Chapter 11 · Igneous Petrology

Problem set · Sharp, Principles of Stable Isotope Geochemistry, 1st ed. (2007) · Answers →

Problem 1

Construct a diagram similar to Fig. 11.12, assuming the same conditions as the original diagram, but infiltration of seawater instead of meteoric water. (See Field and Fifarek, 1985, for other examples.)

[Worksheet constructed from the conditions used in the printed answer, with seawater (δ = 0) as the infiltrating fluid; the closed-system exchange arrangement is reconstructed, check vs print. The hydrogen column uses a W/R ratio RHW times the oxygen value for the same water passage.]

Problem 2

For olivine with a composition of Mg1.5Fe0.5SiO4, how many micromoles of O2 are extracted when 1 mg is fluorinated (e.g., with 100% yield)?

[Worksheet constructed; molecular weight as in the printed answer.]

Problem 3

If all carbon in the Earth’s crust is derived from the mantle without fractionation, and the δ13C value of the mantle is given as −5.7‰, then what are the proportions of carbonate to reduced carbon if the δ13C value of each is 0‰ and −25‰, respectively?

[Worksheet constructed.]

Problem 4

Explain why mantle eclogites have such a wide range of δ18O values, while peridotites have a very narrow range.

Problem 5

Why do diamonds show such a large range of δ13C values, while carbonatites have a very narrow range?

Problem 6

  1. The δ13C values of methane and CO2 from fluid inclusions in olivine from a mantle xenolith are −9.25 and −5.60‰, respectively. Find the temperature of equilibration, given that the equation of fractionation is
    10³lnα = −0.62·10⁹/T³ + 6.616·10⁶/T² + 6.04·10³/T − 3.08
  2. Why didn’t the methane and CO2 reequilibrate during cooling?

[Worksheet constructed. Adjust the trial T until the residual goes to zero.]

Problem 7

In a scenario in which a pluton is immediately emplaced at a shallow level and meteoric water circulates through the pluton at 450 °C, (a) what is the δ18O value of the first fluid to fully equilibrate with the rock and (b) how would you expect the isotopic composition to change over time? Use the quartz–water fractionation equation

10³lnαqz–H2O = 3.13·10⁶/T² − 2.94Matsuhisa et al., 1979

a δ18O value of 7.5‰, and −8‰ for the quartz in granite and meteoric water, respectively.

[Worksheet constructed.]

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.