Growth Kinetics and Morphology of Barite Crystals Derived from Face

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Growth kinetics and morphology of barite crystals derived from face-specific growth rates Jose R. A. Godinho, and Andrew G. Stack Cryst. Growth Des., Just Accepted Manuscript • DOI: 10.1021/cg501507p • Publication Date (Web): 30 Mar 2015 Downloaded from http://pubs.acs.org on April 7, 2015

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Crystal Growth & Design

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Growth kinetics and morphology of barite crystals derived from facespecific growth rates

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Jose R. A. Godinho*1, Andrew G. Stack1

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Abstract

Chemical Sciences Division, Oak Ridge National Laboratory, PO Box 2008, MS-6110, Oak Ridge, TN 37831 USA. [email protected]

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We investigate the growth kinetics and morphology of barite (BaSO4) crystals by measuring the growth rates of the (001), (210), (010) and (100) surfaces using vertical scanning interferometry. Solutions with saturation indices 1.1, 2.1 and 3.0 without additional electrolyte, in 0.7 M NaCl or in 1.3 mM SrCl2 are investigated. Face-specific growth rates are inhibited in the SrCl2 solution relative to a solution without electrolyte, except for (100). Contrarily, growth of all faces is promoted in the NaCl solution. The variation of face-specific rates is solution-specific, which leads to a change of the crystal morphology and overall growth rate of crystals.

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The measured face-specific growth rates are used to model the growth of single crystals. Modeled crystals have a morphology and size similar to those grown from solution. Based on the model the time dependence of surface area and growth rates is analyzed. Growth rates change with time due to surface area normalization for small crystals and large growth intervals. By extrapolating rates to crystals with large surfaces areas, a time-independent growth rates are 0.783, 2.96, 0.513 mmol·m-2·h-1, for SI = 2.1 solutions without additional electrolyte, NaCl and SrCl2, respectively.

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Keywords: growth rate, morphology, kinetics, crystal, surface orientation

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Barite crystals grown from solution and modeled (top left) using a novel method presented in the manuscript.

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ACS Paragon Plus Environment

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Growth kinetics and morphology of barite crystals derived from facespecific growth rates

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Jose R. A. Godinho*1, Andrew G. Stack1

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Abstract

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We investigate the growth kinetics and morphology of barite (BaSO4) crystals by measuring the growth rates of the (001), (210), (010) and (100) surfaces using vertical scanning interferometry. Solutions with saturation indices 1.1, 2.1 and 3.0 without additional electrolyte, in 0.7 M NaCl or in 1.3 mM SrCl2 are investigated. Face-specific growth rates are inhibited in the SrCl2 solution relative to a solution without electrolyte, except for (100). Contrarily, growth of all faces is promoted in the NaCl solution. The variation of face-specific rates is solution-specific, which leads to a change of the crystal morphology and overall growth rate of crystals.

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The measured face-specific growth rates are used to model the growth of single crystals. Modeled crystals have a morphology and size similar to those grown from solution. Based on the model the time dependence of surface area and growth rates is analyzed. Growth rates change with time due to surface area normalization for small crystals and large growth intervals. By extrapolating rates to crystals with large surfaces areas, a time-independent growth rates are 0.783, 2.96, 0.513 mmol·m-2·h-1, for SI = 2.1 solutions without additional electrolyte, NaCl and SrCl2, respectively.

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Introduction

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Understanding the kinetics and mechanisms of barite (BaSO4) growth is important for several environmental and industrial reasons. For example, barite precipitates as scale during oil and gas extraction due to the mixing of formation waters rich in Ba , with surface or seawater rich in SO . The precipitates can clog pipes, and reduce permeability in the formation, which reduces the efficiency of the extraction and increases production costs.1,2 Due to the similar reactivity of aqueous barium and radium, radium mobility in the subsurface can be limited by its incorporation into barite.3 This has led to interest in using barite as a scavenger for radium, e.g., as a reactive barrier as part of a spent nuclear fuel disposal strategy.4,5 The increase in oil and gas production using hydraulic fracturing techniques has resulted in significant quantities of flowback water containing barium and radium.6-8 Barium has been detected in effluent of municipal wastewater treatment plants that handled hydraulic fracturing flowback water7 and in downstream sediments.8 Induced precipitation of barite from the wastewater (either above-ground or in the subsurface) is a possible strategy for removing both barium and radium from these fluids.6

Chemical Sciences Division, Oak Ridge National Laboratory, PO Box 2008, MS-6110, Oak Ridge, TN 37831 USA. [email protected]


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Growth of barite has been studied most frequently by measuring the advance of monomolecular or bimolecular steps on cleaved (001) and (210) surfaces using atomic force microscopy9-15 (AFM); a common approach to study single crystal growth from aqueous solutions.16 This method has the advantage of allowing the visualization of the growing surface structures with near molecular-scale resolution. Some studies have linked the movement of these steps to atomicscale reactions, such as those discovered by molecular simulation.17-19 However, due to the small field of view and the necessity of using near atomically-flat surfaces, experimental studies have been limited to the surfaces of a crystal that are readily cleaved, which are not always representative of all surfaces of a crystal. For example, natural barite crystals can exhibit a wide array of morphologies comprising varying proportions of surfaces different from the cleavable (001) and (210) surfaces.20 These in turn can be composed of different types of structures, each with a different reactivity and specific growth rate.21-23 Surfaces different from the cleavage orientations have recently been shown to provide useful insights about the kinetics and mechanisms of mineral dissolution and precipitation24,25 and specifically the variation of rates with reaction time.26,27

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Another traditional method used to study barite growth includes measurements of changes in solution concentration during growth of seed crystals.28 This approach allows one to calculate the overall growth rate of a mineral phase from a solution. The growth rate is usually normalized to the average surface area of the starting seed material measured by gas adsorption methods or a geometric surface area in which the particles are approximated as spheres. Furthermore, changes of surface area occurring during growth are not accounted for in the normalization. Another disadvantage of this method is that it does not allow one to study the role of individual surfaces during growth and is often difficult to link growth rates to reactions at specific surface sites. For example, the concentration and composition of the electrolyte and the presence of impurity ions that can interact with growth sites can promote or inhibit specific reactions affecting the growth kinetics and crystal shape.29-31

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The morphology of barite crystals is known to vary depending on the solution composition.32-35 At this time, however, the link between crystal-face specific growth rates and crystal morphology has not been studied experimentally. Historically, equilibrium crystal morphology have been derived from the lattice geometry,36 estimates of the attachment energy of new molecules to the crystal19,37 and surface energies.38 Recently developed computer simulation methods such as kinetic Monte Carlo could potentially account for surfacespecific reactions,39-42 especially when coupled to molecular simulation techniques.43 Although those methods have successfully predicted crystal morphologies observed experimentally in a qualitative fashion, little quantitative and predictive information about the growth rates of crystal faces has yet been reported.


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Our goal in this study is to model growth of barite single crystals using the facespecific growth rates of four main crystal surfaces measured in solutions with different compositions. A model is used to calculate surface area and volume of single crystals as a function of time, which is used study the growth kinetics of barite. The error introduced by neglecting the variation of surface area during a growth interval when normalizing growth rates is discussed and calculated as a function of crystal size and length of the growth interval. The work presented here is divided in four sections: a) the growth rates perpendicular to four different surface orientations are measured; b) barite crystals are grown from solution; c) the measured growth rates are used to model the growth of barite single crystals; d) the overall growth kinetics is studied using the surface area and volume of modeled crystals at different growth times.

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Methods

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Composition and structure of optically clear crystals of barite (China) were confirmed by laser ablation inductively coupled plasma mass spectrometry and single crystal X-ray diffraction. Single crystals were cut along {010} and {100} and cleaved along the {001} and {210} planes. Cut samples were embedded in epoxy resin and polished down to a 20 nm colloidal silica finishing. These orientations were chosen because they are the only surfaces found on crystals grown experimentally, are the main surfaces exposed on barite crystals found in nature,20 and include three perpendicular directions sufficient to represent a crystal in three dimensions.

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All solutions were prepared just before each experiment by dilution of 0.01 M BaCl2, Na2SO4 and SrCl2, and 3 M NaCl stock solutions prepared from p.a. anhydrous Na2SO4 (Acros), lab. grade anhydrous BaCl2 (Fischer Scientific), 99 % SrCl2·6H2O (Sigma-Aldrich), and > 99.5 % NaCl (Sigma-Aldrich). Solution compositions were calculated using PHREEQC 2.15.0 and the saturation index (SI) was calculated from equation 1:

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= log

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aBa and aSO4 refer to the activity of barium and sulfate ions in solution (calculated

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using the default Davies equation used in PHREEQC), respectively, and Ksp refers to the solubility product of barite (10-9.97). The following solutions containing 1:1 ratio of SO4-2 and Ba+2 activity coefficients were studied: 1) SI = 1.1 in water; 2) SI = 2.1 in water; 3) SI = 2.1 in 0.7 M NaCl; 4) SI = 2.1 in 1.3 mM SrCl2; 5) SI = 3.0 in water (ion activities and concentrations in Supporting Information, Tab. S1). The concentration of electrolytes used in 3 and 4 are typical concentrations of NaCl found in seawater and strontium in formation waters. The pH of all solutions was 5.3 ± 0.1 and remained constant throughout the experiments. Prior to use, all glassware was left in a 1.5 N HCl solution for 48 hours to remove adsorbed contaminants, and then rinsed with distilled water. Samples were reacted at ambient laboratory temperature, 22.2 ± 0.3 °C. To

eq. 1


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minimize the effect of changing saturation index due to precipitation, all experiments using SI = 2.1 or 3.0 were conducted in a flow-through system where BaCl2 and Na2SO4 solutions are mixed in a stirred T-junction just prior to contacting the reacting surface.

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The growth rates perpendicular to each of the four surfaces were measured in separate experiments. Each surface was partially masked using cyanoacrylate glue and then reacted under a continuously flowing solution at 100 ml·h-1 over 5 hours. The cyanoacrylate mask was then removed with acetone and the thickness of the grown layer was measured from profiles across the interface between the layer and the masked area using an optical profilometer (Wyko, NT9100) equipped with vertical scanning interferometry (VSI) lenses with 50x magnification. For each surface, 10 profiles across the interface were used to calculate the average thickness of the grown layer, which was used to calculate the face-specific growth rate. The deviation from the average value was used to calculate the error.

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To determine the growth morphology and size of crystals in solutions 1-5, barite was grown on soda-lime glass beads 14 - 40 µm diameter. Solutions were continuously flowed on the surface of the beads for up to 20 hours. After the reaction, the beads were washed with distilled water and then with acetone. After drying, samples were carbon-coated and analyzed with scanning electron microscope (SEM) (JOEL, JSM-6060). As no crystals could be observed at SI = 1.1 after 10 hours, the beads were left in 100 ml solution for 885 hours with a constant stirring 125 rotations per minute and the solution was changed every 72 hours.

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Growth of barite crystals was modeled using the SHAPE 7.3 software (Kingsport, TN, USA). Input parameters were the calculated face-specific growth rates of the four studied surfaces.

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Results

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Perpendicular Growth Rates

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The growth rates perpendicular to the four studied surfaces were calculated from the measured thickness of the layer grown in solutions 1 - 4 (Tab. 1). It was not possible to measure the growth rates of crystals grown in a solution with SI = 3.0 due to homogeneous nucleation of a precipitate that sinks and incorporates into the growing surfaces, and the development of irregular topographies. The solution composition affects the growth rates along the different directions disproportionately. The proportionality factor (F) in table 1 indicates the proportionality of the increase (F > 1) or decrease (F < 1) of the growth rate of a surface in a given solution, relative to the growth rate of the same surface measured in the solution with SI = 2.1 and no additional electrolyte. In a solution with SI = 1.1 and no additional electrolyte, the growth rates are about 5 times


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slower than in the solution with SI = 2.1. In a solution with strontium chloride, growth of most surfaces is inhibited, most pronounced on (010), but with the exception of (100). The growth rate of (100) is slightly higher, although the difference is within the experimental variability. In a sodium chloride electrolyte, the growth rates increase by a factor (FNaCl) in the range 2 - 2.6 for surfaces (210), (001) and (010), and by a factor of 7 for surface (100). Thus, NaCl causes a preferential enhancement of growth on the (100) surface.

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The roughness developed on the growing surfaces caused a variability of up to 30 % of the growth rate. The sources of roughness were the uneven growth from screw dislocations on surfaces (001) and (010) (e.g. Fig. 1a), the formation of a multi-stepped surface on surface (100) (Fig. 1b), incorporation of crystals nucleated in solution into the growing surface, or imperfections on the original surface caused by polishing or other defects.

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Table 1. Face-specific growth rates (nm·h-1) calculated from the thickness of the layer grown after 5 hours measured by VSI on the (100), (010), (001) and (210) surfaces of crystals grown in different solutions: 1) SI = 1.1 and no additional electrolyte; 2) SI = 2.1 and no additional electrolyte; 3) SI = 2.1 and 1.3 mM SrCl2; 4) SI = 2.1 and 0.7 M NaCl. Uncertainties are standard deviations derived from the experimental variability caused by surface roughness. Fn is the ratio between the growth rate of a surface in solution n and the growth rate of the same surface in a solution with SI = 2.1 without electrolyte. Surface (100) (010) (001) (210)

SI = 1.1, no electrolyte 8±2 44 ± 8 13.4 ± 0.6 19 ± 3

F1.1 0.2 0.1 0.2 0.2

SI = 2.1, no electrolyte 30 ± 10 320 ± 30 60 ± 10 90 ± 30

SI = 2.1, 1.3 mM SrCl2 40 ± 10 70 ± 20 23 ± 3 32 ± 4

FSr 1.3 0.2 0.4 0.4

SI = 2.1, 0.7 M NaCl 210 ± 60 620 ± 20 130 ± 20 240 ± 30

FNaCl 7.0 2.0 2.2 2.6

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Figure 1. VSI images of surfaces after 5 hours of growth in a solution with SI = 2.1 without additional electrolyte, a) (001) surface, note the high structures that correspond to hillocks grown from screw dislocations that are elongated along the [010] direction; b) (100) surface, note the ridges formed parallel to [001]. The orientation of the surfaces is shown.

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Nucleation and Growth From Solution

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Barite crystals were not observed on glass beads after a growth period of 885 hours in a solution with SI = 1.1, using SEM. After 5 hours in a solution with SI = 2.1 without additional electrolyte, nucleation and growth of barite on glass beads yielded crystals of similar size and morphology (Figs. 2a and 2b). The approximate nucleation density in figure 2a is 29 crystals per 100 µm2 of bead surface area. The (210) and (100) surfaces are not well defined, and the crystals are elongated in the [010] direction. In the solution containing SrCl2, smaller crystals homogeneous in size and morphology, and less elongated along the [010] direction are observed (Fig. 2c, see the morphology in Fig. 4b). Significant homogeneous nucleation occurred in the solution containing NaCl. The resulting crystals do not present a homogeneous distribution of sizes (Fig. 2d). The proportion of (100) surface relative to (210) surface is larger and more significant than crystals grown without background electrolyte or with SrCl2 (Fig. 2).


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In a solution with SI = 3.0, homogeneous nucleation occurs instantaneously when the BaCl2 and Na2SO4 solutions are mixed. Crystals formed in solution and on glass beads have a diversity of sizes and morphologies (Fig. 3).

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Figure 2. SE-SEM images of barite crystals nucleated and grown on glass beads or in solution during 5 hours, in different solution compositions. a,b) SI = 2.1, no additional electrolyte; c) SI = 2.1, 1.3 mM SrCl2; d) SI = 2.1, 0.7 M NaCl. Note the specific sizes of crystals in b-d, which are homogeneous in b and c and heterogeneous in d. Details of crystal morphologies can be seen in figure 4.

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Single Crystal Growth Model

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Using the calculated face-specific growth rates (Tab. 1), the growth of a single crystal can be modeled for each solution composition. The morphology, volume, and the relative surface area of each orientation are determined from the model as a function of growth time. For the same solution composition, the morphologies and the sizes of the modeled crystals are similar to those of crystals obtained experimentally (compare the length of crystals in Fig. 4). The relative area of each surface and the total volume of the modeled crystals after 5 hours are indicated in table 2. The percentage of surface area corresponding to each orientation remains constant during growth (Fig. 5), which is consistent with a steady state growth morphology. As no crystals could be grown from a solution with SI = 1.1 the shape and size of the modeled crystal cannot be compared. The

Figure 3. SE-SEM images of barite crystals nucleated and grown during 5 hours in a solution without additional electrolyte and SI = 3.0.


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area of crystals grown without additional electrolyte is dominated by the (100) surface. The area of crystals grown in the SrCl2 solution exhibit mostly the (210) and (001) surfaces, with (210) dominant, and the (100) surface comprises only a small fraction of the total surface. Crystals grown in the NaCl solution exhibit mostly the (001) surface followed by the (210) surface, and to a minor extent the (100) surface.

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Using the volume and surface area of modeled crystals at different growth times, the volume (Velectrolyte) in nm3 and the surface area (Aelectrolyte) in nm2 of a crystal can be defined by polynomial expressions as a function of time (t) in hours (see Supporting Information), equations 2 - 7. All fits have an R2 > 0.9999. These equations can be used to study the growth kinetics as a function of time (see discussion).

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= 1.11 × 10" # − 1.06 × 10 #

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& = 1.51 × 10( # ) − 4.88 × 10 # + 23.9 #

eq. 3

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012 = 8.95 × 10" # − 1.72 × 10) #

eq. 4

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&012 = 4.60 × 104 # ) − 5.54 × 10( # + 8.22 × 105 # eq. 5

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6712 = 2.00 × 10 # − 5.36 × 10) #

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&6712 = 1.78 × 10" # ) − 8.47 × 108 # + 125 #

eq. 2

eq. 6 eq. 7


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Figure 4. Comparison between the sizes and morphologies of experimentally grown (SE-SEM) and modeled barite crystals a) SI = 2.1, no additional background, after 10 hrs; b) SI = 2.1, 1.3 mM SrCl2 after 20 hrs: c) SI = 2.1, 0.7M NaCl after 10 hrs; d) SI = 1.1, no additional background, after 885 hrs (no crystals were observed experimentally for comparison). Crystals were modeled in SHAPE using as input the measured growth rates (Tab. 1). Numbers identify the length (µm) of crystal sides for comparison between experimentally grown and modeled crystals. Grey tones of modeled crystals identify crystal faces: Darker grey, {210}; Medium grey, {100}; Lighter grey, {001}.


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Figure 5. Percentage of the surface area of each crystal face relative to the total surface area of a single crystal modeled for growth from different solution compositions with SI = 2.1.

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Table 2. Partial surface areas and total volume of a modeled single crystal after 5 hours of growth in different solutions with SI = 2.1. Solution electrolyte 2

(100) area µm 2 (210) area µm 2 (001) area µm 3 Volume µm

No electrolyte 1.27 0.68 0.83 0.19

NaCl

SrCl2

3.18 8.65 10.5 368

0.024 0.27 0.21 0.022

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Discussion

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The discussion of the results will be based on the assumption that the solution composition remains approximately constant, thus the perpendicular growth rate of each surface remains constant within the experimental error.37-44 The solution composition is expected to remain constant because we use a flow-through system where the solution is mixed just before entering the reactor. This assumption is validated by the observations that the morphology of crystals remains approximately constant within the first 20 hours of growth (Fig. 4).

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Experimental Growth Rates

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The morphology of a crystal is defined by the slowest growing surfaces, which also determine the overall growth rate of a crystal.45 Here, growth rates of the (010) surface are significantly faster than the growth rates of the other surfaces that were studied (Tab. 1). For that reason the (010) surface is not visible on crystals formed in any of the solution compositions used here. Nevertheless, elongation along [010] was observed in crystals grown in a solution with SI = 2.1, without additional electrolyte (Figs. 2b and 4a), and in the shape of hillocks observed on surface (001) (Fig. 1a). These observations suggest that specific step advances in the [010] direction may play an important role in the molecular scale growth mechanisms.21 This is concordant with previous observations12 that nucleation of kink sites on surface (001) occurs faster along the [010] direction than the advance of the step on the [210] and [100] directions. In any case, it can


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be assumed that surface (010) and other surfaces found in naturally occurring crystals20 but not found on crystals grown in our experiments, do not directly affect the overall growth kinetics under the tested solution compositions.

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Differences in the proportionality factor (F) for each of the surfaces of a crystal grown in some solution (Tab. 1) suggest that the growth mechanisms on each surface are affected differently by each solution. For example, different growth mechanisms such as island nucleation versus advance of steps originating from growth hillocks46-48 or other reactions49-51 may be triggered on the [010] direction between saturation indices between 1.1 and 2.1. Another example suggested by our results is that sodium and/or chloride may adsorb or otherwise interact preferentially on sites on the (100) surface and promote growth more than in the other surfaces. An additional consideration is the saturation index necessary to initiate nucleation of crystals. No crystals were observed on glass beads in a solution with SI = 1.1, despite the fact that the size of crystals modeled using the face-specific growth rates should be larger than 10 µm after 885 hours (Fig. 4d). We suggest that at SI = 1.1 growth may only occur from existing defects in a crystal, e.g. from screw dislocations on the (001) surface. Thus, the barrier of nucleation was not overcome and such information needs to be included in a model that can predict both nucleation and growth. In contrast, at SI = 3.0, crystal agglomerates and twinned crystals with different morphologies clearly resulted from multiple nucleation events per crystal (Fig. 3). The experimental method described here has its strengths at lower saturation indices as it allows growth rates to be calculated in solutions where nucleation does not occur. However, this method is limited at higher saturation indices, where growth is less homogeneous.

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Strontium inhibits growth on the (001), (210) and (010) surfaces, but may slightly promote growth on (100) (Tab. 1). Strontium is known to be incorporated into barite during growth, which forms a solid solution with specific structure and solubility.48 The specific effect of strontium on each surface could be caused by a different incorporation rate taking place on each surface that can result in the formation of (Ba,Sr)SO4 solid solutions within the same crystal.52 It is also possible that strontium inhibits only specific steps,48,53,54 e.g. steps between the (210) and (001) surfaces, and does not inhibit the steps between the (210) and (2190) surfaces. This behavior has been observed for strontium incorporation on calcite steps of different orientation.30,31 These studies have also shown that strontium may modestly enhance monomolecular step velocity at low concentrations, similar to the slight enhancement observed on (100), but inhibit it at higher concentrations. If the phenomenon is crystal-face dependent, but inhibition occurs at a specific concentration for each surface, it could explain why strontium may slightly promote growth on (100) but inhibit it on the other faces. It also suggests that the mechanism of impurity incorporation is important, as


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opposed to solely the incorporation energy in the bulk crystal or the effect of the impurity on the solubility.31

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Growth of all barite surfaces is promoted by NaCl, which is consistent with previous studies of growth on the (001) surface using AFM.13,55 The same studies proposed that the promotion is caused by disruption of solvation at the surface and/or aqueous ions, which facilitates the incorporation of barium and sulfate into the crystal.21 That concept is consistent with the roughly equal promotion of growth on the (001), (210) and (010) surfaces (Tab. 1). An alternative hypothesis is that sodium or chloride specifically adsorb to surface sites involved in growth, facilitating attachment of barium and sulfate ions.17 The significantly higher increase of the growth rate of (100) surface suggests that there exists a specific interaction of Na+ or Cl- ions with (100). This is supported by figures 2d and 4c that shows a well defined (100) surface for crystals grown in the NaCl solution, in contrast with the poorly defined (100) surface of crystals grown without additional electrolyte (Figs. 2b and 4a). The elongation along [010] and the roughness developed during growth on the (100) surface (Fig. 1b) suggest an overlap between the (219 0) and (210) surfaces that results in the formation of a multi-stepped surface instead of an atomically flat (100) surface. Previous studies also observed that the presence of NaCl affects the relative growth velocity of hillocks on the (001) surface along [100] and [010], which is related to the shape of the hillock.12,13

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Overall Growth Kinetics of Barite

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The growth rate of a mineral (R, in units similar to mol·m-2·h-1) is typically calculated by following the variation of a reactant concentration in the growth solution (e.g., disappearance of barium, :[10 %. The error is represented as a function of the time interval (∆t) used to calculate Rt (eq. 8), and the longest axis of the crystal at the beginning of the interval (∆t), thus proportional to the initial surface area. Data refers to a solution with SI = 2.1, no additional electrolyte. Data corresponding to the other solution compositions are shown in the Supporting Information, Fig. S2 50x30mm (600 x 600 DPI)


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Growth Kinetics and Morphology of Barite Crystals Derived from Face

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