GEOTHERMOMETRYGEOBAROMETRY

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TOPIC 7

• GEOTHERMOMETRY-GEOBAROMETRY

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BASIC PRINCIPLE OF GEOTHERMOBAROMETRY

• Consider the reaction
• 2CaMgSi2O6(cpx) Fe2SiO4(ol)
• ? 2CaFeSi2O6(cpx) Mg2SiO4(ol)
• We can calculate
• ?rG 2?fGCaFeSi2O6 ?fGMg2SiO4
• - 2?fGCaMgSi2O6 ?fGFe2SiO4

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• This equation tells us that ln K is a function of
  pressure and temperature. Thus, if we had a rock
  with clinopyroxene and olivine which we can
  assume were in equilibrium, we could calculate ln
  K from a microprobe analysis and an activity
  model. Given an independent estimate of P, we
  could calculate T, or vice versa.
• If the above equation was relatively independent
  of pressure, we could use it as a geothermometer
  even if we did not have an independent estimate
  of pressure. Similarly, if the reaction is
  relatively T-independent, we might have a
  geobarometer.

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CRITERIA FOR GEOTHERMOMETERS AND GEOBAROMETERS

• The ideal geothermometer would depend strongly on
  T and weakly on P.
• The ideal geobarometer would depend strongly on P
  and weakly on T.
• The temperature dependence is given by
• and the pressure dependence is given by

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• Thus, a good geothermometer is one in which the
  absolute value of ?rH is relatively high, and
  ?rV is near zero.
• Conversely, a good geobarometer is one in which
  ?rH is nearly zero and the absolute value of
  ?rV is relatively high.

Potential geothermometer
Potential geobarometer
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OTHER CRITERIA

• 1) Reasonably accurate standard-state
  thermodynamic data are either known or can be
  estimated from simple-system experiments.
• 2) The relationships between activities of the
  relevant components in complex phases and the
  compositions of the phases should be
  well-defined. In practice, reactions involving
  major constituents are generally more useful than
  those involving trace components (as
  concentration increases, ?i ? 0).

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EXCHANGE REACTIONS

• Consider the reaction we wrote previously
• 2CaMgSi2O6(cpx) Fe2SiO4(ol)
• ? 2CaFeSi2O6(cpx) Mg2SiO4(ol)
• This is an exchange reaction in that Fe2 and
  Mg2 simply exchange places between clinopyroxene
  and olivine. It can be written in terms of two
  exchange components, i.e.,
• FeMg-1ol ? FeMg-1cpx
• Exchange reactions usually make good
  geothermo-meters because they typically have
  small ?rV.

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THE GARNET-BIOTITE Fe-Mg EXCHANGE THERMOMETER

• This is based on the reaction
• Fe3Al2Si3O12(grt) KMg3AlSi3O10(OH)2(bt)
• ? Mg3Al2Si3O12(grt) KFe3AlSi3O10(OH)2(bt)
• Now the following must be true at equilibrium
• As a general rule, as temperature increases, K
  begins to approach zero. This is because at
  sufficiently high temperature, the energetic
  distinction between different elements decreases.

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• Most garnets in pelitic rocks contain Fe, Mg, Mn
  and Ca, and most biotites contain Fe and Mg.
  Thus, assuming ideal ionic mixing the activities
  may be written

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• Thus, the equilibrium constant can be written
• When dealing with element partitioning, it is
  common to define a quantity called the
  distribution coefficient

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Plots showing the disposition of garnet-biotite
tie lines at different temperatures on two
different diagrams.
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Three ways of showing the partitioning of Fe and
Mg between two phases such as garnet and biotite.
In (b), KD is the slope and in (c) ln KD is the
intercept at ln (Mg/Fe)Bt 0.
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FERRY SPEAR (1978) CALIBRATION

• From an experimental study, Ferry Spear (1978)
  derived the relationship
• ln KD -2109/T(K) 0.782
• However, it is also possible to derive an
  expression using basic thermodynamic properties.
  If we make the assumptions that ?rCP ? 0, and ?rV
  is independent of pressure and temperature we can
  write

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Plot of ln KD vs. 1/T for experimentally
equilibrated garnet-biotite pairs. P 2.07 kbar.
From Ferry and Spear (1978).
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• The assumption that ?rCP ? 0 is pretty good for
  an exchange thermometer because there is
  substantial cancellation of products and
  reactants. Also, if ?rCP were substantially
  different from zero, the plot of ln KD vs. 1/T
  would be curved.
• Ideal mixing can only be assumed when Fe and Mg
  are the only major components in garnet. Ca-Mg
  mixing is non-ideal and a Margules approach would
  be required.
• How do we apply the geothermometer when dealing
  with zoned garnets?

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P-T diagram in which lines of constant KD for the
garnet-biotite thermometer have been plotted.
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OTHER EXCHANGE GEOTHERMOMETERS

• Fe-Mg exchange between garnet and cordierite.
• Fe-Mg exchange between garnet and clinopyroxene.
• Fe-Mg exchange between garnet and orthopyroxene.
• Fe-Mg exchange between garnet and hornblende.
• Fe-Mg exchange between garnet and chlorite.
• Fe-Mg exchange between garnet and olivine.
• Fe-Mg exchange between biotite and tourmaline.
• Fe-Mg exchange between garnet and phengite.
• Fe-Mn exchange between garnet and ilmenite.
• Stable isotope exchange.

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SOLVUS GEOTHERMOMETERS

• As name implies, these are based on a solvus
  between two immiscible phases. Examples include
• 1) Two-pyroxene geothermometry - distribution of
  Ca and Mg between cpx and opx.
• 2) Calcite-dolomite geothermometry - distribution
  of Ca and Mg between calcite and dolomite.
• 3) Two-feldspar geothermometry - distribution of
  K and Na between alkali feldspar and plagioclase.
• 4) Muscovite-paragonite - distribution of K and
  Na between muscovite and paragonite.

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NET TRANSFER REACTIONS

• Many geobarometers are based on net-transfer
  reactions, i.e., reactions that cause the
  production and consumption of phases. Such
  reactions often result in large volume changes,
  so the equilibrium constant is pressure-sensitive.
  
• An example (garnet-plagioclase-olivine)
• 3Fe2SiO4 3CaAl2Si2O8
• ? Ca3Al2Si3O12 2 Fe3Al2Si3O12

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THE GASP GEOBAROMETER

• GASP Garnet-AluminoSilicate-Plagioclase-quartz
• This is a net transfer geobarometer based on the
  reaction
• 3CaAl2Si2O8 ? Ca3Al2Si3O12 2AlSi2O5 SiO2
• Solid solution of grossular with other garnet
  components, mainly, almandine and pyrope, lowers
  the pressure at which the right-hand side
  assemblage is stable.
• Solid solution of anorthite with albite in
  plagioclase tends to stabilize the left-hand side
  to higher pressures. Because grossular often
  quite dilute, the pressure-lowering effect
  prevails.
• Garnet plagioclase Al2SiO5 quartz is a
  common assemblage in the crust.

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THERMODYNAMICS OF GASPNewton Haselton (1981)

• This geothermometer is based on the thermodynamic
  equation
• Experimental determinations of the P-T curve for
  the end-member reaction (with kyanite) have been
  expressed in the form
• P a bT

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• From Goldsmith (1990) we get
• P(kbars) -2.10 0.0232T(C)
• and the error is expected to be on the order of
  1 kbar.
• The analogous expression for the GASP reaction
  with sillimanite is
• P(kbars) -0.6 0.0236T(C)
• Once you have P(T), then, ?rG(T) -P(T)?rV,
  where P(T) is the breakdown pressure of
  anorthite at a given temperature for the
  end-member reaction, and ?rV -66.2 cm3 mol-1
  at 298 K and 1 bar (the molar volume change for
  the end-member reaction).

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KOZIOL NEWTON (1988) CALIBRATION

• P(kbar) -1.093 0.0228T(C)
• This calibration can be written in the
  alternative form
• 0 -48,357 150.66 T(K) (P-1)(-6.608) RT ln
  K
• Thus, for this calibration we get
• ?rH(298 K,1 bar) -48,357 J mol-1
• ?rS(298 K,1 bar) -150.66 J K-1 mol-1
• ?rV(298 K,1 bar) -6.608 J bar-1 mol-1
• and it is assumed that ?rV is constant and ?rCp
  0.

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• Margules Parameters For Garnet
• Hensen et al. (1975) obtained the expression
• WCa-Mg 7460 - 4.3T(K)
• in calories per MAl2/3SiO4. Which goes into the
  equation
• Note the strong temperature dependence of
  non-ideality.
• The above expression assumes a regular or
  symmetrical solution model, which is usually only
  strictly valid over a narrow range of
  composition. In the work of Hensen et al. (1975)
  the mole fraction of grossular only ranged from
  0.1 to 0.22.

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• Newton et al. (1977) found the relation
• WCa-Mg 3300 - 1.5T(K) (calories per
  MAl2/3SiO4)
• Cressey et al. (1978) studied Ca-Fe mixing in
  garnet. They found that WCa-Fe can be assumed to
  be near zero for most natural garnet
  compositions.
• Additional experimental data suggest that WFe-Mg
  can be neglected relative to WCa-Mg.
• Experimental data suggest that WCa-Mn is probably
  not negligible, so the solution model employed
  here should only be employed for low-Mn garnets.

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• For a ternary garnet solid-solution, the activity
  of the grossular component is given by
• But based on the previous discussion, this
  simplifies to
• Activity Model for Plagioclase
• Based on Kerrick Darkens (1975) Al-avoidance
  model, Newton et al. (1980) gave the following
  equation

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PARTIAL MOLAR VOLUMES OF GROSSULAR

• In garnets where grossular is a minor component,
  the partial molal volume of grossular is
  considerably different from the molal volume.
• The partial molar volume of grossular in solid
  solution with pyrope can be expressed as
• where
• and A 125.25 B -11.205 C -0.512 D
  -0.418 E 0.94 F 0.083. For the
  grossular-almandine join we get A 125.24 B
  -8.293 C -1.482 D -0.480 E 0.914 F
  0.066.

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Partial molal volume curve of Ca3Al2Si3O12 in
pyrope-grossular and almandine-grossular garnets,
as constructed by Cressey et al. (1978).
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Calculated pressures of well-documented
parageneses of garnet plagioclase Al2SiO5
quartz. Open symbols are sillimanite occurrences
and filled symbols are kyanite occurrences.
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P-T diagram contoured for values of Keq for the
GASP geobarometer reaction.
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SOME OTHER NET-TRANSFER EQUILIBRIA

• GRIPS Garnet-Rutile-Ilmenite-Plagioclase-quartz.
  
• Ca3Al2Si3O12 2Fe3Al2Si3O12 6TiO2 ?
  3CaAl2Si2O8 6FeTiO3 3SiO2
• GRAIL Garnet-Rutile-Aluminosilicate-ILmenite-qua
  rtz.
• Fe3Al2Si3O12 3TiO2 ? 3FeTiO3 Al2SiO5 2SiO2

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OTHER GEOBAROMETERS

• Phengite barometry - phengite content of white
  mica.
• Sphalerite barometry - Fe content of ZnS
  coexisting with pyrrhotite and pyrite.
• Magnetite-ilmenite thermometry - Based on two
  reactions
• 4Fe3O4 O2 ? 6Fe2O3
• Fe2TiO4 Fe2O3 ? Fe3O4 FeTiO3
• Hornblende barometry - Based on the Al content of
  hornblende in certain igneous assemblages.

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SOURCES OF ERROR

• 1) Accuracy of experimental calibrations.
• 2) Error in measured ?rV (usually determined
  independently of (1)).
• 3) Analytical imprecision in microprobe analysis.
• 4) Uncertainty of electron microprobe standard
  compositions and correction factors.
• 5) Cross correlations between errors in
  temperature estimates (for barometers) and errors
  in pressure (for thermometers).
• 6) Uncertainties in mineral activity models.
• 7) Geological uncertainty arising from
  compositional heterogeneities.

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P-T diagram showing results from garnet-biotite
thermometry (steep lines) and GASP barometry
(gentle lines). All curves are calculated from a
single set of mineral analyses from Mt.
Moosilauke, NH, USA.
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P-T diagram showing the results of
thermobarometry calculations on sample SC-160
from Coolen (1980) using a consistent set of
thermobarometers.