Crust to Core workshop: An introduction to Perple_X Sevilla, March 2009 Mark Caddick Institute of Mineralogy and Petrology Crust to Core workshop: An introduction to Perple_X Part 1: A very brief introduction American Oxford Dictionary Thermodynamics: the branch of physical science that deals with the relations between heat and other forms of energy (such as mechanical, electrical, or chemical energy), and, by extension, of the relationships and interconvertibility of all forms of energy Capabilities Capabilities Caddick & Thompson, 2008 Capabilities • Construction of simple PT plots relevant to metamorphic rocks • Construction of complex PT plots relevant to metamorphic rocks • Calculating proportions and compositions of minerals as a function of PT Capabilities • Construction of simple PT plots relevant to metamorphic rocks • Construction of complex PT plots relevant to metamorphic rocks • Calculating proportions and compositions of minerals as a function of PT • Understanding how rock composition modifies stable assemblage and mineral compositions Capabilities • Construction of simple PT plots relevant to metamorphic rocks • Construction of complex PT plots relevant to metamorphic rocks • Calculating proportions and compositions of minerals as a function of PT • Understanding how rock composition changes stable assemblage and mineral compositions • Application of these calculations… • PT evolution in continental collision • Granite generation during orogenesis • H2O/CO2 in metamorphism Capabilities • Construction of simple PT plots relevant to metamorphic rocks • Construction of complex PT plots relevant to metamorphic rocks • Calculating proportions and compositions of minerals as a function of PT • Understanding how rock composition changes stable assemblage and mineral compositions • Application of these calculations… • PT evolution in continental collision • Granite generation in the orogenesis • H2O/CO2 in metamorphism • Mantle mineralogy and melting Capabilities • Construction of simple PT plots relevant to metamorphic rocks • Construction of complex PT plots relevant to metamorphic rocks • Calculating proportions and compositions of minerals as a function of PT • Understanding how rock composition changes stable assemblage and mineral compositions • Application of these calculations… • PT evolution in continental collision • Granite generation in the orogenesis • H2O/CO2 in orogenesis • Mantle mineralogy and melting • Fluid production during subduction, predicting seismic properties, thermodynamic data from experiments, etc, etc Boundary conditions & assumptions Garnet can be modelled in 1D: Implying a spherical crystal geometry, sectioned through its centre Modal proportion & composition of phases are defined by phase equilibria constraints: No reaction overstep instantaneous is (currently) permitted, rim equilibration is Bulk-rock composition can be fixed or progressively depleted upon Postulated P-T-t history of the Lesser crystal growth Himalaya, western India After Caddick et al (2007) Fe, Mg, Mn and Ca diffusion data after Carlson (2006): Diffusivities are composition (position in model space) and P,T ‘’’’’’’’’’’’’’’’ The PT(t) path and fO2 conditions are prescribed: Following example is based upon a Lesser Himalayan PT path Goldschmidt 2008, Vancouver An introduction to (or some revision on) thermodynamics dU ≤ TdS - PdV tells us about the energetics of a system without chemical change (i.e a homogenous phase with no compositional change during the process) To describe energetic changes coming from mass transfer we use the concept of chemical potential (Gibbs, 1876) ⎛ ∂U ⎞ µi ≡ ⎜ ⎟ ⎝ ∂n ⎠ i S, V , other components An introduction to (or some revision on) thermodynamics dU ≤ TdS - PdV tells us about the energetics of a system without chemical change (i.e a homogenous phase with no compositional change during the process) To describe energetic changes coming from mass transfer we use the concept of chemical potential (Gibbs, 1876) ⎛ ∂U ⎞ µi ≡ ⎜ ⎟ ⎝ ∂n ⎠ i S, V , other components Summing the energies associated with all components in the system and adding to our combined laws equation yields dU = ΤδΣ − Πδς + ∑ ι −1 µιδνι κ An introduction to (or some revision on) thermodynamics dU = ΤδΣ − Πδς + ∑ ι −1 µιδνι κ Is the fundamental equation that we will use to quantify internal energy This can be transformed to give various combinations of S, V, T and P as the independent variables Gibbs free energy: dG = − ΣδΤ + ς δΠ + ∑ ι −1 µιδνι κ Gibbs free energy will be of most interest to us, since P and T are the most obvious choices of independent variables for geologic application An introduction to (or some revision on) thermodynamics Gibbs free energy: dG = − ΣδΤ + ς δΠ + ∑ ι −1 µιδνι κ ⎛ ∂G ⎞ ⎜⎝ ⎟⎠ = −S ∂T P,ni Change in G with respect to temperature = entropy ⎛ ∂G ⎞ ⎜⎝ ⎟⎠ = V ∂P T ,ni Change in G with respect to pressure = volume dP Σ2 − Σ1 = dT ς − ς (Clausius-Clapeyron) An introduction to (or some revision on) thermodynamics Gibbs free energy: dG = − ΣδΤ + ς δΠ + ∑ ι −1 µιδνι κ Ignoring (for a while) heat capacity, thermal expansion and isothermal compression… • If a chemically closed system has two possible states (configurations of phases), the one with the lowest absolute G at any PT should be more stable • If both have the same absolute G (the ∆G of moving from one state to the other = 0), they have the same relative stability and a reaction between them is stable An introduction to (or some revision on) thermodynamics A: Solid more stable than liquid (low T) B: Liquid more stable than solid (high T) Equilibrium at Teq GLiq = Gsol Melting reaction occurs at Teq Relationship between Gibbs free energy and temperature for the solid and liquid forms of a substance at constant pressure After Winter (2001) An Introduction to Igneous and Metamorphic Petrology Prentice Hall An introduction to (or some revision on) thermodynamics ⎛ ∂G ⎞ ⎜⎝ ⎟⎠ = −S , so Sliquid > Ssolid ∂T P,ni A: Solid more stable than liquid (low T) B: Liquid more stable than solid (high T) Equilibrium at Teq GLiq = Gsol Melting reaction occurs at Teq Relationship between Gibbs free energy and temperature for the solid and liquid forms of a substance at constant pressure After Winter (2001) An Introduction to Igneous and Metamorphic Petrology Prentice Hall An introduction to (or some revision on) thermodynamics Two fundamentally different approaches are commonly-used: Find the lowest absolute G to predict the most stable configuration of phases: e.g Perple_X (Connolly) Find the reactions between phases by finding where G is equal between configurations (∆G = 0): e.g THERMOCALC (Holland & Powell) Both approaches are very simple for chemically simple systems, for example… An introduction to (or some revision on) thermodynamics Sillimanite = Al2SiO5 = Andalusite −TSSillimanite + PVSillimanite = −TSAndalusite + PVAndalusite If we know the entropy and volume of sillimanite and andalusite (which are PT dependent), we can easily calculate the PT line along which they both occur… An introduction to (or some revision on) thermodynamics Sillimanite = Al2SiO5 = Andalusite −TSSillimanite + PVSillimanite = −TSAndalusite + PVAndalusite If we know the entropy and volume of sillimanite and andalusite (which are PT dependent), we can easily calculate the PT line along which they both occur… Chlorite + Garnet + Muscovite = Biotite + Staurolite + Quartz + Water An introduction to (or some revision on) thermodynamics Sillimanite = Al2SiO5 = Andalusite −TSSillimanite + PVSillimanite = − TSAndalusite + PVAndalusite Chlorite + Garnet + Muscovite = Biotite + Staurolite + Quartz + H2O Useful resources: • Frank Spear’s book (Metamorphic PhaseEquilibria and Pressure-Temperature-Time Paths)is pretty good for the thermodynamic laws and their derivation (especially chapter 6) • So are chapters 1-4 of Jamie Connolly’s ETH course notes (http://www.perplex.ethz.ch/thermo_course) An introduction to (or some revision on) thermodynamics Energy can be expressed in numerous ways by combining with previous expressions to give the most useful formulation, e.g H = Υ + Πς = ΤΣ + ∑ ι −1 µινι κ Γ = Υ + Πς − ΤΣ = Η − ΤΣ = ∑ι κ −1 µινι Gibbs free energy: dG = − ΣδΤ + ς δΠ + ∑ ι −1 µιδνι κ Gibbs free energy will be of most interest to us, since P and T are the most obvious choices of independent variables for geologic application An introduction to (or some revision on) thermodynamics dU = ΤδΣ − Πδς + ∑ ι −1 µιδνι κ Is the fundamental equation that we will use to quantify internal energy This can be transformed to give various combinations of S, V, T and P as the independent variables Enthalpy: dH = ΤδΣ + ς δΠ + ∑ ι −1 µιδνι κ Gibbs free energy: dG = − ΣδΤ + ς δΠ + ∑ ι −1 µιδνι κ Gibbs free energy will be of most interest to us, since P and T are the most obvious choices of independent variables for geologic application [...]... independent variables for geologic application An introduction to (or some revision on) thermodynamics Gibbs free energy: dG = − ΣδΤ + ς δΠ + ∑ ι 1 µιδνι κ ⎛ ∂G ⎞ ⎜⎝ ⎟⎠ = −S ∂T P,ni Change in G with respect to temperature = entropy ⎛ ∂G ⎞ ⎜⎝ ⎟⎠ = V ∂P T ,ni Change in G with respect to pressure = volume dP Σ2 − 1 = dT ς 2 − ς 1 (Clausius-Clapeyron) An introduction to (or some revision on) thermodynamics... are chapters 1- 4 of Jamie Connolly’s ETH course notes (http://www.perplex.ethz.ch/thermo_course) An introduction to (or some revision on) thermodynamics Energy can be expressed in numerous ways by combining with previous expressions to give the most useful formulation, e.g H = Υ + Πς = ΤΣ + ∑ ι 1 µινι κ Γ = Υ + Πς − ΤΣ = Η − ΤΣ = ∑ι κ 1 µινι Gibbs free energy: dG = − ΣδΤ + ς δΠ + ∑ ι 1 µιδνι κ Gibbs... laws equation yields dU = ΤδΣ − Πδς + ∑ ι 1 µιδνι κ An introduction to (or some revision on) thermodynamics dU = ΤδΣ − Πδς + ∑ ι 1 µιδνι κ Is the fundamental equation that we will use to quantify internal energy This can be transformed to give various combinations of S, V, T and P as the independent variables Gibbs free energy: dG = − ΣδΤ + ς δΠ + ∑ ι 1 µιδνι κ Gibbs free energy will be of most... potential (Gibbs, 18 76) ⎛ ∂U ⎞ µi ≡ ⎜ ⎟ ⎝ ∂n ⎠ i S, V , other components An introduction to (or some revision on) thermodynamics dU ≤ TdS - PdV tells us about the energetics of a system without chemical change (i.e a homogenous phase with no compositional change during the process) To describe energetic changes coming from mass transfer we use the concept of chemical potential (Gibbs, 18 76) ⎛ ∂U ⎞ µi... reaction between them is stable An introduction to (or some revision on) thermodynamics A: Solid more stable than liquid (low T) B: Liquid more stable than solid (high T) Equilibrium at Teq GLiq = Gsol Melting reaction occurs at Teq Relationship between Gibbs free energy and temperature for the solid and liquid forms of a substance at constant pressure After Winter (20 01) An Introduction to Igneous and Metamorphic... Hall An introduction to (or some revision on) thermodynamics ⎛ ∂G ⎞ ⎜⎝ ⎟⎠ = −S , so Sliquid > Ssolid ∂T P,ni A: Solid more stable than liquid (low T) B: Liquid more stable than solid (high T) Equilibrium at Teq GLiq = Gsol Melting reaction occurs at Teq Relationship between Gibbs free energy and temperature for the solid and liquid forms of a substance at constant pressure After Winter (20 01) An Introduction. .. Himalayan simulation - 1mm crystal Small compositional ‘steps’ Distance, µm No diffusion Distance, µm 20 Myr path with diffusion Red = Fe: Blue = Mg: Black = Mn: Green = Ca 9 Goldschmidt 2008, Vancouver Molefraction, X Molefraction, X Lesser Himalayan simulation - 1mm crystal Distance, µm No diffusion Distance, µm 20 Myr path with diffusion Red = Fe: Blue = Mg: Black = Mn: Green = Ca 10 Goldschmidt 2008,... amount of material present: e.g Volume (V) & Entropy (S) An introduction to (or some revision on) thermodynamics First Law of thermodynamics: The increase in the internal energy (U) of a thermodynamic system is equal to the amount of heat energy (Q) added to the system plus the work (W) done on the system by the surroundings dU = dQ ± dW An introduction to (or some revision on) thermodynamics First... = P •V (P = force/area [N/m2] and V = m3) dU = dQ + PdV An introduction to (or some revision on) thermodynamics Second Law of thermodynamics: This introduces the notion of entropy (S) which relates change in temperature (T) with the heat energy (Q) added to the system: δΘ dS ≥ Τ Which can be substituted into the first law: dU ≤ ΤδΣ − Πδς An introduction to (or some revision on) thermodynamics dU ≤ TdS...Molefraction, X Molefraction, X Lesser Himalayan simulation - 1mm crystal Distance, µm No diffusion Distance, µm 20 Myr path with diffusion Red = Fe: Blue = Mg: Black = Mn: Green = Ca 9 Goldschmidt 2008, Vancouver Molefraction, X Molefraction, X Lesser Himalayan simulation - 1mm crystal Distance, µm No diffusion Distance, µm 20 Myr path with diffusion Red = Fe: Blue =