Mapping three-dimensional dissolution rates of calcite microcrystals

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Mapping three-dimensional dissolution rates of calcite microcrystals: Effects of surface curvature and dissolved metal ions Ke Yuan, Vitalii Starchenko, Sang Soo Lee, Vincent De Andrade, Doga Gursoy, Neil C. Sturchio, and Paul Fenter ACS Earth Space Chem., Just Accepted Manuscript • DOI: 10.1021/ acsearthspacechem.9b00003 • Publication Date (Web): 29 Mar 2019 Downloaded from http://pubs.acs.org on March 29, 2019

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ACS Earth and Space Chemistry

Mapping three-dimensional dissolution rates of calcite microcrystals: Effects of surface curvature and dissolved metal ions Ke Yuan1, Vitalii Starchenko2, Sang Soo Lee1, Vincent De Andrade3, Doga Gursoy3,4, Neil C. Sturchio5, Paul Fenter1* 1. Chemical Sciences and Engineering Division, Argonne National Laboratory. 9700 South Cass Avenue, Lemont, IL 60439; 2. Chemical Sciences Division, Oak Ridge National Laboratory, Oak Ridge, TN, 37830; 3. X-ray Science Division, Argonne National Laboratory. 9700 South Cass Avenue, Lemont, IL 60439; 4. Department of Electric Engineering and Computer Science, Northwestern University, Evanston, IL 60208; 5. Department of Geological Sciences, University of Delaware. Newark, DE 19716. *Correspondence and requests for materials should be addressed to [email protected] Abstract The morphological evolution of micron-sized calcite crystals dissolved in static acidic solutions, with and without dissolved Pb2+ ions, was imaged using transmission X-ray microscopy (TXM). The area-normalized dissolution rates measured by TXM increased with time in both Pb-free and Pb-rich solutions but with distinct morphological evolution. Calcite reacted in Pb-free solutions exhibited rounding at corners and edges with faster dissolution at acute corners/edges than obtuse corners/edges. Numerical simulations indicate that this is controlled primarily by solution mass transport that is faster near the acute corners/edges. In comparison, dissolution of calcite in Pbrich solutions was 50% slower than that in Pb-free solutions and exhibited less rounding at corners. Faces of the calcite rhombs exhibited increased surface roughness and the subsequent development of surface micro-pyramids that formed preferentially near the acute edges of the calcite rhombs. Spatially resolved dissolution rates reveal that pyramid formation is associated with reduced dissolution rates near the pyramid apex. The results demonstrate the role of impurity metal ions in controlling the dissolution rate and the associated complexities in the morphological evolution of dissolving mineral surfaces. Keywords: calcite, Pb2+, dissolution rate, morphological instability, X-ray nanotomography, numerical simulation, micro-pyramid, competitive adsorption 1 ACS Paragon Plus Environment

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1. Introduction Dissolution of carbonate minerals has significant impacts on heavy metal sequestration, global carbon cycle, and alkalinity of surface waters.1-5 The dissolution kinetics of calcite has been extensively investigated. Early dissolution experiments used batch reactors and rotating disk techniques where mass transport effects can be controlled by flow rate or rotation speed.6, 7 The measured mass loss was normalized to an estimated surface area and the rate was expressed in terms of a flux (molcm-2s-1). These studies showed that the dissolution rate of calcite is pHdependent.6 The rapid dissolution at acidic conditions (pH < 3) can be limited by solution mass transport (i.e., diffusion and convection). At neutral to basic pH, dissolution rate is normally limited by surface reactions.8, 9 With the advent of surface microscopies, such as atomic force microscopy (AFM), vertical scanning interferometry (VSI), and digital holography (DH), dissolution rates of calcite (104) surfaces have been shown to have spatial heterogeneity.9-11 For example, variations in microscopic dissolution rates have been characterized through the different step velocities of obtuse and acute surface steps and among different kink sites by using AFM and molecular-scale simulations.11-15 Areas having dislocation induced etch pits, grain boundaries, and high surface roughness dissolve faster than defect-free regions.16-19 Statistical distributions of experimentally observed dissolution rates (sometimes referred to as “rate spectra”) have also been shown to have a time dependence. These probe microscopic techniques measure the morphology of a freshly cleaved calcite (104) surface with sub-nm vertical resolution. However, these methods do not reveal the morphological controls over dissolution at macroscopic edges and corners, which can account for a significant portion of the reactive area of a sub-micron sized crystalline grain. Although the dissolution experiments on single crystal calcite in the size of millimeter to centimeter range have been performed, the local dissolution rate variations in three dimensions (3D) have not been reported.20, 21

The presence of metal ions and organic molecules is well-known to modify the morphology of growth hillocks observed on calcite (104) surfaces.22-24 Depending on the functional group and chirality of the organic molecules, they can selectively adsorb to either acute or obtuse steps, resulting in changes of the step energies and step growth velocities. A similar mechanism applies to metal ions, which favor different surface sites depending on their size and charge.24, 2 ACS Paragon Plus Environment

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majority of these experiments on metal-calcite interactions were conducted under calcite growth conditions. Mechanisms on how impurity metals can influence calcite surface morphology during dissolution need further investigations. Here, we image the spatial and temporal evolution of morphologies of individual calcite crystals (tens of microns in size) in acidic solutions (pH = 2.8) using ex situ synchrotron transmission Xray microscopy (TXM), and use this approach to visualize the local variations of dissolution rates in 3D. In particular, calcite dissolution in Pb-free and Pb-rich solutions are compared based on previous results on Pb-calcite interactions at acidic conditions, where significant changes in surface morphology and dissolution rate were observed with reaction time.26,

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mechanisms (e.g., solution mass diffusion vs. surface energetics) that lead to heterogeneously distributed dissolution rates were modeled numerically for Pb-free solutions. The role of Pb2+ ions in generating complex surface structures is discussed. The 3D rate spectra measured by TXM at the grain-scale provide a new perspective, which fills the gap between the knowledge gained on elementary reaction processes by surface probe microscopy on an ideal flat surface and the information obtained by batch dissolution experiments on mineral powders. 2. Materials and Methods Experiments Calcite crystals of 20 μm to 50 μm in size were grown on Kapton® films in dimensions of 5 mm × 2.5 mm × 0.05 mm by using ammonium diffusion method.28, 29 The dissolution experiments were conducted by reacting these calcite crystals in 10 mL of HCl solution at pH = 2.8 (referred to as a Pb-free solution) and 10 mL of 5 mM Pb(NO3)2 solution at the same pH adjusted by 0.1 M HCl (referred to as a Pb-rich solution) at 25 °C. All solutions were prepared in equilibrium with atmospheric CO2. The solid to liquid mass ratio was estimated to be around 1:100000.26 Samples were gently removed from the solutions at 0.5, 2.0, 4.5, 8.0, 11.5, and 14.5 min, and the remaining reactant solution was flushed away with a calcite saturated solution followed by drying under flowing N2. Fresh acidic solutions were used for each time step when placing crystals back into acidic solutions for further dissolution. The solution pH was nearly unchanged after dissolution (pH-stat system). For example, an increase in pH of less than 0.01 was observed for a reaction period of 6.5 min as measured by an Accumet Basic AB15 pH meter.

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Transmission X-ray microscopy was performed with a monochromatic X-ray at energy of 8 keV at beamline 32-ID-C of Advanced Photon Source, Argonne National Laboratory. The sample was imaged in air with 721 projections spanning over 180° rotation with an exposure time of 1s per image and a field view of 70 µm × 70 µm. The acquired data were processed and reconstructed in TomoPy.30-32 The Fresnel zone plate yielded a resolution of 60 nm as characterized by a Siemens Star standard. The reconstructed 3D image had a voxel size of 54 nm × 54 nm × 54 nm after a 2 × 2 binning and visualized by ParaView.33 Image segmentation was completed in Drishti 2.6, where a threshold value was applied to separate the calcite from the background.34 Volume and surface area were calculated from the segmented images in Fiji ImageJ.35-37 A resampling value within the Particle Analysis Toolbox was used to reduce the noise close to the surface of calcite in order to accurately estimate surface areas (See Supporting Information, Fig. S1). Density of the calcite was assumed to be uniform across the sample. Volumes and masses of the crystals were calculated based on the number of voxels within the segmented images. Simulations The modeling of the calcite crystal dissolution is based on the computational fluid dynamics toolkit: OpenFOAM. We used dynamic mesh approach with surface mesh relaxation to simulate the retreat of the crystal interface due to the dissolution reaction.38 For simplicity the twodimensional simulation domain was generated based on the initial shape and dimensions of the crystal extracted from experimental data. Detailed description of governing equations, their dimensionless form, and boundary conditions for reactant transport can be found in the Supporting Information. The dynamic mesh approach with surface mesh relaxation is described in Ref.38 and modified version used in this study is described in the Supporting Information. The dissolution kinetics of calcite under experimental pH conditions was described by a first order rate equation according to previous measurements39, where the rate is proportional to the local proton concentration. Details of the modeling parameters can be found in the Supporting Information, Table S1. 3. Results 3.1 Area-Normalized dissolution rates


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Each calcite crystal grown on the Kapton film exhibited a different orientation with respect to the Kapton substrate (Fig. 1a). Two groups of samples, each containing four crystals were dissolved in Pb-free and Pb-rich solutions, respectively. Pristine crystals had sharp edges and corners with flat (104) surfaces. A majority of the crystals were isolated, whereas two samples were twinned crystals composed of a main crystal accompanied by a smaller one on the side (Fig. 1a, left column). The volume and surface area of the eight calcite crystals all decreased approximately linearly with time (Fig. 1b, 1c). A few of the smaller calcite crystals reacted in Pbfree solutions were completely dissolved during the experiment. The surface area contribution associated with etch pits and steps on surfaces cannot be resolved with the current instrumental resolution (60 nm). Therefore, the actual surface area can be systematically higher than the values shown here, especially if there is significant surface roughening (as found in Pb-containing solutions).

Figure 1. (a) Morphologies of eight pristine calcite crystals before dissolution in acidic solutions (pH = 2.8). Four calcite crystals were dissolved in Pb-free solutions and four other crystals in 5mM Pb(NO)3 solutions. (b) The volume and (c) surface areas of the calcite crystals decreased with time. 5 ACS Paragon Plus Environment


Symbols of the data points on (b) and (c) represented the corresponding calcite crystals having various orientations and sizes, as shown in (a). The area-normalized dissolution rates (in unit of molecm-2s-1) in Pb-free solutions were systematically higher than those in Pb-rich solutions (Fig. 2). These dissolution rates were calculated from the slopes of the data shown in Fig. 1b (in units of mols-1) divided by the measured surface area at a specific time in Fig 1c. Dissolution rates were found to increase with time in all eight crystals. Two crystals represented by the black and red square symbols showed a significant increase in dissolution rate at the last sampling time. The measured time-dependent dissolution rates increased by an order of magnitude from 1.1710-8 molcm-2s-1 to 2.2010-7 molcm-2s-1, but were generally consistent with previous reported values (i.e., between the dashed lines, Fig. 2).9 The different dissolution rates of crystals measured in the same solution (either Pb-free or Pb-rich) and the variability of the dissolution rates as a function of time for each individual crystal indicates that the orientation and shape of the crystal plays an important role. This observation motivated us to investigate the spatial distribution of dissolution rates on individual calcite crystals as described in the following sections.

Figure 2. Area normalized dissolution rates in units of molecm-2s-1 of calcite crystals in acidic Pb-free and Pb-rich solutions both in pH = 2.8. Dashed lines indicate the range of calcite dissolution rates measured at similar pH conditions as summarized recently9. Symbols correspond to the same calcite crystals indicated in Fig. 1a.


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3.2 Anisotropic dissolution in 3D The influence of the calcite grain morphology on the dissolution rate can be visualized in 3D by superimposing a series of images showing the calcite crystal shape as a function of time (Fig. 3). These surfaces were color-coded and carefully aligned in 3D based on intrinsic wedge-shaped growth defects observed near the calcite growth plane attached to the Kapton substrate, where crystal dissolution did not occur (See an example in Supporting Information Fig. S3). Two representative calcite crystals dissolved in Pb-free (Fig. 3a) and Pb-rich (Fig. 3b) solutions are viewed from two different angles (side and top), respectively. The outer image in gray is the pristine calcite crystal and the inner image in red is the remaining core after the dissolution series, with the intermediate color-coded images in between. Notably, the rate of surface retreat was uneven at different locations on the crystal. In Pb-free solutions, dissolution rates were fastest at corners and edges but slower on the flat faces, leading to a noticeable rounding of the rhombic shape. The four symmetry equivalent acute corners dissolved in Pb-free solutions retreated in a nearly equal rate. Also notable was that surfaces retreated faster at the acute corners (a) than at the obtuse corners (o) (Fig. 3a). The evolution of crystal shape can be quantified by plotting the ratio of SA/V2/3 for each crystal as a function of time. The value of this ratio is characteristic of the crystal morphology with values that range from 6.0 for a cube and 4.8 for a sphere. These results confirm the qualitative assessment that calcite crystals in Pb-free solutions evolve monotonically during dissolution, from the characteristic rhombohedral shape that is similar to a cube to a more rounded shape resembling a sphere (Fig. 3c, data in black). In Pb-rich solutions, a number of differences were observed during dissolution, notably that the rounding of the corners was less pronounced than that in Pb-free solutions (Fig. 3c, data in red) and there was a visible increase in the surface roughness (Fig. 3b). The lack of rounding can be quantified by the ratio SA/V2/3 that was found to be largely constant (or even increased) with increasing dissolution.



Figure 3. Morphologies of two calcite crystals dissolved in acidic (a) Pb-free and (b) Pb-rich solutions (pH = 2.8), respectively. The overlapping crystal surfaces are viewed from side and top perspectives (surfaces at t = 0, 30, 120, 270, 480 and 690/870 s are indicated by gray, olive, green, brown, blue, and red colors, respectively). “a” and “o” indicate the acute and obtuse corners. (c) Evolution of the ratio, SA/V2/3 (where SA = surface area, and V = volume of the crystals), as a function of dissolution time indicating a change in crystal morphology. Symbols of the data points in (c) correspond to the calcite crystals shown in Fig. 1a. 3.3 Dissolution rate maps and rate spectra The local dissolution rates of the calcite crystals were quantified by computing the shortest distance from a given point on a calcite surface to the nearest point on the same calcite surface after dissolution at the subsequent time step. 3D dissolution rate maps and rate spectra in a unit of nm/s were generated (Fig. 4 and Fig. 5) by using the computed distances and the known dissolution times. The results reveal that the dissolution of the calcite rhombs is very complex and evolves both spatially and temporally. The crystal dissolved during the first 0.5 min in Pb-free solutions showed a ~5-fold increase in dissolution rate at edges and corners compared with that at the faces (Fig. 4). Similar trends were observed in the rate map measured at 2.0, 4.5, 8.0, and 11.5 min. In particular, three edges associated with the c axis (and the obtuse corners) had lower dissolution rates than the edges associated with the acute edges and corners. The rate differences between obtuse and acute corners/edges were reduced at 4.5 min and 8.0 min, but the acute corners/edges overall kept a higher dissolution rate. For example, acute corners and the associated edges had a


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rate of around 25 nm/s (Fig. 4, 11.5 min, top view). In contrast, the obtuse corner along the c axis direction had a lower dissolution rate of about 15 nm/s. The histogram of observed dissolution rates provides a complimentary approach to understand these changes and indicates that the dissolution rate distributions evolved in two ways during dissolution. The fastest dissolution rate for the initial sample (~25 nm/sec, at the corners and edges) rapidly decreased as the sharp corners of the rhomb shaped crystals became rounded. A second important trend is that the average dissolution rate increased with increasing reaction time (Fig. 4. rate spectra). Peaks in the 0.5 min, 2.0 min and 4.5 min spectra at ~7 nm/s, correspond to the dissolution rate on the faces of the calcite rhombs that accounted for the largest fraction of the surface area (light blue regions). Rate spectra at 11.5 min show a significant increase in local dissolution rates, especially for rates above 15 nm/s. This trend of increasing dissolution rates with time was consistent with the rise of the area normalized rates in units of molecm-2s-1 shown in Fig. 2. Thus, the increase in the dissolution rate does not simply result from changes in the accessible surface area, but also reflects an increase in the local dissolution rates. (Note that the rates close to 0 nm/s in the spectra result from the unreactive calcite surface that was attached to the Kapton substrate.) These behaviors were reproduced in a separate calcite dissolution experiment performed in a Pb-free solution (Supporting Information, Fig. S4).



Figure 4. 3D dissolution rate map of a calcite crystal dissolved in acidic Pb-free solutions (pH = 2.8). The crystal was viewed from side and top with associated dissolution rate color-coded on the surface. Dissolution rate spectra showed the statistical distribution of the corresponding 3D rate map.


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We used computational fluid dynamics simulations on a 2D geometry to understand whether the experimentally observed differences in surface retreat in a Pb-free solution between obtuse and acute edges were caused by surface energy differences or mass transport effects. (Here the edges and corners of the simulated 2D crystal model the behavior of the faces and edges of the 3D crystal; for consistency, we refer to features using the 3D morphological terminology). Specifically, to assess the role of solution transport in the observed rounding of the crystal shape, we performed a simulation in which all sites on the calcite surface followed the same rate law that was controlled solely by the local concentration of protons in the solution. The result of the simulations provided insights into the observed spatial variation of the dissolution kinetics. When adopting the experimentally measured calcite dissolution rate constant of 0.1 cms-1 from Plummer et al.39, the simulated 2D profile retreated with time but maintained sharp edges (Fig. 5a). This simulation also revealed a retreat of the top edges of the simulated 2D crystal (~10 nm/sec, Fig. 5a) was slower than that observed in the experiment (~17 nm/sec, Fig.3) which suggest that the experiments experienced faster than expected solution mass transport (e.g., due to possible solution advection which was not controlled). We also performed a simulation with a 100-fold increase in reaction rate constant (𝑘 = 10 cm ∙ s ―1) which was chosen to explore how the qualitative behavior of the model would change under diffusion-limited conditions (in contrast with the reaction limited conditions, above). Under these conditions, the 2D crystal became rounded (Fig. 5b), and the acute edges of calcite dissolved faster than the obtuse edges, which closely resemble the experimental observations in Fig. 4. These results can be understood from the simulated proton distribution around the crystal (after one second of dissolution for 𝑘 = 10 cm ∙ s ―1). Although the concentration field evolves in time due to diffusion and surface reactions, this image shows how the corners and edges of the crystal are more exposed to the reactive solution within a region with a larger proton concentration gradient. That is, acute corners and edges have higher surface curvature, and therefore, a thinner diffusion layer and faster mass flow than those at the obtuse corner. Thus, one can expect locally faster dissolution and rounding of edges under these conditions (Fig. 5b), whereas edges remain sharp when the dissolution rate is slower (e.g., limited by the slower surface reactions; Fig. 5a). The orientation of the 2D crystal with respect to the supporting substrate also influenced the dissolution rate at the faces and corners of the crystal. The edge forming an acute angle with the substrate (i.e., near the calcite-substrate interface) had a slower dissolution rate than the more open 11 ACS Paragon Plus Environment


obtuse corner due to the more limited solution mass transport near the substrate. The results are consistent with the experimentally observed lower dissolution rate found in calcite faces near the growth substrate in Fig. 4 (side view).

Figure 5. Simulated dissolution of two-dimensional calcite crystals under (a) surface reactioncontrolled and (b) diffusion-controlled condition. Simulation results at 0.5 min, 2.0 min, 4.5 min, 8.0 min, and 11.5 min were showed. (c) An example of the proton concentration distribution around the crystal after 1 s of dissolution (for the simulation in (b), for 𝑘 = 10 cm ∙ s ―1). Here, 𝑐 = 1 corresponds to the bulk proton concentration of pH 2.8. The details of the model are presented in SI. 3D dissolution rate maps in Pb-rich solutions show more homogeneously distributed rates (Fig. 6). Again, the corners and edges had the fastest initial dissolution rates that decreased with reaction time. The initial observed dissolution rates (~15 nm/s) were approximately half the values observed in Pb-free solutions and the rate differences between obtuse and acute corners were significantly smaller than those in Pb-free solution. The average surface dissolution rate increased from 5.0 nm/s to 7.5 nm/s with increasing time, and local dissolution rates above 15 nm/s were less common in the Pb-rich solution. The rate spectrum width was narrower than in Pb-free solution, indicating that the majority of the surface sites had similar dissolution rates (5 to 8 nm/s). Another calcite crystal dissolved in the same Pb-rich solution showed similar changes (Supporting


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Information, Fig. S5). In brief, dissolution of calcite in Pb-rich solutions was ~2 times slower but was more isotropic than that in Pb-free solutions.

Figure 6. 3D surface dissolution rate map of a calcite crystal dissolved in acidic Pb-rich solutions (pH = 2.8). The crystal was viewed from side and top with associated dissolution rate color-coded on the surface. Dissolution rate spectra showing the statistical distribution of the corresponding 3D rate map. 13 ACS Paragon Plus Environment


A notable difference in the Pb-free solutions is the observation of spatially variable dissolution rates across the rhomb faces, seen as 1 m to 5 m sized regions having a deep blue color in the 4.5 min, 8 min, and 14.5 min images (Fig. 6). These locally low dissolution rates are directly associated with the formation of micro-pyramids (Fig. 7). The formation of these pyramids was initiated on rhomb faces near the edges that are farthest away from the c axis, close to the acute edges/corners (as seen in Fig. 7, 2 min). We also find that the size and number density of the pyramids evolved as a function of time. Similar evolution of the micro-pyramids was observed on three other crystals (Supporting Information, Fig. S6). The shape of these micro-pyramids changed with reaction time. The base planes of the pyramids were more elongated in the 14.5 min sample compared to those at 8.0 min (Fig. 7a). In addition, sector-shaped dissolution patterns were observed on the 4.5 min sample. Two straight edges likely made of obtuse steps close to the c axis are indicated by the red lines (Fig. 7b). We can assess the role of the micro-pyramids by simultaneously imaging the topography and the spatially variable dissolution rates (Fig. 8). The dissolution rate was smallest close to the top of the micro-pyramids (with a rate of 1 nm/sec, which was ~7-times smaller than that seen on the flat rhomb face), and gradually increased to that observed on the calcite (104) surface (Fig. 8a). We also correlated the local dissolution rate with the computed surface normal vector directly. This correlation used the triangular surfaces, each with a size of ~4000 nm2, defined by the calculated mesh grid used to represent the calcite surface morphology. The calculated angles of numerous surface normal vectors were plotted as a polar map (Fig. 8b). These data confirm the topographic analysis, having yellow data points in the middle representing flat regions on the calcite (104) surface, as well as four lobes distributed on the polar map corresponding to the four faces of the micro-pyramids. This clustered distribution of surface normal vectors was consistent with the observation that micro-pyramids found on the same calcite (104) surface had a similar shape. The four faces of the micro-pyramids shown in Fig. 8a had averaged angles of 52, 55, 38, and 43 with respect to the calcite (104) surface. These angles do not match precisely to specific crystallographic planes of calcite, but are similar to that of (-120), (-210), (10-8), and (018) calcite surfaces as reported in the previous study.27


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Figure 7. Morphologies of a calcite crystal dissolved in acidic Pb-rich solutions (pH = 2.8) for 14.5 min viewed from (a) side and (b) top perspectives.



Figure 8. (a) Morphology of micro-pyramids covered calcite (104) surface shown with the local dissolution rate (indicated by color) for the calcite sample at 8 min. (b) Orientation of the surface normal vectors computed from (a). 4. Discussion 4.1 Surface energy vs. mass transport The most significant observation in Pb-free solutions was the uneven dissolution rates between acute and obtuse corners/edges of a calcite crystal. A euhedral calcite crystal has a rhombohedral shape composed of six {104} surfaces (Fig. 9a). The eight corners of the crystal can be separated into two groups: (1) two obtuse corners that are connected directly by the calcite c axis and (2) six other symmetry equivalent acute corners. The higher dissolution rates observed at acute vs. obtuse corners/edges could originate from two reasons: microscopic controls due to elementary step velocities and solution mass transport of reactants. In the first case, areas close to the acute corners/edges can be expected to have high surface energy that will be controlled by the step density and the type of steps. For example, acute corners/edges may have a higher step density or other sites that are known to dissolve faster. Microscopically, the calcite (104) surface has obtuse and acute steps resulting from the intrinsic 16 ACS Paragon Plus Environment

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oblique lattice of calcite.40, 41 Combination of two types of steps (acute vs. obtuse) yields four different kink sites denoted as kaa, kao, koa, and koo (o and a indicate obtuse and acute steps, respectively). Both experimental studies and computational simulations indicate that the dissolution kinetics of these steps and kink sites are distinct.12, 42 In brief, obtuse steps dissolve faster than acute steps, and dissolution at koa and koo kink sites contributes more significantly to the total rate than other kink sites. Obtuse steps and koo kinks that are known to dissolve faster, if present, are expected to be preferentially populated near the obtuse edges associated with the rounding of the crystal shape. However, the obtuse edge was observed to have a lower dissolution rate (Fig. 9b). Thus, the nature of the steps present at different edges is unlikely to be the main controlling factor on the differences in observed dissolution rates between the obtuse and acute edges. Solution mass transport, as represented in the numerical simulations (Fig. 5b), instead appears to be a key factor that influences the spatial variation of dissolution rates. Mass transport is more efficient around the acute corner (Fig. 5c), resulting in higher dissolution rate. Also notable is the observation that dissolution at areas near the inert supporting substrate (Kapton film) was also limited by diffusion because of the boundary effect of the substrate (Fig. 4, side view). Another observation from the data in Fig. 4 is that the average dissolution rate increased with time as indicated by the shift of rate spectra to the right (even when the fastest dissolution rates decreased). This is fully consistent with the increase in the surface area-normalized dissolution rates (Figure 2). We speculate this is caused by the increasing number density of step and kink sites as a result of the rounding of the crystal. As shown in Fig. 4, regions having higher dissolution rates (yellow and green regions) are distributed near the edges and corners, which also have a higher surface curvature than the flat calcite (104) faces (blue regions). Microscopically, these high curvature areas must consist of a high density of step and kink sites (Fig. 9b). That is, as the crystal became more rounded upon extent of dissolution, the fraction of the crystal surface having high curvature increased. This resulted in an increase in the density of steps and kink sites and therefore, the net dissolution rate.



Figure 9. (a) A calcite crystal model and (b) the calcite crystal reacted in acidic Pb-free solutions after 11.5 min. Calcite crystal model and calcite sample were placed in the same orientation. Legend of the color-coded rate map in (b) was the same as shown in Fig. 4. a and o indicated acute and obtuse steps expected to be populated on the calcite surface based on the symmetry of the crystal.

4.2 Evolution of surface micro-pyramids Commonly observed dissolution features on the calcite (104) surface are rhombic etch pits.11, 43 The micro-pyramid formation during dissolution in Pb-containing solutions (as also seen in previous studies27) reveals the time-dependent evolution of micro-pyramids on calcite (104) surfaces. Previous observations of calcite nano-rods/shoots and the current micro-pyramids were shown to be preserved dissolution features consisting of calcite due to surface interactions with cations (e.g., Pb2+ in this study).27, 44 We speculate that adsorption and/or incorporation of Pb2+ at steps may increase the energetic barrier for dissolution at steps and that these sites may be concentrated near the top of the micro-pyramids, which showed the lowest dissolution rate (Fig. 8a). Two questions regarding the formation mechanism of micro-pyramids remain unresolved. First, why do micro-pyramids preferentially form near the edges associated with the acute corners of the calcite rhombs? This observation reveals that not all areas of the (104) faces are equivalent with respect to pyramid formation. The preferential formation near the acute edges may imply, for instance, that it relies on the presence of acute steps that would preferentially form with any rounding of the crystal shape. Also, why does the morphology of the micro-pyramid change as a function of time (e.g., with a base initially having a near square shape and evolving towards an 18 ACS Paragon Plus Environment

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elongated diamond shape, as seen in Fig. 7)? This observation indicates that the pyramidal faces are not crystallographic facets but instead suggests that the evolution of the pyramid is likely to be controlled by locally anisotropic dissolution due to the different types of steps that will be present on each of these faces and their different interactions with Pb. The spatially heterogeneous distribution of micro-pyramids on the faces of the calcite rhombs likely resulted from uneven distribution of energetically different surface sites. Based on previous studies it is known that cations such as Pb2+ (133 pm) which are larger than Ca2+ (100 pm) prefer adsorption at the obtuse steps which is consistent with the observation of the sector-shaped dissolution feature observed in Fig. 7b.45-47 Pb2+ apparently interacted with the two long edges of the sector that are likely composed of obtuse steps as inferred from their orientations to the c axis. However, micro-pyramids developed in regions away from the obtuse corner/edges. This contradiction indicates that adsorption of Pb2+ to obtuse steps was not responsible for the formation of micro-pyramids. Areas close to acute corners/edges had high dissolution rate in Pb-free solution, and were also the regions where micro-pyramids were first observed. These areas are expected to be populated with acute steps, kaa, koa, and kao kink sites (Fig. 9b). Pb2+ likely played an important role in changing the dynamics of these surface sites during dissolution. Binding of Pb2+ to these kink sites and competitive adsorption with Ca2+ may be responsible for the decreased dissolution rate at these regions, but it cannot fully explain how micro-pyramids were formed, which likely involved dynamic retreat and bunching of symmetry related steps that were not resolved by our TXM images. Further work with in situ surface probe microscopies will be needed to reveal these mechanistic processes. 4.3 Comparison between dissolution measurement techniques The 3D dissolution rate map measured by TXM provided ex-situ measurements of the 3D dissolution of individual 20-40 µm sized calcite rhombs with a spatial resolution of ~60 nm. These results complement other techniques and recent results. For example, recent studies reported in situ observations of the dissolution of ~½ mm sized calcite crystals using X-ray micro-tomographic imaging at pH 4, with a spatial resolution of 0.65 µm48. The present TXM results were expressed as a velocity (in units of nms-1), which is 3D analog of the surface-normal dissolution rate measured by VSI and DH. Previously reported calcite dissolution rates measured in-situ by VSI and DH were performed mainly in circumneutral pH9, 10, with corresponding dissolution rates that 19 ACS Paragon Plus Environment


are significantly smaller than those observed here on calcite faces (5 to 10 nms-1), which is primarily due to the lower pH solutions (pH = 2.8) used in this study. Both VSI and DH methods have high vertical resolution (few nanometers), where DH has better temporal resolution (~0.1s) than VSI (~1 s). Both methods image 2D mineral surfaces. The TXM approach used here has a spatial resolution of 60 nm  60 nm  60 nm, which enables the imaging of 3D surface morphology. However, it is not possible to resolve the presence of surface steps and kink sites at this resolution. In addition, due to imaging noise at the mineral-air interface (SI, Fig. S3), errors could be introduced during image segmentation and image alignment process. Thus, smaller dissolution rates (i.e., close to 0 nm/s in the rate spectra) are expected to have higher fractional uncertainties than higher rates. In terms of temporal resolution, the current measurements require about 10 min to 20 min to perform a full 3D scan. High spatial resolution nano-tomographic imaging with a time resolution of 1 minute has been reported recently49, which provides new opportunity for operando studies of the spatially and temporally variable dissolution rate spectra both in situ and in real-time. 5. Conclusions Comprehensive information on the surfaces roughness, defect density, solution chemistry, fluid flow pattern, etc. are often required to predict the macroscopic dissolution rate of calcite.18, 50 Dissolution of individual micro-sized calcite crystals in Pb-free solutions at pH 2.8 revealed that the average dissolution rate of calcite increased with time, and was on the order of 10-8 to 10-7 molcm-2s-1. This behavior is directly associated with the change in crystal shape. Calcite dissolution was highly anisotropic. The measured dissolution rates at different regions of the crystal followed the sequence of acute corners/edges > obtuse corners/edges > faces. The observed evolution of the dissolution rate can be explained by a combination of two factors: mass transport effects at regions of initially high surface curvature (e.g., corners and edges) leads to a rounding of the crystal shape, while the local dissolution rate in rounded regions increases due to the associated increase in the density of steps and kink sites. The presence of Pb2+ ions reduced the average dissolution rate by a factor of ~2, but with local dissolution rates reduced by a factor of ~7. Although the molecular-scale mechanism is as yet unclear, this enabled the systematic formation and growth of micro-pyramids on calcite (104) surfaces in the presence of Pb2+, which we postulate is due to the specific interaction of Pb2+ with 20 ACS Paragon Plus Environment

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step/kink sites. Dissolution in Pb-rich solutions was more spatially uniform compared with that in Pb-free solutions. In part, this may be due to the slower dissolution rates observed in Pb2+ containing solutions (where solution transport may not be a limiting factor). Further investigations are needed to observe the dynamic movement of surface steps that ultimately lead to the formation of micro-pyramids. This behavior is likely controlled by the interaction of Pb with the steps on the calcite surface. Organic molecules and enzyme carbonic anhydrase are often found to increase the dissolution rate,5, 51 whereas cations, such as Mg2+, Co2+, Mn2+, Cu2+, and Ni2+ all have retardation effects on calcite dissolution through competitive adsorption with Ca2+ ions.45-47 We found Pb2+ has a similar retardation effect, but the increase of surface roughness through formation of micropyramids has not been reported in previous studies using other divalent metal ions. These micropyramid features increased the surface roughness of calcite, which could alter the reactivity of calcite, for the uptake of toxic metal ions through adsorption or even for biogeochemical reactions. The more complex surface mesoscale morphologies, such as the presence of micron-sized “valleys” between pyramids, could serve as distinct nucleation sites for precipitation of secondary phases or binding sites for colloidal particles and bacteria. Given the dramatic morphological changes that are observed for Pb2+, we anticipate that the specific behavior (i.e., the dissolution rate inhibition, evolution of surface roughness and the development of mesoscale surface morphologies) may be strongly dependent on the choice of impurity cation. Acknowledgements This work was supported by U.S. Department of Energy (DOE), Office of Science, Office of Basic Energy Sciences, Chemical Sciences, Geosciences, and Biosciences Division under Contract DE-AC02-06CH11357 to UChicago Argonne, LLC, Operator of Argonne National Laboratory (“Argonne”). Argonne, a U.S. Department of Energy Office of Science laboratory. CFD simulations used the advanced mesh relaxation techniques sponsored by the Laboratory Directed Research and Development Program of Oak Ridge National Laboratory, managed by UT-Battelle, LLC, for the U. S. Department of Energy. This research used resources of the Advanced Photon Source, a U.S. DOE Office of Science User Facility, beamline 32-ID-C, operated for the DOE Office of Science by Argonne National Laboratory under Contract No. DE-AC02-06CH11357. The U.S. Government retains for itself, and others acting on its behalf, a paid-up nonexclusive, irrevocable worldwide license in said article to reproduce, prepare derivative works, distribute 21 ACS Paragon Plus Environment


copies to the public, and perform publicly and display publicly, by or on behalf of the Government. The Department of Energy will provide public access to these results of federally sponsored research in accordance with the DOE Public Access Plan. Associated Content Supporting Information. Determination of the calcite surface area; Numerical simulations of dissolution rates and the associated solution concentration field; Alignment of calcite images; Mapping the spatially variable dissolution rates, changes to calcite morphology, and rate distributions both without and with dissolved Pb2+; Additional examples of morphological changes during dissolution in the presence of dissolved Pb2+.

Author Information Corresponding Author E-mail: [email protected] Author Contributions The manuscript was written through contributions of all authors. All authors have given approval to the final version of the manuscript. Competing interests. The authors declare no conflict of interest. References 1.

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Mapping three-dimensional dissolution rates of calcite microcrystals

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