Separation of Strontium and Barium Isotopes Using a Crown-Ether. Different Behaviors of Odd Mass and Even Mass Isotopes.

Nishizawa, Kazushige; Nakamura, Kinya; Yamamoto, Tadashi; Masuda, Takatsugu

doi:10.1080/07366299408918254

Cited by 42 publications

(26 citation statements)

References 6 publications

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“…Recent experiments have shown that chemical equilibrium isotope-exchange separation factors are not necessarily a linear function of the atomic mass differences of the isotopomers (1)(2)(3)(4)(5)(6)(7)(8). The most extensive experiments are those of Fujii et al U between an aqueous phase and an anion-exchange resin.…”

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Second-order correction to the Bigeleisen–Mayer equation due to the nuclear field shift

Bigeleisen

1998

Proc. Natl. Acad. Sci. U.S.A.

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The nuclear field shift affects the electronic, rotational, and vibrational energies of polyatomic molecules. The theory of the shifts in molecular spectra has been studied by Schlembach U between an aqueous phase and an anion-exchange resin. The aqueous phase is principally U(IV); the resin phase is principally U(VI), hydrated or complexed uranyl ion. In each of these exchange reactions the heavy isotope concentrates in the aqueous phase, that is U(IV). The nonlinearity and the fact that the heavy isotope concentrates in the U(IV) species arise from the shift in the minimum of the electronic potential energy due to the different nuclear sizes and shapes of the isotopomers. This is known as the nuclear field shift. A quantitative calculation of this effect (9) is in excellent agreement with experiment.The calculation is based on the addition of a term due to the nuclear field shift to the Bigeleisen-Mayer equation for the logarithm of the isotopic separation factor and the reduced partition-function ratio. Analogous to the Bigeleisen-Mayer function, ᐉn(s͞sЈ)f 0 , we define ᐉn(s͞sЈ)f ns as the nuclear field shift correction and ᐉn(s͞sЈ)f T as the total reduced partitionfunction ratio corrected for the nuclear field shift.The nuclear field shift correction is simply,where (E H°Ϫ E L°) is the difference in the ground state electronic energy.The Bigeleisen-Mayer equation is based on the BornOppenheimer approximation and uses an isotope-independent potential energy; it also assumes simple harmonic vibrations. Because the vibrational force constants are the second derivatives of the electronic energy with respect to the mutual distances between atoms, a correction needs to be applied to ᐉn(sЈ͞sЈ)f 0 for the nuclear field shift. The formal theory of the nuclear field shift on the equilibrium force constant of a diatomic molecule has been given by Schlembach and Tiemann (10). From the theory and their data on the electronic and rotational spectra of diatomic Pb chalcogenides and Tl halides, Tiemann et al. (11) estimated the relative vibrational frequency shifts in these compounds resulting from the nuclear field shifts to be of the order of 10 Ϫ6. I now show that a relative frequency shift of this order of magnitude is a negligible, second-order correction to ᐉn(s͞sЈ)f 0 .In my study of the nonlinearity of the isotope separation factor, I found it convenient to use the first finite polynomial approximation to ᐉn(s͞sЈ)f 0 because this utilizes the isotopomer masses directly.For the present purpose it is more convenient to use the Bigeleisen-Mayer free energy function, G(u ), for the calculation of the correction to ᐉn(s͞sЈ)f 0 . We writewhere u boc ϭ h boc ͞kT and boc is the vibrational frequency corrected for the nuclear field shift and G(u) ϭ 1/2 Ϫ 1͞u ϩ (e u Ϫ 1) Ϫ1). To calculate (Ј boc Ϫ boc ) we set the nuclear field shift correction in the heavy isotope equal to zero. Then,where Ј BO is the Born-Oppenhemier frequency and ⌬Ј p is the perturbation due to the nuclear field shift. In Table 1 S). The correc...

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Second-order correction to the Bigeleisen–Mayer equation due to the nuclear field shift

Bigeleisen

1998

Proc. Natl. Acad. Sci. U.S.A.

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“…It is found that the isotope fractionation of the odd mass number isotope 235 U deviates from the mass-dependent lines defined by even mass number isotopes. The isotope fractionations of fractionation phenomenon used to be called the ''odd-even isotope effect'' (Nishizawa et al 1994) (Fig. 1) but its mechanism was not clear.…”

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confidence: 99%

Nuclear field shift effects on stable isotope fractionation: a review

Yang

Liu

2016

Acta Geochim

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An anomalous isotope effect exists in many heavy element isotope systems (e.g., Sr, Gd, Zn, U). This effect used to be called the ''odd-even isotope effect'' because the odd mass number isotopes behave differently from the even mass number isotopes. This mass-independent isotope fractionation driving force, which originates from the difference in the ground-state electronic energies caused by differences in nuclear size and shape, is currently denoted as the nuclear field shift effect (NFSE). It is found that the NFSE can drive isotope fractionation of some heavy elements (e.g., Hg, Tl, U) to an astonishing degree, far more than the magnitude caused by the conventional mass-dependent effect (MDE). For light elements, the MDE is the dominant factor in isotope fractionation, while the NFSE is neglectable. Furthermore, the MDE and the NFSE both decrease as temperatures increase, though at different rates. The MDE decreases rapidly with a factor of 1/T 2 , while the NFSE decreases slowly with a factor of 1/T. As a result, even at high temperatures, the NFSE is still significant for many heavy element isotope systems. In this review paper, we begin with an introduction of the basic concept of the NSFE, including its history and recent progress, and follow with the potential implications of the inclusion of the NFSE into the kinetic isotope fractionation effect (KIE) and heavy isotope geochronology.Keywords Isotope fractionation Á Mass-dependent effect Á Nuclear field shift effect Á Mass-independent fractionation Á Nuclear volume effect Á Nuclear shape effect

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“…Isotope enrichment factor ε m,138 is defined as, Figure 1 shows isotope enrichment factors reported in the pioneering works on barium isotope effects 15,16) as functions of mass number. In these reports, an unusual property named odd/even isotope effect has been discussed by using a liquidliquid extraction 15) or a liquid chromatography.…”

Section: Methodsmentioning

confidence: 99%

Temperature Dependence of Isotope Effects of Barium Using a Crown Ether

Fujii

Hamanishi

Shibahara

et al. 2002

Journal of Nuclear Science and Technology

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Barium isotopes were fractionated in a liquid-liquid extraction system using a crown ether of dicyclohexano-18-crown-6. The temperature dependence of isotope enrichment factors was investigated at 273.2 to 323.2 K. Within the experimental error, the isotope effects appeared to be ruled by the conventional mass-dependent theory. The maximum isotope effect was observed at 323.2 K, whose isotope enrichment factor for unit mass difference was ε u =−0.00044±0.00013. Relation between ε u and 1/T showed a characteristic curve, but was deviated from a temperature-dependent theory of ε=a/T +b/T 2 . The change in the coefficient a in the present system was discussed by considering the obtained results.

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Separation of Strontium and Barium Isotopes Using a Crown-Ether. Different Behaviors of Odd Mass and Even Mass Isotopes.

Cited by 42 publications

References 6 publications

Second-order correction to the Bigeleisen–Mayer equation due to the nuclear field shift

Second-order correction to the Bigeleisen–Mayer equation due to the nuclear field shift

Nuclear field shift effects on stable isotope fractionation: a review

Temperature Dependence of Isotope Effects of Barium Using a Crown Ether

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