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?
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?
The occupancies would be 0.5 for both Fe and Mg in both sites.
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.
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?
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?
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.