1. H. Craig in Nuclear Geology of Geothermal Areas (Consiglio Nazionale delle Ricerche Pisa Italy 1963) p. 17. For reviews of the application of stable isotopes to the study of fluid-rock interaction see Rev. Mineral. 16 165 (1986).
2. The fractionation factor describes the distribution of isotopes between two phases or species and is defined as α A-B = R A / R B where R denotes the concentration ratio of the heavy and light isotope (for example D/H or 18 O/ 16 O) in the phase or species A or B. Values of the fractionation factor are given in the 1000 ln α notation. The typically required accuracy is 1 to 2 per mil for D-H and 0.1 to 0.2 per mil for 18 O- 16 O fractionation factors.
3. H. C. Urey J. Chem. Soc. (London) 562 (1947); J. Bigeleisen and M. G. Mayer J. Chem. Phys. (1947). The most commonly applied expression uses the reduced partition function ratio for the isotopically substituted molecule: Qh/Ql=(σl/σh)(mh/ml)3/2 ∏i=13N−6(Uhi/Uli) (e−Uhi/2/e−Uli/2)(1−e−Uli/1−e−Uhi)where Q is the reduced partition function (subscript h for the heavy l for the light isotope) σ denotes the symmetry number m is the atomic mass of the isotope of interest and U is an abbreviation for h ν/ kT ( h : Planck's constant; ν: vibrational frequency; k : Boltzmann's constant; T : temperature in Kelvin). The first two terms are the translational and rotational contributions to the reduced partition function ratio which for the purpose of the present study can be taken as classical hence not contributing to isotopic fractionation. The other terms are the vibrational contributions treated in the harmonic approximation. Thus in a very good approximation there are only two variables that determine the magnitude of isotope fractionation that is temperature and the vibrational frequencies. From the reduced partition functions of any two phases or species A and B the equilibrium constant for the isotope exchange between these can be calculated as K A-B = ( Q h / Q l ) A ( Q h / Q l ) B . In most cases K A-B is numerical identical to α A-B . If not a simple practical way to calculate α A-B is to leave out the symmetry number terms. For a detailed discussion see V. I. Ferronsky and V. A. Polyakov Environmental Isotopes in the Hydrosphere (Wiley Chicester UK 1982) pp. 14–43.
4. Effect of pressure on equilibrium isotopic fractionation
5. An optical cell for Raman spectroscopic studies of supercritical fluids and its application to the study of water to 500°C and 2000 bar