![Page 1: Crust to Core workshop: An introduction to Perple_X Sevilla, March 2009 Mark Caddick](https://reader036.vdocuments.us/reader036/viewer/2022062409/56649ccf5503460f9499ae41/html5/thumbnails/1.jpg)
Crust to Core workshop:An introduction to Perple_X
Sevilla, March 2009
Mark Caddick
Institute of Mineralogy and Petrology
![Page 2: Crust to Core workshop: An introduction to Perple_X Sevilla, March 2009 Mark Caddick](https://reader036.vdocuments.us/reader036/viewer/2022062409/56649ccf5503460f9499ae41/html5/thumbnails/2.jpg)
Part 1: A very brief introduction
American Oxford DictionaryThermodynamics: 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.
Crust to Core workshop:An introduction to Perple_X
![Page 3: Crust to Core workshop: An introduction to Perple_X Sevilla, March 2009 Mark Caddick](https://reader036.vdocuments.us/reader036/viewer/2022062409/56649ccf5503460f9499ae41/html5/thumbnails/3.jpg)
Capabilities
![Page 4: Crust to Core workshop: An introduction to Perple_X Sevilla, March 2009 Mark Caddick](https://reader036.vdocuments.us/reader036/viewer/2022062409/56649ccf5503460f9499ae41/html5/thumbnails/4.jpg)
Complex pseudo
Capabilities
Caddick & Thompson, 2008
![Page 5: Crust to Core workshop: An introduction to Perple_X Sevilla, March 2009 Mark Caddick](https://reader036.vdocuments.us/reader036/viewer/2022062409/56649ccf5503460f9499ae41/html5/thumbnails/5.jpg)
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
![Page 6: Crust to Core workshop: An introduction to Perple_X Sevilla, March 2009 Mark Caddick](https://reader036.vdocuments.us/reader036/viewer/2022062409/56649ccf5503460f9499ae41/html5/thumbnails/6.jpg)
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
![Page 7: Crust to Core workshop: An introduction to Perple_X Sevilla, March 2009 Mark Caddick](https://reader036.vdocuments.us/reader036/viewer/2022062409/56649ccf5503460f9499ae41/html5/thumbnails/7.jpg)
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
![Page 8: Crust to Core workshop: An introduction to Perple_X Sevilla, March 2009 Mark Caddick](https://reader036.vdocuments.us/reader036/viewer/2022062409/56649ccf5503460f9499ae41/html5/thumbnails/8.jpg)
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
![Page 9: Crust to Core workshop: An introduction to Perple_X Sevilla, March 2009 Mark Caddick](https://reader036.vdocuments.us/reader036/viewer/2022062409/56649ccf5503460f9499ae41/html5/thumbnails/9.jpg)
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..
![Page 10: Crust to Core workshop: An introduction to Perple_X Sevilla, March 2009 Mark Caddick](https://reader036.vdocuments.us/reader036/viewer/2022062409/56649ccf5503460f9499ae41/html5/thumbnails/10.jpg)
1. Garnet can be modelled in 1D:
Implying a spherical crystal geometry, sectioned through its centre
2. Modal proportion & composition of phases are defined by phase equilibria constraints:
No reaction overstep is (currently) permitted, rim equilibration is instantaneous
3. Bulk-rock composition can be fixed or progressively depleted upon crystal growth
4. Fe, Mg, Mn and Ca diffusion data after Carlson (2006):
Diffusivities are composition (position in model space) and P,T ‘’’’’’’’’’’’’’’’
5. The PT(t) path and fO2 conditions are prescribed:
Following example is based upon a Lesser Himalayan PT path
Boundary conditions & assumptions
Goldschmidt 2008, Vancouver8
Postulated P-T-t history of the Lesser Himalaya, western India. After Caddick et al. (2007).
![Page 11: Crust to Core workshop: An introduction to Perple_X Sevilla, March 2009 Mark Caddick](https://reader036.vdocuments.us/reader036/viewer/2022062409/56649ccf5503460f9499ae41/html5/thumbnails/11.jpg)
Lesser Himalayan simulation - 1mm crystal
No diffusion 20 Myr pathwith diffusion
Red = Fe: Blue = Mg: Black = Mn: Green = Ca
Goldschmidt 2008, Vancouver9
Distance, µm Distance, µm
Mol
efra
ctio
n, X
Mol
efra
ctio
n, X
![Page 12: Crust to Core workshop: An introduction to Perple_X Sevilla, March 2009 Mark Caddick](https://reader036.vdocuments.us/reader036/viewer/2022062409/56649ccf5503460f9499ae41/html5/thumbnails/12.jpg)
No diffusion 20 Myr pathwith diffusion
Red = Fe: Blue = Mg: Black = Mn: Green = Ca
Goldschmidt 2008, Vancouver9
Distance, µm Distance, µm
Mol
efra
ctio
n, X
Mol
efra
ctio
n, X
Lesser Himalayan simulation - 1mm crystal
![Page 13: Crust to Core workshop: An introduction to Perple_X Sevilla, March 2009 Mark Caddick](https://reader036.vdocuments.us/reader036/viewer/2022062409/56649ccf5503460f9499ae41/html5/thumbnails/13.jpg)
No diffusion 20 Myr pathwith diffusion
Red = Fe: Blue = Mg: Black = Mn: Green = Ca
Goldschmidt 2008, Vancouver9
Distance, µm Distance, µm
Mol
efra
ctio
n, X
Mol
efra
ctio
n, X
Lesser Himalayan simulation - 1mm crystal
High-Mn core
Higher Ca than Fe in core
Small compositional‘steps’
![Page 14: Crust to Core workshop: An introduction to Perple_X Sevilla, March 2009 Mark Caddick](https://reader036.vdocuments.us/reader036/viewer/2022062409/56649ccf5503460f9499ae41/html5/thumbnails/14.jpg)
No diffusion 20 Myr pathwith diffusion
Red = Fe: Blue = Mg: Black = Mn: Green = Ca
Goldschmidt 2008, Vancouver10
Mol
efra
ctio
n, X
Mol
efra
ctio
n, X
Distance, µm Distance, µm
Lesser Himalayan simulation - 1mm crystal
![Page 15: Crust to Core workshop: An introduction to Perple_X Sevilla, March 2009 Mark Caddick](https://reader036.vdocuments.us/reader036/viewer/2022062409/56649ccf5503460f9499ae41/html5/thumbnails/15.jpg)
System/components definitions 1
A very quick introduction to (or some revision on) thermodynamics
![Page 16: Crust to Core workshop: An introduction to Perple_X Sevilla, March 2009 Mark Caddick](https://reader036.vdocuments.us/reader036/viewer/2022062409/56649ccf5503460f9499ae41/html5/thumbnails/16.jpg)
American Oxford Dictionary
The first law of thermodynamics states the equivalence of heat and work and reaffirms the principle of conservation of energy. The second law states that heat does not of itself pass from a cooler to a hotter body. Another, equivalent, formulation of the second law is that the entropy of a closed system can only increase. The third law (also called Nernst's heat theorem) states that it is impossible to reduce the temperature of a system to absolute zero in a finite number of operations.
An introduction to (or some revision on) thermodynamics
![Page 17: Crust to Core workshop: An introduction to Perple_X Sevilla, March 2009 Mark Caddick](https://reader036.vdocuments.us/reader036/viewer/2022062409/56649ccf5503460f9499ae41/html5/thumbnails/17.jpg)
A system is some part of the universe that you want to study and understand• The surroundings are everything else in the universe that is not in our system• The system can be open or closed to (isolated from) the surroundings in terms of
both matter and energy
All Changes in a system are associated with the transfer of energy
Natural systems tend toward states of minimum energy
System/components definitions 1
An introduction to (or some revision on) thermodynamics:Some definitions
![Page 18: Crust to Core workshop: An introduction to Perple_X Sevilla, March 2009 Mark Caddick](https://reader036.vdocuments.us/reader036/viewer/2022062409/56649ccf5503460f9499ae41/html5/thumbnails/18.jpg)
An introduction to (or some revision on) thermodynamics:Some definitions
• In our case, a system is likely to be a mineral or a rock
• In this case, it is comprised of chemical components that describe chemical variability in that mineral or a rock
• Typical components might be FeO, MgO and SiO2 used to describe olivine
• A phase is any mechanically separable and chemically homogenous portion of the system, e.g. a melt, a fluid, or a mineral in a rock
• A reaction is anything that changes the nature of the phases within a system
System/components definitions 2
![Page 19: Crust to Core workshop: An introduction to Perple_X Sevilla, March 2009 Mark Caddick](https://reader036.vdocuments.us/reader036/viewer/2022062409/56649ccf5503460f9499ae41/html5/thumbnails/19.jpg)
An introduction to (or some revision on) thermodynamics:Some definitions
• Thermodynamics is primarily concerned with macroscopic energies of microscopic processes that we might or might not fully understand.
• It is convenient to group all of the variables required into two classes:
Intensive variables are independent of the amount of material present:
e.g. Pressure (P) & Temperature (T)
Extensive variables are dependent on the amount of material present:
e.g. Volume (V) & Entropy (S)
System/components definitions 3
![Page 20: Crust to Core workshop: An introduction to Perple_X Sevilla, March 2009 Mark Caddick](https://reader036.vdocuments.us/reader036/viewer/2022062409/56649ccf5503460f9499ae41/html5/thumbnails/20.jpg)
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
First Law
![Page 21: Crust to Core workshop: An introduction to Perple_X Sevilla, March 2009 Mark Caddick](https://reader036.vdocuments.us/reader036/viewer/2022062409/56649ccf5503460f9499ae41/html5/thumbnails/21.jpg)
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.
0 = dQ + dW - dU
W (J) = N•m = P •V (P = force/area [N/m2] and V = m3)
dU = dQ + PdV
First Law
![Page 22: Crust to Core workshop: An introduction to Perple_X Sevilla, March 2009 Mark Caddick](https://reader036.vdocuments.us/reader036/viewer/2022062409/56649ccf5503460f9499ae41/html5/thumbnails/22.jpg)
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:
Which can be substituted into the first law:
Second Law
dS ≥dQT
dU ≤TdS−PdV
![Page 23: Crust to Core workshop: An introduction to Perple_X Sevilla, March 2009 Mark Caddick](https://reader036.vdocuments.us/reader036/viewer/2022062409/56649ccf5503460f9499ae41/html5/thumbnails/23.jpg)
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)
Chemical potential
μi ≡∂U
∂ni
⎛
⎝⎜⎞
⎠⎟S, V , other components
![Page 24: Crust to Core workshop: An introduction to Perple_X Sevilla, March 2009 Mark Caddick](https://reader036.vdocuments.us/reader036/viewer/2022062409/56649ccf5503460f9499ae41/html5/thumbnails/24.jpg)
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)
Summing the energies associated with all components in the system and adding to our combined laws equation yields
Chemical potential
μi ≡∂U
∂ni
⎛
⎝⎜⎞
⎠⎟S, V , other components
dU =TdS−PdV + μidnii−1
k∑
![Page 25: Crust to Core workshop: An introduction to Perple_X Sevilla, March 2009 Mark Caddick](https://reader036.vdocuments.us/reader036/viewer/2022062409/56649ccf5503460f9499ae41/html5/thumbnails/25.jpg)
An introduction to (or some revision on) thermodynamics
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 energy
dU =TdS−PdV + μidnii−1
k∑
Gibbs free energy: dG =−SdT +VdP + μidnii−1
k∑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
![Page 26: Crust to Core workshop: An introduction to Perple_X Sevilla, March 2009 Mark Caddick](https://reader036.vdocuments.us/reader036/viewer/2022062409/56649ccf5503460f9499ae41/html5/thumbnails/26.jpg)
An introduction to (or some revision on) thermodynamics
Gibbs energy
Gibbs free energy: dG =−SdT +VdP + μidnii−1
k∑
∂G
∂T⎛⎝⎜
⎞⎠⎟
P,ni
= −S∂G
∂P⎛⎝⎜
⎞⎠⎟
T ,ni
= V
Change in G with respect to temperature = entropy
Change in G with respect to pressure = volume
dP
dT=
S2 −S1
V2 −V1 (Clausius-Clapeyron)
![Page 27: Crust to Core workshop: An introduction to Perple_X Sevilla, March 2009 Mark Caddick](https://reader036.vdocuments.us/reader036/viewer/2022062409/56649ccf5503460f9499ae41/html5/thumbnails/27.jpg)
An introduction to (or some revision on) thermodynamics
Gibbs energy
Gibbs free energy: dG =−SdT +VdP + μidnii−1
k∑
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.
![Page 28: Crust to Core workshop: An introduction to Perple_X Sevilla, March 2009 Mark Caddick](https://reader036.vdocuments.us/reader036/viewer/2022062409/56649ccf5503460f9499ae41/html5/thumbnails/28.jpg)
An introduction to (or some revision on) thermodynamics
Gibbs energy
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.
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
![Page 29: Crust to Core workshop: An introduction to Perple_X Sevilla, March 2009 Mark Caddick](https://reader036.vdocuments.us/reader036/viewer/2022062409/56649ccf5503460f9499ae41/html5/thumbnails/29.jpg)
An introduction to (or some revision on) thermodynamics
Gibbs energy
∂G
∂T⎛⎝⎜
⎞⎠⎟
P,ni
= −S , so Sliquid > Ssolid
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.
![Page 30: Crust to Core workshop: An introduction to Perple_X Sevilla, March 2009 Mark Caddick](https://reader036.vdocuments.us/reader036/viewer/2022062409/56649ccf5503460f9499ae41/html5/thumbnails/30.jpg)
An introduction to (or some revision on) thermodynamics
Key program differences
Two fundamentally different approaches are commonly-used:
1. Find the lowest absolute G to predict the most stable configuration of phases:
e.g. Perple_X (Connolly)
2. 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…
![Page 31: Crust to Core workshop: An introduction to Perple_X Sevilla, March 2009 Mark Caddick](https://reader036.vdocuments.us/reader036/viewer/2022062409/56649ccf5503460f9499ae41/html5/thumbnails/31.jpg)
An introduction to (or some revision on) thermodynamics
Key program differences
−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…
Sillimanite = Al2SiO5 = Andalusite
![Page 32: Crust to Core workshop: An introduction to Perple_X Sevilla, March 2009 Mark Caddick](https://reader036.vdocuments.us/reader036/viewer/2022062409/56649ccf5503460f9499ae41/html5/thumbnails/32.jpg)
An introduction to (or some revision on) thermodynamics
Key program differences
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
−TSSillimanite + PVSillimanite = −TSAndalusite + PVAndalusite
Sillimanite = Al2SiO5 = Andalusite
![Page 33: Crust to Core workshop: An introduction to Perple_X Sevilla, March 2009 Mark Caddick](https://reader036.vdocuments.us/reader036/viewer/2022062409/56649ccf5503460f9499ae41/html5/thumbnails/33.jpg)
Chlorite + Garnet + Muscovite =Biotite + Staurolite + Quartz + H2O
−TSSillimanite + PVSillimanite =
− TSAndalusite + PVAndalusite
Sillimanite = Al2SiO5 = Andalusite
An introduction to (or some revision on) thermodynamics
![Page 34: Crust to Core workshop: An introduction to Perple_X Sevilla, March 2009 Mark Caddick](https://reader036.vdocuments.us/reader036/viewer/2022062409/56649ccf5503460f9499ae41/html5/thumbnails/34.jpg)
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)
![Page 35: Crust to Core workshop: An introduction to Perple_X Sevilla, March 2009 Mark Caddick](https://reader036.vdocuments.us/reader036/viewer/2022062409/56649ccf5503460f9499ae41/html5/thumbnails/35.jpg)
![Page 36: Crust to Core workshop: An introduction to Perple_X Sevilla, March 2009 Mark Caddick](https://reader036.vdocuments.us/reader036/viewer/2022062409/56649ccf5503460f9499ae41/html5/thumbnails/36.jpg)
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.
Gibbs energy
H =U + PV = TS+ μinii−1
k∑G =U + PV −TS = H −TS = μinii−1
k∑
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
Gibbs free energy: dG =−SdT +VdP + μidnii−1
k∑
![Page 37: Crust to Core workshop: An introduction to Perple_X Sevilla, March 2009 Mark Caddick](https://reader036.vdocuments.us/reader036/viewer/2022062409/56649ccf5503460f9499ae41/html5/thumbnails/37.jpg)
An introduction to (or some revision on) thermodynamics
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 will be of most interest to us, since P and T are the most obvious choices of independent variables for geologic application
Gibbs energy
Enthalpy: dH =TdS+VdP + μidnii−1
k∑
dU =TdS−PdV + μidnii−1
k∑
Gibbs free energy: dG =−SdT +VdP + μidnii−1
k∑