chapter 9: introduction to...

CHAPTER 9: INTRODUCTION TO THERMODYNAMICS Sarah Lambart

RECAP CHAP. 8: SILICATE MINERALOGY

� Orthosilicate: “islands”

� olivine: solid solution, ie physical properties vary between 2 end-members: Forsterite (Mg2SiO4) – Fayalite (Fe2SiO4); structure: chains of M1 sites connected by larger M2 and cross-link by independent SiO4 tetrahedra.

� Garnet: X32+Y2

3+[SiO44-]3 - very various chemical compositions ⇔ in

a lot of different rocks; 2 groups: pyralspite (Y=Al3+) and ugrandite (X=Ca2+)

� Zircon: ZrSiO4 - extremely resistant – minor substitutions of U and Th: used to date rocks.

� Aluminosilicate: Al2SiO5 - 3 polymorphs – metamorphic minerals


� Sorosilicate: double island silicates: Si2O76-

� 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:

� Corderite:

� Tourmaline: in peraluminous granites and metapelites

isostructural

RECAP CHAP. 8: SILICATE MINERALOGY � Inosilicate: simple or double chains

� Simple: pyroxenes XYZ2O6

�  2 groups: orthopyroxenes (orthorhombic) and clinopyroxenes (monoclinic)

�  Orthopyroxene: solid solution enstatite MgSiO3 and ferrosillite FeSiO3

�  Clinopyronenes: (Ca,Na,Mg,Fe,Ti)2(Si,Al)2O6

RECAP CHAP. 8: SILICATE MINERALOGY � Inosilicate: simple or double chains

� Double: amphiboles XYZ2O6

�  W0-1X2Y5Z8O22(OH,F)2: HYDROUS MINERAL

� Most common: Hornblende (Ca,Na)2-3(Mg,Fe,Al)5Si6(Si,Al)2O22(OH,F)2

�  In intermediate igneous rocks


� 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


� 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

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 c n we use simple phase diagrams to understand natural systems?

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.

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

THERMODYNAMICS � Popular Computer Programs for Thermodynamic Calculations

and Modeling: � TWQ: allows the calculations of the position of phase equilibria in P-T,

T-XCO2, and P-XCO2 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

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) ΔGf

� ΔGf varies with P- T condition and its composition X

THERMODYNAMICS: DEFINITIONS � Gibbs free energy of reaction ΔGr: sum of ΔGf on the right-

hand side of the reaction minus sum of ΔGf of the left- hand side �  If ΔGr<0, reaction proceeds to the right

�  If ΔGr>0, reaction proceeds to the left

� Ex.: albite = jadeite + quartz ΔGr(1bar)>0 ⇒ albite is stable, the assemblage jadeite + quartz is unstable.

� ΔGr varies with P-T and X ⇒ phase diagram

THERMODYNAMICS: DEFINITIONS � Gibbs free energy of mineral:

� Unit: joules/mols (or calorie/mole)

� Ex.: enstatite MgSiO3

� ΔGf from pure elements (Mg, Si and O) = ΔGf (enstatite, element) = -1460.9 kJ/mole at room temperature and pressure

� ΔGf (enstatite, oxide) = -35.4 kJ/mole

� Convention: ΔGf (pure element) = 0 – other values of Gibbs free energy are relative values

DETERMINING THE LOCATION OF METAMORPHIC REACTIONS

� (1) albite = jadeite + quartz

� ΔGr = ΔG1 = ΔGf(jadeite,elmt) + ΔGf(quartz, elmt) – ΔGf(albite, elmt) = ΔGf(jadeite,oxide) + ΔGf(quartz, oxide) – ΔGf(albite, oxide)

� At 400°C and 1 GPaΔG1 >0 At 400°C and 1.4 Gpa ΔG1 <0


� 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:

� ΔGr = ΔEr + PΔVr – TΔSr = ΔH-TΔS

Constant (depend on the phase)

More voluminous phase = greater gibbs free energy

Measure of the disorder


� 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:


Constant (depend on the phase)

High volume phase are unstable at HP

High S phase are very stable at HT

THERMODYNAMICS: DEFINITIONS � Gibbs free energy of a reaction:


� 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: cm3/mole

�  S: J/deg-mole 1J = 10 cc-bar


� ΔGr: tells us if a reaction will take place

� ΔHr: tell us how much heat will flow in or out of the reaction:

�  If ΔHr < 0: exothermic reaction (ex.: C + O2 = CO2)

�  If ΔHr > 0: endothermic reaction (ex.: H2O(ice) = H2O(water) )

� ΔSr: tell us whether the products or reactants are more disordered

� ΔVr: tell us whether the products or reactants have greater volumes (ex.: ΔVr (graphite = diamond) <0 )

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 : 1st law of thermodynamic

� dG = TdS-PdV + PdV + VdP – TdS – SdT

� dG = VdP – SdT

� On the reaction curve, dG = 0 ⇒ dP/dT = ΔSP,T/ΔVP,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.: SiO2 at 500°C and 500 MPa

� dG = VdP – SdT or ΔG = VΔP – SΔT

� We can treat P and T separately:

� GP2 – GP1 = V(P2 – P1) if T and V constant

� For P2 = 500 MPa and P1 = 0.1 MPa, V = 22.69·10-6 m3; GP1 = -856300J/mol (low-quartz – from dataset) GP2 = -856300 + 22.69·10-6(500·106 – 0.1·106)= -844957 J

�  ΔG = VΔP – SΔT

� GT2 – GT1 = -S(T2-T1) if P = 500 MPa

� GT2 = GT1 – S0.1MPa (773 – 298)= - 844957 – 41.46(773 – 298) = -864650.5 J

�  G(α-qtz) at 500 MPa and 500°C ~ -864.7 kJ

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


� Melting curve - dP/dT = ΔS / ΔV Clapeyron

�  1.Does the liquid or solid have the larger volume/unit mass? Usually liquid. (except H2O)

�  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.


� 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).

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

chapter 9: introduction to...

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