Unraveling the Effects of Strontium Incorporation on Barite Growth – In

Article Cite This: Cryst. Growth Des. XXXX, XXX, XXX−XXX

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Unraveling the Effects of Strontium Incorporation on Barite GrowthIn Situ and Ex Situ Observations Using Multiscale Chemical Imaging Juliane Weber,*,† Jacquelyn N. Bracco,‡ Jonathan D. Poplawsky,§ Anton V. Ievlev,§ Karren L. More,§ Matthias Lorenz,§ Angela L. Bertagni,∥ Sarah A. Jindra,∥ Vitaliy Starchenko,† Steven R. Higgins,∥ and Andrew G. Stack† Crystal Growth & Design Downloaded from pubs.acs.org by KAOHSIUNG MEDICAL UNIV on 08/17/18. For personal use only.

†

Chemical Science Division and §Center for Nanophase Materials Sciences, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37830, United States ‡ Argonne National Laboratory, Chicago, Illinois 60646, United States ∥ Wright State University, Dayton, Ohio 45435, United States S Supporting Information *

ABSTRACT: 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 highresolution 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.

1. INTRODUCTION

even background electrolytes, affect mineral growth rates by modifying the orientation, velocities, and densities of steps on the surface.11,19−28 To accurately model the impact of impurities on mineral growth, process-based models will need to be able to incorporate all of these effects. Current process-based models based of the effect of impurities on rates primarily consider two main driving factors: incorporation12,21 and step-pinning.11,29 In the “incorporation” concept, it is assumed that the impurity becomes incorporated, which increases lattice strain, and thereby changes the mineral solubility, the effective supersaturation and subsequently the growth rate. In the “steppinning” concept, the basic assumption is that the impurities inhibit growth by adsorbing to sites on the mineral surface and blocking the attachment of the mineral’s constituent ions. However, observations have been made in previous experimental studies that cannot be explained by either of the two concepts. For example, solubility changes observed in the

Accurate prediction of mineral precipitation and dissolution is important for several energy-related topics, such as long-term safety of spent nuclear fuel disposal, oil/gas extraction, hydraulic fracturing, and geothermal energy production.1−3 Recently developed process-based mineral growth models have shown great promise in accurately predicting mineral growth rates,2,4−10 as well as accounting for the effect of impurities on mineral growth.11,12 During crystal growth, toxic and potentially harmful elements, including radionuclides or heavy metals, can incorporate into minerals, which potentially can be engineered to sequester these elements.3,13,14 Understanding the underlying mechanisms of how impurities affect mineral growth could benefit strategies to prevent technically enriched naturally occurring radioactive material (TENORM) buildup generated during oil/gas or geothermal energy production.15,16 Also, this knowledge would provide fundamental information for paleo-climate research which greatly relies on the assumption that distribution/partitioning factors of certain elements and minerals represent paleo-environments.17,18 In previous studies, it was demonstrated that impurities, which can be coprecipitating cations, anions, or © XXXX American Chemical Society

Received: June 1, 2018 Revised: July 23, 2018 Published: July 26, 2018 A

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direct correlation exists between growth rate and incorporation rate has been elusive. This is because methods with a limited spatial resolution and chemical sensitivity have been applied, such as scanning electron microscopy,19,24,25 or where highly localized high-resolution methods (transmission electron microscopy, TEM) have been used, the growth rate was not analyzed.53 Here, we combine analyses of both surface morphology and chemical composition of the same newly grown solid with high-resolution/high-sensitivity morphological and chemical imaging measurements to access both growth and incorporation rates on the same sample. Our novel approach consists of combining both topography observations and subsequent solid composition characterization. Step velocities, step densities, growth rates and growth hillock morphology were measured in situ using hydrothermal atomic force microscopy (HAFM). Combining this with ex situ in-depth chemical imaging of the resulting solids led to insights into incorporation extent and homogeneity. For this, we employed a combination of high-resolution chemical imaging techniques: scanning transmission electron microscopy with energy dispersive spectrometry (STEM-EDS), atom probe tomography (APT), and time-of-flight secondary ion mass spectrometry combined with atomic force microscopy (AFM-ToFSIMS). By using this multimodal approach, the solution and solid composition are directly comparable, thereby providing a more complete picture of the effect strontium has on Barite growth.

experimental system calcite with strontium-bearing solutions did not match predictions, which lead to the development of the layer-by-layer theory.30−32 This theory can be employed to qualitatively explain growth observations but does not allow for predictions. Similarly, for the mineral magnesite (MgCO3) growing in calcium-containing solutions, incorporation into the solid was demonstrated without an effect on the crystal growth rate, which cannot be explained by any of the above-mentioned concepts.33 Given the wide range of behaviors reported, an investigation is warranted of the effect of an impurity on the crystal growth rate correlated to direct measurements of its incorporation into the crystal structure. This would allow for better predictions because it would allow us to test hypotheses for which mechanism described above is most likely to act on a system under given solution conditions. Here, we use the Barite (BaSO4) system, growing in aqueous solutions containing strontium, as a model crystal-impurity system to understand the link between the incorporation rates of impurity cations and their effect on sparingly soluble mineral growth rates. In addition to being an excellent model crystal, Barite is known to incorporate toxic elements (e.g., 226Ra, 210 Pb, or 90Sr)3,34−39 and it may be possible to use its incorporation of these for their sequestration. Barite forms a complete isostructural solid solution (space group Pnma)40 with celestite41 and could potentially be used to immobilize 90 Sr contamination3,38 present at some US Department of Energy (DOE) sites.42 However, due to differences in cation radius (Ba = 1.61 Å and Sr = 1.44 Å)43 and solubilities (solubility product constant Ksp for Barite = 10−9.97 and celestite = 10−6.63 at 25 °C),44 most BaxSr1xSO4 solid solution crystals found in nature have compositions close to the endmembers.38 The thermodynamics of the BaxSr1xSO4 solid solution have been the subject of research for several decades,38,45 but recently, Heberling et al.46 provided an extensive summary and pointed out the substantial need for a well-defined interaction parameter. Interaction parameters for the BaxSr1xSO4 solid solution obtained from several modeling methods were determined in a more recent study47 by Vinograd et al. placing the BaxSr1−xSO4 solid solution as a regular solid solution with an interaction parameter WBa−Sr = 4.95 ± 0.75 kJ/mol at 298 K. In general, solid solutions are described and classified based on the deviation of the thermodynamic properties of the solid solution from a hypothetical mechanical mixture between the two endmembers of the solid solution. Different models can be used to describe the shape of the excess free enthalpy of mixing curve, which uses the interaction parameter as a measure to describe the ideality of a solid solution. For a complete introduction into solid solution-aqueous solution thermodynamics, the reader is referred to the reviews by Prieto et al.48 and Glynn and Reardon.49 In the case of the BaxSr1−xSO4 solid solution this means that the solid solution is termed “regular” because the excess free enthalpy of mixing can be described by a function of composition which is symmetric around XBa = XSr = 0.5. Traditionally, analysis of the hillock morphology during growth has been made in AFM mineral growth studies, including step velocities and step densities to determine growth rates.50−52 Recent progress in analytical techniques has allowed the combination of measurements of the morphology during growth with the characterization of the solid afterward, investigating specifically the effect of manganese,19 iron,53 or cadmium24,25 on calcite growth. However, establishing if a

2. MATERIALS AND METHODS Two different sets of mineral growth experiments were conducted on separate crystals of Barite, named lowSrBa and highSrBa, which led to two different solids that were characterized in situ during growth using HAFM and afterward the compositions of these two crystals were examined ex situ using STEM-EDS, APT, and AFM-ToF-SIMS. In the experiment lowSrBa, solutions with three different aqueous strontium-to-barium ratios, [Sr]/[Ba]aq of 0.5, 1, and 5 (denoted by SrBa0.5, SrBa1, SrBa5, respectively), were introduced into the HAFM fluid cell during Barite crystal growth on the (001) Barite surface. The second crystal, highSrBa, is more complex. First, the same compositions for the first three solutions (denoted SrBa0.5, SrBa1, and SrBa5, respectively) were chosen to reproduce experiment lowSrBa. After this, we regrew a pure Barite hillock morphology using a series of strontium-free solutions. These solutions had a saturation index (SI, defined by SI = log

{Ba 2 +}{SO4 2 −} ) K sp,barite

of 0.53 and 1. After the

steady-state Barite hillock morphology was re-established, solutions with higher [Sr]/[Ba]aq of 16, 22, 44, and 68 (SrBa16, SrBa22, SrBa44, SrBa68) were introduced. A full list of solution compositions for both the lowSrBa and highSrBa crystals is given in the Supporting Information (Table S 1 and Table S 2). For the TEM-EDS, AFMToF-SIMS and APT analyses of the solid grown under SrBa16, SrBa22, SrBa44, and SrBa68, we have observed one layer of Sr-rich Barite, for which we calculated an average [Sr]/[Ba]aq of 36.5 (named SrBa37) which will be used in diagrams for growth rate and incorporation analyses. Step velocities of the ⟨120⟩ Barite steps were determined using the angle method54 based on the difference in the angle of the ⟨120⟩ Barite step in a sequential up and down scans. For [010] steps, step displacement over time was directly measured. Both methods are explained in detail in the Supporting Information. Due to significant roughening of the steps (compare with videos contained in the Supporting Information) during the exposure of the Barite to the higher [Sr]/[Ba]aq solutions, step velocities could not be obtained for all [Sr]/[Ba]aq. B

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Figure 1. Step velocity νs dependence on ratio of aqueous barium and strontium cations [Ba]/[Sr]aq. ⟨120⟩ step velocities are given in green and show a decrease with increasing [Ba]/[Sr]aq. In red, [010] step velocities are given, which show an increase with increasing [Sr]/[Ba]aq. Fit functions for the ⟨120⟩ and [010] step growth are displayed. HAFM-images (a-c) show how strontium in solution affects Barite hillock morphology. All images have roughly the same crystallographic orientation. the Land method,54 whereas [010] were analyzed by the direct method57 (described in the Supporting Information). After the HAFM observations, the Barite crystal was recovered, dried with a N2 sparge and coated with a ∼50 nm thick carbon layer using a Crossington 208 carbon coater (TedPella Inc., USA) to enhance conductivity for focused ion beam (FIB) preparation, AFMToF-SIMS measurements, and to avoid recrystallization of the solid driven by air humidity. Prior to FIB preparation, high conductivity silver glue was applied to further enhance conductivity of the sample and minimize thermal drift during preparation. 2.3. FIB Preparation. Both APT tips and TEM lamella were prepared using a FEI Nova 200 dual beam instrument (Thermo Scientific, USA). Lift-out location for TEM lamellae and APT wedges were located at the middle of the hillock; specific lift-out locations for single APT tips are given in the Supporting Information. Established protocols for Barite samples39,58 were modified in order to obtain lamellae with a thickness 1. The shift in growth mechanisms suggests the mechanisms of strontium incorporation into the growing solid may change as well. The steps become increasingly rougher with increasing [Sr]/[Ba]aq ratio as well. Similar increased step roughness caused by the presence of impurities was observed in studies D

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Figure 2. Hillock morphology as well as spatial Sr- and Ba-distribution determined by AFM-ToF-SIMS in lowSrBa (a-c, g) and highSrBa (d-f). Due to oversaturation of the detector for the main barium isotope signal, the 137Ba isotope distribution is displayed here. The lowSrBa images and the highSrBa show, respectively, the same hillock. Intensities in Ba and Sr signal, respectively, are shown on a scale from low (black) to high (yellow). Preferential incorporation of Sr into the [010] step direction is visible in (f). The region of lower Sr concentration between the outer and inner rim in (f) is due to the regrowth of the Barite hillocks with Sr-free solutions in highSrBa before exposing the hillocks again to solutions of higher Sr concentrations. (g) shows a topography corrected 3D reconstruction of the Sr-distribution within the lowSrBa hillock (a-c).

strontium on Barite growth by ⟨120⟩ steps that is observed at [Sr]/[Ba]aq < 1.

more celestite-like morphology comprised of [010] steps that develops at [Sr]/[Ba]aq > 1 overcomes the inhibiting effect of E

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Figure 3. APT results of highSrBa. Spatial distribution of Sr atoms in APT_1 (a) and APT_2 (b). Plots are concentration profiles along the arrow. Three different levels of [Sr]/[Ba]s in the solid are visible relating to the three different [Sr]/[Ba]aq solutions (SrBa0.5, SrBa1, and SrBa5) the solid was exposed to.

step orientation (at low saturation index).62 The reason may be the different crystallography of Barite relative to calcite, which includes a 21 screw axis on the growth hillocks does not allow a distinction between preferred incorporation into obtuse and acute steps as they form bilayer steps. Similar to the observed shift in growth morphology, the strontium incorporation also shifts from homogeneous incorporation along the edges of the hillock to a preferential incorporation into the [010] direction at higher [Sr]/[Ba]aq (Figure 2d, e). This preferential strontium incorporation could be due to the earlier proposed facilitated attachment of strontium ions to the [010] step direction compared to ⟨120⟩ step direction. Since celestite is in the same space group as Barite,73 it has a 21 screw axis parallel to the c axis, which is inferred from crystallography. As mentioned above, the conditions used in our study are not suited for pure celestite growth as the solutions are undersaturated with respect to pure celestite (SIcelestite = −2.6 to −0.7). This indicates that the incorporation mechanism of an intermediate phase BaxSr1−xSO4 is distinct from the pure phase incorporation mechanism. 3.3.1. Understanding the Strontium Distribution with Depth − [Sr]/[Ba]aq < 5. To resolve the thickness of the individual layers, as well as analyze the strontium incorporation

To summarize the results of in situ HAFM measurements: we observed a shift of growth morphology from ⟨120⟩ step growth typical for Barite to [010] steps typical for celestite at a [Sr]/[Ba]aq ratio of 1 which is in good agreement with literature.22 Due to the shift in step advance orientation for higher [Sr]/[Ba]aq, it appears the inhibiting effect of strontium on growth rate at lower [Sr]/[Ba]aq ratios in solution can be overcome. This shift likely indicates a change in the strontium incorporation mechanism as well, which cannot be sufficiently investigated by AFM topography characterization only. To link growth morphology/rate and the rate of impurity incorporation, we employed high-resolution chemical imaging techniques described below. 3.3. Strontium Incorporation into the Barite Solid. By characterizing both samples from lowSrBa and highSrBa with a prototype AFM-ToF-SIMS, we observed the precise extent of incorporation of strontium into the newly grown Barite. At lower [Sr]/[Ba]aq, the strontium incorporated into the Barite hillock is spatially homogeneous along the newly grown edges of the hillock (Figure 2 a-c). This is in contrast to the previous studies of impurity incorporation on other solid solutions, e.g. (Ca,Mg)CO 3 and (Ca,Mg)CO 3 , 71 where strontium is preferentially incorporated into the obtuse step orientation,72 and magnesium is preferentially incorporated into the acute F

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Figure 4. STEM-EDS mapping of a cross-section TEM lamellae prepared from the solid from highSrBa. The elemental map (a) shows the strontium distribution (red). The bold arrow indicates location and direction of the line scan in (b). Numbers (1), (2) and (3) indicate three different Sr-levels matching different [Sr]/[Ba]aq in experiment highSrBa. The yellow marker indicates the location of the mineral surface.

rate, we used APT on solids from highSrBa. We examined two APT tips of the highSrBa experiments, APT_1 (8.1 million atoms collected) and APT_2 (31.9 million atoms collected). Both these APT measurements comprised two different sections of strontium layers grown under low (≤5) [Sr]/ [Ba]aq (as same solutions were used in the first part of highSrBa and lowSrBa, representing experiment lowSrBa) and under higher (>5) [Sr/]/[Ba]aq. For the section of APT_1 and APT_2 representing the lowSrBa experiment, the three different levels of strontium incorporation into the newly grown Barite solids were easily resolved in the one-dimensional concentration profiles through these layers (Figure 3), matching the three different [Sr]/ [Ba]aq ≤ 5 solutions to which the solid was exposed to during mineral growth (Figure 3). 3D strontium atom maps of each sample are shown in Figure 3 with strontium-enriched (strontium in solution) and strontium-depleted (no strontium in solution) layers identified. Additional APT data (3D maps of all other elements, peak identification and mass spectra) are given in the Supporting Information. The first two layers exhibit the same [Sr]/[Ba]s ratio, within error, in both the APT_1 and APT_2 measurements ([Sr]/[Ba]aq = 0.5 led to a [Sr]/[Ba]s of 0.02, and [Sr]/[Ba]aq = 1 led to a [Sr]/[Ba]s of 0.04 in both APT samples). However, there is a significant difference in the [Sr]/[Ba]s ratio in the solid when grown under solutions containing [Sr]/[Ba]aq = 5 ([Sr]/[Ba]s of 0.12 for APT_1 and 0.06 for APT_2). One possible reason for this could be the shift in growth mechanism favoring [010] steps we observed with the HAFM for [Sr]/[Ba]aq > 1. This shift in growth mechanism led to a localized growth rate and possible preferential incorporation as observed in AFM-ToF-SIMS. APT samples have a size of about 70 nm radius and therefore give highly localized compositional analyses. APT_1 and APT_2 were sampled from different parts of the hillock with the lift out position for APT_1 being from a preferential incorporation region. Therefore, we can reasonably assume that the [Sr]/[Ba]s ratio in the solid of APT_1 resembles the more representative value of the areas of the surface that were still growing. 3.3.2. Understanding the Strontium Distribution with Depth − [Sr]/[Ba]aq ≫ 5. We observed a layered strontium distribution with depth by EDS characterization of the TEM lamellae for the sample exposed to higher [Sr]/[Ba]aq (Figure

4). This layered distribution can be correlated to the experimental conditions under which the solid was grown. An underlying thin layer (marked 1) of strontium stems from growth under aqueous [Sr]/[Ba]aq ≤ 5, a thicker strontium-free layer (marked 2) represents strontium-free regrowing of the hillock in highSrBa and then a homogeneous strontium-rich localized surface precipitate (marked 3) originated from growth under aqueous [Sr]/[Ba]aq ≥ 5. These observations are in good agreement with our APT observations (Figure 3). The strontium-rich top layer grown under exposure to solutions SrBa16, SrBa22, SrBa44, and SrBa68 exhibited up to 32 at. % strontium representing a Ba0.05Sr0.95SO4 solid solution and showed a homogeneous Sr-distribution. The average thickness of the precipitate determined from growth analyses was 56.7 ± 4.7 nm. This matches well with our APT_1 reconstruction, which indicated a height of the Sr-rich precipitate of 44 nm (Supporting Information, Figure S7). The [Sr]/[Ba]s ratio in the Sr-rich precipitate determined by APT indicates a BaxSr1−xSO4 solid solution of Ba0.60Sr0.40SO4, which slightly underestimates the Sr-content in comparison to EDS determined Ba0.05Sr0.95SO4 solid solution. When comparing low [Sr]/[Ba]aq ratios with [Sr]/[Ba]s, we can reasonably fit data obtained from APT_1 to a linear fit function (Figure 5) indicating a direct correlation between [Sr]/[Ba]aq and [Sr]/[Ba]s. In contrast to the observations at lower [Sr]/[Ba]aq, the [Sr]/[Ba]s produced by growth in high [Sr]/[Ba]aq is independent of the aqueous composition. Despite four different [Sr]/[Ba]aq introduced in the solution, only one [Sr]/[Ba]s is observed in both STEM-EDX (Figure 4) and APT (Figure 5 and Figure S21) characterization. Therefore, we represent this continuous [Sr]/[Ba]s by two representative values (green diamond marker for [Sr]/[Ba]s obtained from TEM characterization and black diamonds for [Sr]/[Ba]s obtained from APT) in Figure 5. This result suggests that the incorporation extent shifts with the change in growth mechanism described above. At low [Sr]/[Ba]aq, strontium is incorporated along the edges of the growing hillock uniformly. This incorporation could be described by a partitioning factor. At [Sr]/[Ba]aq ≫ 5, however, strontium incorporation shifts toward a localized incorporation which is apparently independent of the [Sr]/ [Ba]aq. Incorporation extent under these conditions could not be described by a partitioning factor. G

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[Sr]/[Ba]aq = 37) of 1.92 × 104 μmol/m2/s (TEM) and 1.5 × 104 μmol/m2/s (APT_1) show a good agreement and are similar to the pure Barite growth rate. Therefore, we can state that the inhibiting effect of strontium on Barite growth is partially overcome by the shift in growth mechanism from ⟨120⟩ to [010] step growth. 3.5. BaxSr1−xSO4 Solid Solution  Thermodynamic Considerations. Thermodynamic relations between solid solutions and aqueous solution (SS-AS) systems (with solubility products KBA and KCA, activity coefficients γBA and γCA, and mole fractions XBA and XCA for the endmembers BA and CA of a (B,C)A solid solution respectively) can be conveniently described by Lippmann diagrams for SS-AS systems.3,48,49 Here, the two alternate equilibrium conditions are used to describe the equilibrium situation in the SS-AS XB, aq

system. The solutus (ΣΠeq = 1/ K

BAγBA

+

XC , aq KCAγCA

) is used to

describe the solution side of the solid solution-aqueous solution system. For the solid side, the solidus equation (∑∏eq = KBAγBAXBA + KCAγCAXCA) is used. We will use this diagram to explore whether the experimental results can be explained based on equilibrium thermodynamics (Figure 7).

Figure 5. Relation between [Sr]/[Ba]aq and [Sr]/[Ba]s measured by APT and STEM-EDX. For [Sr]/[Ba]aq below a threshold value of 5, a linear relation (R2 value of linear fit included) was observed, whereas at [Sr]/[Ba]aq ≫5, the [Sr]/[Ba]s is constant for different [Sr]/[Ba]aq values.

3.4. Growth Rate Analysis. A clear decrease in Barite growth rate is observed with increasing [Sr]/[Ba]aq, which is reproducible in two types of growth rate measurements (HAFM and APT) (Figure 6) for [Sr]/[Ba]aq ≤ 5. Growth

Figure 7. Lippmann diagram for BaxSr1−xSO4 solid solution based on W = 4.75 ± 0.75 kJ/mol with logKspBarite = −9.48 and logKspcelestite = −5.6771 at 108 °C giving the total supersaturation product for both solid (solidus) and solution (solutus) as a function of composition. Green triangle represent strontium solutions used in the experiments. Orange square represent solid composition analyzed by STEM-EDS and red diamonds are derived from APT characterization.

Figure 6. Barite growth rate at SI 0.5 as a function of [Sr]/[Ba]aq for all methods used in this work, showing a decrease in growth rate for [Sr]/[Ba]aq up to 5 followed by an increase in growth rate at [Sr]/ [Ba]aq in solution. The inset highlights the first data points up to [Sr]/ [Ba]aq ratio of 1.

Solid activity coefficients γBA and γCA were calculated using the Thompson-Waldbaum equation.74 In Figure 7, solution compositions for this study are indicated on the solutus by green markers and at near-equilibrium conditions, these solution compositions are related to the solid compositions on the left (solidus) curve. As a comparison, the observed solid compositions are marked in red on the solidus. There is a significant difference between equilibrium and measured solid compositions, especially with respect to incorporation at higher aqueous Sr-concentrations. There are four different [Sr]/ [Ba]aq ratios resulting in a single [Sr]/[Ba]s. However, the Lippmann diagram is somewhat limited in its application as it provides only the supersaturation with respect to a solid of a fixed composition. There are two different functions available in literature, the β-function45,75 and the δ-function,76 to

rates determined by these two methods showed a good agreement with each other with a small overestimation by APT and/or underestimation by HAFM on growth rates (Table S 3, Supporting Information). TEM EDS map analyses at higher [Sr]/[Ba]aq (= 37) showed an increased growth rate relative to the HAFM and APT measurements, and likely indicates that the shift in growth mechanism suggested from the HAFM step velocities, despite the high uncertainty mentioned above, does indeed translate to an increase in growth rate, on average, over the average crystal. This is in good agreement with observations from the APT_1 measurement, where the detection of the overlying sputtered carbon layer indicated that the full strontium-rich layers was measured. Both final growth rates under [Sr]/[Ba]aq > 5 (calculated average of H

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kinetics and reaction mechanisms in this system, we employed kinetic process modeling of the step velocities. We used the Stack-Grantham-Bracco-Higgins (SGBH) model5 to fit the step velocity data using a Newton−Raphson minimization, shown in Figure 1. In previous papers,8,60 we have compared other currently available process-based models of the effect of impurities on mineral growth, e.g. Nielsen et al.12 based on the Zhang and Nancollas model79 to the SGBH model and demonstrated the suitability of the SBGH for our data. Therefore, we will not include a comparison with the Zhang and Nancollas-style models in our paper. To account for the shift in growth morphology from ⟨120⟩ to [010] step growth, two different fit functions were employed. Following Bracco et al.,11 the first part of the model includes the effect of strontium as an inhibitor for Barite ⟨120⟩ step velocity. Due to the limited number of solution conditions measured, for simplicity we assume that kink site propagation and nucleation are equal, therefore the ⟨120⟩ step velocity, is defined as υs = aR kn (1)

evaluate the supersaturation of a given aqueous solution with respect to a solid with a changing composition. Calculation of these supersaturation functions indicated that the solutions applied in our experiments are not supersaturated with respect to a BaxSr1−xSO4 solid solution over the complete range of aqueous solutions applied here. There are several possible reasons to explain this discrepancy between theoretical expectations and the observed experimental values (Figure 7). One issue is that, despite recent computational advances, the thermodynamics of the BaxSr1−xSO4 solid solution still remain the subject of discussion and experimental studies at thermodynamic equilibrium conditions are needed to confirm the findings on the interaction parameters. Therefore, the discrepancy can be partially attributed to uncertainty in the interaction parameter for the solid solution. In addition, several potential sources of error exist on both the solution and solid side of the diagram curve during their derivation in experiments and their analysis. To account for this, we assumed at least 15% uncertainty, but that still does not explain the observed discrepancy. We can therefore conclude that kinetic influences are present and significantly affecting the extent of impurity incorporation in the system. The presence of kinetic influences can be tested by using the distribution coefficient77 (see Thien et al. 2014 for a recent summary of application and nomenclature in geoscience). Often used to indicate the trace element partitioning between an aqueous/melt phase and a solid, the total distribution coefficient is the ratio of two aqueous and solid distribution coefficients (DBa − Sr =

[Sr] [Ba] solution

( BaSr )solid

With a as kink depth normal to the step (a = 0.72 nm for Barite) and where Rkn is the rate of kink site nucleation, defined as R kn⟨120⟩ =

fractionation factor DSr−Ba = 3 (±1) × 10−2 based on APT characterization of strontium incorporation during low [Sr]/ [Ba]aq. At higher [Sr]/[Ba]aq, the strontium incorporation is no longer spatially homogeneous and cannot be accounted for by a single distribution coefficient (Individual values under these conditions are given in the Supporting Information). By comparing this value to the thermodynamic equilibrium distribution coefficient (DBa − Sr =

K sp0

γ Barite Barite

γ celestite celestite

),

78

kBa[Ba] + k SO4[SO4 ]

− k −kn (2)

With kBa being the first-order rate constant for attachment of barium ions, and kSO4 as the first-order rate constant for attachment of sulfate ions and k‑kn as a pseudozero order combined detachment rate constant and kink site density. To model the step velocities under influence of low strontium concentrations, we employed the correction factor introduced in Bracco et al.11

). We determined an average

K sp0

kBa[Ba]k SO4[SO4 ]

cf⟨120⟩ =

1 + KS − Ba[Ba] 1 + KS − Ba[Ba] + KS − Ba[Sr ]

(3)

with Ks‑Ba treated as adjustable fit parameters (Table 1 and Figure 1). Here, strontium is treated as an impurity which is

we can

Table 1. Estimated Rate Constant for the Kinetic Process Model for the ⟨120⟩ Step Growth and for ⟨010⟩ Step Growth

state whether our experiments have reached thermodynamic equilibrium. A WH = 4.95 ± 0.75 kJ/mol41 was used to calculate solid activities based on the Thompson-Waldbaum model.74 The thermodynamic equilibrium distribution coefficient for compositions from x = 0 to x = 0.5 are 2.24 × 10−4 to 4.96 × 10−5. Our experimentally determined distribution coefficient is more than 2 orders of magnitude higher. Therefore, it can be concluded that our system is not at thermodynamic equilibrium even at lower [Sr]/[Ba]aq. Thus, we cannot use an approach based solely on equilibrium thermodynamics like the Lippmann diagram to describe the observed levels of Sr incorporation. To some degree, the uncertainty associated with our experimental data as well as with the interaction parameter41 contributes to this. In addition, we can speculate that defect-driven incorporation on steps as observed here at the growth hillocks, is indeed different from defect-free incorporation as likely implicitly assumed in the interaction parameter definition. Therefore, we included kinetics in order to interpret our data sufficiently. 3.6. Process-Based Model of Step Velocities−inhibition Effect of Mineral Growth by Impurities. Because the above discussion clearly indicates that there is an influence of

⟨120⟩ step growth kBa (s−1) kSO4 (s−1) k−kn (s−1) Ks‑Sr Ks‑Ba χ2

1.0 × 105 5.3 × 105 1.61 1.2 × 104 3.9 ×104 173.31

[010] step growth kSr (s−1) kSO4 (s−1) k−kn (s−1) Ks‑Ba Ks‑Sr χ2

1.6 × 104 1.6 × 104 0 13.402

poisoning Barite growth. Based on HAFM morphology observations, this premise can be justified as growth predominantly oriented in the ⟨120⟩ direction and only minor amounts of strontium were incorporated into the steps. That is, 0−12% strontium in the solid was observed under solution conditions where ⟨120⟩ step growth was active (Figure 5) suggesting that the error introduced by neglecting strontium’s contribution to the step velocity is small. Regardless, including both barium and strontium as conI

DOI: 10.1021/acs.cgd.8b00839 Cryst. Growth Des. XXXX, XXX, XXX−XXX

Crystal Growth & Design

Article

Figure 8. Scheme summarizing the transition in step growth direction from ⟨120⟩ step growth to [010] step growth due to elevated [Sr]/[Ba]aq ratio. Cations (Barium in green and strontium in red) are shown as circles, anions (sulfate) as triangles due to tetrahedral coordination of SO42− anions.

in which the Barite was grown. By comparing [Sr]/[Ba]s and [Sr]/[Ba]aq ratios with expected values based on thermodynamics as well by comparing distribution coefficients, it was determined thermodynamics alone were likely not determining the [Sr]/[Ba]s. A greater incorporation of strontium into Barite was observed than would be thermodynamically predicted, which is likely due to a change in the mechanisms of crystal growth from dominated by ⟨120⟩ Barite-like steps to [010] celestite-like steps. This shift in growth mechanism is accompanied by an increase in the amount of strontium incorporated into the solid. The implications of this observation for crystal growth in the presence of impurities in general is clear: 1) reaction mechanisms are important to know in order to predict the extent of impurity incorporation and shift in rate; 2) reaction mechanisms can change with changing solution conditions, resulting in differing growth rates and incorporation extents; and 3) these may be specific to the system of interest depending on mineral’s composition and structure, the identity of the impurity, and the solution conditions.

tributing elements to the step growth did not result in an improved fit. After the transition to [010] step growth at [Sr]/[Ba]aq > 1, a second fit function was employed to model the [010] steps. As described above, this is based on the HAFM observations which indicated a shift from Barite ⟨120⟩ step growth to the growth of a strontium-containing phase elongated in [010] as observed for pure celestite growth.60 Based on our solid characterization showing that the newly grown steps are mainly comprised of celestite, we used a fit function for pure celestite growth neglecting the barium present in the solution. This approximation is supported by the data in Figure 5 showing only 20% barium in the newly grown areas of the surface. Including the minor amounts of barium present as an impurity poisoning the celestite growth did not improve the fit and is therefore not shown here. This is consistent when we compare the ratio of the impurity with the main constituent cation (in this hypothetic modeling case of barium poisoning celestite growth [Ba]/[Sr]aq) with our impurity-solid system studied through experiments ([Sr]/[Ba]aq). The highest experimental [Ba]/[Sr]aq ratio is