This document last updated on 12Jan2011
EENS 2120
Petrology
Tulane University
Prof. Stephen A. Nelson
Ternary Phase Diagrams
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 curves. These curves 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.
Ternary Phase Diagrams
1/12/2011
Page 1 of 11
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View Full DocumentNote 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
Ternary Phase Diagrams
1/12/2011
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