A modified surface kinetic model for calcium and strontium isotope fractionation during calcite precipitation

Abstract

The Ca and Sr isotope fractionation factors (\(\mathrm{\Delta^{44/40}Ca}\) and \(\mathrm{\Delta^{88/86}Sr}\)), as well as the bulk Sr partition coefficient (\(K\)), depend on calcite precipitation rates in both experimental and natural settings. These processes are expected to be controlled by surface kinetics. Ten years ago, Depaolo (2011) proposed a surface reaction model that successfully explained the kinetic effects on \(\mathrm{\Delta^{44/40}Ca}\) and \(K\). With new observations of \(\mathrm{\Delta^{88/86}Sr}\), the limitation of this model emerges. Here, we develop a modified surface reaction model with separate contributions from two underlying precipitation mechanisms, namely spiral growth and surface nucleation. We derive the most representative model by synthesizing general forms with simple but justifiable assumptions of surface reaction kinetics. Our modified model successfully explains observations of the precipitation rate dependence of \(\mathrm{\Delta^{44/40}Ca}\), \(\mathrm{\Delta^{88/86}Sr}\), and \(K\), as well as their correlations. Our findings suggest that surface reactions during calcite precipitation solely regulate these parameters, regardless of diffusion. The revised model can be readily integrated with existing stoichiometric models and offers important implications for interpreting carbonate stable Ca and Sr isotope compositions, as well as the partitioning and isotope fractionation of other trace elements during carbonate precipitation.