Answers · Sharp, Principles of Stable Isotope Geochemistry, 1st ed. (2007) · ← Problems
The closure temperature is 561 °C. Solving equation (12.13) for the conditions given in Table 12.P3 gives a cooling rate of 120 °C/Ma for quartz and almost the same for magnetite. [The printed answer to part (b) does not appear in the extraction; check vs print.]
Although the whole-rock values are different, the two lithologies could be in isotopic equilibrium. Because the mica schist has a higher silica content, it will tend to have more minerals that concentrate 18O. This does not mean that the two rocks are not in equilibrium, however. One way of testing this possibility is to analyze minerals that are common to both lithologies. If they have the same δ18O values, then the lithologies could be in equilibrium.
Cherts are chemical sediments, and their δ18O values are generally over 30‰. But because the two lithologies are in equilibrium (δ18O is the same for both units), you cannot determine whether the quartzite was a sandstone (whose normal δ18O values are around 13‰) or a chert that has reequilibrated with the volumetrically dominant surrounding pelites. Thus, your measurements are inconclusive.
Temperatures indicate that all three minerals are in equilibrium at 638 °C. Projecting this hypothesis onto the diagram, with the additional constraint that the temperature and pressure must lie on the andalusite–sillimanite univariant curve, corresponds to a very low pressure of about 1.6 kbar.
Not printed in the 1st ed.
Transcribed from Z. Sharp, Principles of Stable Isotope Geochemistry, 1st ed. (Pearson Prentice Hall, 2007), end-of-chapter problem set (published source). Reference-scale names are written VSMOW, VPDB and VCDT where the original used SMOW, PDB and CDT, with the original numerical constants unchanged; historical usages (e.g. Craig's definition of SMOW) are kept as printed.
The source PDF's text layer scrambles mathematics, so equations and some values were reconstructed during transcription. Bracketed notes and anything tagged reconstructed or check vs print are editorial (constructed), not part of the original, and the warn-tagged items should be verified against the print copy.