Langmuir 1998, 14, 4967-4971
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Dissolution Kinetics of the Barium Sulfate (001) Surface by Hydrothermal Atomic Force Microscopy Steven R. Higgins,* Guntram Jordan, and Carrick M. Eggleston Department of Geology and Geophysics, University of Wyoming, Laramie, Wyoming 82071-3006
Kevin G. Knauss Earth Sciences Division, Lawrence Livermore National Laboratory, Livermore, California 94550 Received June 5, 1998 Dissolution of the BaSO4(001) surface was studied for the first time by hydrothermal atomic force microscopy. Step velocities and pit nucleation rates as a function of temperature along with observations of surface morphology led to the conclusion that the dissolution process is most accurately described by a two-dimensional birth-and-spread model.
I. Introduction The fundamental surface processes (e.g., kink/step nucleation and growth) that govern the aqueous dissolution of solids have been recognized for nearly a century.1 However, direct observation of the kinetics of these processes requires, in many cases, lateral resolution only attainable by scanning probe microscopy (SPM). Mineral dissolution is important in many geochemical processes (e.g., exerting a degree of control over global climate). Of the numerous mineral phases found in ground and subsurface waters as well as soils and sediments, most ((hydr)oxides, silicates, and some salts) dissolve in roomtemperature aqueous solution at rates far too low for direct observation by SPM.2 To observe the microscopic dissolution kinetics of these relatively insoluble minerals, temperatures must be increased. While phase contrast and differential interference contrast optical microscopy are viable high-temperature, in-situ imaging methods, they are limited in lateral resolution due to the diffraction limits of visible light. Here, we present for the first time experimental measurements of the mineral Barite (BaSO4) (001) surface dissolution kinetics using a novel hydrothermal atomic force microscope (AFM).3 Because BaSO4 has low solubility, its dissolution and precipitation represent a control on the concentration and mobility of barium in surface and subsurface water. Barite dissolution and growth are also important to offshore oil and gas exploitation because Barite scale deposits may precipitate in well casings. Predicting how, and at what rate, solids dissolve under certain conditions requires a thorough understanding of the fundamental surface reaction mechanisms. In this letter, we present hydrothermal AFM results that provide a link between atomic-scale rates and macroscale observables.
by cleaving with a knife edge. Samples were mounted in the AFM fluid cell using a Ti wire; no adhesives were used. In all experiments, deionized water (resistivity g 18 MΩ cm) was used without the addition of further reagents. The water was contained in a heated Ti bomb/reservoir pressurized with 6.8-bar high-purity N2. Flow rates were maintained at 330 mg/ min by a mass flow controller. Higher flow rates had no effect on the observed dissolution kinetics, indicating that the surface reactions were not influenced by the diffusion of reactants or products to the bulk solution. Fluid cell temperature was maintained with a resistive heater/controller system coupled to a K-type thermocouple. We used a novel high-temperature AFM designed in our laboratories3 and capable of operating in hot aqueous solutions up to 150 °C under constant flow conditions. Cantilevers were uncoated single-crystal Si probes with a 0.02-0.1-N/m spring constant. Contact forces were maintained below 10 nN.
III. Results and Discussion
* To whom correspondence should be addressed. Tel.: (307) 7663318. Fax: (307) 766--6679. E-mail:
[email protected].
The cleavage morphology on our Barite samples was similar to morphologies reported by others (e.g., BaSO4,4 SrSO45). The orientation of steps generated by cleavage generally does not represent the preferred orientation of steps during dissolution. We estimate that the time required for room-temperature dissolution to remove cleavage artifacts could exceed 24 h, but at the temperatures in our AFM (90-125 °C), the cleavage structure is removed within 30 min. Figure 1 shows two sequential AFM images of a Barite (001) surface in water at 125 °C. Steps comprising the walls of the etch pit are aligned along 〈120〉 and 〈010〉 . All steps have dissolved (i.e., retreated) between Figure 1a and Figure 1b. Step velocities are higher for 〈120〉 steps than for 〈010〉 steps, and the differing retreat velocities ultimately govern the aspect ratio of growing pits. The pits, which are comprised primarily of double-layer steps (7.1-Å height), also contain single-layer steps (3.5-Å height) in the uppermost and lowermost layers. The single-layer steps in the uppermost layer (labeled “1”, Figure 1a) are curved, in contrast to the straight double-layer steps in the pit walls. The intersection of retreating steps results in local edge orientations not necessarily belonging to 〈120〉
(1) Stranski, I. N. Z. Phys. Chem. 1928, 136, 259. (2) Dove, P. M.; Platt, F. M. Chem. Geol. 1996, 127, 331. (3) Higgins, S. R.; Eggleston, C. M.; Knauss, K. G.; Boro, C. O. Rev. Sci. Instrum., in press.
(4) Putnis, A.; Junta-Rosso, J. L.; Hochella, M. F. Geochim. Cosmochim. Acta 1995, 59, 4623. (5) Seo, A.; Shindo, H. Appl. Surf. Sci. 1994, 82/83, 475.
II. Experimental Section Our selected specimens (from Cumberland, England) were optically clear and colorless. Clean (001) surfaces were prepared
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Figure 1. Pair of time-sequential deflection mode AFM images (8 µm × 8 µm) of Barite(001) in water at 125 °C taken at (a) t ) 0 s and (b) t ) 127 s. The steps labeled “1” are single-layer (3.5-Å height) steps. Opposing arrows in (a) show the intersection of retreating steps resulting in unbounded step retreat, labeled “U” in (b).
or 〈010〉 . An example of this can be seen in Figure 1a (marked with opposing arrows) where the step intersection creates a step morphology not bounded by either pit. A kink birth-and-spread mechanism governs “bounded” step motion, but “unbounded” steps (marked “U” in Figure 1b) need not nucleate kinks and thus retreat at higher velocities. Rapid motion of “unbounded” steps also was h 4).6 found for CaCO3 (101 Barite (space group Pnma) has unit cell parameters a ) 8.87 Å, b ) 5.45 Å, and c ) 7.14 Å. There is a 21 screw axis parallel to 〈001〉 . A single molecular layer (3.5-Å thick) has Pm plane group symmetry; the directions [10] and [1 h 0] are inequivalent.4 As a result, a 3.5-Å deep pit in the Barite(001) surface develops three sides; one side with [010] alignment and the other two with [120] and [1 h 20] alignment. Figure 2a (125 °C) shows two singlelayer triangular pits nucleated at different times within the bottom of a multilayer pit. Their individual orientations are opposite each other because they exist in neighboring layers. The velocity of the lower pit vertexes is higher than that of the upper pit edges such that the lower pit vertexes “catch up” to the upper pit edges, forming (6) Jordan, G.; Rammensee, W. Geochim. Cosmochim. Acta 1998, 62, 941.
Letters
a segment in the pit edge with double-layer height (marked “D”, Figure 2b). This increase in step height causes the velocity of the pit edge to increase. In Figure 2c, a new single-layer pit has nucleated in the pit bottom whose vertexes eventually reach the next higher layer pit edges, causing the other three edges of the second pit to accelerate. Figure 2d shows the alternating single- and double-layer step structure that defines the walls of each pit (single-layer steps are highlighted with lines). The single-layer steps assume the velocity of the double-layer step by receiving double-layer kinks propagating into the single-layer step.7 At 107 °C (Figure 3), the velocities of single-layer 〈120〉 and 〈010〉 steps in the lowest layer are 1.5 and 0.81 nm/s, respectively; these rates are 0.8 and 0.11 nm/s slower, respectively, than the 2.3 and 0.92 nm/s velocity of the corresponding double-layer steps. Similar trends in the single-layer/double-layer velocities were found at 90 and 125 °C. We speculate that there is a greater steric hindrance associated with the mechanism for dissolution on single-layer steps relative to that of double-layer steps. Figure 4a shows an image (2700 nm × 2700 nm) of a Barite (001) surface immersed in water at 125 °C. This is one of a sequence of images of an area with widely varying step density (C, nm-1). By measuring the step velocity (G, nm/s) in regions of high C (0.11 nm-1) and low C (0.015 nm-1), we find step velocities of 1.73 ((0.04) nm/s for 〈010〉 steps in high C regions and 1.80 ((0.05) nm/s for 〈010〉 steps in low C regions (Figure 4b). Although the step velocity is dependent on step height, it is independent of step density. G〈120〉 was found to be independent of C as well, with typical values of 3.0 nm/s under these conditions. These results suggest that the kinetics of step retreat are not significantly affected by surface (i.e., twodimensional (2D)) or near-surface (i.e., three-dimensional (3D) diffusion gradients.8 The ability to measure the temperature dependence of step velocities allows us to calculate activation energies for different step directions. Figure 5a gives ln G versus 1/T (Arrhenius plot). Within statistical error, the activation energy for step retreat along 〈120〉 (34 ( 4 kJ/mol) is not significantly different from the value obtained along 〈010〉 (31 ( 6 kJ/mol). To compare our microscopic results with macroscopic dissolution rates (i.e., rates averaged over the entire surface area of crystal particles in aqueous suspension), we must consider various models for calculating macroscopic rates from microscopic data. Considering the one-dimensional kink birth-and-spread model of step motion by Frank,9 eq 1 expresses step velocity as
G = a(2ig)1/2,
when L
(2gi )
1/2
> 10
(1)
where i (nm-1s-1) is the rate of double-kink nucleation per unit length at a step, g (nm s-1) is the rate of singlekink propagation, a (nm) is the unit lattice dimension, and L (nm) is the length of the step. Therefore, the temperature dependence of G will give an activation energy for step motion approximated by the average of the double-kink nucleation and single-kink propagation activation energies. The measured activation energy then is an effective activation energy and the kinetics for i and g cannot be discriminated without direct access to the (7) Higgins, S. R.; Jordan, G.; Eggleston, C. M. 1998, in preparation. (8) Chernov, A. A.; Nishinaga, T. Growth shapes and their stability at anisotropic interface kinetics: Theoretical aspects for solution growth. In Morphology of Crystals, Part A; Sunagawa, I., Ed.; Terra Scientific: Tokyo, 1987; p 207. (9) Frank, F. C. J. Cryst. Growth 1974, 22, 233.
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Figure 2. Sequence of height mode AFM images ((a-c): 1370 nm × 1370 nm, (d): 1220 nm × 1220 nm) of Barite(001) in water at 125 °C. The vertexes of the triangular monolayer pit in the lowest layer in (a) retreat faster than the steps in the next highest layer, resulting in their intersection in (b). (c) shows a newly formed pit whose vertexes will eventually reach the next highest layer’s monolayer steps. In (d), the lines show the positions of the monolayer steps, demonstrating the complex step morphology within the pit walls.
temperature. By measuring the slope of the pit walls, we calculated the step density C (nm-1) within the walls. This local step density will depend on G and the rate I′ of pit formation. The rate of monolayer pit formation (I′) is
I′ ) CG
Figure 3. Plot of relative displacement of double-layer steps with respect to single-layer steps versus time at 107 °C. The slope of each data set equals the difference between doublelayer and single-layer step velocities for a given step orientation.
individual kink dynamics. Thus, the level of detail at which we can use kinetic models is limited to two and three dimensions. As outlined below, dissolution can be modeled in an analogous manner to the one-dimensional model above using two independent surface observables: The rate of monolayer pit formation I′ (s-1) and the step velocity G (notation extended from Frank9). We have chosen I′ in our notation to distinguish it from I, the rate of purely random monolayer pit nucleation. In our experiments, the average slope of the pit walls decreased with increasing
(2)
and is independent of G. By plotting ln I′ versus 1/T, we find the activation energy for the vertical growth rate of a pit to be 11 ((10) kJ/mol (Figure 5b). If we assume that vertical pit growth occurs primarily at line defects exposed at the surface, then we expect that the rate of pit nucleation will vary for each pit depending on the precise nature of each defect. The macroscopic surface velocity, G (nm/s), for any crystalline material will take on a form similar to that of eq 2:
G ) hmCG
(3)
where C and G are the average step density and velocity, respectively, and hm is the height of a monolayer plane. As in the case of one-dimensional step retreat,9 and assuming random pit nucleation, the surface velocity can be approximated by a two-dimensional pit birth-andspread model:10
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Figure 4. (a) Height/deflection mode mixed AFM image (2700 nm × 2700 nm) at 125 °C showing an etch pit whose surrounding region has low step density (C ) 0.015 nm-1) while the region in the lower right corner has high step density (C ) 0.11 nm-1). (b) Plot of step position versus time for steps in both high and low step density regions of (a). The nearly equal slopes of the two data sets show that step velocity is independent of step density.
(Ga)
G = hmI1/3
2/3
(4)
Equations 4 and 5 give a reasonable approximation to the dissolution rate when etch pits are truncated to the extent that aI′/G > hpF1/2, where hp (nm) is the average truncated pit depth. However, if we consider a surface consisting exclusively of stepped pit walls, then C ) I′/G such that eq 3 becomes
G ) hmI′
and the macroscopic surface dissolution activation energy will be equal to a 33% and 67% weighted sum of the pit nucleation and step retreat activation energies, respectively. The surface dissolution rate (R, mol/(m2s)) is simply VmG, where Vm is the crystal molar volume. However, there is a severe flaw in using eq 4 to predict the Barite (001) dissolution rate because this model assumes random two-dimensional nucleation (I), whereas our measurements of I′ overestimate I by up to 9 orders of magnitude due to nonrandom pit nucleation at defects. Because the majority of the pits on Barite (001) appear to be related to linear defects, we normalize I with respect to the surface density F (nm-2) of outcropping defects such that
I ) a2FI′
Figure 5. (a) ln G versus 1/T for the 〈010〉 and 〈120〉 steps giving activation energies for step retreat of 31 (( 6) and 34 (( 4) kJ/mol, respectively. (b) ln I′ versus 1/T for the calculated rate of pit formation based on eq 2. The average activation energy for pit formation is 11 (( 10) kJ/mol. The error bars (shown for only one data set) are large due to a wide distribution of pit wall step densities.
(5)
Equations 4 and 5 predict a very weak dependence of dissolution rate on defect density, consistent with other experimental observations.11-15 (10) Nielsen, A. E. J. Cryst. Growth 1984, 67, 289. (11) Schott, J.; Brantley, S.; Crerar, D.; Guy, C.; Borcsik, M.; Willaime, C. Geochim. Cosmochim. Acta 1989, 53, 373. (12) Blum, A. E.; Yund, R. A.; Lasaga, A. C. Geochim. Cosmochim. Acta 1990, 54, 283. (13) Murr, L. E.; Hiskey, J. B. Metall. Trans. B 1981, 12, 255. (14) Casey, W. C.; Carr, M. J.; Graham, R. A. Geochim. Cosmochim. Acta 1988, 52, 1545.
(6)
Equation 6 shows that the macroscopic dissolution rate will be proportional to the monolayer pit nucleation rate I′, and be independent of F (for F > 0) and G. This specific situation can be described by a three-dimensional nucleation birth-and-spread model (with hill-and-valley morphology) which is quantitatively equivalent to Sangwal’s16 polynuclear two-dimensional nucleation (no spreading) model. Based on eq 6, the maximum macroscopic (001) dissolution rate will be 7.6 × 10-7, 1.0 × 10-6, and 1.0 × 10-6 mol m-2 s-1, at 90, 107, and 125 °C, respectively. The macroscopic (001) dissolution activation energy in the three-dimensional nucleation model is the same as the activation energy for vertical pit growth (e.g., 11 kJ/ mol) and the dissolution rate is determined by eq 6 (see Table 1). In contrast, our experimental activation energies applied to the two-dimensional polynuclear birth-andspread model ( eq 4) predicts a macroscopic (001) dissolution activation energy of 25 (( 7) kJ/mol and dissolution rates given in Table 1. As the closest available comparison, macroscopic bulk dissolution activation energies for Barite under similar conditions range from 25 to (15) Holdren, G. R.; Casey, W. H.; Westrich, H. R.; Carr, M.; Boslough, M. Chem. Geology 1988, 70, 79. (16) Sangwal, K. Etching of Crystals. Theory, Experiment, and Application; North-Holland: Amsterdam, 1987.
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Table 1. Summary of Predicted Macroscopic (001) Dissolution Rates (mol/m2 s) and Activation Energy (kJ/mol) Based on the Two-dimensional Birth-and-spread, and the Three-dimensional Nucleation Models
T ) 90 °C T ) 107 °C T ) 125 °C ED (kJ/mol)
2D birth-and-spread (mol/(m2s))
3D nucleation (mol/(m2s))
bulk data (mol/(m2s))a
5.0 × 10-6 7.4 × 10-6 1.1 × 10-5 25 ((7)
7.6 × 10-7 1.0 × 10-6 1.0 × 10-6 11 ((10)
1.1 × 10-7 1.7 × 10-7b 2.5 × 10-7b 25-32
a Experimental bulk dissolution rates and energies are shown for comparison from refs 17 and 18. b Extrapolation based on activation energy.
32 kJ/mol.17,18 If we assume that these reported activation energies resulted from a majority of (001)-dissolved species, then we can say, based on activation energies and surface morphology, that dissolution of Barite (001) is best described by a two-dimensional birth-and-spread model. However, this assumption must be validated by further experiments (e.g., surface-limited macroscale dissolution by the channel flow cell (CFC) method19) and theoretical work, as it appears neither model, taken exclusively, predicts reasonable dissolution rates, activation energies, and surface morphologies. (17) Dove, P. M.; Czank, C. A. Geochim. Cosmochim. Acta 1995, 59, 1907. (18) Bovington, C. H.; Jones, A. L. Trans. Faraday Soc. 1970, 66, 764. (19) Tam, K. Y.; Compton, R. G.; Atherton, J. H.; Brennan, C. M.; Docherty, R. J. Am. Chem. Soc. 1996, 118, 4419.
Summary We have measured various step retreat rates and activation energies for the dissolution of Barite (001) using a novel new hydrothermal AFM at temperatures previously inaccessible by in-situ AFM. Application of crystal dissolution models shows that activation energies for Barite (001) dissolution will be determined by either threedimensional pit nucleation or a combination of pit nucleation and step retreat. Although the dissolution activation energy of 25 kJ/mol in light of the Barite (001) surface morphology and previously reported bulk activation energies suggests that a two-dimensional polynuclear birth-and-spread model is applicable, predicting, in general, macroscopic dissolution kinetics from AFM measurements requires further study (both experimental and theoretical) from a surface-limited macroscopic perspective in order to improve the quantitative treatment of defects. Acknowledgment. The authors wish to acknowledge the curators of the University of Wyoming mineral repository for donation of the Barite specimens, the U.S. Department of Energy, Office of Basic Energy Sciences (No. KC040302 to K.G.K. and No. DE-FG03-96SF14623 to C.M.E.), and the National Science Foundation (No. EAR9634143 to C.M.E.) for financial support. G.J. acknowledges support from the German Academic Exchange Service (DAAD). LA9806606
