecithin NaC, sodium choiate W, water. Also a, lamellar liquid crystalline phase b, cubic liquid crystalline phase c, hexagonal liquid crystalline phase d, micellar phase (42). Expressed as wt%.

Tan = 1550°C the binary eutectic temperatures 1362°C (quartz-diopside), 1270°C (diopside-anorthite), and 1368°C (quartz-anorthite) and the ternary eutectic temperature of 1200 °C. The composition of the ternary eutectic is 30 mass% quartz, 33 mass% diopside, and 37 mass% anorthite (Clark et al., 1962 Osborn and Tail, 1952). The ternary phase diagram discussed above refers to high-fired calcareous UMtic clays with the four components Si02, AI2O3, CaO, and MgO, but fails to incorporate an important fifth component such as Fe203. Hence, even more complex phase relations must be considered in appropriate multicomponent (quaternary, quinary, hexanary,... multinary) systems. 

Analogous to ternary systems, a quaternary system can be represented in a three-dimensional prism, but having a square as prism base with the four components at the comers. An example is given in Figure 3.6a for four arbitrary components A, B, C, and D. Again, only simple eutectic binary systems A/B, B/C, C/D, and A/D are assumed. In order to simplify the interpretation of such quaternary phase equilibria, as for ternary systems, usually isothermal slices of the three-dimensional representation of the phase diagram are considered. 

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