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Quantitative 3D Visualization of the Growth of Individual Gypsum Microcrystals: Effect of Ca :SO Ratio on Kinetics and Crystal Morphology 2+

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Michael M. Mbogoro, Massimo Peruffo, Maria Adobes-Vidal, Emma L. Field, Michael A. O'Connell, and Patrick R. Unwin J. Phys. Chem. C, Just Accepted Manuscript • Publication Date (Web): 18 May 2017 Downloaded from http://pubs.acs.org on May 30, 2017

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The Journal of Physical Chemistry

Quantitative 3D Visualization of the Growth of Individual Gypsum Microcrystals: Effect of Ca2+:SO42Ratio on Kinetics and Crystal Morphology Michael M. Mbogoro,† Massimo Peruffo,‡ Maria Adobes-Vidal, Emma L. Field, Michael A. O’Connell# and Patrick R. Unwin* Electrochemistry and Interfaces Group, Department of Chemistry, University of Warwick, Coventry, CV4 7AL, U.K.

* To whom correspondence should be addressed: Tel: (+44) (0)24 7652 3264 Email: [email protected] †

Present address: Isis Innovation Ltd. Buxton Court, 3 West Way, Oxford, OX2 0SZ, United Kingdom. Email: [email protected] ‡

Present address: Johnson Matthey Fuel Cells, Lydiard Fields, Great Western Way, Swindon, SN5 8AT, United Kingdom. Email: [email protected] # Present address: National Physical Laboratory. Hampton Road, Teddington, Middlesex, TW11 0LW, United kingdom. Email: [email protected] 1

ACS Paragon Plus Environment


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Abstract The kinetics of crystal growth of gypsum is determined by measuring the 3D time-evolution of isolated microcrystals (~ 10 µm characteristic dimension) by in-situ AFM. By coupling such measurements to a well-posed diffusion model, the importance of mass transport to the overall rate can be elucidated readily. Indeed, because microscale interfaces that act as source or sink sites are characterized by intrinsically high diffusion rates, it is possible to study crystal growth free from mass transport effects in many instances. In the present study, a particular focus is to elucidate how the ratio of Ca2+ to SO2-4 ions at constant supersaturation influences the rate of growth at the major crystal faces of gypsum. It is found that growth at the {100} and {001} faces, in particular, are highly sensitive to solution stoichiometry, resulting in needle-like crystals forming in Ca2+-rich solutions and plate-like crystals forming in SO 4 -rich solutions. The 2-

maximum growth rate occurs with a stoichiometric solution of Ca2+:SO42- The much slower growing basal {010} face also shows a stoichiometry dependence and growth is found to occur at step sites in growth hillocks. Importantly, overall growth rates derived by measuring the volumetric expansion of microcrystals by 3D in-situ AFM are in reasonable agreement with previous bulk studies on suspensions. This study is a further illustration that the study of individual microcrystals is a powerful approach for resolving face-resolved kinetics and in providing a link between microscopic observations and macroscopic rates in bulk systems. In this study it has further been possible to link face-resolved kinetics to the resulting crystal morphology.

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Introduction The elucidation of crystal growth kinetics and mechanisms requires an intimate knowledge of the relationship between interfacial flux and the underlying local microscopic events on the crystal surface.1-2 Moreover, the reliable analysis of the kinetic regime demands a demarcation between mass transport (typically diffusion) of species to the crystal surface, and the various surface processes (attachment, detachment and diffusion of species on the crystal surface) which lead to the incorporation of these species into the crystal lattice.1 Recognizing that crystal growth (and dissolution) is inherently spatially heterogeneous, scanning probe techniques such as atomic force microscopy (AFM)3-7 among others,8-9 have proven valuable for the investigation of processes at the microscopic and nanoscopic level.10-11 However, such studies have tended to employ macroscopic crystal surfaces, with the probe only investigating the behavior of a tiny portion of the crystal surface12-15 which may not necessarily be representative;16-17 and where the region imaged can be greatly influenced by processes outside that region.18 There are notable examples where there is a significant mismatch in nanoscale/microscale kinetic measurements, determined via AFM, and macroscopic (bulk) kinetics.19-20 In this paper, we use a novel microcrystal configuration to track the growth of microcrystals in 3D over time by in-situ AFM, and develop a complementary diffusion model via a finite element method analysis, which allows us to determine the prevailing kinetic regime. This approach has several attributes: (i) mass transport (diffusion) between bulk solution and the crystal is high (concentration boundary layer of the order of the crystal size), and can be modeled, pushing the reaction further towards surface-kinetic control compared to other techniques, so that surface kinetic values can be obtained; (ii) the contributions of all the exposed

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faces to the growth/dissolution kinetics can be measured and the influence of flux processes at each face can be accounted for; (iii) the AFM tip is much less invasive with micro-interfaces21 than with macroscopic interfaces18 and any effect of the tip on mass transport is readily treated. Thus, the use of AFM to study microcrystals constitutes a powerful and general methodology that enables the determination of intrinsic face-dependent growth (or dissolution) rates. 18, 22-25 The focus of the studies herein is gypsum (CaSO4⋅2H2O), which is one of the most abundant sulfate minerals,26-27 of geological28-30 and technological importance.31-35 Despite this, the growth kinetics of gypsum is less well studied than for other calcium minerals,36-41 particularly at the local (single crystal face) level. The vast majority of bulk42-46 and microscopic2,

47-49

gypsum crystal growth studies have focused on stoichiometric solutions,

where the ratio of the activity of reagent ions matches the ion ratio in the crystal lattice,

r = (aCa2+ aSO2- ) = 1. The effect of varying individual ion concentrations (at a particular 4

supersaturation) - which could be mechanistically revealing - is somewhat underexplored. Understanding how the solution stoichiometry (r) influences crystal growth rates is fundamentally important because some studies4,

37, 40, 50

have found that varying solution

composition has a dramatic effect on crystal nucleation and, in addition, the morphology of the resulting grown crystals.51 Herein, the effect of varying solution stoichiometry on face-specific crystal growth rates is investigated over a wide range of r. In addition to 3D visualization, we also investigate the surface topography of the basal {010} surface of gypsum microcrystals to obtain insights into the growth mechanism of this surface.

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Experimental Solutions. All chemicals were purchased from Sigma-Aldrich, UK, and solutions were prepared using Milli-Q reagent grade water (Millipore) with a typical resistivity of 18.2 MΩ cm (25oC). Crystal seeding solutions were prepared by mixing equal volumes of 0.04 M CaCl2⋅2H2O and 0.04 M Na2SO4. Separate stock solutions of 0.56 M CaCl2⋅2H2O and 0.56 M Na2SO4 were made and used to prepare growth solutions with r = 7.12, 4.00, 1.01, 0.25 and 0.133. Each stock solution and growth solution was prepared immediately prior to AFM experiments. For growth studies, the saturation state, S = IAP/Ksp where IAP is the ionic activity product of ions (Ca2+ and SO2-4 ) and Ksp is the solubility product of gypsum (10-4.61),52 was maintained at ~ 1.9 (except for r = 7.12 where S ~ 1.8). The ionic strength and chemical speciation were calculated for each growth solution using the numerical code MINEQL+ (Environmental Research Software, Hallowell, ME).53-54 Table 1 provides a summary of the composition of all growth solutions used. It is evident that the ion pair, CaSO4, in the solution is a significant species but is essentially constant (10 mM) for all solutions. Note that there is some change in the ionic strength, but this is taken into account in calculating the driving force, S, and the variation is insignificant in comparison to the kinetic effects demonstrated herein.

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Table 1: Summary of solutions used for growth experiments free ion activity /10-3 ion pair concentration (mM) ionic Strength (M)

S

r

Ca2+

SO 4

CaSO4

0.13

2.5

18.8

10.4

0.27

1.92

0.25

3.4

13.7

10.3

0.20

1.90

1.01

6.9

6.8

10.4

0.15

1.92

4.00

13.6

3.4

10.3

0.19

1.89

7.12

17.8

2.5

10.5

0.25

1.81

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Crystal growth experiments. Details of the crystal seeding procedure are described in the Supporting Information, section S1. Following the seeding process, the formation of gypsum microcrystals was characterized by Micro-Raman spectroscopy (see Supporting Information, section S2). All growth experiments were conducted at room temperature (23 ± 1 ºC) under conditions open to the atmosphere. MINEQL+ simulations revealed a negligible change in speciation between a system closed and open to the atmosphere. Individual microcrystals for imaging purposes were selected based on their size (maximum initial dimension 10 ± 3 µm), morphology (monoclinic structure devoid of obvious macroscopic steps and defects) and isolation (distance between adjacent crystals > 20-fold the characteristic length scale of a crystal under observation). The imposed restrictions satisfied the conditions necessary for a microscopically active surface to be essentially diffusionally isolated from neighboring crystals, simplifying the treatment of mass transport and ensuring high intrinsic diffusion rates to the microcrystal of interest. In addition, based on the crystal size and coverage on the functionalized glass surface, and the crystal growth rates deduced (vide infra) it was reasonable to assume that the growth solution was not depleted in a significant way for the duration of a typical growth experiment (~ 60-90 min).

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A 4 mL aliquot of growth solution was transferred through a filter (0.20 µm pore, Sartorius Ministart High-Flow, UK) to the in-situ AFM cell, using a 10 mL syringe (Becton Dickinson S.A. Plastipak, Spain). The AFM (BioScope Catalyst, Bruker, Billerica, MA) was positioned on an optical microscope (Leica Microsystems DMI 4000, Germany) equipped with differential interference contrast (DIC). The optical microscope was used to locate microcrystals for AFM imaging and to allow positioning of the AFM tip on the microcrystal surface. After a period of equilibration (~ 10 min), the growth of gypsum microcrystals was visualized over time via in-situ AFM using the ScanAsyst mode, a PeakForce Tapping (Bruker, Billerica, MA) based imaging technique that uses an auto-optimization protocol of scan parameters to obtain topographical images at high resolution. All measurements were carried out using 120 µm long silicon nitride cantilever tips (SNL-type, Bruker, Billerica, MA) with a resonant frequency of ∼ 65 kHz, a nominal spring constant of ∼ 0.35 N m-1, a tip height of 2.5 – 8 µm, a front angle of 15 ± 2.5 °, a back angle of 25 ± 2.5 °, and tip radius of curvature of 2 – 3 nm. The 3D visualization of microcrystals permitted analysis of growth along specific crystallographic directions. Growth rates were measured from consecutive frames acquired during a 1 h period at ~ 6 min per frame with a resolution of 128 lines and 512 samples per line. The images were obtained at a 0 ° scan angle and a scan rate of 0.35 Hz. This is less than one might use for high-resolution 2D imaging, but here the goal was to obtain crystal geometric parameters as a function of time and this resolution was sufficient for such measurements. In addition to visualizing entire microcrystals in 3D with AFM, ex-situ 2D images were also obtained. In this case, the image resolution was typically 1024 lines and 512 samples per line. All topographical (3D and 2D) images produced were analyzed using WYKO Vision Software (Veeco Instruments, Inc, Vision 4.10).

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Simulations. Numerical simulations were executed on a Dell Intel Core 2 Quad 2.13 GHz computer equipped with 16 GB of RAM and running Windows 7 Professional 64 bit. Modeling was performed using the commercial finite element method package Comsol Multiphysics 4.2 (Comsol AB, Sweden). 3D simulations using the “mass transport of diluted species” module were carried out with > 106 tetrahedral mesh elements and the mesh resolution was refined to be the finest in the vicinity of the crystal surface. The model considered the growth of an isolated gypsum microcrystal in quiescent supersaturated solution and used face-dependent crystal growth rates (normal to face) obtained directly from in-situ crystal growth experimental measurements to predict interfacial concentrations around the growing crystal in order to deduce the growth regime, i.e., mass transport vs. kinetic control (vide infra). The simulated static crystal geometry was approximated to the monoclinic structure of gypsum crystal, which mimicked the morphology and dimensions of crystals grown experimentally (vide infra). The adoption of a static crystal for modeling was reasonable as crystal growth rates were low, such that the timescale for the change in crystal size was slow compared to the timescale for diffusion to a crystal. The mass transport of species to the crystal surface was described by the steady-state diffusion equation (eq 1): Di ∇ 2Ci = 0

(1)

where Di is the diffusion coefficient and Ci is the concentration of species i, where i is Ca2+ or SO2-4 . Diffusion coefficients used for the purposes of simulations were 0.792 × 10-5 cm2 s-1 and 1.065 × 10-5 cm2 s-1 for Ca2+ and SO2-4 , respectively,55 i.e. all ions considered to be free, and assumed to be constant over the entire domain. Note that, CaSO4 ion pair was ignored, because the goal of the simulation was to elucidate whether mass transport was important. By considering

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only the free ions, the simulation was simplified and identified the maximum possible perturbation in the ion concentrations due to growth process. The simulation domain is shown in Figure 1 where the boundary conditions on the numbered boundaries are described in the text. Boundaries 1-3 represent the predominant {010}, {001} and {100} crystal growth faces, respectively. Experimentally determined face-specific fluxes, J⊥{hkl} (mol m-2 s-1), were used as inputs for predicting the near-interface concentration of Ca2+ and SO2-4 ions at each face, as governed by: (2) where n is the inward pointing unit normal to the surface. Boundary 4 represents the inert glass substrate where there is no normal flux of any species: (3) Boundaries 5-9 define boundaries sufficiently far from the crystal that bulk solution conditions, as described by equation 4, prevail:

Ci = Ci ,b

(4)

where Ci,b is the bulk concentration of species i. The domain size as defined by boundaries 5-9 was designed such that the shortest distance between a crystal face (boundaries 1-3) and the domain walls was at least a 20-fold the characteristic length of a typical crystal under observation.

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Figure 1: Simulation domain used for finite element simulations of face-specific crystal growth fluxes (not to scale). The numbers represent boundaries used in simulations and described in the text.

Results and Discussion Characterization of seed crystals. Raman spectroscopy confirmed that the microcrystals resulting from the seeding process were gypsum crystals (see Supporting Information, section S2). Gypsum microcrystals presented a tabular habit reflecting the monoclinic crystal structure elongated on the [001] direction.56 The seeds were typically single crystals of 10 ± 3 µm length with a height of ~ 1 µm (growth in the [010] direction) and were largely devoid of macrosteps and large defects. Occasionally, some of the crystals formed were twinned or in small clusters, but their occurrence was not common. Figure 2 (a-b) shows an AFM image of a typical grown microcrystal highlighting the dominant {hkl} faces and the corresponding crystal structure (Figure 2 (c-e)). The number density of crystals on the surface was typically ca. 2 × 103 cm-2.

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Figure 2: Typical AFM images of a grown gypsum crystal: (a) top view highlighting the dominant crystallographic directions (the scale bar represents 2 µm) and (b) the crystal morphology in 3D. Gypsum structure showing (c) the (100) and (d) (001) steps of the CaSO4 bilayer and (e) the basal (010) surface. Imaging 3D growth kinetics: face-specific growth rates. In-situ AFM allowed the measurement of crystal size, for all three dimensions as a function of time, providing both the overall volume crystal growth rate and individual face-specific growth rates. A time-lapse sequence of AFM images (top view) of two growing crystals in r = 1 solution at times of: (a, e) 530 s, (b, f) 1200 s, (c, g) 2430 s, and (d, h) 3650 s is shown in Figure 3. In these, and all other time sequences, the times relate to the end of the image. The growth rate is slow compared to the image acquisition time (∼6 min) and growth rates are obtained from displacement-time plots so

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that as long as the time is defined in a consistent manner on each image, it does not matter whether the beginning or end time of an image is considered. It is evident that the imaged crystal increased in all dimensions with time. Under this condition (r = 1), the crystals were observed to become elongated on the [001] direction (preferential growth at the {100} face) indicating facespecific growth kinetics anisotropy, which we consider later.

Figure 3: Typical AFM height images (top view) of two seed crystals in r = 1 solution after growth for (a, e) 530 s, (b, f) 1200 s, (c, g) 2430 s and (d, h) 3650 s. The scale bar represents 2 µm. 12


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A summary plot of crystal expansion in the dominant exposed faces, namely {100}, {001} and {010}, as a function of time for an r = 1 solution, as determined by AFM is shown in Figure 4. The growth velocities, v⊥{hkl} (nm s-1) were found to follow the trend; v⊥{010} < v⊥{001} < v⊥{100}. For these and all other cases (0.13 < r < 7.12), the plots were found to be reasonably linear. For each AFM image, the average length of a crystal in a particular direction was determined from several (~ 5) cross-sections across the entire span of the crystal image. Crystal height data were determined from these cross-sections and the error bars represent standard deviations. For each r value, at least three crystals were visualized and analyzed in this way and it was found that the growth rates measured for each exposed face were highly reproducible (small standard error), and essentially independent of the initial crystal morphology (aspect ratio of faces {100}, {001} and {010}) and size, suggesting our system was free of mass transport limitations. A summary of the corresponding face-specific growth rates (velocities), derived from the slopes of these plots, is shown in Table 2.

Figure 4: Crystal expansion normal to the principle faces: {100} (black), {001} (red) and the basal {010} surface (blue), as a function of time, for growth in a stoichiometric (r = 1) solution.

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Table 2: Summary of all face-specific displacement velocities

Face-specific growth rates (nm s-1) r

{100} face

{001} face

{010} face

0.13

0.27± 0.12

0.39 ± 0.10

0.06 ± 0.02

0.25

0.40 ± 0.10

0.40 ± 0.06

0.08 ± 0.03

1.01

0.76 ± 0.09

0.51 ± 0.08

0.03 ± 0.01

4.00

0.60 ± 0.11

0.32 ± 0.08

0.04 ± 0.01

7.12

0.22 ± 0.07

0.07 ± 0.02

0.01 ± 0.005

Face-specific fluxes, J⊥{hkl} (mol m-2 s-1) were calculated as the product of face-specific velocities (v{hkl}) and the molar density of gypsum crystal (13400 mol m-3).57 Figure 5 shows plots of face-specific growth fluxes, as a function of solution stoichiometry (r) for the 3 principal crystal faces. Maximum lateral (J⊥{100} and J⊥{001}) rates were observed at stoichiometric growth conditions (r = 1), highlighting the need for equimolar amounts of Ca2+ and SO 4 ions for crystal 2-

growth in these directions. This observation is consistent with a recent model which has proposed that faster growth rates under stoichiometric conditions may be explained by the easier transport of the neutral complex on the crystal surface, and the growth units may then be supplied to the growth sites when the ion pair is close to surface growth sites.58 As r deviated from 1, growth rates on the {100} and {001} faces slowed, but with J⊥{100} diminishing more sharply for r < 1 conditions, than for r > 1, relative to J⊥{001}.

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Figure 5: Summary plot of face-specific growth fluxes to the following faces: {100} (black); {001} (red); and {010} face (blue), as a function of solution stoichiometry (r). For r < 1, growth of the {100} face decreased steadily with smaller r values, to achieve similar fluxes as for the (otherwise slower moving) {001} face at r = 0.25. The growth rate decreased further still at r < 0.25, ultimately to values lower than those observed for the {001} 2face, indicating that low concentrations of Ca2+ ions (compared to SO 4 ) limited growth on the

{100} face, in particular. Conversely, under similar conditions (r < 1), the growth flux for the {001} face appeared to plateau at a value of ca. 6 µmol m-2 s-1, and further reduction of the bulk Ca2+ concentration in the regime covered had negligible effect on the growth rate of this face. For r > 1, the decrease in J⊥{100} with increasing r was more gradual than the decrease in rates observed at r < 1. However, at r = 7.5 (maximum r value), J⊥{001} diminished to a value similar to that observed at r = 0.133 (minimum r value), suggesting that crystal growth on the {100} face, is sensitive to SO2-4 ion concentration in similar way to Ca2+ concentration, particularly at extreme r values. This significant drop in growth rate is too large to be a result of the slightly lower supersaturation (S = 1.8) used in this particular case compared to other r values (S = 1.9); see Table 1. At these extreme values, r = 0.133 and r = 7.12, J⊥{100} is evidently smaller by a factor of ~ 5 compared to rates for stoichiometric conditions (r = 1). Although the

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ionic strength is also lower at extreme r values (Table 1), the studies have been carried in a fairly narrow band of (relatively high) ionic strength, such that the small ionic strength variation is unlikely to be a significant factor in the observed trend of rate vs. r. Over the entire range of r, growth of the {010} crystal surface was found to be slow relative to the other faces, consistent with the {010} basal surface being the most stable face.59 However, in addition, there was a subtle decrease in J⊥{010} with increasing r. The growth behavior of this face may be rationalized based on bonding in the crystal in the [010] direction, with a discontinuity of the periodic bond chain. Previous studies2, 49 have alluded to the CaSO4 bilayer as a repeat unit for growth (and dissolution). Effect of r = (aCa2+ aSO 2- ) on crystal morphology. The observed trends in face-specific 4

velocities, v⊥{hkl} (Table 2) or equivalent fluxes, over a range of r (Figure 5) were predictably manifest in the morphology of the growing crystals. Figure 6 shows AFM height images of crystals grown with r values of (a-b) 0.133, (c-d) 1 and (e-f) 7.12 where (a), (c) and (e) are crystals after the initial scan and (b), (d) and (f) are the same crystals after growth for ~3600 s. When grown in the SO2-4 rich solution (Figure 7 (a-b)), the ratio of lateral rates of growth were found to be v⊥{100} / v⊥{001} ≈ 0.7 (Table 2), producing a plate-like crystal morphology with comparable dimensions in the [100] and [001] directions. As r increased to stoichiometric levels (r = 1), v⊥{100} / v⊥{001} ≈ 1.5 thus producing crystals slightly elongated in the [001] direction (Figure 7 (d)). In Ca2+ rich solution (r = 7.12), the velocity ratio, v⊥{100} / v⊥{001} ≈ 3 and the crystal morphology is more needle-like with a significant elongation in the [001] direction (relatively faster displacement of the {100} face). These findings for individual microcrystals are in quantitative agreement with previous morphological assessment of gypsum crystals grown in bulk suspensions,60-61 where SO2-4 -rich solutions (r < 1) produced large plate-like crystals 16


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compared to a needle-like habit observed for r = 1, confirming the validity of our approach, in which we are also able to deduce face-specific growth rates.

Figure 6: AFM height images of crystals grown with r values of (a-b) 0.133, (c-d) 1 and (e-f) 7.12 where (a), (c) and (e) are crystals initially and (b), (d) and (f) are after growth for ~3600 s. The scale bar represents 2 µm. Insights from simulations: mass transport vs. surface kinetic control. Finite element method analysis has been proven to be an excellent computational tool for the analysis of mass transport in a vast variety of environments, including in-situ AFM.24, 62 For example, previous studies from this group and others,18, 62 have demonstrated that when only a tiny portion of a crystal surface is investigated, a surface kinetic controlled regime might be unattainable even though high convective rates of solution through the AFM cell are used, because mass transport in the region of the AFM measurement is hindered by the AFM tip. We also reported how the surface processes imaged in the AFM scan area during crystal dissolution were strongly influenced by reactive fluxes from active regions of the crystal outside that area, and highlighted the

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importance of knowing in detail the hydrodynamic behavior in the AFM fluid cell as well as the processes occurring on the crystal surface in the area outside that image by AFM in order to provide reliable intrinsic rates from AFM data.18 Herein, these problems are overcome by imaging entire isolated microcrystals (≤ 10 µm in the largest dimension). Mass transport to an isolated microscopic active surface is very high and well-defined, as evident from electrochemical studies of work in the field of ultramicroelectrodes,63 as the concentration boundary size is of the order of the crystal size. Moreover, AFM tips have little influence on diffusion to such microscale reactive surfaces, provided that the surrounding area is inert,21-23 which greatly simplifies the treatment of mass transport and one can generally ignore the tip to a reasonable approximation. The model considered the growth of an isolated gypsum microcrystal in quiescent supersaturated solution. The crystal face growth rates (flux of species per unit area) were input into the finite element simulations to predict the interfacial activities (of Ca2+ and SO2-4 ions) at the crystal surface during growth as well as concentration gradients at the interface. Table 3 summarizes all near-interface concentrations at specific crystal faces, deduced from the simulations, for the range of r studied. The focus of the data in the Table 3 is on the limiting ion (lowest bulk concentration), which will show the biggest relative change in concentration during crystal growth. It is evident that the surface concentration values for all crystal faces remain essentially the same as the bulk concentration (< 1% difference between surface and bulk concentrations). This is consistent with crystal growth being limited by surface kinetics64 for the entire range of r studied, i.e. species diffuse to the surface much faster than they are integrated into the crystal surface. Thus, the growth rates measured, such as those in Figure 5, represent intrinsic rates free from mass transport (diffusion) effects.

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Table 3: Summary of interfacial concentrations for each measured crystal face concentration of limiting ion /mM r

{100}

{001}

{010}

face

face

face

2.5

2.48

2.48

2.48

3.4

3.38

3.38

3.38

6.8

6.79

6.79

6.79

limiting ion

bulk

0.13

Ca2+

0.25

Ca2+

1.01 Ca2+ and SO2-4 4.00

SO 4

2-

3.4

3.39

3.39

3.39

7.12

SO2-4

2.5

2.49

2.50

2.48

Relationship between microscopic fluxes, macroscopic growth rates and previous studies. The 3D visualization data allowed overall crystal growth rates, J (mol m2 s-1), to be deduced readily:

J=

dV (t ) ρ × dt A(t )

(5)

where t is time (s), V(t) is the time-dependent crystal volume (m3), ρ is the molar density of gypsum crystal (13400 mol m-3) and A(t) is the time-dependent total crystal surface area (m2) exposed to solution. Growth rates averaged over the time course of measurements were found to be 1.7 (±0.3) ×10-6 mol m-2 s-1, 2.5 (±0.4) ×10-6 mol m-2 s-1 and 1.5 (±0.2) ×10-6 mol m-2 s-1 for r = 0.133, 1 and 7.12, respectively. In part, the trend of these values mirrors that found for facespecific growth rates, where the highest rates were deduced at r = 1. However, the average rates determined are sensitive to the surface areas of each exposed crystal face and the corresponding reactivity of the individual faces. For instance, at r = 1, the anisotropy in face-specific growth rates resulted in a needle-like crystal morphology, which increases the basal plane area (due to

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Page 20 of 34

relatively fast lateral growth in [001] direction) while the faster moving {100} face area remains comparatively small (as a consequence of slow basal plane growth). The slowest growing face, the basal {010} plane has significant influence on the overall (volumetric) rate of crystal growth. The rates of growth of single isolated microcrystals analyzed in this work can be compared to kinetic measurements in a seeded suspension. Previous studies of this type have monitored growth kinetics by tracking changes in the bulk solution via conductivity measurements,45, 65 titration,66-68 potentiometry44, 46 and spectrometry.69 A study by Zhang and Nancollas61 at comparable supersaturation (1.54 ≥ S ≤ 1.84) using suspensions at relatively high ionic strength (in 0.5 M KCl), determined average growth rates to be: 3.22 ×10-6 mol m-2 s-1, 1.8 ×10-6 mol m-2 s-1 and 8.4 ×10-7 mol m-2 s-1 for r = 0.1, 2 and 10, respectively. Thus, the values in our study and previous bulk measurements correlate reasonably well. Other kinetic studies60-61,

70-71

on bulk suspensions suggested that gypsum growth

followed a 2nd order rate law on supersaturation at close to equilibrium conditions and in low ionic strength solutions. This body of work thus appeared to corroborate either the Burton, Cabrera and Frank (BCF)72 crystal growth model, characterized by the advancement of spiral hillocks on the dominant F-faces of a crystal, or a ‘layer-by-layer’ growth model.73-75 With the development of AFM, it was possible to discriminate between competing theories by probing the surface topography during growth on the cleaved basal {010} surface of natural gypsum samples at close to equilibrium conditions.

2, 47-49

The existence of 2D layers with few spirals were

observed, thus supporting the ‘layer-by-layer’ growth model. In this work, in addition to tracking the 3D growth of microcrystals, the morphology of the dominant {010} basal plane was investigated to provide further information on the mechanism of crystal growth on this face. This was considered valuable because, as mentioned

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earlier, previous AFM studies have focused on macroscopic crystals2, 47-49, 76 and it is of great interest to identify any similarities and differences between synthetically grown microcrystals and natural cleaved macro-crystal surfaces. Figure 7 shows images of a typical crystal imaged in air on the combined AFM-optical microscope system, with (a) showing an optical image of a typical microcrystal with small areas highlighted in red where AFM imaging was carried out revealing (b) a growth hillock with a nucleation point where steps originate and propagate across the surface. [100]-oriented steps are shown in (c), which is an area of the surface some distance from the nucleation point, where there is a large step spacing compared to the closely spaced [001]-oriented steps. In (d) [001]oriented steps close to the crystal edge are shown. A cross-section perpendicular to [100]oriented steps in Figure 7 (c), is plotted in Figure 7 (e), revealing the step heights and spacing between [100]-oriented steps. These steps are consistent with the CaSO4 bilayer height in the unit cell of gypsum crystal which has a thickness of ~0.76 nm.77 Close to the crystal edge (Figure 7 (d)), the cross-section over slow moving [001]-oriented steps is plotted in Figure 7 (f) reveals them to be multilayered with heights of > 20 nm.

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Figure 7: (a) Optical image depicting typical crystal in air with small areas on the basal {010} surface magnified via AFM to reveal (b) growth hillock with a nucleation point in the center, which acts as a source of steps. Image (c) is an area away from the source where fast moving [100]-oriented steps have a large step spacing, with much more closely spaced [001]-oriented steps. Image (d) is close to the crystal edge where only the [001]-oriented steps are evident. The cross-sections in (c) and (d) are shown in (e) and (f), respectively, and serve to highlight a large difference in step heights in the different regions of the crystal surface.

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Conclusions We have investigated the growth behavior of isolated gypsum microcrystals via in-situ 3D AFM imaging, and determined the process to be controlled by surface-kinetics with no influence of bulk solution to surface diffusion. The growth kinetics for the edge-like faces, i.e. {100} and {001} faces, were found to be highly sensitive to the ratio of Ca2+ to SO2-4 ions in the growth solution, effecting the morphology of crystals as growth progressed. In SO2-4 -rich solutions crystals adopted plate-like shapes, while in Ca2+-rich solutions, they formed a needle-like morphology. This finding highlights an asymmetric dependence of face-specific growth on the solution stoichiometry. Ex-situ analysis of the basal {010} surface topography inferred that [100]-oriented steps propagate much faster than those that are [001]-oriented. The considerable anisotropy of step velocities was evident during in-situ growth measurements on the {010} surface, in which only [001]-oriented steps could be monitored by AFM. The approach described herein should be generally applicable to crystal growth (and dissolution); its merits being the possibility of measuring overall crystal growth rates, the ability to decouple mass transport and surface kinetic effects, and the possibility of obtaining facespecific growth (dissolution) kinetics from the time-dependent analysis of the morphology of a single microcrystal

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Supporting Information Substrate preparation and crystal seeding process and characterization of seeded crystals by Raman spectroscopy. Electronic Supporting Information files are available without a subscription to ACS Web Editions. The American Chemical Society holds a copyright ownership interest in any copyrightable Supporting Information. Files available from the ACS website may be downloaded for personal use only. Users are not otherwise permitted to reproduce, republish, redistribute, or sell any Supporting Information from the ACS website, either in whole or in part, in either machine-readable form or any other form without permission from the American Chemical Society. For permission to reproduce, republish and redistribute this material, requesters must process their own requests via the RightsLink permission system. Acknowledgements This work was supported by the European Research council (ERC-2009-AdG247143QUANTIF) which funded P.R.U., M.P. and M.M.M. M.A-V acknowledges funding from the European Union under a Marie Curie Initial Training Network FP7-PEOPLE-2012_ITN Grant Agreement Number 31663 CAS-IDP. M.A.O’C was supported by EPSRC/Syngenta (CTA studentship). We thank Dr. James Iacobini for assistance with Raman spectrometry.

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