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Ternary Phase Diagrams EENS 211 Tulane University Ternary Phase Diagrams
This document last updated on 14-Oct-2003

Earth Materials Prof. Stephen A. Nelson

Crystallization in Ternary Systems I. Equilibrium Crystallization Where all 2 Component Systems are Binary Eutectic Systems. Figure 1 shows a three dimensional representation of the three component (ternary) system ABC. Note thatcomposition is measured along the sides of the basal triangle and temperature (or pressure) is measured vertically. The top of the figure shows a surface with contour's representing lines of constant temperature. These contours are called isotherms. Note that the eutectic points in each of the binary systems project into the ternary systems as lines. These lines are called boundary curves, and anycomposition on one of these curves will crystallize the two phases on either side of the curve. Figure 2 shows the same figure in two dimensions as seen from above. The boundary curves and isotherms are also shown projected onto the basal triangle. Note how the temperature decreases toward the center of the diagram In Figure 3 we trace the crystallization of composition X. Figure 3 is the same as Figure2, with the isotherms left off for greater clarity.

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10/14/2003

Ternary Phase Diagrams

Note that the final solid must consist of crystals A + B + C since the initial composition is in the triangle ABC. At a temperature of about 980° the liquid of composition X would intersect the liquidus surface. At this point it would begin to precipitate crystals of C. As temperatureis lowered, crystals of C would continue to precipitate, and the composition of the liquid would move along a straight line away from C. This is because C is precipitating and the liquid is becoming impoverished in C and enriched in the components A + B.

At a temperature of about 820°, point L in Figure 3, we can determine the relative proportion of crystals and liquid. % crystals = a/(a+b)*100% liquid = b/(a+b)*100 With further cooling, the path of the liquid composition will intersect the boundary curve at point 0. At the boundary curve crystals of A will then precipitate. The liquid path will then follow the boundary curve towards point M. The bulk composition of the solid phase precipitated during this interval will be a mixture of A + C in the proportion shown by point P. At pointM, the bulk composition of the solid phases so far precipitated through the cooling history lies at point N (the extension of the straight line from M through the initial composition X). At this time the % solid will be given by the distances : (distanceMX/distanceMN)*100 and the % liquid by the distances: (distanceXN/distanceMN)*100 Note, however, that the solid at this point consists of crystalsof A and crystals of C. So, we must further break down the percentages of the solid. This is done as follows: The percentage of the solid that is A will be given by the distance from C to N relative to the distance between A and C; i.e. by the formula: %A in solid = (distanceNC/distanceAC)*100 Similarly, the percentage of the solid consisting of crystals of C is given by the formula: %C in solid= (distanceAN/distanceAC)*100 Page 2 of 11 10/14/2003

Ternary Phase Diagrams We can now calculate the exact percentage of all phases present in composition X at a temperature of 660° (where the liquid composition is at point M). The following formulae apply: %A crystals = %A in the solid * %crystals/100 or %A = (distanceNC/distanceAC)*100 * (distanceMX/distanceMN) and %C crystals = %C in thesolid * % crystals/100 or %C = (distanceNA/distanceAC)*100 * distanceMX/distanceMN

Note also that we can determine the composition of all phases present in the system at this point. The composition of the liquid is given by reading the composition of point M off the basal triangle. Since it is a mixture of A, B, and C, it will have a composition expressed in terms of the percentages of A, B,...