Construction of a Triangular Stability Diagram

Terri Woods, East Carolina University

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Summary

An interactive powerpoint presentation walks students step-by-step through the process of generating a triangular diagram for the system K2O-Al2O3-SiO2. A Word document provides the thermodynamic data and instructions necessary to create their own diagram for the CaO-MgO-SiO2 system. An answer key is also provided.
Students will:
- Calculate mineral compositions in mole percent and plot on a triangular diagram.
- Determine which is the stable mineral at the apices.
- Draw in all possible tie-lines connecting coexisting minerals.
- Eliminate unstable collinear phases.
- Eliminate crossing tie-lines.
- Determine stable mineral assemblages for bulk-rock compositions provided.

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Context

Audience

graduate and upper level undergraduate course in low-temperature geochemistry

Skills and concepts that students must have mastered

Balancing chemical reactions not involving redox.

Recognizing "go/no-go" reactions and using Gibbs Free Energies to determine which way the reaction goes (i.e., which is the stable equilibrium assemblage).

How the activity is situated in the course

This classroom activity is pursued after introducing Gibbs Free Energies, "go/no-go" reactions, plotting mineral compositions on triangular diagrams, and uses of Mineral Stability diagrams.
It is part of a sequence of exercises related to constructing and interpreting stability diagrams.

Goals

Content/concepts goals for this activity

Plotting mineral compositions on a triangular diagram
Using Gibbs Free Energy to calculate which minerals are stable by constructing "go/no-go" reactions relating various mineral assemblages

Recognizing that tie-lines connect assemblages of stable minerals

Using a triangular diagram to determine what minerals are stable for a specific bulk-rock composition

Higher order thinking skills goals for this activity

Understanding the concept of collinear phases on a stability diagram.

Recognizing the significance of "crossing tie-lines" on a triangular stability diagram and eliminating unstable mineral assemblages.

Reinforcing the concept of mass balance

Other skills goals for this activity

Description and Teaching Materials

An interactive powerpoint presentation walks students step-by-step through the process of generating a triangular diagram for the system K2O-Al2O3-SiO2.

You may also want to have them complete the class template below as you guide them step-by-step through the construction of this diagram. This template starts them off with a detailed description of the first calculation and then lets them complete the construction of the reactions and the ∆Gr calculations for the rest. You may or may not want to include the balanced reactions and completed ∆Gr calculations in this template.

Also uploaded below are potential diagrams to hand out as they complete successive steps in the process.

A Word document provides the thermodynamic data and instructions necessary to create their own diagram for the CaO-MgO-SiO2 system.

The final diagram is also provided.


Powerpoint tutorial for diagram construction (PowerPoint 2007 (.pptx) 1006kB Nov30 21)
Class template for student use during tutorial (Microsoft Word 2007 (.docx) 216kB Nov30 21)
Diagrams to accompany class template (Acrobat (PDF) 818kB Nov30 21) 
Triangular Diagram Exercise (Microsoft Word 2007 (.docx) 14kB Nov30 21) 

Teaching Notes and Tips

I suggest going through the tutorial in class with the students allowing them to complete each step and record on their class template before clicking to show the correct answer to them on the screen. I also provide this tutorial to them online so they can refer to it when they are doing their problem set for the CaO-MgO-SiO2 system. For more advanced students it can serve as a stand-alone activity permitting them to quickly review the construction and use of such diagrams.

As we progress through the tutorial in class, I regularly check with students to ensure they understand where the answers are coming from and feel comfortable that they could repeat these steps on their own for their problem set.

I find I need to constantly remind them to check that the reactions they write are mass balanced.

Assessment

Did they plot compositions and lines correctly on diagram?
Did they correctly eliminate crossing tie-lines and duplicate phases at apices?
Did they write all the necessary, correct, balanced chemical reactions?
Did they correctly calculate and interpret Gibbs Free Energies of reaction?
Did they correctly plot bulk rock chemistries provided and identify the stable mineral under those conditions?

References and Resources

This activity is related to a SERC activity called: "Plotting Compositions in 2-D and 3-D Space:, which focuses almost entirely on how to plot compositions on binary and triangular diagrams. The present activity approaches the concept differently and goes into considerably more detail on how to do the calculations which determine which assemblages of minerals are stable.

This activity is related to another SERC activity called: "Three Component Systems and Their Reactions", however my activity does not involve Gibbs Phase Rule or adding together reactions.

Finally, the SERC activity called: "Steve Nelson's: Triangular Plots in Metamorphic Petrology" has some similarities with the current activity.

The latter two SERC activities mentioned above are more advanced than the one described here.

Although my search was far from exhaustive, I was unable to find information about my particular activity online or in commonly used geochemistry texts.

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