Using in situ atomic force microscopy, the growth rates of the obtuse and acute step orientations on the {101̅ 4} calcite surface were measured at two saturation indices as a function of the aqueous calcium-to-carbonate ratio and aqueous strontium concentration. The amount of strontium required to inhibit growth was found to correlate with the aqueous calcium concentration, but did not correlate with carbonate, suggesting that strontium inhibits attachment of calcium ions to reactive sites on the calcite surface. Strontium/ calcium cation exchange selectivity coefficients, K ex , are estimated at 1.09 ± 0.09 and 1.44 ± 0.19 for reactive sites on the obtuse and acute step orientations, respectively. The implication of this work is that, to avoid poisoning calcite growth, the concentration of calcium should be higher than the quotient of the strontium concentration and K ex , regardless of the saturation index. Previous analytical models of nucleation of kink sites on steps are expanded to include growth rates at multiple saturation indices and the effect of strontium. The rate constants for calcium attachment are found to be similar for the two step orientations, but those of carbonate vary significantly. This work will have implications for natural or engineered calcite growth, such as to sequester subsurface strontium contamination.

The three-dimensional structure of the barite (001)−water interface was studied using in situ specular and nonspecular X-ray reflectivity (XR). Displacements of the barium and sulfate ions in the surface of a barite crystal and the interfacial water structure were defined in the analyses. The largest relaxations (0.13 Å lateral and 0.08 Å vertical) were observed for the barium and sulfate ions in the topmost unit cell layer, which diminished rapidly with depth. The best fit structure identified four distinct adsorbed species, which in comparison with molecular dynamics (MD) simulations reveals that they are associated with positions of adsorbed water, each of which coordinates one or two surface ions (either barium, sulfate, or both). These water molecules also adsorb in positions consistent with those of bariums and sulfates in the bulk crystal lattice. These results demonstrate the importance of combining highresolution XR with MD simulations to fully describe the atomic structure of the hydrated mineral surface. The agreement between the results indicates both the uniqueness of the structural model obtained from the XR analysis and the accuracy of the force field used in the simulations.

Ionically bonded minerals are ubiquitous and play a determinative role in controlling the mobility of toxic metals in natural environments. However, little is known about the mechanism of ion uptake by these mineral surfaces. Here, the sorption of strontium ions (Sr 2+ ) to the barite (001)−water interface was studied using a combination of synchrotron X-ray scattering and three types of computational simulations (density functional theory, classical molecular dynamics (CMD), and CMD-metadynamics). In situ resonant anomalous X-ray reflectivity (RAXR) revealed that Sr 2+ adsorbed on the barite surface as inner-sphere surface complexes and was incorporated within the outermost barite atomic layers. Density functional theory combined with CMD simulations confirmed the thermodynamic stability of these species, demonstrating almost equal magnitudes in the free energy of sorption between these species. Metadynamics simulations showed a more detailed feature in the free energy landscape for metal adsorption where adsorbed Sr 2+ are stabilized in as many as four distinct inner-sphere sites and additional outer-sphere sites that are more diffuse and less energetically favorable than the inner-sphere sites. All three techniques confirmed Sr 2+ adsorbs inner-sphere and binds to oxygens in the top two surface sulfate groups. The energy barriers among the inner-sphere sites were significantly lower compared with those for constituent cation Ba 2+ , implying fast exchange among adsorbed Sr 2+ species. The Sr 2+ uptake measured by RAXR followed a Frumkin isotherm defined with an apparent free energy of sorption, ΔG Sr ≈ − 22 kJ/mol, and an effective attractive interaction constant, γ ≈ − 4.5 kJ/mol, between sorbed Sr 2+ . While the observed free energy can be mostly explained by the (CMD) Helmholtz free energy of adsorption for Sr 2+ , ΔF Sr = −15.3 kJ/mol, the origin of the sorbate−sorbate correlation could not be fully described by our computational work. Together, these experimental and computational results demonstrate the complexity of Sr 2+ sorption behavior at the barite (001) surface.

Quantitative prediction of mineral reaction rates in the subsurface remains a daunting task partly because a key parameter for macroscopic models, the reactive site density, is poorly constrained. Here we report atomic force microscopy (AFM) measurements on the {1014} calcite surface of monomolecular step densities, treated as equivalent to the reactive site density, as a function of aqueous calcium-to-carbonate ratio and saturation index. Data for the obtuse step orientation are combined with existing step velocity measurements to generate a model that predicts overall macroscopic calcite growth rates. The model is quantitatively consistent with several published macroscopic rates under a range of alkaline solution conditions, particularly for two of the most comprehensive data sets, without the need for additional fit parameters. The model reproduces peak growth rates, and its functional form is simple enough to be incorporated into reactive transport or other macroscopic models designed for predictions in porous media. However, it currently cannot model equilibrium or pH effects and it may overestimate rates at high aqueous calcium-to-carbonate ratios. The discrepancies in rates at high calcium-to-carbonate ratios may be due to differences in pretreatment, such as exposing the seed material to SI ≥ 1.0 to generate/develop growth hillocks, or other factors.

The rate of growth of ionic minerals from solutions with varying aqueous cation:anion ratios may result in significant errors in mineralization rates predicted by commonly-used affinitybased rate equations. To assess the potential influence of solute stoichiometry on barite growth, step velocities on the barite (001) surface have been measured at 108°C using hydrothermal atomic force microscopy (HAFM) at moderate supersaturation and as a function of the aqueous barium:sulfate ratio (r). Barite growth hillocks at r ~ 1 were bounded by steps, however at r < 1, kink site densities increased, steps followed a direction vicinal to , and the [010] steps developed. At r > 1, steps roughened and rounded as the kink site density increased. Step velocities peaked at r = 1 and decreased roughly symmetrically as a function of r, indicating the attachment rates of barium and sulfate ions are similar under these conditions. We hypothesize that the differences in our observations at high and low r arise from differences in the attachment rate constants for the obtuse and acute steps. Based on results at low r, the data suggests the attachment rate constant for barium ions is similar for obtuse and acute steps. Based on results at high r, the data suggests the attachment rate constant for sulfate is greater for obtuse steps than acute steps. Utilizing a step growth model developed by Stack and Grantham (2010)

Sorption of ions at the mineral–water interface is an important factor that determines the fate of toxic metals in the environment. Here, we use barite as a model substrate to understand the interaction of toxic-metal lead (Pb) with ionic crystals. The coverage and location of Pb sorbed to the (001) surface was measured as a function of aqueous Pb concentration ([Pb]aq) using in situ specular resonant anomalous X-ray reflectivity (RAXR) to determine the sorption capacity and process. The results show that Pb sorption occurs via incorporation (primarily within the top barite layer ∼3 Å in depth) and adsorption (mostly as an inner-sphere complex at ∼2 Å in height) simultaneously. Both the incorporated and adsorbed Pb coverages increase with increasing [Pb]aq up to [Pb]aq ≈ 200 μM, above which the adsorbed fraction increases more rapidly than the incorporated fraction. This enhanced adsorption has a height distribution that is further extended (≥15 Å from the surface) than that observed in lower [Pb]aq. This change in distribution is interpreted as arising from additional sorption of outer-sphere species or Pb-bearing phases precipitated on the surface. Desorption experiments in Pb-free solutions show that the incorporated fraction is more resistant to removal than the adsorbed fraction, consistent with the speciation-dependent stabilities premised in the classical sorption models.

Impurity ions influence mineral growth rates through a variety of kinetic and thermodynamic processes that also affect partitioning of the impurity ion between the solid and solution. Here, the effect of an impurity ion, strontium, on Barite (BaSO4) (001) growth rates was studied using a combination of high-resolution in situ microscopy with ex situ chemical imaging techniques. In the presence of strontium, ⟨120⟩ steps roughened and bifurcated. The overall Barite growth rate also decreased with increasing aqueous strontium-to-barium ratio ([Sr]/[Ba] aq ) < 1. Analysis of the reacted solids using chemical imaging techniques indicated strontium incorporated uniformly across all step orientations into the Barite growth hillock for [Sr]/[Ba] aq < 1. However, at [Sr]/[Ba] aq > 5, steps with an apparent [010] orientation were expressed and growth in the [010] step direction led to an increase in the overall growth rate of the surface. Strontium became preferentially incorporated into the [010] step direction, rather than being homogeneously distributed. The [Sr]/[Ba] s in the newly grown solid was found to correlate directly with that of solutions at [Sr]/[Ba] aq < 5, but not for higher [Sr]/[Ba] aq . Solid composition analyses indicate that thermodynamic equilibrium was not achieved. However, kinetic transport modeling successfully reproduces the shift in growth mechanism.

Sparingly soluble sulfate minerals, particularly barite (BaSO 4 ), present an ideal system to understand mineral−water interfacial reactions. The model system barite has been used to develop crystal nucleation, growth, recrystallization, and pore-scale reactive transport models, both for the end-member cases, and in the presence of impurities that form isostructural solid solutions (Sr, Pb, Ra). Here, we present a comprehensive picture of the current body of research on sulfate minerals and their solid solution reactivity over spatiotemporal scales ranging from the molecular scale in picoseconds to the pore-scale in years of reaction time. Understanding reactivity of minerals at the pore-scale begins at the atomic-level where the structure of the mineral surface influences interfacial water structuring, and hence mineral reactivity. This review covers the inherently multiscale nature of mineral reactivity, ranging from atomic-scale interfacial structure to mesoscale impurity incorporation during recrystallization to pore-scale reactive transport models. In each topic, we identify gaps in knowledge, difficulties in cross-scale analyses, and future challenges in prediction of mineral growth, nucleation, and impurity transport across scales.