Metamorphic Petrology
Deferral Coursework July-August 2021 – s
Answer all 3 questions in this workbook, then save the file as a PDF and submit this via the submission point in the Assment folder of GG536 on studentcentral.
Practical 1 Mineral Stability.
Consult lecture notes and read the following before attempting to answer questions
We need to know under what conditions minerals form and are stable to interpret the geological history of an area. Information is obtained by experimental or calculation and is generally presented in terms of a pressure – temperature phase diagram. Calculation of phase boundaries involves the use of thermodynamics, the study of the flow of energy, but it does not give any information about the rate of a reaction, that is given by the role of kinetics. In geological reactions the stable state with the lowest free energy is given by G (Gibbs free energy). A reaction is favoured if there is a decrease in G.
In the phase diagram below, in region X GCALCITE is less than GARAGONITE therefore the reaction aragonite → calcite is favoured in this region and visa-versa for region Y. On the phase boundary (marked by line A – B) X GCALCITE equals GARAGONITE.
The position of a phase boundary depends on the differences in density of two minerals and the degree of disorder of the minerals, which is expressed as entropy (S). Entropy increases as a substance passes from the solid state to liquid state to gaseous state. Entropy increases also increases as substances are mixed together. Reactions in which there is an increase in entropy tend to occur spontaneously. If we increase the pressure on a system it will favour the higher density phase. If we increase the temperature of the system it will favour the higher entropy (more disordered) phase.
Although many phases are thermodynamically unstable they persist because of an energy hurdle which makes their transformation extremely slow. For example most metamorphic minerals are thermodynamically unstable at Earth surface conditions but persist because they are metastable, requiring activation energy to progress the reaction to move the system to the stable state with the lowest free energy is given by G (Gibbs free energy). Related to this, minerals of the same composition but different crystal structures are polymorphs. In metamorphic petrology there are two types of transformation, ‘displacive’(involving only the bending of bonds), and reconstructive, involving the breaking and reforming of bonds. The type of polymorphic transition determines how sluggish or otherwise a polymorphic transition occurs.
Practical 1 Questions
The reaction between calcite and quartz to give wollastonite and carbon dioxide (vapour) is shown in the phase diagram above.
Which side possesses the higher entropy, calcite + quartz or wollastonite + CO2 state your reasons in the text box below
At what temperature does wollastonite + CO2 become stable at P = 1Kbar ?
Which has the higher entropy silica glass or crystalline quartz ?
Which has the higher entropy calcite or aragonite ?
Which has the higher entropy diamonds or graphite or coal ?
Why does aragonite occur at Earth surface conditions ? state your reasons
The figure above is the SiO2 phase diagram
Which phase has the higher density low quartz (trigonal) or high quartz (hexagonal) ?, state your reasons
Which phase has the higher entropy – low quartz or high quartz, state your reasons
Why can tridymite often be seen in hand samples at room temperature but high quartz never is ?
Which SiO2 solid phase shows the greatest density ?
Which SiO2 phase shows the greatest entropy ?
How many divariant fields are shown in the SiO2 diagram ?
The diagram above is the phase diagram for H2O
What has the higher entropy water or solid or gas?
How many degrees of freedom exist at the H2O triple point ? use the phase rule explain your reason
Practical 2: The Diagenesis Metamorphic Transition
Be sure to go through the virtual lecture before attempting this practical.
Sample K.I calibrated Sample K.I calibrated
S1 0.31 S6 0.41
S2 0.35 S7 0.38
S3 0.4 S8 0.36
S4 0.45 S9 0.31
S5 0.44 S10 0.29
The picture above shows folded turbidites with positions from which samples were acquired. The table above gives the x-ray diffraction Kubler Index for illite crystallinity. Which Kubler index zone(s)are present, approximately what temperature range have the rocks encountered, and how do the findings relate to the geological structure present. Answer in text box below
Practical 3 Geothermobarometry
Be sure to fully engage with the virtual lecture on Geothermobarometry before attempting this practical
Image courtesy J.Ciborowski
The above thin section sketch shows garnets with inclusions of biotite, plagioclase, kyanite, and quartz. The garnet, plagioclase and biotite were analysed by electron probe in the centre of the garnet (area 1) and in the vicinity of the rim of the garnet. The resultant data is presented in the table below, as wt% oxide and recast as formula units for the respective minerals. Use the formula units data for the following calculations.
Geothermometry
Very often, garnets become chemically zoned as they grow in a changing P-T field. Consider the assemblage garnet + biotite. Both of these minerals contain Fe and Mg that can be exchanged between them as temperature and/or pressure change. We can write an equilibrium constant, KD, for this reaction, that relates the ratios of Mg/Fe in both minerals at a given temperature and pressure. Some equilibrium constants are primarily a function of temperature. This is the case for Fe-Mg exchange between garnet and biotite.
KD =
Geobarometry
Some element exchanges involve minerals that have very different molar volumes (densities). The following reaction involves the exchange of Ca between plagioclase and garnet:
3 CaAl2Si2O8 (An in plagioclase) = Ca3Al2Si3O12 (Grossular in garnet) + 2 Al2SiO5 (Sil) + SiO2 (Qtz)
To measure the distribution of Ca in coexisting garnet and plagioclase we calculate the KD of the reaction:
KD =
Where XCa Garnet = (Ca /Ca + Mn + Mg + Fe) and XCa Plagioclase = (Ca / Ca + Na + K). Note that at high pressure there is fairly strong dependence of the exchange reaction on temperature. Therefore, to get an accurate determination of pressure an independent determination of temperature has to be made. Consequently the garnet-biotite Fe-Mg geothermometer is employed together with the GASP geobarometer. The diagram below shows contoured KD values for the GASP barometer (dotted line) and Garnet – biotite thermometer (dashed lines). The GASP barometer is generally considered accurate to ± 1.5Kbar, the garnet – biotite geothermometer ± 50°C.
Practical 3 Question
Employing the KD equations given for the GASP geobarometer and the Garnet-Biotite geothermometer and, working from the formula units values given for plagioclase, biotite and garnet in the table provided,
- Calculate the P-T conditions for garnet growth in areas 1 and 2. Show your workings and plot the points on the P-T graph provided.
- Briefly provide a hypothesis defining which metamorphic facies series the rock relates to and the likely tectonic setting in the text box overleaf
Sample Solution
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