Estimating the Triple-Point Isotope Effect and the Corresponding Uncertainties for Cryogenic Fixed Points

The sensitivities of melting temperatures to isotopic variations in monatomic and diatomic atmospheric gases using both theoretical and semi-empirical methods are estimated. The current state of knowledge of the vapor-pressure isotope effects (VPIE) and triple-point isotope effects (TPIE) is briefly summarized for the noble gases (except He), and for selected diatomic molecules including oxygen. An approximate expression is derived to estimate the relative shift in the melting temperature with isotopic substitution. In general, the magnitude of the effects diminishes with increasing molecular mass and increasing temperature. Knowledge of the VPIE, molar volumes, and heat of fusion are sufficient to estimate the temperature shift or isotopic sensitivity coefficient via the derived expression. The usefulness of this approach is demonstrated in the estimation of isotopic sensitivities and uncertainties for triple points of xenon and molecular oxygen for which few documented estimates were previously available. The calculated sensitivities from this study are considerably higher than previous estimates for Xe, and lower than other estimates in the case of oxygen. In both these cases, the predicted sensitivities are small and the resulting variations in triple point temperatures due to mass fractionation effects are less than 20 μK.