doi:10.1016/j.gca.2003.12.013 Determination of the mass-dependence of cadmium isotope fractionation during evaporation FRANK WOMBACHER, 1, * ,† MARK REHK ¨ AMPER, 2 and KLAUS MEZGER 1 1 Institut fu ¨r Mineralogie, Universita ¨t Mu ¨nster, Corrensstr. 24, 48149 Mu ¨nster, Germany 2 Institute of Isotope Geology and Mineral Resources, ETH Zu ¨rich, NO C61, CH-8092 Zu ¨rich, Switzerland (Received March 11, 2003; accepted in revised form December 23, 2003) Abstract—Mass fractionation laws relate the fractionation factor  A for one isotope ratio to the fractionation factor  B for a second isotope ratio of the same element, with a fractionation exponent  such that  A =  B  . The exponent  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  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 3 0, respectively. Large isotope fractionations (up to 10% for 106 Cd/ 114 Cd) were found to accompany the evaporation of molten Cd into vacuum at about 180°C. The slopes of the fractionation lines (-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 -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 3 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. Copyright © 2004 Elsevier Ltd 1. INTRODUCTION Chemical or biochemical reactions and physical processes can generate mass-dependent stable isotope fractionations as the result of equilibrium isotope exchange or kinetic isotope separation. A quantitative physicochemical understanding of stable isotope effects was first developed by Urey (1947), Bigeleisen and Mayer (1947), and Bigeleisen (1949). Follow- ing earlier work of Matsuhisa et al. (1978), Young et al. (2002) inferred that the mass-dependences, which result from kinetic and equilibrium isotope fractionation, differ slightly. This dif- ference arises because kinetic isotope effects are due to atomic or molecular motions that can often be described using classical mechanics, whereas equilibrium isotope fractionation is a quan- tum phenomenon (Young et al., 2002). The limited Mg isotope data that is available for chondrules and evaporation residues from chondrules, appear to confirm the kinetic mass-depen- dence inferred from theory (Young et al., 2002). Further evi- dence for slightly different mass-dependences is provided by precise measurements of oxygen isotopes that were fraction- ated in the hydrological cycle (Miller, 2002; Meijer and Li, 1998) and by biologic mechanisms (Angert et al., 2003). Apart from these investigations, differences in mass-depen- dences have so far gained little attention, which is due in part to limitations in measurement precision. However, state of the art gas source mass spectrometry and MC-ICPMS (multiple collector inductively coupled mass spectrometry) now allow very precise stable isotope ratio measurements for a wide range of elements and thus render such studies possible (Young et al., 2002). Mass-dependences are of interest for several reasons. First, precise data on fractionation line slopes provide a new perspective for the interpretation of physicochemical isotope effects. Second, a firm understanding of mass-dependences is necessary for a rigorous evaluation of mass-independent iso- tope fractionations (Miller, 2002; Young et al., 2002; Angert et al., 2003). As demonstrated by Esat et al. (1986), a careful evaluation of mass-dependences is also required for other iso- tope anomalies if large mass-dependent isotope fractionations are present. For the present study, we investigated the mass-dependence for the evaporation of molten Cd into vacuum. Because sam- ples of the residual Cd melt displayed strongly fractionated isotope compositions, the mass-dependence was precisely con- strained and this allowed further insight into the isotope frac- tionation mechanism that accompanied the evaporation pro- cess. * Author to whom correspondence should be addressed (fwombacher@ifm-geomar.de). † Present address: IFM-GEOMAR Leibniz-Institute fu ¨ r Meereswissen- schaften, Wischofstr. 1-3, 24148 Kiel/Germany. Pergamon Geochimica et Cosmochimica Acta, Vol. 68, No. 10, pp. 2349 –2357, 2004 Copyright © 2004 Elsevier Ltd Printed in the USA. All rights reserved 0016-7037/04 $30.00 + .00 2349