Geology 2142

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Geology 2142

• Element Partitioning and Element Activity in
  Minerals

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Element variation

• Majority of elements in a rock do not form their
  own minerals
• Concentration is too low
• Instead they enter the common rock-forming
  minerals
• Certain elements taken into minerals
  preferentially e.g. Ni into olivine

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Partitioning

• Elements preferentially accepted by certain
  minerals said to be partitioning into the mineral
• We will deal with partitioning between minerals
  and magma
• Same principles apply to mineral mineral
  partitioning or mineral - fluid

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General Principles

• Define whether or not an element is accepted by a
  mineral by defining a partition coefficient (D
  not to be confused with D in the diffusion
  equations)
• Dconcentration in mineral / concentration in
  melt

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What factors control D?

• Partition coefficient is sensitive to
• Temperature
• Pressure
• Composition of the mineral
• Composition of the magma

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What use is D?

• In the form quoted it is not much use in
  thermodynamic calculations
• VERY useful in modelling petrogenesis of magmas
• Fractionation
• Uses a bulk partition coefficient

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How is D measured?

• By experiment
• Synthesis of a mineral / melt system under
  equilibrium conditions
• From glassy volcanic rocks
• Measurement of composition of coexisting glass
  and phenocrysts
• Problems of disequilibrium

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Values of D

• Clinopyroxene

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What Do the Values Mean?

• Values greater than 1
• Element is accepted by the mineral
• Compatible element
• Values less than 1
• Element is not accepted by the mineral
• Incompatible element

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Significance of Compatibility

• During magma crystallisation the incompatable
  elements will be enriched in the liquid
• During magma crystallisation the compatable
  elements will be depleted in the liquid

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Significance of Compatibility

• During melting the incompatible elements will be
  enriched in the liquid when the amount of melting
  is small
• As the amount of melting increases the enrichment
  in incompatible elements is swamped and the magma
  becomes enriched in compatible elements

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Temperature Dependence of D

• Expressed as
• Where A and B are constants and T is in K

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Pressure Dependence of D

• Very few experiments performed to date
• Pressure can have a large effect on crystal
  structure
• Phase transitions
• Closing of structure with increased P
• Might expect the pressure dependence to be the
  inverse of that for T

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Composition Dependence

• Difficult to separate T effects from X effects
• In some cases can see a strong effect of
  composition
• Ni partitioning between olivine and melt is
  strongly dependent on the MgO content of the
  olivine
• REE partitioning between garnet and melt

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Activity another thermodynamic variable

• Natural minerals in solid solutions have
  compositions different to those used in
  experiments
• We determine phase diagrams for pure phases e.g.
  pure diopside and pure anorthite
• BUT in real rocks we rarely if ever have the pure
  phases

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Activity and Composition

• Changing the composition of the phase will change
  the position of phase boundaries
• We must correct for these variations
• HOW?
• Use the activity of the end-member phases as they
  occur in the mineral

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What is Activity?

• Activity is the thermodynamically effective
  concentration of a component in a solution

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Example 1

• Pure H2O has an activity aH2O 1
• In a mixture of H2O and CO2, aH2O is less than 1
• How much less?
• Depends on the relative proportion of CO2 and H2O
• Mole fraction

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Example 2.

• Pure jadeite (NaAlSi2O6) has ajd1
• An intermediate pyroxene somewhere in the solid
  solution space has ajd lt 1
• The actual activity will depend on the exact
  composition of the mineral.

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What use is activity?

• If we know activities of end member components in
  a mineral we can calculate the offsets of
  equilibrium curves relative to the pure system
• Important in geothermobarometry
• Important in igneous petrology

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Problem

• Activity Composition (a X) relations are
  complex and poorly understood
• Can only be determined by experimentation

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Derivation of Activity

• Activity is a dimensionless ratio
• It is the ratio of the fugacity of a component in
  the natural solution and the fugacity of that
  component in the standard state
• Standard state is the phase occuring as pure
  component at the pressure and temperature of
  interest (always 1)

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What is Fugacity

• Fugacity is the pressure of a component in the
  gas phase coexisting with a mineral in its
  natural or standard state

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Fugacity and Partial Pressure

• CO2 in pop separates into gas phase more easily
  than H2O
• Bottle sealed
• Space above pop filled by CO2 at pressure greater
  than atmospheric

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Fugacity and Partial Pressure

• Open pop
• Gas escapes
• Pressure in space above pop decreases
• Bubbles form in opo since CO2 in gas phase and
  CO2 in pop not at equilibrium concentrations

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Fugacity and Partial Pressure

• Reseal bottle
• Bubbles will continue to exsolve until
  concentration of gas in space above pop is in
  equilibrium with the concentration of gas in the
  pop.
• Thats why pop goes flat after you open the
  bottle a few times

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Fugacity and Partial Pressure

• How much pressure in gas space due to CO2 and how
  much to H2O?
• Measure using a membrane permeable to CO2
• Allows measurement of pressure due to CO2
• Do same for H2O
• Total pressure PH2O PCO2
• PH2O and PCO2 called partial pressures

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Partial Pressure and Composition

• Express relation between partial pressure and
  composition in terms of mole fraction
• moles CO2/ moles CO2 H2O mole fraction CO2

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Ideal Gas

• In an ideal gas PVnRT
• Also no interaction between molecules
• Collisions are perfectly elastic
• Real gases non ideal
• Have finite volume at TO K
• Have interactions between molecules
• PVnRT breaks down for real gases

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Fugacity

• In an ideal gas (VRT/P) we can write an
  expression that relates the free energy of the
  gas (G) to its pressure
• If we write pressure in bars then
• This means that pressure is a measure of the free
  energy of an ideal gas BUT

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Fugacity

• At high P gases are not ideal but the equation
  that we made is easy to work with so we invent a
  function (f) called fugacity so that
• Fugacity measures the free energy of a real gas
  in the same way that P measures the free energy
  of an ideal gas
• We relate f to P by the fucacity coefficient g

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The Fugacity Coefficient

• We define g as fPg
• For an ideal gas g1fP
• We can find values for the fugacity coefficient
  at various P and T for H2O and CO2 in the
  literature.
• Determinations require large amounts of
  thermodynamic data that can only be obtained by
  experiment.

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Chemical Potential (?)

• For component i, chemical potential is the change
  in G of the phase resulting from a change in the
  number of moles of that component when P, T and
  number of moles of all other components remains
  constant

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Chemical Potential - 2

• Rewrite as
• Where is a function only of pressure and
  temperature and is the chemical potential of i in
  the solid solution in the standard state

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Compare
For gas pressure
Chemcal potential
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Chemical Potential and Activity

• Chemical potential in this simple form does not
  work for non-ideal solutions
• Introduce activity (analogous to fugacity in
  gases) to fix the problem
• Where

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The Activity Coefficient

• The activity coefficent (?i) is a measure of the
  departure of the system from ideality
• Can be greater or less than 1
• At standard state, elements and compounds have an
  activity coefficient of 1 and therefore an
  activity of 1

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Henrys Law

• If we take a dilute solution we find that in
  these, activity is directly proportional to mole
  fraction
• kh is a proportionality constant called the
  Henrys law constant
• Only works over a limited compositional range

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Summary

• Element partitioning
• Compatible elements taken up easily by a mineral
• Incompatible element rejected by a mineral
• Partition coefficient
• D
• D of 1 or more element is compatible
• D of 1 or less (usually much less) element is
  incompatible

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Summary

• Solid solution leads to problems in modeling
  phase equilibria
• Get around this by dealing with solid solutions
  as mixtures
• For gases concept of partial pressure
• For solids use of mole fraction

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Summary

• These simplistic ideas break down in the real
  world
• Non-ideal behaviour leads to development of
  concepts of
• Fugacity
• Activity
• Defined in same way one refers to gases and the
  other to solids