## COMPOSITIONS, PROPORTIONS AND TIE LINES

### System Displaying Solid Solution

The system Di-Ab-An will be examined. In this system liquids undergoing crystallization will produce two-phase assemblages:

1. diopside of fixed composition, and;
2. plagioclase of variable composition.

No three phase assemblage of solids + liquid is possible as in the previous ternary systems examined. This is because of the complete solid solution between Ab and An, which yields plagioclase, of variable composition, and the lack of a ternary eutectic.

### Compositions and Proportions

Point A has a bulk composition of 50% Di, 23% Ab and 27% An, determined by drawing a series of lines (the magenta lines) through A parallel to the outer edges of the triangle.

On cooling, Liquid A will result in a solid mixture of Di and Pl, the proportions of which can be determined by applying the lever rule to a line drawn from Di, through A to the Ab-An join (Point B):

• % Di = AB/DiB * 100 =
• % Pl = ADi/DiB *100 =

The composition of the Di is fixed at the composition point of Di (100% Di, 0% Ab and 0% An).

The composition of the Pl is determined along the Ab-An join at Point B, again by applying the lever rule:

• % An = AbB/AbAn *100 =
• % Ab = BAn/AbAn *100 =

### Liquid Compositions, Plagioclase Compositions and Tie Lines

Along the boundary curve separating the field of Di + L from Plss + L, two solid phases (Di and Plss) coexist with a single liquid. These three phases can be joined together with three tie lines:

1. DiY
2. DiX
3. XY, where
• Di represents the composition of diopside
• Y represents the composition of the plagioclase in equilibrium with liquid X and solid Di;
• X represents the composition of the liquid in equilibrium with Solid Di and PlY.

Note that the apex of this small triangle which lies on the boundary curve represents the liquid composition and points down the boundary curve, in the direction of decreasing temperature.

A specific liquid composition on the boundary curve coexists only with a plagioclase of specific composition;

e.g. liquid X coexists with Di and Pl of composition Y.

The tie line joining PlY with the liquid at X must be determined experimentally, it is not obvious from simply examining the diagram.

Diopside of fixed composition can coexist with any composition of plagioclase. This is readily apparent from examining the phase diagram. We can draw a series of tie lines (Click Here) which radiate from the Di apex to the Ab-An join, spanning the range of plagioclase compositions from 100% Ab - 0% An to 0% Ab - 100% An.