Phase Diagrams Notes

Week 6b – Phase diagrams I

Recap from Week 2

• Phase rule: $F + P = C + 2$
  • $C$ = components
  • $P$ = phases
  • $F$ = degrees of freedom
  • Integer = intensive variables (P & T)

Endmembers of Melting / Crystallisation

• Equilibrium (batch): The crystals remain in equilibrium with the melt.
• Fractional: The crystals and melt are immediately separated.

Binary Phase Diagrams

• Often composition vs. temperature.
• Melt at high temperature.
• Stable minerals indicated on x-axis.
• Solids at low temperature.
• Pure endmembers + melt.
• Eutectic (A + B = L): First and last melt at eutectic

Binary Phase Diagrams - Solid Solutions

• Solid solutions have loops.
• Melting occurs below liquidus.
• Solidus is temperature of 100% solidification.
• Complete solid solution of A-B.
• 2-phase region within binary loop.

Binary Phase Diagrams - Lever Rule

• Lever rule for composition & proportions
• Given a phase diagram with temperature (°C) vs composition (A, B) and regions for L (liquid), AB (solid solution), and AB+L (solid solution + liquid):
  • $X_{melt}$
  • $X_{solid}$
  • $x_{AB}$
  • $x_L$
  • $[x<em>{AB} / (x</em>{AB} + x_L)] * 100 = \% \text{ solid}$
  • $[x<em>L / (x</em>{AB} + x_L)] * 100 = \% \text{ liquid}$

New Concepts in Phase Diagrams

• Intermediate phases have individual stability fields.
• Congruent Melting (C = L):
  • Melts have same composition as solid.
• Thermal Divide:
  • Splits the binary into 2 diagrams.
  • Bulk compositions on one side of thermal divide can never produce melts/solids on the opposite side.

More New Concepts in Phase Diagrams

• Peritectic Point
• Incongruent Melting (C = A + L):
  • Melts have a different composition (must be another solid).

Miscibility Loops

• Solvus that creates two diverging compositions as function of temperature.
• Can be liquid-liquid or solid-solid immiscibility.

Example: Leucite-Kspar System

• Diagram showing temperature vs. Wt% SiO2 with leucite, K-feldspar, quartz, and tridymite.
• Illustrates peritectic and eutectic points.
• Shows the compositions and phases present at various temperatures for a system with 70% KAISi2O6 - 30% SiO2.

Reading Resources

• Essential: Chapter 2 of Essentials of Igneous & Metamorphic Petrology
• Optional:
  • Chapter 8 of Open Petrology
  • Chapter 11 of Principles of Igneous and Metamorphic Petrology

Practical Work

• Week 6b: Binary phase diagrams [~1.5 hours for Q1 & 2, Q3-5 for more practice later]
• Practice interpreting binary phase diagrams
• Drawing batch vs. fractional paths
• Calculating mineral/melt compositions and proportions
• Identifying features of phase diagrams you need to know how to do this…