INTRODUCTION

Ternary phase diagrams are 3 component systems. To construct a ternary diagram it is

necessary to know the three binary systems for the three components. Ternary

diagrams have a vertical temperature axis.

The actual ternary diagram may be represented as a three dimensional form or more

commmonly as a two dimensional projection of the liquidus surface onto the base of

the triangle created when the three binary diagrams are joined together. This irregular

triangle is often transformed into an equililateral triangle to facilitate presentation and

interpretation.

For experimentally studied ternary systems the liquidus surface may be contoured

with the temperature interval representing the contour interval. The fields indicated on

the ternary diagram represent the primary phase fields, of solid phases in equilibrium

with liquid, present on the liquidus surface.

The lines or curves which separate primary phase fields, the red, blue and magneta

lines on the above image, are referred to as Cotectic Lines or Boundary Curves,

along which 3 phases are in equilibrium - two solids and a liquid.

Straight lines which join the composition points of two phases whose primary phase

fields share a common boundary curve are called Alkemade Lines. Thus the edges of

the triangle are Alkemade Lines as they join the individual phases AB, AC and BC,

which share a boundary curve. Alkemade lines are a specific type of tie line.

PHASE RULE

Applying the Phase Rule to Ternary Diagrams

To refresh your memory the phase relates the number of phases present in the

system, the the number of components which define the system and the degrees of

freedom displayed the by the system at equilibrium.

Phase Rule P + F = C + 1

With referernce to the hypothetical ABC system:

1. At Point 1 Point 1 lies in the C + L field

o P = 2 - Solid C and Liquid o C = 3 - three components A, B and C o F = 2 - two degrees of freedom, giving a divariant surface o To maintain equilbrium, i.e. to keep Solid C and Liquid as the stable

phases, temperature and composition may both vary independently of each other .

2. At Point 2 Point 2 lies on the Boundary Curve which separates the field of Solid A + LIquid from the field of Solid C + Liquid.

o P = 3 - Solid A, Solid C and Liquid o C = 3 - three components, A, B and C o F = 1 - One degree of freedom, giving a univariant line. o To maintain equilibrium between the three phases i.e. to stay on the

boundary curve, only temperature or pressure may be changed independently, fixing one automatically fixes the other.

3. At Point E Point E represents the ternary eutectic, where the three fields A + L, B + L and C + L meet.

o P = 4 - Solid A, Solid B, Solid C and Liquid o C = 3 - three components, A, B and C o F = 0 - No degrees of freedom, yielding an invariant point. o To maintain equilibrium, i.e. to have all four phases stable and in

euilibrium the position of the eutectic is fixed in terms of temperature and composition, changing either will result in a shift of the system away from the eutectic.

DETERMINING COMPOSITION ON TERNARY

DIAGRAMS

Compositions in Ternary Diagrams

All compositions, e.g., bulk compositions, liquid compositions, compositions of solid

phases, on ternary diagrams are expressed in terms of the three end member

components which define the system. These three components are located a the apices

of the triangle.

Each apex on the triangle representing the ternary system represents 100% of the

component at that apex. The side of the triangle, directly opposite the apex, represents

0% of the apex component. Compositions of points which lie along the outside edge

of the triangle are simply a mixture of the two components at each end of the tie line,

with 0% of the third component.

The composition of points which lie inside the area of the triangle can be determined

by using either of the following methods.

1. Method 1 - Triangular Grid In this method a grid is constructed on the diagram. This grid is most commonly set up representing a 10% incremental increase in the components. To determine the composition of a point within the triangular area of the diagram a series of three lines are drawn through the point of intersest, with each line parallel to a side of the triangle. With these lines in place the percentage of each component in the compostion of the point can readliy be determined.

2. Method 2 - Two Line Method In this method only two lines are drawn, through the point of interest, parallel to any two sides of the triangle. The intersection of these two lines with the third side divides this side into three line segments. The lengths of the individual line segments are proportional to the relative amounts of the three components.

The two methods outlined above assumed an equilateral triangle, however both

methods can be applied when dealing with a non-equilateral or scalene triangle in

nature.

Determining Compositions

To determine the composition of a point lying inside the triangular diagram, a series

of three lines through the point of interest, with each line parallel to a side of the

triangle are drawn, as shown on the above image.

With these lines in place the composition of each point in terms of the end member

components can be read directly from the diagram.

On the overhead:

1. Point E has a composition of 36% A, 43% B and 21% C. 2. Point 1 has a composition of 19% A, 30% B and , 51% C. 3. Point 2 has a composition of 45% A, 23% B and 32%C. 4. Point e3 has a composition of 60% A, 0% B and 40% C.

NOTE: The compositions total 100%!

HYPOTHETICAL TERNARY SYSTEMS

Hypothetical Ternary Systems - Without Solid Solution

(a) congruently melting compound BC, 2 eutectics; (b) congruently melting compound, BC, 1 eutectic, 1 peritectic; (c) incongruently melting compound BC, 1 eutectic, 1 peritectic; (d) congruently melting compound ABC, 3 eutectics; (e) incongruently melting compound ABC, 1 eutectic, 1 distributary peritectic,

1 tributary peritectic.

Hypothetical Ternary Systems - With Partial to Complete Solid Solution

(a) limited solid solution of A with B or C

(b) complete solid solution between B and C (c) congruently melting compound BC, in complete solid solution with A (d) incongruently melting compound BC in complete solid solution with A.

Systems displaying complete solid solution will not contain a ternary eutectic. (e) complete solid solution between B and C, but with a ternary minimum (M)

between the fields of A + L and BCSS + L. The BC binary system displays a binary minimum (m), as in the Ab-Or system. Instead of a eutectic in this system a thermal valley exists between M and m and represents the lowest temperature at which a liquid exists.

Ternary Phase Diagrams - General Rules

1. A congruently melting compound will lie within the primary phase field for that compound.

2. An incongruently melting compound will not lie in the field of that compound. 3. Ternary diagrams which do not exhibit solid solution effects will contain at

least one ternary eutectic, i.e. the lowest temperature at which liquid can exist.

4. In systems with no solid solution conjugation lines or Alkemade lines within such systems are thermal barriers.

5. Ternary systems which contain an incongruently melting compound will contain at least one ternary peritectic.

6. Ternary systems which exhibit complete solid solution effects will not contain a ternary eutectic within the triangular area representing the system.

7. For any ternary diagram identify all Alkemade lines. For every boundary curve there exists an Alkemade line.

8. Consider the relation between a boundary curve and its pertinent Alkemade line;

o i) The actual or projected intersections between boundary curve and its pertinent Alkemade line represents a temperature maximum of the boundary curve.

o ii) If tangents drawn from the boundary curve intersect the pertinent Alkemade line, then that part of the boundary curve is a subtraction curve.

o iii) If tangents drawn from the boundary curve intersect an extension of the pertinent Alkemade line, then that part of the boundary curve is a reaction curve.

9. After the thermal slopes, i.e. the direction of falling temperature, of the boundary curves are determined, the various ternary invariant points can be identified as either eutectic, tributary or distributary reaction points.

DEFINITIONS

Subtraction Curve - That part of the boundary curve along which crystalline material

precipitates from the liquid.

Reaction Curve - That part of the boundary curve along which crystalline materials

both precipitate and dissolve.

DIRECTIONS OF FALLING TEMPERATURE

For ternary systems where actual isotherms are not known it is still possible to

determine the dirctions that temperatures will fall by examining the relationship

between tie lines and boundary curves.

Determining the directions of falling temperature

1. Temperatures fall away from the three apices along the edges of the triangle.

2. The point of intersection of a tie line joining two compounds, that share a

boundary curve, with the boundary curve or an extension of the curve

represents a thermal maximum along the pertinent section of the boundary

curve.

These relationships can be illustrated by examing the hypothetical ABC system.

1. The primary fields A + L and B + L share a boundary curve, and the tie line or

Alkemade line joining the two solid phase is the AB side of the triangle,

therefore the temperature along the boundary curve separating the A + L field

from the B + L field must move away from the point of intersection along the

boundary curve.

2. The dashed line joining A and BC represents an Alkemade line, which crosses

the boundary curve between the A + L and BC + L fields. Therefore the point

of intersection is a temperature maximum, and temperatures fall away, in both

direction, from the point of intersection.

3. Compound BC is congruently melting, its bulk composition point lies within

the primary phase field of BC + L.

This system exhibits two ternary eutectics, the arrows along the boundary curves

converge at the eutectics.

Ternary peritectics occur in systems containing

both congruent and incongruently melting compounds.

At ternary peritectics, the following relationships of boundary curves are possible:

1. tributary - where two boundary curves come into the triple point and one goes

out, or

2. distributary - where one boundary curve comes into the triple point and two

curves go out.

ISOTHERMAL SECTIONS

One method of examining the phase relationships within a ternary system is by the

construction of isothermal sections through the diagram, parallel to the base.

An isothermal section is a representation of the stable phases for different

compostions which have been quenched to the same temperature.

The isothermal sections to be examined are derived from the liquidus diagram, where

we are looking at the phases present between the liquidus and the solidus.

The best way to view Isothermal Sections is by examining a simple ternary system.

1. Simple Ternary System

A simple ternary system with a single eutectic. The individual isotherms (in

blue) are labelled T5 through T1, such that T5 > T4 > T3 > T2 > T1. The

cotectic curves (in magenta) separate the three primary phase fields A + L, B +

L and C + L from each other.

2. Isothermal Section at T > temperature of melting of Pure B (TB)

In this section, made at a temperature above the highest temperature on the

diagram, so we are above the liquidus, there exists a single "one-phase field"

consisting entirely of melts throughout the system, regardless of the

compostion. Another way of looking at this is that no matter what the

composition of the system, it will be 100% melt.

3. T5 Isotherm

For this section, which is at a temperature that intersects the liquidus but not a

cotectic curve, the one-phase melt field has become smaller and we have the

addition of two "two-phase fields": B + Liq and C + Liq. The boundaries of the

melt field are the appropriate contour line representing the isotherm for this

section. In each of the two-phase fields, radiating tie lines (in red) are shown

connecting coexisting melt and crystal compositions. These tie lines link solid

crystals, of fixed composition, (the point from which the tie lines radiate) with

liquid of a variety of compositions, represented along the liquidus.

4. T4 Isotherm

The one-phase melt field has decreased in size, as the temperature of the

iosthermal section is lowered. At the same time the two-phase fields of B + Liq

and C + Liq have increased and been joined by the two-phase field A + Liq.

5. T3 Isotherm

The one-phase field continues to shrink while the three two-phase fields increse

in size.

6. T2 Isotherm

In this isothermal section the isotherm has intersected the cotectic curves (in

magenta) as well as the liquidus surface. In addition to the one-phase melt field,

which continues to decrease in size, and the three two-phase fields, three three-

phase fields are present. In each three-phase field a melt of fixed composition

(on the cotectic) and crystals of two solids coexist, e.g. A + B + Liq, A + C +

Liq and C + B + Liq. Note that only one melt composition can exist in a three-

phase field, whereas any number of melts (on the contour line along the

boundary of teh melt field) can exist in a two-phase field.

7. T1 Isotherm

The one-phase melt field has decreased, the two-phase fields have gotten

smaller and the three-phase fields have increased.

8. Isothermal section at T < temperature of the eutectic (TE)

For this isothermal section, which is at a temperature below the temperature of

the eutectic, i.e. below the solidus, then the entire diagram is a three-phase

field, A + B + C, with no melt remaining and the system at every compostion

will consist entirely of some combination of A, B and C.

INTRODUCTION

Ternary System #1 - An-Wo-Sp System

System 1 - Anorthite - Wollastonite - Sphene System

This is a simple ternary system, with no solid solution, exhibiting a single ternary

eutectic. Along the edges of the triangle there exists a binary eutectic in each of the

simple binary systems, e.g. Wo-An, Wo-Sp and An-Sp.

The three components which define the system are:

Anorthite - CaAl2Si2O8 Wollastonite - CaSiO3 Sphene - CaSiTiO5

On the image above note that the liquidus surface slopes down from each apex of

the triangle towards the eutectic inside the diagram. Any liquids present in the

system and which undergo crystallization will travel down the liquidus surface

towards the eutectic. On ternary systems we will be tracing out the path the liquid

follows, and as we will see it is possible to predict the path any liquid will follow

during crystallization.

Remember you are looking at a map of the liquidus surface so that the fields present

are labelled as a solid + liquid, e.g. Wo + L. The cotectic boundaries, shown in purple,

separate the individual fields from each other. The isotherms are labelled in red and

marked as dashed blue lines.

EQUILIBRIUM CRYSTALLIZATION

Composition X

Since we are examining equilibrium crystallization, the final solid must have the same

bulk compostion as the initial liquid. The bulk composition of X, in tems of the three

end member components which define the system, is 60% Wo, 20% An, 20% Sp. The

compostion of X is determined by drawing a series of lines (the red lines) through X

parallel to the sides of the triangle and the corresponding percentage of each

component can be calculated.

As these are the only phases present in this ternary system and all three coexist at the

ternary eutectic, the liquid must move to the eutectic. The final liquid will be a

mixture of An Wo and Sp, in the proportions of the eutectic.

So we know what our initial liquid composition is and we know what our final liquid

composition will be - What path will the liquid follow?

The path followed by the liquid is shown as the blue line on the image.

1. To begin, X is at some temperature well above the liquidus and as such is 100% liquid. As the temperature drops to the liquidus the system still consists of 100% liquid 0% solid.

2. Upon cooling to the liquidus, the bulk composition does not change, and reaches the liquidus at point X, which lies in the field of Wo + L. At this point Wo begins to crystallize and it is in equilibrium with liquid. Due to the crystallization of Wo, the liquid composition must change, i.e., it is becoming depleted in the Wo component and enriched in the An and Sp components. The result is that the liquid composition moves directly away from the Wo composition point.

3. As the liquid moves away from X towards Z, it is changing in the following way: o It is becoming depleted in Wo. Wo is being removed from the liquid

into solid Wo crystals, and o It is becoming enriched in An and Sp, it is moving towards the An-Sp

side of the diagram. 4. At Point Z

The two phases in equilibrium are Wo and L. Two questions to ask here are: 1. What are the proportions of Wo and L at Z? 2. What are the compostions of Wo and L at Z?

Proportions

Applying the lever rule at Z will provide the proportions of Wo and L.

o % Wo = XZ/WoZ *100 = 24% o % L = WoX/WoZ * 100 = 76%

Compositions

The composition of the two phases Wo and L at Z, must be expressed in terms

of the three end member components of the ternary diagram An, Wo and Sp.

o The solid Wo is pure Wo (100%Wo, 0% An, 0% Sp). o The liquid composition can be determined by drawing a series of three

lines through Z, with each line parallel to one side of the triangle. This gives a composition for the liquid of 47% Wo, 27% Sp and 25% An.

5. As crystallization continues from Z to P, Wo continues to crystallize and the liquid continues to move directly away from Wo.

6. At P, which lies on the cotectic between the field of Wo + L and Sp + L. Sp begins to crystallize along with the Wo, because the liquid has reached the

boundary curve between the fields of Wo + L and Sp + L. The result is that the liquid composition now moves down the boundary curve towards E as both Wo and Sp are removed from the liquid.

7. At Q Here three phases are in equilibrium, Wo + Sp + L. The proportion of solid (Wo+Sp) to liquid (L) and the composition of the solid and liquid phases can be determined. In order to calculate these values we must first draw a line from Q, the point of interested, through X, our bulk composition, back to intersect the edge of the triangle. This line on the image extends from Q through X to T. Proportions of Solid to Liquid

o % Solid (Wo+Sp) = QX/QT * 100 = 45% o % Liquid (L) = TX/QT *100 = 55%

Proportion of Wo to Sp

o % Wo = TSp/WoSp * 100 = 89% o % Sp = TWo/WoSp * 100 = 11%.

Compositions of Phases

o Solid Wo is pure Wo (100% Wo, 0% Sp, 0% An) o Solid Sp is pure Sp (0%Wo, 100% Sp, 0% An) o The liquid composition can be determined by drawing a series of lines

through Q, with each line parallel to one side of the triangle. 8. Crystallization of Wo and Sp together continues from Q to E. 9. At E, the ternary eutectic

Wo and Sp continue to crystallize and are joined by An, with all three crystallizing together, in the proportions given by the eutectic. The system stays at the temperature of the eutectic until the last droplet of liquid crystallizes into the last grains of Wo, Sp and An. The compostion of the last liquid last liquid to exist in the system is represented by E. The proportions of the solid phases in the final solid after the last liquid has crystallized is given by X (60% Wo, 20% Sp, 20% An) - OUR INITIAL BULK COMPOSITION!

In order to maintain equilibrium as the solid phases are crystallized the liquid

composition is constantly changing as represented by the path from X to P to E, the

solid blue line on the diagram.

FRACTIONAL CRYSTALLIZATION

Composition X

For fractional crystallization of composition X, the path followed by the liquid is the

same as the path followed during equilibrium crystallization.

The only difference is that the final solid mixture will consist of Wo, Sp and An in the

proportions given by the bulk composition of the last residual liquid remaining after

the removal of solid crystals prior to the liquid reaching the eutectic.

INTRODUCTION

The Forsterite - Anorthite - Silica System

This system exhibits an incongruently melting compound (En) along the binary join

Fo-Si. This system also exhibits a ternary eutectic and a ternary peritectic. Things to

note about this system are:

1. Melting and crystallization relationships in this system are ternary except along the Fo-An join where spinel appears on the liquidus.

2. The En-An join or tie line (dashed green line) divides the triangular area of the Fo-An-Si diagram into two smaller triangular areas:

o Fo-En-An triangle o En-Si-An triangle.

These two triangles (shown on the inset of the diagram) tell us something

about the final solid compositions that will be present as a result of

crystallization of a liquid and whether that liquid will move to the peritectic or

eutectic as a result of crystallization. At the peritectic and the eutectic the

three phases in equilibrium with liquid are Fo + En + An and En + Si +An,

respectively, - the same phases that make up the two small triangles.

o For equilibrium crystallization any staring composition that begins in the Fo-En-An triangle will move to the peritectic, where crystallization will cease and the last liquid will have a composition of the peritectic.

o Compositions that start in the En-Si-An triangle will move to the eutectic, where crystallization will cease and the last liquid will have a composition of the eutectic.

3. Also in the system the boundary curve separating the fields of Fo + L from En + L is a reaction curve, labelled with a double arrow, and involves a reaction relationship during crystallization:

En ===> Fo + L

This is the same reaction we studied when examining the binary Fo - Qtz

system.

EQUILIBRIUM CRYSTALLIZATION 1

Composition X

Point X

The bulk composition of X can be determined by drawing three lines (the magenta

lines) through X, parallel to each side of the large triangle Fo-An-Si. Using this

method we get a compostions of 70% Fo, 18% Si and 12% An. For equilbrium

crystallization the final product must have the same bulk composition as the initial

starting composition.

Point X also lies in the small triangle Fo-En-An, therefore the final solid must be a

mixture of the three phase that define this small triangle. The proportions of these

three phases, present at X, can be determined again by drawing three lines (the dashed

black lines) through X, but parallel to the sides of the Fo-An-En triangle. The final

solid will be a mixture of 28% Fo, 60% En and 12% An. These three phase in the

final solid coexist at P, the peritectic, so the last liquid will have a composition

equivalent to that of the peritectic.

The path followed by the liquid is shown in red, with the sequence of events as

follows:

1. Cool the liquid down until it reaches the liquidus. 2. At the liquidus Fo begins to crystallize and the Fo is in equilibrium with liquid.

The liquid composition moves directly away from Fo, as it is being depleted in Fo.

3. From X to Y, Fo continues to crystallize and the liquid moves along the path, represented by the red line, constantly changing composition.

4. At Y, which lies on the boundary curve between the fields of En + L and Fo +L. This cotectic curve is a reaction curve denoted by the double arrow. The reaction taking place is

Fo====> En + L

At Y Fo is resorbed, melted back into the liquid and En begins to crystallize

with both phases in equilibrium with liquid, represented by Y.

5. From Y to Point Q Fo continues to be resorbed, En crystallizes and both of these are in equilibrium with the liquid, the composition of which is moving down the boundary curve from Y to Q.

6. At Q Point Q lies along the cotectic curve separating the En + L field from the Fo + L field. At Q we can determine:

1. The proportion of solid Fo + En to L. To do this we must draw a tie line from Q through X, back to the En-Fo join (Point A).

% Solid (Fo+En) = XQ/AQ * 100 = 64% We can also determine the ratio or Fo:En at Q

% Fo = AEn/FoEn * 100 = 52% % En = FoA/FoEn *100 = 48%

% L = AX/AQ * 100 = 36% 2. The proportion of F being melted and En crystallizing.

To do this we must draw a line which is tangential to the cotectic curve from Q back to intersect the the extension of the Fo-En tie line - Line segment QC.

Ratio of Fo being resorbed: En crystallizing = EnC/FoC = 1:1.65. From this ratio it can be seen that much more En is forming than Fo being resorbed.

3. The composition of all phases present. Fo is Pure Fo (100% Fo, 0% Si, 0% An) En is pure En (68% Fo, 32% Si, 0% An) Liquid composition is represented by point Q - draw three lines

through Q parallel to the outside edges of the large triangle and get a compostion in terms of the three end member components Fo, Si and An. I haven't done it, you know how to, give it a try!

7. From Q to the peritectic (P). Fo resorbtion continues as does En crystallization. 8. At the peritectic Fo continues to be resorbed, En continues to crystallize and

An begins to crystallize. The liquid stays at the point represented by the peritectic until all the liquid has been used up, leaving a solid mixture of Fo + En + An, in the proportions 26:60:12 - the proportions we calculated above using the small Fo-En-An triangle.

9. EQUILIBRIUM CRYSTALLIZATION 2 10. 11. EQUILIBRIUM CRYSTALLIZATION OF Z

12. Composition Z lies on the En-An join, therefore the final solid must be a

mixture of En and An in the proportions En:An = 70:30 - NO Fo or Si in the

final solid.

For equilibrium crystallization of Z, the final liquid is situated at P and it

behaves like composition X previously looked at.

At P, Fo is being resorbed and En and An are crystallizing from a liquid with a

composition of the peritectic.

This resorbtion and crystallization contiunes until the last grain of Fo is

resorbed into the last droplet of liquid which crystallizes into the last grains of

En and An.

13. 14. EQUILIBRIUM CRYSTALLIZATION OF A

15. Composition A lies in the En-Si-An triangle, so it's last liquid must lie at E, the

eutectic, where En + Si +an are in equilibrium.

As this composition is initially in the Fo + L field, once it reaches the liquidus,

it will begin to crystallize Fo and move directly away from Fo towards the En-

Fo boundary curve. At the boundary curve the Fo will be resorbed and the En

will crystallize, with the liquid composition moving down the boundary curve

towards P.

The proportion of Fo to be resorbed is very small, so at some point along the

boundary curve all the Fo will be removed. This point can be located by

drawing a line through A from En to intersect the boundary curve ( Point R). At

this point all the Fo is resorbed, but En continues to crystallize, so the liquid

now moves off the boundary curve, directly away from En into the En + L

field.

Crystallization of En continues until the boundary curve between the fields of

En + L and An + L is reached (Point S), where An begins to crystallize along

with the En. The liquid moves down the boundary curve from S to E.

At E En and An continue to crystallize and are joined by Si. The liquid

composition stays at E until all the liquid is used up and the final solid that

results is a mixture of En-An-Si.

16. 17. EQUILIBRIUM CRYSTALLIZATION OF W

18. Composition W lies in the En + L field, so at the liquidus temperature En

crystallizes and the liquid moves directly away from En to the boundary curve

between En + L and Si +L (Point V), where Si joins En in crystallizing.

The liquid moves down the boundary curve from V to E, where An joins En

and Si in crystallizing. At E all three solids phases crystallize until all the liquid

is used up. The location of Composition W in the small triangle En-An-Si tells

us that the final solid must be a mixture of these three phases.

It should be noted that on the phase diagram that nowhere do Fo and Si coexist

together.

FRACTIONAL CRYSTALLIZATION

Batch Fractionation

The paths followed for liquids which undergo batch fractional crystallization will be

dependant on where the individual batches of crystals are removed from the system

and the composition of the residual liquid after removal.

For Composition X if fractionation occurs between X and Z, the removal of the Fo

crystals will yield a dunite, leaving a residual liquid of composition Z. If this is the

only place where fractionation occurs then the last liquid will end up at P, leaving a

solid mixture of En and An.

If crystallization continues from Z to Q, Fo and En will be removed producing a

peridotite, which is either olivine-rich or enstatite-rich, depending on which phase is

dominant.

By fractionating at Q, the liquid now moves off the boundary curve directly away

from En, towards A.

From Q to A, En crystallizes and the liquid composition moves away from Q. At A,

En and An crystallize together and the liquid moves down the boundary curve towards

E, where Si joins En and An, giving a solid which has enstatite anorthite and quartz -

a quartz norite.

The bulk composition of the final solid is given by point Q, the position where the last

batch of crystals were removed.

Pure Fractionation

The paths followed for liquids which undergo pure fractional crystallization will all

end at the eutectic, regardless of the initial liquid composition.

For Composition X the final liquid remaining after pure fractional crystallization will

have the composition of the eutectic. The final solid will be a mixture of Si + En +

An, in the proportions given by E in the En-Si-An triangle.

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

Start with an initial liquid represented by Point A.

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

o Di represents the composition of diopside o Y represents the composition of the plagioclase in equilibrium with

liquid X and solid Di; o 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.

EQUILIBRIUM CRYSTALLIZATION 1

Composition A

For an initial liquid of composition A the final solid after Equilibrium crystallization

must be a mixture of Di and plagioclase of composition B (PlB), in the proportions

determined above.

The path followed by the liquid is shown in blue, with the sequence of events as

follows:

1. Above the liquidus surface we have 100% liquid. 2. Cool this liquid to the liquidus 3. At the liquidus, Di begins to crystallize and is in equilibrium with liquid. The

liquid composition moves directly away from Di towards the boundary curve. 4. From A to C, Di contiunes to crystallize and the liquid moves along the path,

constantly changing composition to remain in equilibrium with the Di forming. 5. At Point C, on the boundary curve

Pl begins to crystallize along with the Di and these two solid phases are in equilibrium with Liquid.

1. The composition of the Di is fixed.

2. The composition of the Pl, represented by Point D, will have an An content greater than B (the final Pl composition in equilibrium with Di). The actual plagioclase composition, i.e. the position of Point D between Ab and An, forming here must be determined experimentally. However, intuitively, we know from our examination of the Ab-An binary system that at equilibrium, the liquid is always more Ab-rich than the coexisting Pl, so the plagioclase must lie on the An side of the final Pl composition.

3. The composition of the Liquid is represented by Point C.

Note that the three points above, Di, C and D, form a triangle (the purple

lines). The bulk composition A, lies on or very close to the Di-C join, which lies

directly opposite D (the Plagioclase apex), giving <<< 1% Pl in the proportions

of the three phases which coexist for composition A at Point C.

6. As cooling continues, the liquid composition moves down the boundary curve from C to E.

7. At E, in equilibrium we have Di, Pl, represented by point F, and Liquid represented by point E. These three phases are linked by the green tie lines. Note that the position of the green triangle has shifted from that of the purple triangle by rotating about the Di apex, common to both, resulting in the shifting of both the liquid composition, from C to E, and the plagioclase composition, from D to F, to more Ab-rich/An-poor compositions.

8. As cooling continues, the liquid composition moves down the boundary curve from E to G.

9. At G, in equilibrium we have Di, Pl, represented by point H, and Liquid represented by point G. These three phases are linked by the red tie lines. Note that the position of the red triangle has shifted from that of the purple and green triangles, again by rotating about the Di apex, common to all three, resulting in the shifting of both the liquid composition, from E to G, and the plagioclase composition, from F to H, to more Ab-rich/An-poor compositions.

10. When the plagioclase has reached it's final composition (Point B), the last liquid is consumed. The composition of the last liquid given by I, expressed in terms of the three end member components Di, Ab and An, on the boundary curve. The cyan tie

lines join the Di, the last Liquid composition - I, and the final plagioclase composition - B. Examining the cyan triangle shows that the initial bulk composition point A now lies along the Di-PlB edge of the triangle, representing <<< 1% liquid, telling us that crystallization has ceased. The final solid mixture present consists of % Di and % plagioclase of composition B.

The important things to remember about equilibrium crystallization in this system are:

1. Equilibrium between the plagioclase and the liquid must be maintained as: 1. The liquid migrates down the boundary curve it continuously reacts

with the previously formed plagioclase, causing the liquid to become more sodic, i.e. more Ab-rich;

2. While at the same time the liquid continues to precipitate plagioclase with a higher soda content, i.e. more Ab-rich.

2. Tie lines which join liquid compositions along the boundary curve with plagioclase compositions along the Ab-An join must be determined experimentally.

EQUILIBRIUM CRYSTALLIZATION 2

Composition X

For an intitial liquid of composition X, the final solid after equilibrium must be a

mixture of plagioclase of composition N and Di, in the proportions given by applying

the lever rule to the line DiN.

The path followed by the liquid is shown in blue, with the sequence of events as

follows:

1. Above the liquidus surface we have 100% liquid. 2. Cool this liquid to the the liquidus. 3. On cooling to the liquidus, the liquid first crystallizes an An-rich plagioclase,

represented by Point T. The actual composition of the plagioclase forming

from the liquid can not be worked out by examining the diagram, it must be determined experimentally.

4. As cooling continues the liquid moves down the liquidus surface from X to S, precipitating a more Ab-rich plagioclase, while the previously formed An-rich plagioclase becomes more sodic by reacting with the liquid. This double reaction between the liquid and solid causes the liquid to migrate in a curved path to the boundary curve at S. The actual liquid path must be determined experimentally.

5. At S, on the boundary curve. Di begins to crystallize and is in equilibrium with Pl represented by Point R and a liquid of composition S. To maintain equilibrium the liquid and the plagioclase compositions are constantly changing, such that each successive liquid is more Ab-rich and each new plagioclase grain is more Ab-rich than the previous one.

6. From S to Q to O the liquid composition moves down the boundary curve. Each new liquid is in equilibrium with a new plagioclase of composition R, P and N respectively, linked by appropriate coloured tie lines. The last drop of liquid is used up at O, yielding a solid mixture of Di and Pl of composition N, in the proportions given by X.

FRACTIONAL CRYSTALLIZATION

Fractional Crystallization

For fractional crystallization, early formed plagioclase does not react with the liquid.

The result is that the liquid will migrate to a lower point on the boundary curve than

for the same bulk composition which has undergone equilibrium crystallization.

Examination of plagioclase in igneous rocks indicates that such a process of

incomplete reaction is common, as observed in the presence of zoned plagioclase

grains which exhibit normal, reverse and oscillatory zoning.

For pure fractional crystallization the last liquid would have a composition

represented by the binary eutectic composition on the Di-Ab join and would produce a

solid mixture of Di and Ab in the proportions given by this binary eutectic.