Ternary Phase Diagrams EENS 211 Tulane University Earth Materials Prof Stephen A Nelson Ternary Phase Diagrams This document last updated on 14 Oct 2003 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 that composition 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 any composition 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 Figure 2 with the isotherms left off for greater clarity Page 1 of 11 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 temperature is 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 point M 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 crystals of 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 the solid 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 and C The composition of the solids are 100 A and 100 C i e they are pure solid phases not mixtures With further cooling the liquid composition will move to the ternary eutectic E at a Temperature of about 650 at which point crystals of B will precipitate The temperature will remain constant until all of the liquid is used up The final crystalline product will consist of crystals of A B C in the proportions given by the initial composition X Crystallization will proceed in an analogous manner for all other compositions in the ternary system To summarize we can express the path of crystallization for composition X in an abbreviated form as follows T 980 All Liquid 980 680 Liq C 680 650 Liq C A T 650 Liq C A B T 650 C A B all solid Page 3 of 11 10 14 2003 Ternary Phase Diagrams At any temperature an isothermal planecan be constructed through the system that will show the phases present for all compositions in the ternary system Such an isothermal plane for the system ABC at 700 is shown in Figure 4 II Crystallization in Ternary Systems that Contain a Compound that Melts Congruently A ternary system that has a binary system with a compound that shows congruent melting melts to a liquid of its own composition is shown in Figure 5 Also shown is the binary system X Y that contains the intermediate compound W The result of the addition of this intermediate compound is essentially that the ternary system XYZ is divided into two smaller ternary systems represented by triangles WYZ and XWZ Page 4 of 11 10 14 2003 Ternary Phase Diagrams Crystallization in this system is illustrated in Figure 6 where the isotherms have been removed for simplicity We first note that any composition within the triangle WYZ must end up with crystals of W Y Z in the final crystalline product compositions in the triangle XWY will end up with crystals of X W Y and compositions on the line WZ must end up with crystals of W Z only Consider first crystallization of composition A in Figure 6 Crystallization begins at about 1160 with separation of crystals of Z The composition of the liquid then changes along a straight line away from Z When the temperature reaches about 680 the liquid composition has intersected the boundary curve at point B At this time crystals of W begin to separate and with further lowering of temperature the liquid moves along the boundary curve B E1 precipitating crystals of Z W When the liquid reaches the ternary eutectic E1 crystals of X begin to separate along with crystals of W and Z The temperature remains constant at 640 until all of the liquid is used up leaving a final product of crystals of X W Z in the proportions of the