Questions and Problems

1. What is the coordination number of the M1 site?
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6-fold (octahedral)
2. What is the coordination number of the M2 site?
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6-fold (octahedral)
3. One of the purposes of Redfern et al.'s study was to investigate whether the M1 and M2 sites "behaved" differently at different temperatures. One type of such site "behavior" involves how (and under what physical conditions) a site discriminates between different ions having different ionic radii. If a site shows a preference for one type of ion over another, the site is said to be "ordered". If a site shows no preference for one type of ion over another one, the site is "disordered".
   
   Look up the ionic radius of Mg and Fe in 6-fold coordination in your mineralogy textbook. Are they exactly the same, or different?
   
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They are slightly different: Mg=0.72; Fe=0.78
4. Click on Edit > Structure to determine the site occupancies for Mg and Fe in each of the downloaded structure files (site occupancy is the atomic proportion of a given element occupying that site, averaged over the entire crystal). Remember that the olivine composition synthesized for the exeriments in this study contains precisely the same amount of Fe as Mg. If the M1 and M2 sites did not discriminate between cations of different size, what would you expect the site occupancies to be?
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The occupancies would be 0.5 for both Fe and Mg in both sites.
5. Using a spreadsheet program like Excel, make a table with the following three columns: Temperature, Fe in M1 site, and Mg in M1 site. Use the data in your table to make a plot of Fe(M1) and Mg(M1) (both on the y-axis) versus Temperature (on the x-axis). Use this plot to answer the following questions.
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6. If Fa₅₀ olivine was crystallized at 1200 °C from a basaltic magma, which site, M1 or M2, would contain more Mg?
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The M1 site would contain more Mg than the M2 site.
7. At low temperatures (100-400 °C), is the Fa₅₀ olivine structure ordered or disordered with respect to the M1 and M2 sites?
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Disordered
8. As temperature is increased from 100 to 400 °C, does the Fa₅₀ olivine structure get more or less ordered? Is this what you would expect based on how disorder (a type of randomness or entropy) generally changes with increasing temperature?
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At low temperatures, the olivine structure becomes more disordered with increasing T. This is what you would expect, since entropy (and randomness) tends to increase with increasing T.
9. At what temperatures does the olivine structure show a totally disordered state with respect to crysatllographic placement of Fe and Mg?
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About 630 °C
10. As temperature is increased above this temperature, does the Fa₅₀ olivine structure generally get more or less ordered? Is this what you would expect based on how disorder (a type of randomness or entropy) generally changes with increasing temperature?
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At higher temperatures, the olivine structure becomes more ordered with increasing T. This is not what you would expect, since entropy (and randomness) tends to increase with increasing T.
11. Does the olivine crystal structure vary its M1/M2 site ordering over the 100-1250 °C range in temperature in a linear fashion?
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The order/disorder process is not linear with respect to T. The authors of this study suggest that several factors may be responsible for the geometries of the M1 and M2 sites: (1) vibrational entropy, (2) crystal field effects, and (3)changes in bond characteristics.