Lecture 6 (9/27/2006)Lecture 6 (9/27/2006)

Crystal ChemistryCrystal Chemistry

Part 5: Part 5: Mineral ReactionsMineral Reactions

Phase Equilibrium/StabilityPhase Equilibrium/StabilityIntro to Physical ChemistryIntro to Physical Chemistry

Mineral Reactions in Igneous Mineral Reactions in Igneous EnvironmentsEnvironments

Mineral Reactions in Metamorphic Mineral Reactions in Metamorphic EnvironmentsEnvironments

0 200 400 600 800

2

4

6

8

10

12

14

16

0

6

12

18

25

31

37

43

50

0

Conditionsnot foundin crust

THERMAL (CONTACT) METAMORPHISM

BURIAL METAMORPHISM

LOW-GRADE REGIONAL METAMORPHISM

HIGH-GRADE REGIONAL METAMORPHISM

HIG

H PR

ESSUR

E META

MO

RPH

ISMZONE OFPARTIALMELTING

CRUSTALGEOTHERM

TEMPERATURE (centigrade )

Role of Volatiles Role of Volatiles (H(H22O & COO & CO22))

Catalyzes reactionsCatalyzes reactions Mobility during Mobility during

metamorphism leads metamorphism leads to non-isochemical to non-isochemical reactionsreactions

Dehydration and Dehydration and decarbonation during decarbonation during prograde reactionsprograde reactions

Lack of volatiles slows Lack of volatiles slows retrograde reactionsretrograde reactions

Prograde/

Prograde/

Dehydration

Dehydration

Retrograde

Retrograde

Mineral Reactions in Near-Mineral Reactions in Near-surface Environmentssurface Environments

Chemical WeatheringChemical Weathering conversion of minerals into simple layered conversion of minerals into simple layered

silicates (montmorillonite and kaolinite)silicates (montmorillonite and kaolinite) de-silicificationde-silicification dissolution of cations (Nadissolution of cations (Na++, K, K++, Ca, Ca++++, Mg, Mg++++)) e.g. K-felspar + acidic water Muscovite + silica + Ke.g. K-felspar + acidic water Muscovite + silica + K++

Muscovite + acidic water Kaolinite + KMuscovite + acidic water Kaolinite + K++

Mineral Reactions in High Mineral Reactions in High Pressure Environments Pressure Environments

Conversion to high Conversion to high density polymorphsdensity polymorphs

Increase in Increase in Coordination Coordination Numbers of cation Numbers of cation sitessites

Mineral Stability/EquilibriumMineral Stability/Equilibrium

Phase StabilityPhase Stability defined by the state (solid, defined by the state (solid, liquid, gas or vapor) and internal structure liquid, gas or vapor) and internal structure of a compositionally homogeneous of a compositionally homogeneous substance under particular external substance under particular external conditions of pressure and temperatureconditions of pressure and temperature

A A MineralMineral of constant composition is of constant composition is considered a solid phaseconsidered a solid phase

Phase (or mineral) stability is commonly Phase (or mineral) stability is commonly portrayed on a portrayed on a Pressure-Temperature Pressure-Temperature Phase DiagramPhase Diagram

Phase DiagramsPhase DiagramsOne Component Multi-component

Stability, Activation Energy and Stability, Activation Energy and EquilibriumEquilibrium

StabilityStability of a phase (or mineral) is related to its internal of a phase (or mineral) is related to its internal energy, which strives to be as low as possible under the energy, which strives to be as low as possible under the external conditions.external conditions.

MetastabilityMetastability exists in a phase when its energy is higher exists in a phase when its energy is higher than P-T conditions indicate it should be. than P-T conditions indicate it should be.

Activation EnergyActivation Energy is the energy necessary to push a is the energy necessary to push a phase from its metastable state to its stable state.phase from its metastable state to its stable state.

EquilibriumEquilibrium exists when the phase is at its lowest energy exists when the phase is at its lowest energy level for the current P-T conditions. (Two minerals that level for the current P-T conditions. (Two minerals that are reactive with one another, may be found to be in are reactive with one another, may be found to be in equilibrium at particular P-T conditions which on phase equilibrium at particular P-T conditions which on phase diagrams are recognized as phase boundaries)diagrams are recognized as phase boundaries)

Recognize that by these definitions, most metamorphic Recognize that by these definitions, most metamorphic and igneous minerals at the earth’s surface are and igneous minerals at the earth’s surface are metastable and out of equilibrium with their environment!metastable and out of equilibrium with their environment!

Phase ComponentPhase Component ComponentsComponents are the chemical entities are the chemical entities

necessary to define all the potential necessary to define all the potential phases in a system of interestphases in a system of interest

Thermodynamics (P Chem)Thermodynamics (P Chem)

Theoretical basis of phase equilibriumTheoretical basis of phase equilibrium Three Laws of ThermodynamicsThree Laws of Thermodynamics

1.1. Internal Energy (E)Internal Energy (E) dE = dQ – dWdE = dQ – dW

QQ – heat energy – heat energy

WW – work = F * dist = P * area *dist = P * V – work = F * dist = P * area *dist = P * V

at constant pressure - at constant pressure - dW = PdVdW = PdV

So, So, dE = dQ – PdVdE = dQ – PdV dV – thermal expansion dV – thermal expansion

Second and Third Laws of Second and Third Laws of ThermodynamicsThermodynamics

2. All substances strive to be at the 2. All substances strive to be at the greatest state of disorder (highest greatest state of disorder (highest Entropy-SEntropy-S) for a particular T and P. ) for a particular T and P.

dQ/T = dSdQ/T = dS

3. At absolute zero (03. At absolute zero (0ººK), Entropy is K), Entropy is zerozero

Gibbs Free EnergyGibbs Free Energy

G G – the energy of a system in excess of its – the energy of a system in excess of its internal energy. (This is the energy necessary for internal energy. (This is the energy necessary for a reaction to proceed) a reaction to proceed)

G = E + PV - TSG = E + PV - TSdG = VdP – SdTdG = VdP – SdT

at constant Tat constant T ( (δδG/G/δδP)P)TT = V = Vat constant Pat constant P ( (δδG/G/δδT)T)PP = -S = -S

Stable phases strive to have the lowest GStable phases strive to have the lowest GTherefore, the phase with the highest density at a Therefore, the phase with the highest density at a

given pressure and the highest entropy at a given given pressure and the highest entropy at a given temperaturetemperature will be preferredwill be preferred

Relationship of Gibbs Free Energy to Relationship of Gibbs Free Energy to Phase EquilibriumPhase Equilibrium

Clapeyron EquationClapeyron Equation

Defines the state of equilibrium between Defines the state of equilibrium between reactants and product in terms of S and Vreactants and product in terms of S and V

dGdGrr = V = VrrdP – SdP – SrrdTdTdGdGpp = V = VppdP – SdP – SppdTdT

at equilibrium:at equilibrium: V VrrdP – SdP – SrrdT = VdT = VppdP – SdP – SppdTdTor: (Vor: (Vp p –V–Vrr) dP = (S) dP = (Sp p –S–Srr) dT ) dT

or: dP/dT = or: dP/dT = ΔΔS / S / ΔΔVVThe slope of the equilibrium curve will be The slope of the equilibrium curve will be

positive if S and V both decrease or positive if S and V both decrease or increase with increased T and Pincrease with increased T and P