why temperature of mineral formation determined from clumped isotope measurements is independent of the isotopic composition of the water in which it formed.
https://www.sciencedirect.com/science/article/pii/S0016703718304241
*The clumped (13Csingle bond18O) isotope composition of echinoid calcite: Further evidence for “vital effects” in the clumped isotope proxy
By : Amelia J.Davies & Cédric M.John
Geochimica et Cosmochimica Acta Volume 245, 15 January 2019, Pages 172-189
Abstract
Carbonate clumped isotope thermometry is based on the thermodynamically dependent relative abundance of 13Csingle bond18O bonds (quantified as Δ47) within the carbonate crystal lattice. The clumping of 13Csingle bond18O in carbonates is based on a self-reaction of isotope exchange that occurs rapidly at near neutral pH. Similar Δ47-temperature relationships between biogenic and inorganically precipitated carbonate in initial studies led to the promise of a proxy free of biologically driven disequilibrium effects, commonly referred to as “vital effects”. This has been largely the case for most organisms investigated. Biologically mediated disequilibrium precipitation has however been reported in corals and cephalopods and brachiopod molluscs. Echinoderms, despite their complex inter-cellular bio-mineralization strategy, large inter-skeletal fractionation of δ18O, δ13C and rapid calcite precipitation have however not been previously investigated with regards to their clumped isotope composition. We present clumped isotopic composition (Δ47) of 25 inter-skeletal elements of 5 echinoid species with varying growth temperatures. We found no statistically significant inter-skeletal variation in Δ47 in all echinoid species measured, a surprising find given the important inter-skeletal variability reported for δ13C and δ18O. Our echinoid Δ47-temperature calibration however shows a statistically significant positive offset from Δ47-temperature calibration for inorganic calcite of 0.014‰. The pattern of isotopic fractionation in δ18O and Δ47 of echinoderms is not consistent with CO2 hydration or hydroxylation, diffusion or the high-Mg calcite composition of echinoid calcite. Positive offsets in the Δ47 of echinoid calcite may however relate to deviations in the pH of the calcifying fluid from the pH at which equilibrium calcite is precipitated.
Without getting too far into the physical chemistry weeds, I think it's helpful to look at the formula for Δ47. You're essentially looking at how much more common clumped heavy molecules are than you'd expect based on the presence of molecules with single heavy isotopes. Intuitively, that comparison provides some control for isotopic environment, and empirically, that seems to hold.
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