Bigeleisen—Mayer equation

Bigeleisen J (1949) The relative velocities of isotopic molecules. J Chem Phys 17 675-678 Bigeleisen J (1955) Statistical mechanics of isotopic systems with small quantum corrections. I. General considerations and the rule of the geometric mean. J Chem Phys 23 2264-2267 Bigeleisen J (1998) Second-order correction to the Bigeleisen-Mayer equation due to the nuclear field shift. Proc National Acad Sci 95 4808-4809... 

The ratio of ionimtion constants E /K[, can be expressed as an isotopic exchange efiuilibrium, the constant for which can in principle l)e evaluated by the relevant form of the Bigeleisen-Mayer equation, eq. (17), where S3anmetry numbers have been cancelled out (96,97). 

Bigeleisen and Mayer (Historical Vignettes 4.1 and 4.2), recognizing that the term in Equation 4.78 involving isotopic masses would always cancel in the calculation of... 

Considerations like the above led the German statistical mechanician L. Waldman independently to an equation similar to the (si/s2)f equation of Bigeleisen and Mayer. The foregoing can be regarded as an independent proof of the Teller-Redlich product rule but this statement depends on the assumption of no rotational-vibrational interaction. 

Using a sum-of-squares rule from theoretical vibrational spectroscopy, Bigeleisen and Mayer (1947) then showed that, under the conditions relevant to Equation (4),... 

Mossbauer spectroscopy involves the measurement of minute frequency shifts in the resonant gamma-ray absorption cross-section of a target nucleus (most commonly Fe occasionally Sn, Au, and a few others) embedded in a solid material. Because Mossbauer spectroscopy directly probes the chemical properties of the target nucleus, it is ideally suited to studies of complex materials and Fe-poor solid solutions. Mossbauer studies are commonly used to infer properties like oxidation states and coordination number at the site occupied by the target atom (Flawthome 1988). Mossbauer-based fractionation models are based on an extension of Equations (4) and (5) (Bigeleisen and Mayer 1947), which relate a to either sums of squares of vibrational frequencies or a sum of force constants. In the Polyakov (1997)... 

Based on equation 11.41, the difference between the Helmholtz free energies of formation of two isotopic molecules with respect to their gaseous atoms depends on the shift of vibrational frequencies between heavy and light isotope-bearing compounds—i.e., according to Bigeleisen and Mayer (1947),... 

Table 11.4 Separative effect / and isotopic fractionation constant K for heavy isotopes, computed through equation 11.47. is angular totally symmetric stretching frequency derived from Raman spectra (see Bigeleisen and Mayer, 1947 for references).

The theory of IEs was formulated by Bigeleisen and Mayer.9 The IE on the acid-base reaction of Equation (1) is defined as the ratio of its acidity constant KA to the acidity constant of the isotopic reaction, Equation (2). The ratio KJ KA is then the equilibrium constant XEIE for the exchange reaction of Equation (3). That equilibrium constant may be expressed in terms of the partition function Q of each of the species, as given in Equation (4), which ignores symmetry numbers. 

The expected characteristics of 7 can best be determined by an examination of the original derivation of the Y equation. Bigeleisen and Mayer (7) derived the equation... 

In the G(w)-approximation, introduced by Bigeleisen and Mayer (8) and later extended to higher orders by Bigeleisen (4), the reduced partition function ratio (Equation 1) is expanded in terms of the isotope frequency shifts, Au, = — Ui. The first three terms are... 

The theory of stable isotope exchange was described by Urey (1947) and Bigeleisen and Mayer (1947), and has been reviewed and elaborated many times (Javoy 1977, Clayton 1981, O Neil 1986, Hoefs 1997, Criss 1999 Chacko et ak, this volume Cole and Chakraborty, this volume). Only the basic equations need be given here. 

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