Isotope Fractionation and Mathematical Approximations Used in Isotope Fractionation
What is Isotope Fractionation?
Isotope fractionation is the process by which stable isotopes are separated based on their mass rather than their chemical properties. This natural process occurs in three main ways:
1. Isotopic Exchange Reactions
Isotope fractionation can occur during conventional exchange reactions, such as when oxygen isotopes exchange between quartz and magnetite.
2Si16O2 + Fe318O4 = 2Si18O2 + Fe316O4The fractionation is controlled by bond strength, with lighter isotopes forming weaker bonds compared to heavier isotopes.
2. Kinetic Processes
Kinetic isotope fractionation happens when a reaction does not go to completion. It reflects the readiness of a particular isotope to react, with fractionation occurring due to differences in reaction rates of isotopes.
3. Physico-Chemical Processes
These include processes such as evaporation, condensation, melting, crystallization, and diffusion, where isotopes fractionate based on their physical and chemical properties.
How is Isotope Fractionation Defined?
Isotope fractionation between two substances, A and B, is quantified using the fractionation factor α:
Fractionation Factor (α)
The fractionation factor is defined as:
αA-B = (Isotope ratio in A) / (Isotope ratio in B)For instance, in the exchange between 18O and 16O between magnetite and quartz, the fractionation factor is:
αquartz-magnetite = ((18O / 16O)in quartz) / ((18O / 16O)in magnetite)If isotopes are randomly distributed in the compounds, α is related to the equilibrium constant K such that α = K1/n, where n is the number of atoms exchanged.
What are the Mathematical Approximations Used in Isotope Fractionation?
Per Mil Value
Values for α are close to unity and are typically expressed in the third decimal place, referred to as the per mil value (e.g., 1.009 can be expressed as 9.0 per mil).
1000ln(α) Approximation
A useful approximation is:
1000 ln(α) ≈ XFor example, if α = 1.009, then 1000 ln(α) = 9.0. This relationship often shows a smooth and linear function of 1/T2 for mineral-mineral and mineral-fluid pairs.
Equation for Fractionation Factor
The fractionation factor can be approximated by:
1000 ln αquartz-magnetite = (6.29 × 106) / T2where T is in kelvin, and the constants A and B are determined experimentally (e.g., for quartz-magnetite, A = 6.29 and B = 0).
Difference in δ Values
The difference in δ values between two minerals, denoted as Δ, approximates 1000 ln α when δ values are less than 10:
Δqz-mgt = δqz - δmgt ≈ 1000 ln αqz-mgtSummary
Isotope fractionation is crucial for understanding natural processes based on isotope mass differences. It occurs through exchange reactions, kinetic processes, and physico-chemical processes, and is quantified using fractionation factors. Mathematical approximations, including per mil values and ln(α) relationships, provide insights into isotopic behavior across different substances.
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