Determination of the mass-dependence of cadmium isotope fractionation during evaporation

Abstract

Mass fractionation laws relate the fractionation factor α A for one isotope ratio to the fractionation factor α B for a second isotope ratio of the same element, with a fractionation exponent β such that α A = α B β. The exponent β defines the mass-dependence of the mass fractionation law and thus determines the slope of a mass fractionation line in linearized three isotope space. The generalized power law (GPL) defines β as a function of a variable exponent n. The laws that aim to describe equilibrium and kinetic isotope fractionations are special cases of the GPL with n = −1 and n → 0, respectively. Large isotope fractionations (up to 10% for 106Cd/ 114Cd) were found to accompany the evaporation of molten Cd into vacuum at about 180°C. The slopes of the fractionation lines (β-values) were obtained by analyzing the Cd isotope compositions of the evaporation residues relative to the starting material with two different multiple collector-ICPMS instruments. For the most fractionated sample, the difference between the theoretical β-values, that describe kinetic and equilibrium isotope fractionation, is 10 to 20 times larger than the measurement uncertainty. A mass-dependence with n = −0.35 was determined for this sample. This result differs significantly from the value that would be expected for simple kinetic evaporation (n → 0), which is governed by the diffusion of monatomic Cd from the melt into vacuum. The observed “non-kinetic” mass-dependence probably results from partial recondensation (back reaction) of Cd vapor into the melt phase. This interpretation requires that equilibrium evaporation of Cd at about 180°C is associated with significant isotope fractionation. The present study demonstrates that the mechanism of isotope fractionation can be investigated by studying the associated mass-dependence, which can be determined by measuring the isotope ratios of a fractionated product relative to the starting material. The quantification of mass fractionation line slopes with the GPL should aid the interpretation of mass-dependent and small mass-independent isotope effects.