A step-by-step tutorial

Ternary Crystallization

Click to continue

TiO2

ZrTiO4

Al2O3Al2TiO5

ZrO2

1580°

1590°1610°

Most of this tutorial is automated, but at several points, a click is required to move on. Anytime this is the case, a

“Click to continue” message will appear in the lower left corner.

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

Click to continue

Crystallizationmade up of six simple steps

Keep in mind that a crystallization path simply traces the makeup of

the liquid present as a given composition cools

Click to continue

TiO2

ZrTiO4

ZrO2

Al2O3

Al2TiO5

Constructing the Diagram

Identify primary phase fields

Draw Alkemades lines

Identify direction of falling temperature on boundary lines.

TiO2

ZrTiO4

Al2O3Al2TiO5

ZrO2

1580°

1590°1610°

Now the diagram is ready fora crystallization path . . .

Process

Click to continue

TiO2

ZrTiO4

Al2O3Al2TiO5

ZrO2

1580°

1590°1610°

AlAl22TiOTiO55

TiO2

ZrTiO4

ZrO2

Al2O3

Al2TiO5

ProcessLocate the composition you will be crystallizing

Starting and Ending Points

for example . . .

Locate the end point associated with the compositiontriangle you are in . . .

ZrOZrO22

ZrTiOZrTiO44

Now you know where you areand where you’re going,

but how do you get there?

Click to continue

TiO2

ZrTiO4

Al2O3Al2TiO5

ZrO2

1580°

1590°1610°

TiO2

ZrTiO4

ZrO2

Al2O3

Al2TiO5

ProcessIdentify the phase field where the composition lies

Primary Phase Field

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

The crystallization path continues directly away from ZrO2, as it is the only thing crystallizing out until the path reaches a boundary line

Then what??

ZrOZrO22

For more on the relationship between liquid composition and crystallization path, click here:

Click to continue

TiO2

ZrTiO4

Al2O3Al2TiO5

ZrO2

1580°

1590°1610°

TiO2

ZrTiO4

ZrO2

Al2O3

Al2TiO5

ProcessWhen the crystallization path reaches the boundary

line, a second solid beings to crystallize

Boundaries

Upon reaching the boundary line, the crystallization path turns and follows the boundary line down (according to the arrows) to the end point

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

But what happens at the endpoint?

Click to continue

TiO2

ZrTiO4

Al2O3Al2TiO5

ZrO2

1580°

1590°1610°

Click to continue

TiO2

ZrTiO4

ZrO2

Al2O3

Al2TiO5

ProcessAt the endpoint, all remaining liquid crystallizes

(that’s what makes it the endpoint)

Final Crystallization

JUST BEFORE FINAL CRYSTALLIZATION:The percentages of liquid and solid present can be determined using the lever rule back through

the original point

Liquid

Solid

ZrO2

ZrTiO4

The relative amounts of the species of crystals can also be determined using the

lever rule along the side of the composition triangle

TiO2

ZrTiO4

Al2O3Al2TiO5

ZrO2

1580°

1590°1610°

Click to continue

TiO2

ZrTiO4

ZrO2

Al2O3

Al2TiO5

ProcessAt the endpoint, all remaining liquid crystallizes

(that’s what makes it the endpoint)

Final Crystallization

And after final crystallization?

The composition of the liquid can be found using the method of parallel lines

over the entire diagram

ZrO2

Al2O3

TiO2

JUST BEFORE FINAL CRYSTALLIZATION:The percentages of liquid and solid present can

be determined using the lever rule.

TiO2

ZrTiO4

Al2O3Al2TiO5

ZrO2

1580°

1590°1610°

TiO2

ZrTiO4

ZrO2

Al2O3

Al2TiO5

ProcessAt the endpoint, all remaining liquid crystallizes

(that’s what makes it the endpoint)

Final Crystallization

What else can a crystallization path tell

you?

ZrO2

Al2TiO5

ZrTiO4

JUST AFTER FINAL CRYSTALLIZATION:Remember that this is an isoplethal analysis;

the overall composition has not changed.

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.

Click to continue

TiO2

ZrTiO4

Al2O3Al2TiO5

ZrO2

1580°

1590°1610°

Click to continue

TiO2

ZrTiO4

ZrO2

Al2O3

Al2TiO5

ProcessNot 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

Instantaneous Crystallization

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

For example . . .

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

Now the tangent . . .

Think of Calculus - to find an instantaneous change we find a derivative, which is also a tangent line

TiO2

ZrTiO4

Al2O3Al2TiO5

ZrO2

1580°

1590°1610°

Click to continue

TiO2

ZrTiO4

ZrO2

Al2O3

Al2TiO5

Process

Think of Calculus - to find an instantaneous change we find a derivative, which is also a tangent line

ZrO2

ZrTiO4

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

Instantaneous Crystallization

To find the instantaneous crystallization along a boundary line, we follow the

same procedure

Draw the tangent line to the crystallization path . . .

Use the lever rule on the side of the composition triangle . . .

TANGENT LINES

The lever rule shows us that ZrO2 is being resorbed

For more on resorption:

Click to continue

Example Overall Composition

Instantaneous Crystallization Composition

TiO2

ZrTiO4

Al2O3Al2TiO5

ZrO2

1580°

1590°1610°

TiO2

ZrTiO4

ZrO2

Al2O3

Al2TiO5

Now that we know how this works, let’s watch what happens as we travel down the crystallization path . . .

0%

20%

40%

60%

80%

100%

ZrO2 ZrTiO4 Al2TiO5Liquid

0%

20%

40%

60%

80%

100%

ZrO2 ZrTiO4 Al2TiO5

Click to continue

Example Overall Composition

Instantaneous Crystallization Composition

TiO2

ZrTiO4

Al2O3Al2TiO5

ZrO2

1580°

1590°1610°

TiO2

ZrTiO4

ZrO2

Al2O3

Al2TiO5

Initially, only ZrO2 crystallizes out, so the remaining liquid becomes more and more rich in the other two components

0%

20%

40%

60%

80%

100%

ZrO2 ZrTiO4 Al2TiO5Liquid

0%

20%

40%

60%

80%

100%

ZrO2 ZrTiO4 Al2TiO5

Click to continue

Example Overall Composition

Instantaneous Crystallization Composition

TiO2

ZrTiO4

Al2O3Al2TiO5

ZrO2

1580°

1590°1610°

TiO2

ZrTiO4

ZrO2

Al2O3

Al2TiO5

0%

20%

40%

60%

80%

100%

0%

20%

40%

60%

80%

100%

ZrO2 ZrTiO4 Al2TiO5Liquid

ZrO2 ZrTiO4 Al2TiO5

Still within the ZrO2 primary phase field, so it is the only solid

Click to continue

Example Overall Composition

Instantaneous Crystallization Composition

TiO2

ZrTiO4

Al2O3Al2TiO5

ZrO2

1580°

1590°1610°

TiO2

ZrTiO4

ZrO2

Al2O3

Al2TiO5

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

0%

20%

40%

60%

80%

100%

-20%0%

20%40%60%80%

100%120%

ZrO2 ZrTiO4 Al2TiO5Liquid

ZrO2 ZrTiO4 Al2TiO5

Click to continue

Example Overall Composition

Instantaneous Crystallization Composition

TiO2

ZrTiO4

Al2O3Al2TiO5

ZrO2

1580°

1590°1610°

TiO2

ZrTiO4

ZrO2

Al2O3

Al2TiO5

Travelling down the boundary, less ZrO2 is being resorbed, and ZrTiO4 continues to crystallize

0%

20%

40%

60%

80%

100%

-20%0%

20%40%60%80%

100%120%

ZrO2 ZrTiO4 Al2TiO5Liquid

ZrO2 ZrTiO4 Al2TiO5

Click to continue

Example Overall Composition

Instantaneous Crystallization Composition

TiO2

ZrTiO4

Al2O3Al2TiO5

ZrO2

1580°

1590°1610°

TiO2

ZrTiO4

ZrO2

Al2O3

Al2TiO5

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 0%

20%

40%

60%

80%

100%

-20%0%

20%40%60%80%

100%120%

ZrO2 ZrTiO4 Al2TiO5Liquid

ZrO2 ZrTiO4 Al2TiO5

Click to continue

Example Overall Composition

Instantaneous Crystallization Composition

TiO2

ZrTiO4

Al2O3Al2TiO5

ZrO2

1580°

1590°1610°

TiO2

ZrTiO4

ZrO2

Al2O3

Al2TiO5

0%

20%

40%

60%

80%

100%

0%

20%

40%

60%

80%

100%

ZrO2 ZrTiO4 Al2TiO5Liquid

ZrO2 ZrTiO4 Al2TiO5

Just before final crystallization, there is still a significant amount of liquid, and the amount of ZrTiO4 is equal to the amount of ZrO2

Also, the tangent to the crystallization path falls directly on ZrTiO4, so there is no more resorption

Click to continue

Example Overall Composition

Instantaneous Crystallization Composition

TiO2

ZrTiO4

Al2O3Al2TiO5

ZrO2

1580°

1590°1610°

TiO2

ZrTiO4

ZrO2

Al2O3

Al2TiO5

Just after final crystallization, all of the liquid has turned into solid and the crystallization path is complete

0%

20%

40%

60%

80%

100%

0%

20%

40%

60%

80%

100%

ZrO2 ZrTiO4 Al2TiO5Liquid

ZrO2 ZrTiO4 Al2TiO5

Notice that a large amount of ZrO2 and

AlTiO5 crystallize immediately below the eutectic temperature

Click to repeat

Finished That’s all there is to ternary crystallization - hope this helped

Click for menu MENU

TiO2

ZrTiO4

Al2O3Al2TiO5

ZrO2

1580°

1590°1610°

TiO2

ZrTiO4

ZrO2

Al2O3

Al2TiO5