A stepbystep tutorial

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Ternary Crystallization
A step-by-step tutorial
Most of this tutorial is automated, but at
several points, a click is required to move on.
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message will appear in the lower left corner.
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Crystallization made up of six simple steps

• Constructing the Diagram
• Starting and Ending Points
• Primary Phase Field
• Boundaries
• Final Crystallization at the Endpoint
• Instantaneous Crystallization at any Point on the
  Path

Keep in mind that a crystallization path simply
traces the makeup of the liquid present as a
given composition cools
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Constructing the Diagram
Identify primary phase fields
Draw Alkemades lines
Identify direction of falling temperature on
boundary lines.
ZrO2
ZrTiO4
Now the diagram is ready for a crystallization
path . . .
Al2O3
TiO2
Al2TiO5
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Starting and Ending Points
Locate the composition you will be crystallizing
ZrO2
for example . . .
Locate the end point associated with the
composition triangle you are in . . .
ZrTiO4
ZrO2
ZrTiO4
Now you know where you are and where youre
going, but how do you get there?
Al2O3
TiO2
Al2TiO5
Al2TiO5
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Primary Phase Field
Identify the phase field where the composition
lies
ZrO2
The first thing to crystallize out is the
compound associated with the primary phase field
ZrO2 is the only thing crystallizing out, so the
amount of ZrO2 in the liquid is decreasing while
the amounts of the other components in the liquid
remain the same - the path starts directly away
from pure ZrO2
ZrO2
The crystallization path continues directly away
from ZrO2, as it is the only thing crystallizing
out until the path reaches a boundary line
ZrTiO4
Al2O3
TiO2
Then what??
Al2TiO5
For more on the relationship between liquid
composition and crystallization path, click here
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Boundaries
When the crystallization path reaches the
boundary line, a second solid beings to
crystallize
Upon reaching the boundary line, the
crystallization path turns and follows the
boundary line down (according to the arrows) to
the end point
ZrO2
As the path continues down the boundary line, two
solids crystallize out - the compounds associated
with the phase fields on either side of the
boundary
ZrTiO4
Al2O3
TiO2
Al2TiO5
But what happens at the endpoint?
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Final Crystallization
At the endpoint, all remaining liquid
crystallizes (thats what makes it the endpoint)
ZrTiO4
Liquid
JUST BEFORE FINAL CRYSTALLIZATION The
percentages of liquid and solid present can be
determined using the lever rule back through the
original point
ZrO2
ZrO2
The relative amounts of the species of crystals
can also be determined using the lever rule along
the side of the composition triangle
Solid
ZrTiO4
Al2O3
TiO2
Al2TiO5
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Final Crystallization
At the endpoint, all remaining liquid
crystallizes (thats what makes it the endpoint)
TiO2
JUST BEFORE FINAL CRYSTALLIZATION The
percentages of liquid and solid present can be
determined using the lever rule.
Al2O3
ZrO2
The composition of the liquid can be found using
the method of parallel lines over the entire
diagram
ZrO2
ZrTiO4
Al2O3
TiO2
Al2TiO5
And after final crystallization?
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Final Crystallization
At the endpoint, all remaining liquid
crystallizes (thats what makes it the endpoint)
ZrTiO4
Al2TiO5
ZrO2
JUST AFTER FINAL CRYSTALLIZATION Remember that
this is an isoplethal analysis the overall
composition has not changed.
ZrO2
Once the final endpoint has been reached, only
solids exist. The identity and relative amounts
of these solids can be found by using the method
of parallel lines at the starting point, within
the composition triangle.
ZrTiO4
Al2O3
TiO2
Al2TiO5
What else can a crystallization path tell you?
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Instantaneous Crystallization
Not only can you find the overall composition of
each phase present along a crystallization path,
but you can also determine the percents of solids
crystallizing at any instant in time along the
path
TANGENT LINES
To find how much of which solids are in the
process of crystallizing out at any instant,
draw a tangent line to the crystallization path
at that point
ZrO2
For example . . .
Now the tangent . . .
ZrTiO4
Within the primary phase field, there is only one
solid crystallizing, so we already knew that 100
of the solid crystallizing at that point is ZrO2
Al2O3
TiO2
Al2TiO5
Think of Calculus - to find an instantaneous
change we find a derivative, which is also a
tangent line
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Instantaneous Crystallization
Not only can you find the overall composition of
each phase present along a crystallization path,
but you can also determine the percents of solids
crystallizing at any instant in time along the
path
ZrTiO4
ZrO2
TANGENT LINES
To find the instantaneous crystallization along a
boundary line, we follow the same procedure
ZrO2
Draw the tangent line to the crystallization path
. . .
ZrTiO4
Use the lever rule on the side of the composition
triangle . . .
The lever rule shows us that ZrO2 is being
resorbed
Al2O3
TiO2
Al2TiO5
For more on resorption
Think of Calculus - to find an instantaneous
change we find a derivative, which is also a
tangent line
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Now that we know how this works, lets watch what
happens as we travel down the crystallization
path . . .
Overall Composition
ZrO2
Instantaneous Crystallization Composition
ZrTiO4
Al2O3
TiO2
Al2TiO5
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Initially, only ZrO2 crystallizes out, so the
remaining liquid becomes more and more rich in
the other two components
Overall Composition
ZrO2
Instantaneous Crystallization Composition
ZrTiO4
Al2O3
TiO2
Al2TiO5
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Overall Composition
Still within the ZrO2 primary phase field, so it
is the only solid
ZrO2
ZrO2
ZrTiO4
Al2TiO5
Liquid
Instantaneous Crystallization Composition
ZrTiO4
Al2O3
TiO2
Al2TiO5
ZrO2
ZrTiO4
Al2TiO5
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At the boundary, ZrTiO4 begins to crystallize.
The tangent line to the crystallization path
shows that ZrO2 is being resorbed, so it shows up
as negative crystallization
Overall Composition
ZrO2
ZrO2
ZrTiO4
Al2TiO5
Liquid
Instantaneous Crystallization Composition
ZrTiO4
Al2O3
TiO2
Al2TiO5
ZrO2
ZrTiO4
Al2TiO5
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Overall Composition
Travelling down the boundary, less ZrO2 is being
resorbed, and ZrTiO4 continues to crystallize
ZrO2
ZrO2
ZrTiO4
Al2TiO5
Liquid
Instantaneous Crystallization Composition
ZrTiO4
Al2O3
TiO2
Al2TiO5
ZrO2
ZrTiO4
Al2TiO5
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A small amount of ZrO2 is still being resorbed.
The amount of ZrTiO4 is increasing faster than
the amount of ZrO2, but the overall amount is
still less because ZrO2 had such a
head start
Overall Composition
ZrO2
ZrO2
ZrTiO4
Al2TiO5
Liquid
Instantaneous Crystallization Composition
ZrTiO4
Al2O3
TiO2
Al2TiO5
ZrO2
ZrTiO4
Al2TiO5
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Just before final crystallization, there is still
a significant amount of liquid, and the amount of
ZrTiO4 is equal to the amount of ZrO2
Overall Composition
Also, the tangent to the crystallization path
falls directly on ZrTiO4, so there is no more
resorption
ZrO2
ZrO2
ZrTiO4
Al2TiO5
Liquid
Instantaneous Crystallization Composition
ZrTiO4
Al2O3
TiO2
Al2TiO5
ZrO2
ZrTiO4
Al2TiO5
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Just after final crystallization, all of the
liquid has turned into solid and the
crystallization path is complete
Overall Composition
Notice that a large amount of ZrO2 and AlTiO5
crystallize immediately below the eutectic
temperature
ZrO2
ZrO2
ZrTiO4
Al2TiO5
Liquid
Instantaneous Crystallization Composition
ZrTiO4
Al2O3
TiO2
Al2TiO5
ZrO2
ZrTiO4
Al2TiO5
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Finished
Thats all there is to ternary crystallization -
hope this helped
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