Temperature-dependent fractionation

Calcium carbonate is also the main constituent of the shells of sea animals, which make their shells from elements acquired from the surrounding waters. Now, the degree of fractionation of the oxygen isotopes as well as the formation of mineral carbonates and of animal shells in sea waters are determined on the basis of the temperature-dependent fractionation of the isotopes of oxygen the oxygen isotope composition of these materials reflects, therefore, the temperature at the time of their formation. Thus determining the isotope ratio between the stable isotopes of oxygen... 

Figure 10. Summary of experimentally determined fractionation factors for Ca isotopes in the formation of foraminifera and coccolith shell carbonate, and for rapid inorganic precipitation of aragonite from an Mg-Ca-Cl solution. Data for the foraminifer G. ornatissima and the coccolith E. huxleyi are from De La Rocha and DePaolo (2000). Data on G. sacculifer are from Nagler et al. (2000). Data for O. universa and aragonite are from Gussone et al. (2003). Two of the forams and the coccolith E. huxleyi have similar fractionation behavior, with an overall fractionation factor of-1 to -1.5%o, and a small temperature dependence of about 0.02 per °C. The foram G. sacculifer appears to have a strongly temperature dependent fractionation factor.

A further advancement comes from inter-laboratory comparison of two standards having different isotopic composition that can be used for a normalization procedure correcting for all proportional errors due to mass spechomehy and to sample preparation. Ideally, the two standard samples should have isotope raUos as different as possible, but still within the range of natural variations. There are, however, some problems connected with data normalization, which are still under debate. For example, the CO2 equilibration of waters and the acid extraction of CO2 from carbonates are indirect analytical procedures, involving temperature-dependent fractionation factors (whose values are not beyond experimental uncertainties) with respect to the original samples and which might be re-evaluated on the normalized scale. 

Heterogeneities in stable isotopes are difficult to detect, because stable isotope ratios are affected by the various partial melting-crystal fractionation processes that are governed by temperature-dependent fractionation factors between residual crystals and partial melt and between cumulate crystals and residual liquid. Unlike radiogenic isotopes, stable isotopes are also fractionated by low temperature surface processes. Therefore, they offer a potentially important means by which recycled crustal material can be distinguished from intra-mantle fractionation processes. 

It should be mentioned that most authorities (17) consider the solid solubility of silicon in nickel to be several per cent in the temperature region of this study. The present sample contained only 0.3 per cent Si. This would indicate that a temperature-dependent fraction of the total finds it more economical, from the free energy standpoint, to occur as a surface phase. It may be that certain types of catalyst poisoning consist of the formation of surface phases of this kind on normally active regions of the catalyst. 

The temperature-dependent fractionation of oxygen isotopes between calcite (ct) and water (w), can be written in terms of the isotopic exchange reaction ... 

C of calcite tests assuming that the calcite was precipitated in equilibrium with the ECO2, correcting for the temperature-dependent fractionation Sb(a) between C02(aq) and dissolved bicarbonate according to Mook et al. (1974) ... 

Rewriting equation (1) in terms of the time and temperature dependent fractional conversion, F(t,T), we obtain... 

The acoustic polarons are metastable or unstable. In the case of metastable polarons, the acoustic polaron states may be partially occupied at higher temperatures. Therefore, positrons spend on average a temperature-dependent fraction / of their life in the metastable state. The interesting case is when the decay rate of the metastable state is smaller than or comparable to the positron annihilation rate. 

---