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The Kinetics of Calcite Growth: Interpreting Chemical Affinity-Based Rate Laws Through the Lens of Direct Observation 1

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Henry. H. Teng , Patricia M. Dove and James J. De Yoreo 1 Department of Geology George Washington University Washington, D.C. 20052 2 Department of Geological Sciences Virginia Polytechnic Institute and State University Blacksburg, VA 24061 3 Department of Chemistry and Materials Science Lawrence Livermore National Laboratory Livermore, CA 94550

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ABSTRACT Chemical affinity-based rate laws are used across the geochemical and materials communities to quantify mineral/material corrosion and growth kinetics. These rate expressions are founded in assumptions regarding reaction mechanism with little evidence for surface processes. Using Atomic Force Microscopy (AFM), this study demonstrates the dependence of growth kinetics upon the structures of dislocation sources. In situ observations show that the dominant mode of growth occurs by hillock development initiated at complex sources. Derivations of surface process-based rate expressions show a complex dependence of rate on chemical affinity. This dependence is approximated by second order affinity-based rate laws only under the special conditions that 1) growth proceeds by development of single sourced spirals and 2) growth occurs at very near equilibrium conditions where spiral formation is the only operative mechanism. This suggests that growth experiments that measure temporal changes in solution chemistry yield a composite rate that arises from the contributions of the different hillock types. Hence, chemical affinity-based rate laws do not generally give meaningful interpretations of growth mechanism. By combining direct observations with macroscopic methods that monitor temporal changes in solution chemistry, rate laws with greater predictive capabilities may be possible. INTRODUCTION The abundance of calcium carbonate minerals throughout natural and engineered earth systems has motivated investigations of calcite crystallization over the last century. It is widely recognized that an understanding of the kinetics and mechanisms governing growth is of first order importance for predicting mineralization and thus, acquiring the ability to control it. Advances in controlling or directing the growth of carbonate minerals hinge upon clarifying two uncertainties: (1) The dependence of growth mechanism upon supersaturation; (2) The microscopic surface processes that control the macroscopic manifestations of overall growth rates. Answers to these questions establish the knowledge base for constructing general models that quantify growth in complex mixtures of organic and inorganic constituents. They also establish relationships between microscopic processes and macroscopic growth rates determined by what are known as ’bulk’ methods throughout the scientific literature. However, a review of the findings published to date suggests that these issues have not been adequately explored. Growth studies conducted over a wide range of supersaturations have e