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

Mineral Reactions in Igneous Environments

Mineral Reactions in Metamorphic Environments

Role of Volatiles (H 2 O & CO 2 ) Catalyzes reactions Catalyzes reactions Mobility during metamorphism leads to non-isochemical reactions Mobility during metamorphism leads to non-isochemical reactions Dehydration and decarbonation during prograde reactions Dehydration and decarbonation during prograde reactions Lack of volatiles slows retrograde reactions Lack of volatiles slows retrograde reactions Prograde/Dehydration Retrograde

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

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

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 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 A Mineral of constant composition is considered a solid phase Phase (or mineral) stability is commonly portrayed on a Pressure-Temperature Phase Diagram Phase (or mineral) stability is commonly portrayed on a Pressure-Temperature Phase Diagram

Phase Diagrams One ComponentMulti-component

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. 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. 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. 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) 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!

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

Thermodynamics (P Chem) Theoretical basis of phase equilibrium Theoretical basis of phase equilibrium Three Laws of Thermodynamics 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

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 (0 º K), Entropy is zero

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 – 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 temperature will be preferred

Relationship of Gibbs Free Energy to Phase Equilibrium

Clapeyron Equation Defines the state of equilibrium between reactants and product in terms of S and V Defines the state of equilibrium between reactants and product in terms of S and V dG r = V r dP – S r dT dG p = V p dP – S p dT at equilibrium: V r dP – S r dT = V p dP – S p dT or: (V p –V r ) dP = (S p –S r ) 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