Questions: Stable Isotope Fractionation

Question 1

Two coexisting minerals -- quartz and magnetite -- are analyzed for oxygen isotopes. The fractionation between them (delta-18O-quartz minus delta-18O-magnetite) is 6 per mil. How is this used as a geothermometer?

• A. Larger fractionation indicates higher temperature
• B. The fractionation between coexisting minerals decreases with increasing temperature; a calibrated relationship between the fractionation factor and temperature (typically 1000*ln(alpha) proportional to 1/T^2) allows calculation of the equilibrium temperature from the measured isotopic difference
• C. The absolute delta-18O value of either mineral gives the temperature directly
• D. Oxygen isotope thermometry only works for igneous rocks

Answer: (B)

Equilibrium isotope fractionation between two phases decreases systematically with increasing temperature because thermal energy increasingly overcomes the small bond-energy differences between isotopes. The quartz-magnetite fractionation has been experimentally calibrated: 6 per mil corresponds to approximately 600 C. Smaller fractionation would indicate higher temperature, larger fractionation would indicate lower temperature.

Question 2

Kinetic isotope fractionation always favors the lighter isotope in the product.

• T. True
• F. False

Answer: True

Kinetic fractionation arises because lighter isotopes have higher velocities (at the same kinetic energy) and lower activation energies for bond breaking. In unidirectional or incomplete processes -- diffusion, evaporation, biological reactions -- the lighter isotope reacts or moves faster, becoming enriched in the product relative to the reactant. This is why evaporated water vapor is enriched in H-16O relative to H-18O, and why biologically fixed carbon (organic matter) is enriched in 12C relative to 13C.

Question 3

Explain why stable isotope fractionation decreases with increasing temperature and what this means for isotope geothermometry.

Model answer: Fractionation arises from differences in zero-point vibrational energy between isotopically substituted molecules. At low temperatures, these differences are significant relative to thermal energy (kT), causing strong preferential partitioning of heavy isotopes into phases with higher bond stiffness. As temperature increases, thermal energy dominates over zero-point energy differences, the vibrational energy levels converge, and fractionation decreases -- approaching zero at very high temperatures where all isotopes behave identically. For geothermometry, this T-dependence means the isotopic difference between coexisting minerals is a monotonic function of temperature, enabling temperature calculation from measured isotopic compositions.

The 1/T^2 dependence of fractionation is the physical basis of isotope geothermometry: at high T, phases are isotopically similar; at low T, they diverge.