Transcript Chapter 27 Thermodynamics of Metamorphic Reactions

Thermodynamics and P-T
Today
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Updates
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Lecture outline:
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Gibbs free energy
Reactions
P-T estimates
Prograde Sequence and Facies
Index minerals make zones, but COMPOSITION DEPENDENT
Change in composition, means change in minerals occurring
 Chlorite zone.
Chlorite
 Biotite zone.
Biotite
 Garnet zone.
Cordierite
 Staurolite zone.
Andalusite
 Kyanite zone.
Sillimanite
 Sillimanite zone.
=> Facies is better to compare different metamorphic rocks
Prefix and mineral texture
High Strain Rocks
High Strain Rocks
Rock types to expect with depth/deformation
Why do we care about metamorphic
rocks?
Thermodynamics
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Consider a chemical system in terms of energy
Natural systems tend toward states of minimum energy
(and maximum entropy)
Energy States
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Unstable: falling or rolling
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Stable: at rest in lowest
energy state
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Metastable: in low-energy
perch
Figure 5-1. Stability states. Winter (2001) An Introduction to
Igneous and Metamorphic Petrology. Prentice Hall.
Gibbs Free Energy
Gibbs free energy is used to describe chemical energy
Gibbs free energy for 1 phase:
G = H - TS
Where:
G = Gibbs Free Energy
H = Enthalpy (heat content)
T = Temperature in Kelvins
S = Entropy (can think of as randomness)
Change in Gibbs f.e. in reaction
DG for a reaction of the type:
2A + 3B =C +4D
DG = S (n G)products - S(n G)reactants
= GC + 4GD - 2GA - 3GB
What side of the reaction is more stable?
Gibbs f.e. @ different PT
From 2nd law of thermodynamics, can derive for other PT:
dG = VdP - SdT
(Spear, Ch 6)
where V = volume and S = entropy (both molar)
We can use this equation to calculate G for any phase at any T and P
by integrating
GT
2
P2
- GT P =
1
1
P2
T2
1
1
VdP - SdT

P
T
For a reaction:
Now consider a reaction, we can then use the equation:
dDG = DVdP - DSdT
(ignoring DX)
DG for any reaction = 0 at equilibrium
Initial roundup
So:
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G measures relative chemical stability
Get G from H and S measurements
Expand to other PT mathematically
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Need change in V, S:
• dV/dP is the coefficient of isothermal compressibility
• dS/dT is the heat capacity (Cp)
Result of changing composition
Effect of adding Ca to “albite = jadeite + quartz”
DGT, P = DGoT, P + RTlnK
DGoT, P = equilibrium (= 0 at some P and T)
Changing Ca => RTlnK
We could assume ideal solution and
K=
X
Pyx
Jd
X
Q
SiO 2
Plag
Ab
X
All coefficients = 1
Chemical potential - 
RT ln K term and chemical potential:
At constant P&T:
G = ∑ *n
( = chem. pot., n = moles)
 for component I (think phase diagrams) in phase A is:
i,A = i,o + RT ln ai,a (a = activity, i,o =  STP)
General case:
aA + bB = cC + dD
K=
RTlnK = RTln{(aC*aD)/(aA*aB)}
c
C
a
A
d
a
aD
a
aB b
Compositional variations
Effect of adding Ca to albite = jadeite + quartz
DGP, T = DGoP, T + RTlnK
numbers are values for K
Figure 27-4. P-T phase diagram for the reaction Jadeite + Quartz = Albite for various values of K. The equilibrium curve for K =
1.0 is the reaction for pure end-member minerals (Figure 27-1). Data from SUPCRT (Helgeson et al., 1978). Winter (2001) An
Introduction to Igneous and Metamorphic Petrology. Prentice Hall.
Geothermobarometry
Use measured distribution of elements in coexisting
phases from experiments at known P and T to estimate P
and T of equilibrium in natural samples
Geothermobarometry
The Garnet - Biotite geothermometer
lnKD = -2108 · T(K) + 0.781
DGP,T = 0 = DH 0.1, 298 - TDS0.1, 298 + PDV + 3 RTlnKD
ln K D =
-DH - PDV  1  DS
 
3R
 T  3R
52 ,090  2.494P  MPa 
T  C =
- 273
19.506 - 12.943 ln K D
o
Figure 27-5. Graph of lnK vs. 1/T (in Kelvins) for the Ferry and Spear (1978) garnet-biotite exchange equilibrium at 0.2 GPa from
Table 27-2. Winter (2001) An Introduction to Igneous and Metamorphic Petrology. Prentice Hall.
Geothermobarometry
The Garnet - Biotite geothermometer
Figure 27-7. Pressure-temperature diagram similar to Figure 27-4 showing lines of constant KD plotted using equation (27-35) for the
garnet-biotite exchange reaction. The Al2SiO5 phase diagram is added. From Spear (1993) Metamorphic Phase Equilibria and PressureTemperature-Time Paths. Mineral. Soc. Amer. Monograph 1.
Geothermobarometry
The GASP geobarometer
Figure 27-8. P-T phase diagram showing the
experimental results of Koziol and Newton
(1988), and the equilibrium curve for reaction
(27-37). Open triangles indicate runs in which
An grew, closed triangles indicate runs in which
Grs + Ky + Qtz grew, and half-filled triangles
indicate no significant reaction. The univariant
equilibrium curve is a best-fit regression of the
data brackets. The line at 650oC is Koziol and
Newton’s estimate of the reaction location based
on reactions involving zoisite. The shaded area is
the uncertainty envelope. After Koziol and
Newton (1988) Amer. Mineral., 73, 216-233
Geothermobarometry
The GASP geobarometer
Figure 27-8. P-T diagram contoured for equilibrium curves of various values of K for the GASP geobarometer reaction: 3 An = Grs + 2
Ky + Qtz. From Spear (1993) Metamorphic Phase Equilibria and Pressure-Temperature-Time Paths. Mineral. Soc. Amer. Monograph 1.
Geothermobarometry
Precision and Accuracy
Figure 27-15. P-T diagram illustrating the calculated uncertainties from various sources in the application of the garnet-biotite
geothermometer and the GASP geobarometer to a pelitic schist from southern Chile. After Kohn and Spear (1991b) Amer. Mineral., 74,
77-84 and Spear (1993) From Spear (1993) Metamorphic Phase Equilibria and Pressure-Temperature-Time Paths. Mineral. Soc. Amer.
Monograph 1.