Isothermal SectionsIsothermal Sections

Isothermal sections in ternary phase diagrams are Isothermal sections in ternary phase diagrams are horizontal slices through the three dimensional diagram. horizontal slices through the three dimensional diagram. All points on the section are at the same temperature, All points on the section are at the same temperature, unlike the normal view of the ternary diagram where the unlike the normal view of the ternary diagram where the liquidus surface is seen.liquidus surface is seen.

Drawing isothermal sections in ternary phase diagrams, Drawing isothermal sections in ternary phase diagrams, with no solid solutions, is a relatively simple procedure if with no solid solutions, is a relatively simple procedure if it is gone about in a very systematic manner. The next it is gone about in a very systematic manner. The next few slides will demonstrate this step by step process.few slides will demonstrate this step by step process.

The diagram used in this tutorial is Fig. 630 in The diagram used in this tutorial is Fig. 630 in Phase Phase Diagrams for Ceramists: Volume 1Diagrams for Ceramists: Volume 1. It will be helpful to . It will be helpful to follow along using the book, as many of the details are follow along using the book, as many of the details are hard to see.hard to see.

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L

Tracing IsothermsTracing Isotherms

Trace the boundary of Trace the boundary of the diagram.the diagram.

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Identify and trace all the isotherms of Identify and trace all the isotherms of the temperature for which you want the the temperature for which you want the isothermal section, in this case 1400 isothermal section, in this case 1400 ooC.C.

Identify the portion of the Identify the portion of the diagram where the liquidus diagram where the liquidus surface is still below the surface is still below the temperature of interest and temperature of interest and label this section: Liquid (L).label this section: Liquid (L).

Intersection of Boundary Lines and Intersection of Boundary Lines and IsothermsIsotherms

At any point where the At any point where the traced isotherm intersects traced isotherm intersects a phase boundary line, a phase boundary line, including the edge of the including the edge of the diagram, draw a line from diagram, draw a line from the intersection point the intersection point back to the composition back to the composition on either side of the on either side of the phase boundary line. phase boundary line.

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From each composition From each composition that a line was drawn that a line was drawn back to, draw tie lines to back to, draw tie lines to the liquidus line(s).the liquidus line(s).

Alkemades LinesAlkemades Lines

Draw in any alkemades Draw in any alkemades lines that don’t come into lines that don’t come into contact with the liquidus contact with the liquidus line(s), or cross any of line(s), or cross any of the tie lines drawn so far.the tie lines drawn so far.

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Identifying Phase RegionsIdentifying Phase Regions

To understand the last step it is necceasary to describe To understand the last step it is necceasary to describe the different regions of the isothermal section first.the different regions of the isothermal section first.

There should now be up to four different regions on the There should now be up to four different regions on the isothermal section. isothermal section. – Liquid region, composed entirely of a liquid of varying Liquid region, composed entirely of a liquid of varying

composition. This region was labeled on the first slide.composition. This region was labeled on the first slide.– Two Phase region, composed of a solid and a liquid. The Two Phase region, composed of a solid and a liquid. The

composition of the liquid is found using the tie lines that were composition of the liquid is found using the tie lines that were drawn in on the second slide. This region shares a border with drawn in on the second slide. This region shares a border with the Liquid region.the Liquid region.

– Three Phase region, composed of two compositions and one Three Phase region, composed of two compositions and one unvarying liquid composition. This region is easily recognized by unvarying liquid composition. This region is easily recognized by its sole point of contact with the Liquid region.its sole point of contact with the Liquid region.

– Solid region, composed of three solids. This region is triangular, Solid region, composed of three solids. This region is triangular, and has no contact with the Liquid region.and has no contact with the Liquid region.

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LabelingLabeling

Identify the phases present Identify the phases present in each of the three different in each of the three different types of regions, and label types of regions, and label each of the different regions each of the different regions in the diagram. in the diagram.

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– Three Phase RegionsThree Phase Regions

– Solid RegionsSolid Regions

– Two Phase RegionsTwo Phase Regions

Phases Present

SiO2 + LiquidCaO ·SiO2 + Liquid3CaO ·2SiO2 + Liquid2CaO ·SiO2 + Liquid2CaO ·SiO2 + LiquidCaO ·Al2O3 ·2SiO2 + LiquidCaO ·6Al2O3 + Liquid2CaO ·Al2O3 ·SiO2 + Liquid2CaO ·Al2O3 ·SiO2 + Liquid3Al2O3 ·2SiO2 + LiquidCaO ·Al2O3 + Liquid12CaO ·7Al2O3 + Liquid3CaO ·Al2O3 + Liquid

L3

L1L2

L4

L5

L6

L7

L8

L9

L10

L11

SiO2 + CaO ·SiO2 +

L1

CaO ·SiO2 + 3CaO ·2SiO2 +

L2

3CaO ·2SiO2 + 2CaO ·SiO2 +

L3

2CaO ·SiO2 + 2CaO ·Al2O3 ·SiO2 +

L4

2CaO ·Al2O3 ·SiO2 + CaO ·6Al2O3 +

L5

CaO ·6Al2O3 + CaO ·Al2O3 ·2SiO2 +

L6

CaO ·Al2O3 ·2SiO2 + 3Al2O3 · 2SiO2 +

L7

3Al2O3 · 2SiO2 + SiO2 +

L8

2CaO ·SiO2 + 3CaO · Al2O3 +

L9

2CaO ·SiO2 +2CaO ·Al2O3 ·SiO2 +

L10

2CaO ·Al2O3 ·SiO2 +CaO · Al2O3 +

L11

2CaO ·SiO2 +3CaO ·SiO2 +3CaO · Al2O3

3CaO ·SiO2 +CaO +

3CaO · Al2O3

3CaO · Al2O3 +2CaO ·Al2O3 ·SiO2 +

CaO ·2Al2O3

2CaO ·Al2O3 ·SiO2 +CaO ·2Al2O3 +CaO ·6Al2O3

CaO ·6Al2O3 +CaO ·Al2O3 ·2SiO2 +

Al2O3

Al2O3 +CaO ·Al2O3 ·2SiO2 +

3Al2O3 ·2SiO2

Things To RememberThings To Remember

Use the representative tie lines to determine the Use the representative tie lines to determine the percent of each phase present in a Two Phase percent of each phase present in a Two Phase region, and to determine the liquid composition.region, and to determine the liquid composition.

Use parallel lines in the Three Phase and the Solid Use parallel lines in the Three Phase and the Solid regions to determine the percent of each phase regions to determine the percent of each phase present.present.

If making the isothermal section on a copy of a If making the isothermal section on a copy of a diagram, use colored pencils for the different steps.diagram, use colored pencils for the different steps.

Use tracing paper when the best results are desired. Use tracing paper when the best results are desired.

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