Ch 27 Thermo
-
Upload
jiggycheng -
Category
Documents
-
view
218 -
download
0
Transcript of Ch 27 Thermo
-
8/12/2019 Ch 27 Thermo
1/39
Thermodynamics
Begin with a brief review of Chapter 5
Natural systems tend toward states of minimum energy
-
8/12/2019 Ch 27 Thermo
2/39
Energy States
Unstable:falling or rolling
Stable:at rest in lowestenergy state
Metastable:in low-energyperch
Figure 5.1.Stability states. Winter (2010) An Introduction to Igneous
and Metamorphic Petrology. Prentice Hall.
-
8/12/2019 Ch 27 Thermo
3/39
Gibbs Free Energy
Gibbs free energy is a measure of chemicalenergy
Gibbs free energy for aphase:
G = H - TS
Where:
G = Gibbs Free Energy
H = Enthalpy (heat content)
T = Temperature in Kelvins
S = Entropy (can think of as randomness)
-
8/12/2019 Ch 27 Thermo
4/39
Thermodynamics
DG for a reactionof the type:2 A + 3 B = C + 4 D
DG = S(n G)products- S(n G)reactants= GC+ 4GD- 2GA- 3GB
The side of the reaction with lower G will be more stable
-
8/12/2019 Ch 27 Thermo
5/39
Thermodynamics
For other temperatures and pressures we can use the equation:
dG = VdP - SdT (ignoring DX for now)
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
zzG G VdP SdTT P T P
T
T
P
P
2 1 11
2
1
2
2- = -
If V and S are constants, our equation reduces to:
GT2 P2- GT1 P1= V(P2- P1) - S (T2- T1)
-
8/12/2019 Ch 27 Thermo
6/39
Now consider a reaction, we can then use the equation:
dDG = DVdP - DSdT (again ignoring DX)
G for any reaction = 0 at equilibrium
-
8/12/2019 Ch 27 Thermo
7/39
Worked Problem #2 used:
dDG = DVdP - DSdT
and G, S, V values for albite, jadeite and quartz tocalculate the conditions for which DG of the reaction:
Ab + Jd = Q
is equal to 0
from G values for each phase at 298K and 0.1 MPa calculate DG298, 0.1for the
reaction, do the same for DV and DS
DG at equilibrium = 0, so we can calculate an isobaric change in T that would
be required to bring DG298, 0.1to 0
0 - DG298, 0.1= -DS (Teq- 298) (at constant P)
Similarly we could calculate an isothermal change
0 - DG298, 0.1= -DV (Peq- 0.1) (at constant T)
Mineral S(J) G (J) V
(cm3/mol)
Low Albite 207.25 -3,710,085 100.07
Jadeite 133.53 -2,844,157 60.04
Quartz 41.36 -856,648 22.688
From Helgeson et al. (1978).
Table 27-1.Thermodynamic Data at 298K and
0.1 MPa from the SUPCRT Database
Method:
-
8/12/2019 Ch 27 Thermo
8/39
NaAlSi3O8= NaAlSi2O6+ SiO2
P - T phase diagram of the equilibrium curveHow do you know which side has which phases?
Figure 27.1. Temperature-pressure
phase diagram for the reaction:
Albite = Jadeite + Quartz
calculated using the program TWQ
of Berman (1988, 1990, 1991).
Winter (2010) An Introduction toIgneous and Metamorphic
Petrology. Prentice Hall.
-
8/12/2019 Ch 27 Thermo
9/39
pick any two points on the equilibrium curve
dDG = 0 = DVdP - DSdT
ThusdP
dT
S
V=
D
D
Figure 27.1. Temperature-pressure
phase diagram for the reaction:
Albite = Jadeite + Quartz
calculated using the program TWQ
of Berman (1988, 1990, 1991).
Winter (2010) An Introduction toIgneous and Metamorphic
Petrology. Prentice Hall.
-
8/12/2019 Ch 27 Thermo
10/39
Return to dG = VdP - SdT, for an isothermal process:
G G VdPP PP
P
2 11
2
- =z
Gas Phases
For solids it was fine to ignore V as f(P)
For gases this assumption is shitty
You can imagine how a gas compresses as P increasesHow can we define the relationship between V and P for a gas?
-
8/12/2019 Ch 27 Thermo
11/39
Gas Pressure-Volume Relationships
Ideal Gas
As P increases V decreases
PV=nRTIdeal Gas Law P = pressure
V = volume
T = temperature
n = # of moles of gas R = gas constant
= 8.3144 J mol-1K-1
P x V is a constant at constant T
Figure 5.5.Piston-and-cylinder apparatus to
compress a gas. Winter (2010) An Introduction to
Igneous and Metamorphic Petrology. Prentice Hall.
-
8/12/2019 Ch 27 Thermo
12/39
Gas Pressure-Volume Relationships
Since
we can substitute RT/P for V (for a single mole of gas), thus:
and, since R and T are certainly independent of P:
G G VdPP PP
P
2 11
2
- =z
G GRT
PdPP P
P
P
2 11
2
- =z
zG G RT P dPP P PP
2 11
2
- = 1
-
8/12/2019 Ch 27 Thermo
13/39
Gas Pressure-Volume Relationships
And since
GP2- GP1= RT ln P2- ln P1= RTln(P2/P1)
Thus the free energy of a gas phase at a specific P and T, when
referenced to a standard atate of 0.1 MPa becomes:
GP, T- GT= RTln(P/Po)
G of a gas at some P and T = G in the reference state (same T and 0.1 MPa)
+ a pressure term
1
xdx x=
zln
o
-
8/12/2019 Ch 27 Thermo
14/39
Gas Pressure-Volume Relationships
The form of this equation is very useful
GP, T- GT= RT ln(P/Po)
For a non-ideal gas(more geologically appropriate) the same
form is used, but we substitute fugacity (f )for P
wheref = gP gis the fugacity coefficient
Tables of fugacity coefficients for common gases are available
At low pressures most gases are ideal, but at high P they are not
o
-
8/12/2019 Ch 27 Thermo
15/39
Dehydration Reactions
Mu + Q = Kspar + Sillimanite + H2O
We can treat the solids and gases separately
GP, T- GT= DVsolids(P- 0.1) + RTln(P/0.1) (isothermal)
The treatment is then quite similar to solid-solid reactions, but
you have to solve for the equilibrium P by iteration
-
8/12/2019 Ch 27 Thermo
16/39
Dehydration Reactions
(qualitative analysis)
dP
dT
S
V=
D
D
Figure 27.2. Pressure-temperature
phase diagram for the reaction
muscovite + quartz = Al2SiO5+ K-
feldspar + H2O, calculated using
SUPCRT (Helgeson et al., 1978).
Winter (2010) An Introduction to
Igneous and Metamorphic Petrology.
Prentice Hall.
-
8/12/2019 Ch 27 Thermo
17/39
Solutions: T-X relationships
Ab = Jd + Q was calculated forpurephases
When solid solution results in impure phases
the activity of each phase is reduced
Use the same form as for gases (RT ln P or ln f)Instead of fugacity, we use activity
Ideal solution: ai= Xi n = # of sites in the phase on
which solution takes placeNon-ideal: ai= giXi
where giis theactivity coefficient
n
n
-
8/12/2019 Ch 27 Thermo
18/39
Solutions: T-X relationships
Example: orthopyroxenes (Fe, Mg)SiO3 Real vs. Ideal Solution Models
Figure 27.3. Activity-composition relationships for the enstatite-ferrosilite mixture in orthopyroxene at 600oC and 800oC. Circles are data
from Saxena and Ghose (1971); curves are model for sites as simple mixtures (from Saxena, 1973) Thermodynamics of Rock-Forming
Crystalline Solutions. Winter (2010) An Introduction to Igneous and Metamorphic Petrology. Prentice Hall.
-
8/12/2019 Ch 27 Thermo
19/39
Solutions: T-X relationships
Back to our reaction:
Simplify for now by ignoring dP and dT
For a reaction such as:
aA + bB = cC + dD
At a constant P and T:
where:
D DG G RT KP T P T
o
, ,= - ln
K cc
D
d
A
a
B
b=
a a
a a
-
8/12/2019 Ch 27 Thermo
20/39
Compositional variations
Effect of adding Ca to albite = jadeite + quartz
plagioclase = Al-rich Cpx + Q
DGT, P= DGo
T, P+ RTlnK
Lets say DGo
T, Pwas the value that we calculated forequilibrium in the pure Na-system (= 0 at some P and T)
DGoT, P = DG298, 0.1+ DV (P - 0.1) - DS (T-298) = 0
By adding Ca we will shift the equilibrium by RTlnK
We could assume ideal solution and
K JdPyx
SiO
Q
Ab
Plag=X X
X
2 All coefficients = 1
-
8/12/2019 Ch 27 Thermo
21/39
Compositional variations
So now we have:
DGT, P= DGo
T, P+ RTln since Q is pure
DGo
T, P= 0 as calculated for the pure system at P and TDGT, Pis the shifted DG due to the Ca added (no longer 0)
Thus we could calculate a DV(P - Peq
) that would bring
DGT, Pback to 0, solving for the new Peq
X
X
JdPyx
Ab
Plag
-
8/12/2019 Ch 27 Thermo
22/39
Compositional variations
Effect of adding Ca to albite = jadeite + quartz
DGP, T= DGo
P, T+ RTlnKnumbers 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 (2010) An Introduction to
Igneous and Metamorphic Petrology. Prentice Hall.
-
8/12/2019 Ch 27 Thermo
23/39
Geothermobarometry
Use measured distribution of elements in coexistingphases from experiments at known P and T to estimate P
and T of equilibrium in natural samples
-
8/12/2019 Ch 27 Thermo
24/39
Geothermobarometry
The Garnet - Biotite geothermometer
ToC Initial
X(Fe-Bt)
Final
X(Fe-Bt)
Final
X(Fe-Grt)
Final
(Mg/Fe)Grt
Final
(Mg/Fe)Bt
K T
Kelvins
1/T
Kelvins
lnK
799 1.00 0.750 0.905 0.105 0.333 0.315 1072 0.00093 -1.155
799 0.50 0.710 0.896 0.116 0.408 0.284 1072 0.00093 -1.258
749 0.50 0.695 0.896 0.116 0.439 0.264 1022 0.00098 -1.330
738 1.00 0.730 0.906 0.104 0.370 0.281 1011 0.00099 -1.271698 0.75 0.704 0.901 0.110 0.420 0.261 971 0.00103 -1.342
698 0.50 0.690 0.896 0.116 0.449 0.258 971 0.00103 -1.353
651 0.75 0.679 0.901 0.110 0.473 0.232 924 0.00108 -1.459
651 0.50 0.661 0.897 0.115 0.513 0.224 924 0.00108 -1.497
599 0.75 0.645 0.902 0.109 0.550 0.197 872 0.00115 -1.623
599 0.50 0.610 0.898 0.114 0.639 0.178 872 0.00115 -1.728
550 0.75 0.620 0.903 0.107 0.613 0.175 823 0.00122 -1.741
550 0.50 0.590 0.898 0.114 0.695 0.163 823 0.00122 -1.811
601 0.50 0.500 0.800 0.250 1.000 0.250 874 0.00114 -1.386
601 0.25 0.392 0.797 0.255 1.551 0.164 874 0.00114 -1.807
697 0.75 0.574 0.804 0.244 0.742 0.329 970 0.00103 -1.111
697 0.25 0.468 0.796 0.257 1.137 0.226 970 0.00103 -1.487
Table 27-2.Experimental results of Ferry and Spear (1978) on a Garnet-Biotite Geothermometer
-
8/12/2019 Ch 27 Thermo
25/39
Geothermobarometry
The Garnet - Biotite geothermometer
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 (2010) An Introduction to Igneous and Metamorphic Petrology. Prentice Hall.
lnKD= -2108 T(K) + 0.781
DGP,T= 0 = DH 0.1, 298- TDS0.1, 298+ PDV + 3 RTlnKD
D
H P V 1 SK
3R T 3R ln
-D - D D =
o
D
52 090 2 494P MPaT C 273
19 506 12 943 K
, .
. . ln
= -
-
h b
-
8/12/2019 Ch 27 Thermo
26/39
Geothermobarometry
The Garnet - Biotite geothermometer
Figure 27.6. AFM projections showing the relative distribution of Fe and Mg in garnet vs. biotite at approximately 500oC(a)and 800oC (b).
From Spear (1993)Metamorphic Phase Equilibria and Pressure-Temperature-Time Paths. Mineral. Soc. Amer. Monograph 1.
G h b
-
8/12/2019 Ch 27 Thermo
27/39
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 Al2SiO5phase diagram is added. From Spear (1993)Metamorphic Phase Equilibria and Pressure-Temperature-
Time Paths. Mineral. Soc. Amer. Monograph 1.
G h b
-
8/12/2019 Ch 27 Thermo
28/39
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 Newtons 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
G h b
-
8/12/2019 Ch 27 Thermo
29/39
Geothermobarometry
The GASP geobarometer
Figure 27.98. 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
Table 27-3 Mineral Compositions Formulas and End-
G h b
-
8/12/2019 Ch 27 Thermo
30/39
Wt. % Oxides Garnet Biotite Muscovite Plagioclase
SiO2 37.26 34.22 44.50 64.93
Al2O3 21.03 18.97 34.50 22.59
TiO2 1.23 0.40 FeO 32.45 17.50 0.70
MgO 2.46 9.98 0.46
MnO 6.08 0.12 0.02
CaO 1.03 0.01 0.03 2.90
Na2O 0.27 1.64 9.36
K2O 7.79 8.05 0.45
Total 100.31 90.09 90.30 100.23
Si 3.00 5.43 6.17 2.84
AlIV
2.00 2.57 1.83 1.17
AlVI
0.98 3.81
Ti 0.15 0.04
Fe 2.19 2.32 0.08
Mg 0.30 2.36 0.10
Mn 0.42 0.02 0.00 Ca 0.09 0.00 0.14
Na 0.08 0.44 0.83
K 1.58 1.42 0.03
Fe/(Fe+Mg) 0.88 0.50 0.46
Prp 10 An 14
Alm 73 Ab 83
Sps 14 Or 3
Grs 3From Hodges and Spear (1982) and Spear (1993).
Table 27-3. Mineral Compositions, Formulas, and End-
Members for Sample 90A from Mt. Moosilauke, New
Hampshire
Cations
Geothermobarometry
G h b
-
8/12/2019 Ch 27 Thermo
31/39
Figure 27.10.P-T diagram showing the results of garnet-biotite geothermometry (steep lines) and GASP barometry (shallow lines) for sample
90A of Mt. Moosilauke (Table 27.4). Each curve represents a different calibration, calculated using the program THERMOBAROMETRY, by
Spear and Kohn (1999). The shaded area represents the bracketed estimate of the P-T conditions for the sample. The Al2SiO5invariant point
also lies within the shaded area.
Geothermobarometry
-
8/12/2019 Ch 27 Thermo
32/39
Figure 27.11.P-T phase diagram calculated by TQW 2.02 (Berman, 1988, 1990, 1991) showing the internally consistent reactions between
garnet, muscovite, biotite, Al2SiO5and plagioclase, when applied to the mineral compositions for sample 90A, Mt. Moosilauke, NH. The
garnet-biotite curve of Hodges and Spear (1982)Amer. Mineral., 67, 1118-1134 has been added.
Geothermobarometry
TWQ and THERMOCALC accept mineralcomposition data and calculate equilibrium
curves based on an internally consistent set of
calibrations and activity-composition mineral
solution models.
Rob Bermans TWQ 2.32 program calculated
relevant equilibria relating the phases in sample
90A from Mt. Moosilauke.
TWQ also searches for and computes all
possible reactions involving the input phases, a
process called multi-equilibrium calculations
by Berman (1991).
Output from these programs yields a single
equilibrium curve for each reaction and shouldproduce a tighter bracket ofP-T-Xconditions.
G th b t
-
8/12/2019 Ch 27 Thermo
33/39
Figure 27.12.Reactions for the garnet-biotite geothermometer and GASP geobarometer
calculated using THERMOCALC with the mineral compositions from sample PR13 of Powell
(1985). A P-T uncertainty ellipse, and the optimal AvePT ( ) calculated from correlated
uncertainties using the approach of Powell and Holland (1994). b. Addition of a third
independent reaction generates three intersections (A, B, and C). The calculated AvePT lies
within the consistent band of overlap of individual reaction uncertainties (yet outside the ABC
triangle).
GeothermobarometryTHERMOCALC (Holland and Powell) also based on an internally-consistent dataset
and produces similar results, which Powell and Holland (1994) call optimal
thermobarometryusing the AvePT module.
THERMOCALC also considers activities of each end-member of the phases to be
variable within the uncertainty of each activity model, defining bands for each
reaction within that uncertainty (shaded blue).
Calculates an optimal P-T point within the correlated uncertainty of all relevant
reactions via least squares and estimates the overall activity model uncertainty.
The P and T uncertainties for the Grt-Bt and GASP equilibria are about 0.1 GPa and75oC, respectively.
A third independent reaction involving the phases present was found (Figure 27.12b).
Notice how the uncertainty increaseswhen the third reaction is included, due to the
effect of the larger uncertainty for this reaction on the correlatedoverall uncertainty.
The average P-T value is higher due to the third reaction, and maybe consideredmore reliable when based on all three.
G th b t
-
8/12/2019 Ch 27 Thermo
34/39
Figure 27.13.P-T pseudosection calculated by THERMOCALC for a computed average composition in NCKFMASH for a pelitic
Plattengneiss from the Austrian Eastern Alps. The large + is the calculated average PT (= 650oC and 0.65 GPa) using the mineral data of
Habler and Thni (2001). Heavy curve through AvePT is the average P calculated from a series of temperatures (Powell and Holland, 1994).The shaded ellipse is the AvePT error ellipse (R. Powell, personal communication). After Tenczer et al. (2006).
GeothermobarometryThermobarometry maybest be practiced
using thepseudosectionapproach of
THERMOCALC (or Perple_X), in which aparticular whole-rock bulk composition is
defined and the mineral reactions delimit a
certain P-T range of equilibration for the
mineral assemblage present.
The peak metamorphic mineral assemblage:
garnet + muscovite + biotite + sillimanite +
quartz + plagioclase + H2O, is shaded (andconsiderably smaller than the uncertainty
ellipse determined by the AvePT approach).
The calculated compositions of garnet,
biotite, and plagioclase within the shaded
area are also contoured (inset). They
compare favorably with the reported
mineral compositions of Habler and Thni(2001) and can further constrain the
equilibrium P and T.
-
8/12/2019 Ch 27 Thermo
35/39
G th b t
-
8/12/2019 Ch 27 Thermo
36/39
Figure 27.15. The results of applying the garnet-biotite geothermometer of Hodges and Spear (1982) and the GASP geobarometer of Koziol
(1988, in Spear 1993) to the core, interior, and rim composition data of St-Onge (1987). The three intersection points yield P-T estimates which
define a P-T-t path for the growing minerals showing near-isothermal decompression. After Spear (1993).
Geothermobarometry
P-T-t Paths
G th b t
-
8/12/2019 Ch 27 Thermo
37/39
Figure 27.16. Clockwise P-T-t paths for samples D136 and D167 from
the Canadian Cordillera and K98-6 from the Pakistan Himalaya.
Monazite U-Pb ages of black dots are in Ma. Small-dashed lines are
Al2SiO5polymorph reactions and large-dashed curve is the H2O-
saturated minimum melting conditions. After Foster et al. (2004).
GeothermobarometryP-T-t Paths
Recent advances in textural geochronology have allowed age
estimates for some points along a P-T-t path, finally placingthe t term in P-T-t on a similar quantitative basis as P and
T.
Foster et al. (2004) modeled temperature and pressure
evolution of two amphibolite facies metapelites from the
Canadian Cordillera and one from the Pakistan Himalaya.
Three to four stages of monazite growth were recognized
texturally in the samples, and dated on the basis of U-Pb
isotopes in Monazite analyzed by LA-ICPMS.
Used the P-T-t paths to constrain the timing of thrusting
(pressure increase) along the Monashee dcollement in
Canada (it ceased about 58 Ma b.p.), followed by
exhumation beginning about 54 Ma.
Himalayan sample records periods of monazite formation
during garnet growth at 82 Ma, followed by later monazite
growth during uplift and garnet breakdown at 56 Ma, and a
melting event during subsequent decompression.
Such data combined with field recognition of structural
features can elucidate the metamorphic and tectonic history
of an area and also place constraints on kinematic andthermal models of orogeny.
G th b t
-
8/12/2019 Ch 27 Thermo
38/39
Figure 27.17. An illustration of precision vs. accuracy. a. The shots are precise because successive shots hit near the same place
(reproducibility). Yet they are not accurate, because they do not hit the bulls-eye. b. The shots are not precise, because of the large scatter, but
they are accurate, because the average of the shots is near the bulls-eye. c. The shots are both precise and accurate. Winter (2010) An
Introduction to Igneous and Metamorphic Petrology. Prentice Hall.
Geothermobarometry
Precision and Accuracy
G th b t
-
8/12/2019 Ch 27 Thermo
39/39
Figure 27.18. 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)
F S (1993) M t hi Ph E ilib i d P T t Ti P th Mi l S A M h 1
Geothermobarometry
Precision and Accuracy