旗开得胜 Lecture 5: Higher-dimensional isotope relationships
H1. Multiple isotopes of the same element; Non-mass dependent (NMD)
fractionation-θ
H2. Difference in isotope composition for the same element at different
sites in a molecule (site-specific isotope effect)-SP
H3. Multiple isotopologues of the same molecule (clumped isotope
system)-?
H4. Coupled isotope behavior for multiple elements in a single ion or
molecule-Ζ
So far, we've been dealing mainly with the behavior of isotope ratio of two isotopes of an element, one major and one minor during various processes. What about the additional ratios we can have for an element that has more than two stable isotopes? What about the isotope ratio difference of the same element at between different sites in a molecule?
What about the relationship among the many ratios we can have for a molecule that has multiple isotopologues? What about the behavior of isotope ratios of different elements in a single complex ion, e.g. δD and δ18O in H2O, or δ34S and δ18O in SO42–?
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H1: Elements with multiple isotopes
M1 (major), M2 (minor), M3 (minor)
According to Bigeleisen (1965), Science, v. 147, No. 3657, at higher temperatures a very good approximation holds that
ln ? = (Δm/m×m’) × force constant.
Force constant is a measure of the strength of the chemical binding.
θ = ln?17(17?16)/17?16force ln?18?constant(18?16)/18?16?force constant*
The two force constants are essentially the same at high T limit, when molecule dissociate into free gaseous atom. (e.g. CO ? C + O)
The above relationship can be expressed as ?(M2/M1) = [?(M3/M1)]θ
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in which,
??M3M2?M1?M2M3?M1For example,
θ ≈ (18/17)×(17-16)/(18-16) = 0.5305
The above θ and M relationship shows that the mass differences
determine the θ or S value. We therefore call the fractionation relationship as mass-dependent fractionation.
But this value is applicable only in high-T dissociation case. In other low-T cases, the θ (e.g. for α17/α18) value changes slightly, ranging from 0.500 to 0.5305 for oxygen and from 0.505 to 0.515 for sulfur, for example.
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【北大 稳定同位素分馏】PKU Lecture 5-Higher dimensional
