CHAPTER 9: INTRODUCTION TO THERMODYNAMICS. Sarah Lambart

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1 CHAPTER 9: INTRODUCTION TO THERMODYNAMICS Sarah Lambart

2 RECAP CHAP. 8: SILICATE MINERALOGY Orthosilicate: islands olivine: solid solution, ie physical properties vary between 2 endmembers: Forsterite (Mg 2 SiO 4 ) Fayalite (Fe 2 SiO 4 ); structure: chains of M1 sites connected by larger M2 and cross-link by independent SiO4 tetrahedra. Garnet: X 3 2+ Y 2 3+ [SiO 4 4- ] 3 - very various chemical compositions in a lot of different rocks; 2 groups: pyralspite (Y=Al 3+ ) and ugrandite (X=Ca 2+ ) Zircon: ZrSiO 4 - extremely resistant minor substitutions of U and Th: used to date rocks. Aluminosilicate: Al 2 SiO 5-3 polymorphs metamorphic minerals

3 RECAP CHAP. 8: SILICATE MINERALOGY Sorosilicate: double island silicates: Si 2 O 6-7 epidote: rich in Ca LT/LP metamorphic rocks (greenshist facies) Allanite: rich in La - accessory mineral in granitoid Lawsonite: LT/HP metamorphism (blueschist facies) in basic rock Cyclosilicate: ring of 3,4 or 6 tetrahedra Beryls: isostructural Corderite: Tourmaline: in peraluminous granites and metapelites

4 RECAP CHAP. 8: SILICATE MINERALOGY Inosilicate: simple or double chains Simple: pyroxenes XYZ 2 O 6 2 groups: orthopyroxenes (orthorhombic) and clinopyroxenes (monoclinic) Orthopyroxene: solid solution enstatite MgSiO 3 and ferrosillite FeSiO 3 Clinopyronenes: (Ca,Na,Mg,Fe,Ti) 2 (Si,Al) 2 O 6

5 RECAP CHAP. 8: SILICATE MINERALOGY Inosilicate: simple or double chains Double: amphiboles XYZ 2 O 6 W 0-1 X 2 Y 5 Z 8 O 22 (OH,F) 2 : HYDROUS MINERAL Most common: Hornblende (Ca,Na) 2-3 (Mg,Fe,Al) 5 Si 6 (Si,Al) 2 O 22 (OH,F) 2 In intermediate igneous rocks

6 RECAP CHAP. 8: SILICATE MINERALOGY Phyllosilicates sheet silicates Structures: TO, TOT, TOT+c, TOT+O Di- (trivalent cations) or trioctahedral (divalent cations) Perfect cleavage Important ones: Serpentine group (TO) Talc (TOT) Micas (TOT + c) Clay minerals: from chemical weathering

7 RECAP CHAP. 8: SILICATE MINERALOGY Tectosilicates framework Si:O ratio= 1:2 Silica group: 9 polymorphs Feldspar group: 2 solid solutions: Ab-Or and Ab-An Feldspatoids: in Si-poor rocks never associated with Qz

8 GOAL CHAPTERS 9 TO 11 How can we determine the stability range of a mineral assemblage? What are the effects of a change of parameters (P, T, fluids) on a stable mineralogical assemblage? How cn we use simple phase diagrams to understand natural systems?

9 THERMODYNAMICS The Oxford Dictionary definition: "Thermodynamics: the theory of the relations between heat and mechanical energy, and of the conversion of either into the other." science that tells us which minerals or mineral assemblages will be stable under different conditions.

10 THERMODYNAMICS The Oxford Dictionary definition: "Thermodynamics: the theory of the relations between heat and mechanical energy, and of the conversion of either into the other." science that tells us which minerals or mineral assemblages will be stable under different conditions = forward modeling + science that allows us to use mineral assemblages and mineral compositions to determine the conditions at which a rock formed = thermobarometry

11 THERMODYNAMICS Popular Computer Programs for Thermodynamic Calculations and Modeling: TWQ: allows the calculations of the position of phase equilibria in P-T, T-XCO 2, and P-XCO 2 space. (Windows easy to use) Thermocalc: performs the same calculations as TWQ for a much larger number of phases and includes more complicated types of calculations. MELTS family: allows thermodynamic calculations to be made for equilibria involving magmas. Perplex: thermodynamic calculation package suitable for rapidly creating phase diagrams of all types

12 THERMODYNAMICS: DEFINITIONS A system: a portion of the universe that you wish to study Change in the system = transfer of energy Natural systems tend toward states of minimal energy Gibbs free energy of formation: energy associated with the formation of a phase (mineralogical or not) ΔG f ΔG f varies with P- T condition and its composition X

13 THERMODYNAMICS: DEFINITIONS Gibbs free energy of reaction ΔG r : sum of ΔG f on the righthand side of the reaction minus sum of ΔG f of the left- hand side If ΔG r <0, reaction proceeds to the right If ΔG r >0, reaction proceeds to the left Ex.: albite = jadeite + quartz ΔG r (1bar)>0 albite is stable, the assemblage jadeite + quartz is unstable. ΔG r varies with P-T and X phase diagram

14 THERMODYNAMICS: DEFINITIONS Gibbs free energy of mineral: Unit: joules/mols (or calorie/mole) Ex.: enstatite MgSiO 3 ΔG f from pure elements (Mg, Si and O) = ΔG f (enstatite, element) = kj/mole at room temperature and pressure ΔG f (enstatite, oxide) = kj/mole Convention: ΔG f (pure element) = 0 other values of Gibbs free energy are relative values

15 DETERMINING THE LOCATION OF METAMORPHIC REACTIONS (1) albite = jadeite + quartz ΔG r = ΔG 1 = ΔG f (jadeite,elmt) + ΔG f (quartz, elmt) ΔG f (albite, elmt) = ΔG f (jadeite,oxide) + ΔG f (quartz, oxide) ΔG f (albite, oxide) At 400 C and 1 GPaΔG 1 >0 At 400 C and 1.4 Gpa ΔG 1 <0

16 THERMODYNAMICS: DEFINITIONS Gibbs free energy of a phase: G = E + PV TS = H-TS with P and T: pressure and temperature, V: volume, E: internal energy, H: enthalpy, S: entropy, of the phase, such as: H = E + PV Gibbs free energy of a reaction: ΔG r = ΔE r + PΔV r TΔS r = ΔH-TΔS Constant (depend on the phase) More voluminous phase = greater gibbs free energy Measure of the disorder

17 THERMODYNAMICS: DEFINITIONS Gibbs free energy of a phase: G = E + PV TS = H-TS with P and T: pressure and temperature, V: volume, E: internal energy, H: enthalpy, S: entropy, of the phase, such as: H = E + PV Gibbs free energy of a reaction: ΔG r = ΔE r + PΔV r TΔS r = ΔH-TΔS Constant (depend on the phase) High volume phase are unstable at HP High S phase are very stable at HT

18 THERMODYNAMICS: DEFINITIONS Gibbs free energy of a reaction: ΔG r = ΔE r + PΔV r TΔS r = ΔH-TΔS P and T: intensive variables = do not depend on the size of the system or the amount of material present G,E, H, V and S: extensive variables = depend on the size of the system or the amount of material present Units: P: bar, kbar, Pa, Gpa G, E, H: J/mole V: cm 3 /mole S: J/deg-mole 1J = 10 cc-bar

19 THERMODYNAMICS: DEFINITIONS ΔG r : tells us if a reaction will take place ΔH r : tell us how much heat will flow in or out of the reaction: If ΔH r < 0: exothermic reaction (ex.: C + O 2 = CO 2 ) If ΔH r > 0: endothermic reaction (ex.: H 2 O(ice) = H 2 O(water) ) ΔS r : tell us whether the products or reactants are more disordered ΔV r : tell us whether the products or reactants have greater volumes (ex.: ΔV r (graphite = diamond) <0 )

20 PHASE DIAGRAMS = result of thermodynamic calculations = graphical representation of equilibrium relationship between minerals 3 main kind of phase diagrams:

21 PHASE DIAGRAMS = result of thermodynamic calculations = graphical representation of equilibrium relationship between minerals 3 main kind of phase diagrams:

22 PHASE DIAGRAMS = result of thermodynamic calculations = graphical representation of equilibrium relationship between minerals 3 main kind of phase diagrams:

CLAUSIUS CLAPEYRON EQUATION G = E + PV TS dg = de + PdV + VdP TdS SdT de= dq PdV = TdS PdV : 1 st law of thermodynamic dg = TdS-PdV + PdV + VdP TdS SdT dg = VdP SdT On the reaction curve,

23 CLAUSIUS CLAPEYRON EQUATION G = E + PV TS dg = de + PdV + VdP TdS SdT de= dq PdV = TdS PdV : 1 st law of thermodynamic dg = TdS-PdV + PdV + VdP TdS SdT dg = VdP SdT On the reaction curve, dg = 0 dp/dt = ΔS P,T /ΔV P,T : slope of the reaction define equilibrium between reactants and products in terms of volume and entropy Slope: positive if both ΔV and ΔS increase (or decrease)

CLAUSIUS CLAPEYRON EQUATION Ex.: SiO 2 at 500 C and 500 MPa dg = VdP SdT or ΔG = VΔP SΔT We can treat P and T separately: G P2 G P1 = V(P 2 P 1 ) if T and V constant For P 2 = 500 MPa and P 1 = 0.

24 CLAUSIUS CLAPEYRON EQUATION Ex.: SiO 2 at 500 C and 500 MPa dg = VdP SdT or ΔG = VΔP SΔT We can treat P and T separately: G P2 G P1 = V(P 2 P 1 ) if T and V constant For P 2 = 500 MPa and P 1 = 0.1 MPa, V = m 3 ; G P1 = J/mol (low-quartz from dataset) G P2 = ( )= J ΔG = VΔP SΔT G T2 G T1 = -S(T 2 -T 1 ) if P = 500 MPa G T2 = G T1 S 0.1MPa ( )= ( ) = J G(α-qtz) at 500 MPa and 500 C ~ kj

25 PHASE DIAGRAM CONSTRUCTION One component (ex.: water) The Gibbs and Clapeyron Equations allow us to estimate phase diagrams with extrapolations from laboratory measurements. The lines show where equilibrium conditions (ΔG = 0) occur. Clapeyron tells us the slope

PHASE DIAGRAM CONSTRUCTION Melting curve - dp/dt = ΔS / ΔV Clapeyron 1.Does the liquid or solid have the larger volume/ unit mass? Usually liquid. (except H 2 O) 2.

26 PHASE DIAGRAM CONSTRUCTION Melting curve - dp/dt = ΔS / ΔV Clapeyron 1.Does the liquid or solid have the larger volume/ unit mass? Usually liquid. (except H 2 O) 2. High pressure favors low volume, so which phase should be stable at high P? Solid 3.Does liquid or solid have a higher entropy? Liquid High temperature favors randomness, so which phase should be stable at higher T? Liquid is more random, expect at high T. 5. Both ΔV and ΔS increase to right. We can thus predict that the slope of solid-liquid equilibrium should be positive and that increased pressure raises the melting point.

27 PHASE DIAGRAM CONSTRUCTION Our experiments and calculations allow us to construct the 3-D plot in (a), and to project the mineral with the lowest free energy at each PT onto the graph in (b).

28 The KSA Phase diagram allows us to assign PT conditions to various Plate Tectonic settings

Silicates. The most common group of minerals forming the silicate Earth

Silicates. The most common group of minerals forming the silicate Earth Silicates The most common group of minerals forming the silicate Earth 25% of all minerals (~1000) 40% of rock forming minerals 90% of earth s crust i.e those minerals you are likely to find ~100 of earth