Ternary Crystallization ZrTiO4 Al2O3 Al2TiO5 ZrO2 1580° 1590° 1610° A step-by-step tutorial 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. Click to continue

made up of six simple steps 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 Click to continue Click to continue

Now the diagram is ready for a crystallization path . . . Process Constructing the Diagram TiO2 ZrTiO4 Al2O3 Al2TiO5 ZrO2 1580° 1590° 1610° 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 Click to continue

Starting and Ending Points Now you know where you are Process Starting and Ending Points Locate the composition you will be crystallizing ZrO2 TiO2 ZrTiO4 Al2O3 Al2TiO5 ZrO2 1580° 1590° 1610° 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 you’re going, but how do you get there? Al2O3 TiO2 Al2TiO5 Al2TiO5 Click to continue

Identify the phase field where the composition lies Process Primary Phase Field Identify the phase field where the composition lies ZrO2 TiO2 ZrTiO4 Al2O3 Al2TiO5 ZrO2 1580° 1590° 1610° 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 Al2TiO5 Then what?? For more on the relationship between liquid composition and crystallization path, click here: Click to continue

But what happens at the endpoint? Process Boundaries When the crystallization path reaches the boundary line, a second solid beings to crystallize TiO2 ZrTiO4 Al2O3 Al2TiO5 ZrO2 1580° 1590° 1610° 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? Click to continue

Final Crystallization Process Final Crystallization At the endpoint, all remaining liquid crystallizes (that’s what makes it the endpoint) TiO2 ZrTiO4 Al2O3 Al2TiO5 ZrO2 1580° 1590° 1610° 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 Click to continue

Final Crystallization And after final crystallization? Process Final Crystallization At the endpoint, all remaining liquid crystallizes (that’s what makes it the endpoint) TiO2 ZrTiO4 Al2O3 Al2TiO5 ZrO2 1580° 1590° 1610° TiO2 JUST BEFORE FINAL CRYSTALLIZATION: The percentages of liquid and solid present can be determined using the lever rule. Al2O3 ZrO2 ZrO2 The composition of the liquid can be found using the method of parallel lines over the entire diagram ZrTiO4 Al2O3 TiO2 Al2TiO5 And after final crystallization? Click to continue

Final Crystallization What else can a crystallization path tell you? Process Final Crystallization At the endpoint, all remaining liquid crystallizes (that’s what makes it the endpoint) ZrTiO4 TiO2 ZrTiO4 Al2O3 Al2TiO5 ZrO2 1580° 1590° 1610° 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? Click to continue

Instantaneous Crystallization Process 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 TiO2 ZrTiO4 Al2O3 Al2TiO5 ZrO2 1580° 1590° 1610° 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 Click to continue

Instantaneous Crystallization For more on resorption: Process 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 TiO2 ZrTiO4 Al2O3 Al2TiO5 ZrO2 1580° 1590° 1610° 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 Click to continue

Instantaneous Crystallization Composition Example Now that we know how this works, let’s watch what happens as we travel down the crystallization path . . . Overall Composition ZrO2 ZrTiO4 Al2TiO5 Liquid TiO2 ZrTiO4 Al2O3 Al2TiO5 ZrO2 1580° 1590° 1610° ZrO2 Instantaneous Crystallization Composition ZrO2 ZrTiO4 Al2TiO5 ZrTiO4 Al2O3 TiO2 Al2TiO5 Click to continue

Instantaneous Crystallization Composition Example Initially, only ZrO2 crystallizes out, so the remaining liquid becomes more and more rich in the other two components Overall Composition ZrO2 ZrTiO4 Al2TiO5 Liquid TiO2 ZrTiO4 Al2O3 Al2TiO5 ZrO2 1580° 1590° 1610° ZrO2 Instantaneous Crystallization Composition ZrO2 ZrTiO4 Al2TiO5 ZrTiO4 Al2O3 TiO2 Al2TiO5 Click to continue

Instantaneous Crystallization Composition Example Overall Composition Still within the ZrO2 primary phase field, so it is the only solid TiO2 ZrTiO4 Al2O3 Al2TiO5 ZrO2 1580° 1590° 1610° ZrO2 Liquid ZrO2 ZrTiO4 Al2TiO5 Instantaneous Crystallization Composition ZrTiO4 Al2O3 TiO2 Al2TiO5 ZrO2 ZrTiO4 Al2TiO5 Click to continue

Instantaneous Crystallization Composition 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 Example Overall Composition TiO2 ZrTiO4 Al2O3 Al2TiO5 ZrO2 1580° 1590° 1610° ZrO2 Liquid ZrO2 ZrTiO4 Al2TiO5 Instantaneous Crystallization Composition ZrTiO4 Al2O3 TiO2 Al2TiO5 ZrO2 ZrTiO4 Al2TiO5 Click to continue

Instantaneous Crystallization Composition Example Travelling down the boundary, less ZrO2 is being resorbed, and ZrTiO4 continues to crystallize Overall Composition TiO2 ZrTiO4 Al2O3 Al2TiO5 ZrO2 1580° 1590° 1610° ZrO2 Liquid ZrO2 ZrTiO4 Al2TiO5 Instantaneous Crystallization Composition ZrTiO4 Al2O3 TiO2 Al2TiO5 ZrO2 ZrTiO4 Al2TiO5 Click to continue

Instantaneous Crystallization Composition Example 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 TiO2 ZrTiO4 Al2O3 Al2TiO5 ZrO2 1580° 1590° 1610° ZrO2 Liquid ZrO2 ZrTiO4 Al2TiO5 Instantaneous Crystallization Composition ZrTiO4 Al2O3 TiO2 Al2TiO5 ZrO2 ZrTiO4 Al2TiO5 Click to continue

Instantaneous Crystallization Composition Just before final crystallization, there is still a significant amount of liquid, and the amount of ZrTiO4 is equal to the amount of ZrO2 Example Overall Composition TiO2 ZrTiO4 Al2O3 Al2TiO5 ZrO2 1580° 1590° 1610° Also, the tangent to the crystallization path falls directly on ZrTiO4, so there is no more resorption ZrO2 Liquid ZrO2 ZrTiO4 Al2TiO5 Instantaneous Crystallization Composition ZrTiO4 Al2O3 TiO2 Al2TiO5 ZrO2 ZrTiO4 Al2TiO5 Click to continue

Instantaneous Crystallization Composition Example 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 TiO2 ZrTiO4 Al2O3 Al2TiO5 ZrO2 1580° 1590° 1610° ZrO2 Liquid ZrO2 ZrTiO4 Al2TiO5 Instantaneous Crystallization Composition ZrTiO4 Al2O3 TiO2 Al2TiO5 ZrO2 ZrTiO4 Al2TiO5 Click to continue

Finished That’s all there is to ternary crystallization - hope this helped TiO2 ZrTiO4 Al2O3 Al2TiO5 ZrO2 1580° 1590° 1610° MENU Click to repeat Click for menu