Solid Solutions & Phase Diagrams

Solid Solutions & Phase Diagrams

Gibbs Free Energy

• Definition: Gibbs free energy quantifies the stability of a mineral under specific Pressure (P), Temperature (T), and Composition (X) conditions.

Gibbs Free Energy & Reactions

• Calculation: The Gibbs free energy change (9;ΔG_{rxn}9;) for a reaction is calculated as:

  
  ΔG{rxn} = G{products} - G_{reactants}
  

• Interpretation:

  • If ΔG_{rxn} < 0: reaction favors products, proceeds to the right.

  • If ΔG_{rxn} > 0: reaction favors reactants, proceeds to the left.

Example: Calcite–Aragonite

• Reaction: CaCO3 (cc) ightleftharpoons CaCO3 (ar)

• Energy Change:

  • ΔG = G{aragonite} - G{calcite}

  • If G{aragonite} < G{calcite} → ΔG < 0 → aragonite is stable.

  • If G{aragonite} > G{calcite} → ΔG > 0 → calcite is stable.

  • Coexistence occurs at ΔG = 0 (defining the phase boundary).

• Thermodynamic Tables: Provide Gibbs free energies of formation ΔG^ heta_f for minerals in J/mol or Kcal/mol indicating their stability.

Free Energy of Formation

• Definition: ΔG_f is the energy difference between the standard state (298 K, 1 atm) of the element and its state in the mineral at the relevant P,T.

• Comparative Stability: Between two chemically identical minerals, the one with lower free energy is the more stable form.

Quartz Polymorphs & Phase Transformations

• Quartz polymorph transformations can be displacive (atoms shift positions) or reconstructive (bonds are broken and formed).

• Reconstructive Transformation: Involves energy barriers and may lead to metastable phases if crossed too rapidly.

• Metastable phases (e.g., stishovite, coesite) can exist under high P,T conditions but are less stable at Earth's surface.

New Minerals Formation

• New minerals form through chemical reactions that occur under conditions that minimize Gibbs free energy.

Solid Solutions

• Definition: A solid solution is a homogeneous crystal phase where two or more elements can substitute for each other in the lattice without altering the crystal structure, effectively forming a miscible mixture.

Liquidus & Solidus

• Liquidus: The temperature at which a rock or mineral is completely molten.

• Solidus: The temperature below which a rock or mineral is entirely solid.

• Crystallization: Begins as the melt cools and crosses the liquidus, while melting initiates when heating crosses the solidus.

Fractional Crystallization

• Definition: Occurs when forming or melting crystals are separated from the melt, leading to different compositional evolutions of the melt and solid.

• Process: Early-formed minerals are removed from the melt (e.g., olivine in basalt), enriching the remainder in silica and incompatible elements.

Equilibrium Crystallization

• Definition: Involves continuous chemical communication between melt and solid during crystallization, allowing compositions to adjust without separation.

Phase Diagrams

• Purpose: Represent the stable phases (mineral, melt, gas) for given compositions under specific P,T conditions and are crucial for understanding mineral relationships in geological contexts.

Lever Rule

• A tool for determining the relative amounts of two phases in a mixture from the phase diagram, using bus composition and tie-lines:

  • 
    %A = \frac{rs}{qs}, %B = \frac{qr}{qs}
    

• Example Calculation: % solid phase = 67%, % liquid = 33%.

Continuous Solid Solution in Olivine

• Components: Forsterite (Mg2SiO4) and Fayalite (Fe2SiO4) illustrate a continuous solid solution model with varying compositions of melt and crystallization phases at different temperatures.