Lecture 6 (9/27/2006) Crystal Chemistry Part 5: Mineral Reactions Phase Equilibrium/Stability Intro to Physical Chemist

1. Lecture 6 (9/27/2006)Crystal ChemistryPart 5: Mineral ReactionsPhase Equilibrium/StabilityIntro to Physical Chemistry

2. Mineral Reactions in Igneous Environments

3. Mineral Reactions in Metamorphic Environments

4. Role of Volatiles (H2O & CO2) • Catalyzes reactions • Mobility during metamorphism leads to non-isochemical reactions • Dehydration and decarbonation during prograde reactions • Lack of volatiles slows retrograde reactions Retrograde Prograde/ Dehydration

5. Mineral Reactions in Near-surface Environments • Chemical Weathering • conversion of minerals into simple layered silicates (montmorillonite and kaolinite) • de-silicification • dissolution of cations (Na+, K+, Ca++, Mg++) e.g. K-felspar + acidic water Muscovite + silica + K+ Muscovite + acidic water Kaolinite + K+

6. Mineral Reactions in High Pressure Environments • Conversion to high density polymorphs • Increase in Coordination Numbers of cation sites

7. Mineral Stability/Equilibrium • Phase Stability defined by the state (solid, liquid, gas or vapor) and internal structure of a compositionally homogeneous substance under particular external conditions of pressure and temperature • A Mineral of constant composition is considered a solid phase • Phase (or mineral) stability is commonly portrayed on a Pressure-Temperature Phase Diagram

8. Phase Diagrams One Component Multi-component

9. Stability, Activation Energy and Equilibrium • Stability of a phase (or mineral) is related to its internal energy, which strives to be as low as possible under the external conditions. • Metastability exists in a phase when its energy is higher than P-T conditions indicate it should be. • Activation Energy is the energy necessary to push a phase from its metastable state to its stable state. • Equilibrium exists when the phase is at its lowest energy level for the current P-T conditions. (Two minerals that are reactive with one another, may be found to be in equilibrium at particular P-T conditions which on phase diagrams are recognized as phase boundaries) Recognize that by these definitions, most metamorphic and igneous minerals at the earth’s surface are metastable and out of equilibrium with their environment!

10. Phase Component • Components are the chemical entities necessary to define all the potential phases in a system of interest

11. Thermodynamics (P Chem) • Theoretical basis of phase equilibrium • Three Laws of Thermodynamics 1.Internal Energy (E)dE = dQ – dW Q – heat energy W – work = F * dist = P * area *dist = P * V at constant pressure - dW = PdV So, dE = dQ – PdV dV – thermal expansion

12. Second and Third Laws of Thermodynamics 2. All substances strive to be at the greatest state of disorder (highest Entropy-S) for a particular T and P. dQ/T = dS 3. At absolute zero (0ºK), Entropy is zero

13. Gibbs Free Energy • G – the energy of a system in excess of its internal energy. (This is the energy necessary for a reaction to proceed) G = E + PV - TS dG = VdP – SdT at constant T (δG/δP)T = V at constant P (δG/δT)P = -S Stable phases strive to have the lowest G Therefore, the phase with the highest density at a given pressure and the highest entropy at a given temperaturewill be preferred

14. Relationship of Gibbs Free Energy to Phase Equilibrium

15. Clapeyron Equation • Defines the state of equilibrium between reactants and product in terms of S and V dGr = VrdP – SrdT dGp = VpdP – SpdT at equilibrium: VrdP – SrdT = VpdP – SpdT or: (Vp –Vr) dP = (Sp –Sr) dT or: dP/dT = ΔS / ΔV The slope of the equilibrium curve will be positive if S and V both decrease or increase with increased T and P