Scanning-Induced Growth on Single Crystal Calcite with an Atomic

Attempts to achieve similar deposition rates in the absence of scanning require high supersaturations that produce three-dimensional crystal nuclei, w...
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Langmuir 2006, 22, 6931-6938

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Scanning-Induced Growth on Single Crystal Calcite with an Atomic Force Microscope A. L. McEvoy, F. Stevens, S. C. Langford, and J. T. Dickinson* Surface Dynamics Laboratory, Washington State UniVersity, Pullman, Washington 99164-2814 ReceiVed March 28, 2006. In Final Form: May 29, 2006 We report observations of localized growth on the (101h4) surface of single-crystal CaCO3 in supersaturated solutions while scanning with the tip of an atomic force microscope (AFM). At low contact forces, AFM scanning strongly enhances deposition along preexisting steps. This enhancement increases rapidly with increasing solution supersaturation, and is capable of filling in multilayer etch pits to produce defect-free surfaces at the resolution of the AFM. Attempts to achieve similar deposition rates in the absence of scanning require high supersaturations that produce threedimensional crystal nuclei, which are important defects. Localized deposition produced by drawing the AFM tip back and forth across step edges can produce monolayer deposits extending well over a micron from the scanned area. These tip-induced deposits provide convincing evidence for the importance of ledge diffusion in calcite crystal growth.

1. Introduction Mechanical stimulation can have profound effects on the progress of dissolution and growth. Scanning the surface of singlecrystal calcite (CaCO3)1,2 and brushite (CaHPO4‚2H2O)3 with the tip of an atomic force microscope (AFM) at high contact forces in undersaturated solution can dramatically enhance dissolution along preexisting steps. In previous work, we have shown that low contact force scanning on brushite in supersaturated solutions can induce localized growth to produce atomically smooth surfaces.4 In the brushite system, we provided evidence that scanning sweeps loosely adsorbed material from terrace sites into preexisting etch pits, dramatically increasing the material available for deposition along the edge of the pit. In this work, we show that low contact-force scanning can also induce localized atomic layer growth on calcite. The deposition rate is shown to be sensitive to the crystallographic step orientation and the degree of solution supersaturation. To within the resolution of the AFM, deposition during scanning yields atomically flat surfaces. In contrast, surfaces formed by spontaneous deposition at high supersaturations show large defects, including three-dimensional deposits (hillocks) rising some nanometers above the surrounding surface. Many biological, geological, and technological processes involve crystal growth and dissolution. Calcite in particular plays an important role in the exchange of carbon dioxide between the atmosphere, lithosphere, and ocean.5-8 Calcium carbonate (both calcite and aragonite) is also a major component of bones and shells9 and is involved in several pathologies, including arthritis, tendonitis, and kidney stones. Thus controlling calcite growth * Corresponding author. E-mail address: [email protected]. (1) Park, N.-S.; Kim, M.-W.; Langford, S. C.; Dickinson, J. T. J. Appl. Phys. 1996, 80, 2680-2686. (2) Park, N.-S.; Kim, M.-W.; Langford, S. C.; Dickinson, J. T. Langmuir 1996, 12, 4599-4604. (3) Scudiero, L.; Langford, S. C.; Dickinson, J. T. Tribology Lett. 1999, 6, 41-55. (4) Hariadi, R.; Langford, S. C.; Dickinson, J. T. Langmuir 2002, 18, 77737776. (5) Lasaga, A. C. J. Geophys. Res. 1984, 89, 4009-4025. (6) Archer, D.; Maler-Reimer, E. Nature 1994, 367, 260-263. (7) Brady, P. V.; House, W. A. Surface-controlled dissolution and growth of minerals. In Physics and Chemistry of Mineral Surfaces; Brady, P. V., Ed.; CRC Press: Boca Raton, FL, 1996; pp 225-305. (8) Morse, J. W.; Arvidson, R. S. Earth Sci. ReV. 2002, 58, 51-84. (9) Berner, R. A. ReV. Mineral. 1995, 31, 565-583.

and dissolution has potential medical applications. The growth and dissolution of the (101h4) face of calcite in aqueous solution have been extensively studied by atomic force microscopy (AFM).10-24 The effect of moving asperity contacts on localized deposition may have important implications in laboratory experiments as well as natural processes. Our results also suggest that tribologically important planarization processes, such as chemical mechanical planarization (CMP), could benefit from asperity induced deposition as well as material removal processes (wear).25 2. Experimental Section Optical-quality, synthetic calcite from Korth Kristalle (Altenholz, Germany) and Commercial Crystal Laboratory (Naples, Florida) were cleaved into 4 × 4 × 1 mm3 plates. In situ atomic force microscopy (AFM) imaging was performed in the contact mode using a Molecular Imaging PicoScan AFM using commercial Si3N4 (10) Hillner, P. E.; Manne, S.; Gratz, A. J.; Hansma, P. K. Ultramicroscopy 1992, 42-44, 1387-1393. (11) Hillner, P. E.; Gratz, A. J.; Manne, S.; Hansma, P. K. Geology 1992, 20, 359-362. (12) Gratz, A. J.; Hillner, P. E.; Hansma, P. K. Geochim. Cosmochim. Acta 1993, 57, 491-495. (13) Dove, P. M.; Hochella, M. F., Jr. Geochim. Cosmochim. Acta 1993, 57, 705-714. (14) Stipp, S. L. S.; Eggleston, C. M.; Nielsen, B. S. Geochim. Cosmochim. Acta 1994, 58, 3023-3033. (15) Liang, Y.; Baer, D. R.; Lea, A. S. Dissolution of CaCO3(1014) surface. In EVolution of Thin-Film and Surface Structure and Morphology; Demczyk, B. G., Williams, E. D., Garfunkel, E., Clemens, B. M., Cuomo, J. J., Eds.; Materials Research Society: Pittsburgh, PA, 1995; Vol. 355, p 409. (16) Liang, Y.; Baer, D. J.; McCoy, J. M.; Amonette, J. E.; LaFemina, J. P. Geochim. Cosmochim. Acta 1996, 60, 4883-4887. (17) Liang, Y.; Baer, D. R.; McCoy, J. M.; LaFemina, J. P. J. Vac. Sci. Technol. A 1996, 14, 1368-1375. (18) Britt, D. W.; Hlady, V. Langmuir 1997, 13, 1873-1876. (19) Jordan, G.; Rammensee, W. Geochim. Cosmochim. Acta 1996, 60, 50555062. (20) Jordan, G.; Rammensee, W. Surf. Sci. 1997, 371, 371-380. (21) Jordan, G.; Rammensee, W. Geochim. Cosmochim. Acta 1998, 62, 941947. (22) Teng, H. H.; Dove, P. M.; Orme, C. A.; Yoreo, J. J. D. Science 1998, 282, 724-727. (23) Teng, H. H.; Dove, P. M.; Yoreo, J. J. d. Geochim. Cosmochim. Acta 2000, 64, 2255-2266. (24) Shiraki, R.; Rock, P. A.; Casey, W. H. Aquatic Geochem. 2000, 6, 87108. (25) Steigerwald, J. M.; Murarka, S. P.; Gutmann, R. J. Chemical mechanical planarization of microelectronic materials; John Wiley & Sons: New York, 1997.

10.1021/la0608359 CCC: $33.50 © 2006 American Chemical Society Published on Web 07/08/2006

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Figure 1. Twelve consecutive AFM images of a monolayer pit acquired at supersaturation σ ) 3.1, FN ) 11 nN, and a scan speed of 2.9 µm/s. The scanned area was shifted slightly between (e) and (f). tips with typical tip radii of 40 nm. All AFM tips used were from the same wafer and had nominal force constants of either 0.32 or 0.58 nN. Imaging was performed at ambient temperature (22-25 °C) in a fluid cell of approximately 0.5 mL volume. CaCO3 solutions were prepared from reagent grade calcium chloride (CaCl2‚2H2O Baker) and sodium bicarbonate (NaHCO3 Baker). The ionic strength of the solutions was fixed using reagent grade sodium chloride (NaCl Baker). Solution pH was 8.3-8.6. The resulting supersaturation, σ, is given by26

(

σ ) ln

)

aCa2+aCO32Ksp

(1)

where a is the activity of the ionic species and Ksp ) 10-8.34.27 Note that Ksp is referenced to zero ionic activity and ideal crystals (no steps). The solution activities were calculated from product of the corresponding ion concentrations and activity coefficients, γ(, where the activities were estimated from log10 (γ() ) 0.509.z+z-I1/2; z+ ) z- ) 2 (the magnitudes of the ionic charges of Ca2+ and CO32-, respectively) and I is the ionic strength.28

3. Results At supersaturations σ < 0.8, AFM calcite cleavage surfaces [(101h4)] normally display rhombohedral etch pits which grow with time (dissolution). These pits typically have sharp corners and straight edges. In previous work, we have shown that dissolution at step edges in undersaturated solution is dramatically accelerated by scanning at almost any contact force.1 At somewhat higher supersaturations (σ > 0.8), etch pits tend to (slowly) fill in spontaneously. The influence of scanning at these supersaturations depends strongly on the contact force. At high contact forces, FN > 50 nN, local dissolution is observed even at high supersaturations. However, at lower contact forces, scanning significantly enhances deposition in multilayer etch pits at supersaturations of 0.8 < σ < 7. At supersaturations σ > 6, step growth and hillock nucleation are common. Deposition during Square Raster Scanning of Calcite. Figure 1 shows a sequence of 12 AFM images of a monolayerdeep pit imaged at a supersaturation σ ) 3.1, a contact force FN ) 11 nN, and a scan speed of 2.9 µm/s. The measured pit depth is 0.33 nm, consistent with the bulk lattice spacing of calcite, 0.31 nm. After 12 scans, the original pit is completely filled in, leaving a high quality, smooth surface on the nanometer scale. Although some growth is noted outside the scanned area, step advance outside the scan is less than 10% as fast as step advance in the scanned area. Therefore, we conclude that the observed growth is primarily tip-induced. In previous work on single(26) Drever, J. I. The Geochemistry of Natural Waters. 3rd ed.; Prentice Hall: Upper Saddle River, NJ, 1997. (27) Mucci, A. Am. J. Sci. 1983, 283, 780-790. (28) Moore, W. J. Physical Chemistry; Prentice Hall: Englewood Cliffs, NJ, 1962.

Figure 2. Selected AFM images of a small pit two monolayers deep: (a) imaged at σ ) 1.1; (b) imaged immediately after replacing the fluid with solution at σ ) 1.7; (c) after four more scans, which completely filled in the pit. Images were acquired at FN ) 7 nN and a scan speed of 700 nm/s.

crystal brushite (CaHPO4‚2H2O), we attributed this growth to loosely bound surface species that were swept into the pit by the AFM tip. Spontaneous growth or dissolution in calcite etch pits is generally most rapid along the crystallographically equivalent [4h41]+ and [481h]+ steps.11,16,17,29 At pH ) 7, velocity of fast step retreat along [4h41]+ and [481h]+ steps can be 2-4 times greater than the retreat velocity of the [4h41]- and [481h]- steps.17,30 As the solution carbonate concentration increases, the anisotropy in step velocities decreases and can even be reversed.31 In the work described below, virtually all of the scanning-induced growth takes place along the [4h41]+ and [481h]+ steps: the upper- and right-most steps in Figure 1. For the sake of brevity, we designate (29) Liang, Y.; Baer, D. R. Surf. Sci. 1997, 373, 275-287. (30) De Giudici, G. Am. Mineral. 2002, 87, 1279-1285. (31) Lea, A. S.; Amonette, J. E.; Baer, D. R.; Liang, Y.; Colton, N. G. Geochim. Cosmochim. Acta 2001, 65, 369-379.

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Figure 3. AFM images of a larger pit, three monolayers deep: (a) imaged at σ ) 1.1; (b) imaged immediately after replacing the fluid with solution at σ ) 1.7; (c) after two scans; (d) after four scans; and (e) after thirteen more scans, which completely filled in the pit. Images were acquired at FN ) 15 nN and a scan speed of 6.2 µm/s.

the [4h41]+ and [481h]+ steps, where growth is concentrated, fast steps. Conversely, we designate the remaining pair of steps slow steps. At the supersaturations employed in this work, the corner between the two fast steps quickly becomes rounded. In contrast, the other corners remain relatively sharp. This same behavior is observed during spontaneous growth in calcite etch pits at high solution supersaturations or in the presence of certain impurities.32 Between the fifth and sixth scans of Figure 1 (images 1e and 1f), the scan location was shifted slightly to compensate for drift in the AFM position control system. This procedure accelerated deposition during the next few scans. We attribute this acceleration to the introduction of fresh material into the scanned area. Scanning apparently depletes the upper terrace of loosely sorbed species; thus introducing fresh material into the scanned region significantly increases the amount of material swept into the pit. Figure 2a shows an image of an etch pit, two monolayers deep, acquired at σ ) 1.1 and FN ) 7 nN. The solution supersaturation was then raised to σ ) 1.7. Without scanning, no significant step growth was observed in these pits at this supersaturation. With scanning, significant deposition takes place at both levels, as shown in Figure 2b. After four more scans at σ ) 1.7, both levels of the pit had filled in completely, as shown in Figure 2c. At each stage, growth is dominated by advance of the fast steps. Step advance in the multilayer pits is most rapid along the bottom-most step: in Figure 2, the velocities of the bottom-most fast steps are almost twice that of the fast steps in the topmost pit. This velocity difference is strong evidence that growth is not limited by concentration gradients in the solution. Rapid growth along the bottom-most step is consistent with the accumulation of swept material along the bottom terrace. For purposes of forming defect free material, such a sequence is clearly advantageous (the bottom layer fills in first). Tip-induced growth in a three-monolayer pit is illustrated in Figure 3. The first image was scanned at σ ) 1.1 and FN ) 15 nN. The solution was then replaced with a solution of σ ) 1.7. In this series, the bottom-most pit filled in before the second scan was completed. The middle pit required seven more scans to fill in completely, and the topmost pit required 13 more scans. Although deposition is again concentrated along the fast steps in the middle and upper pits of Figure 3, the pattern of deposition is much less uniform than in Figure 2. The upper left corner of these pits, near the intersection of the two fast steps, filled in last. We emphasize that the resulting surfaces are free of observable defects. The kinetics of scanning-induced deposition are indicated in Figure 4, where the pit areas in Figures 2 and 3 are plotted against time on a semilogarithmic scale. (The bottom-most pit in the three pit structure of Figure 3 filled in so rapidly we do not plot it.) The dark lines in Figure 4 represent least-squares fits to a simple model which we describe below. Initially, each pit area falls exponentially with time. As deposition proceeds, the deposition kinetics become superexponential, until (at the (32) Astilleros, J. M.; Pina, C. M.; Ferna´ndez-Dia´z, L.; Putnis, A. Geochim. Cosmochim. Acta 2002, 66, 3177-3189.

Figure 4. Pit areas versus time for the larger pits in (a) Figure 2 and (b) Figure 3. The vertical axis is logarithmic.

resolution of these measurements) the pit area reaches zero. In multiple pit structures, the time constants for deposition in the lower pits are shorter than the time constants for deposition in the upper pits. Note that the pit areas in Figure 4b show no particular discontinuity associated with the uneven pattern of growth in Figure 3. This suggests that material swept to the fast step is deposited, despite irregularities in the location of the deposit. As discussed below, the rate of deposition is initially proportional to the pit area. Later, the contribution of material swept in from outside the pit becomes important, and superexponential kinetics are observed. Scanning-induced growth along fast steps can show fingerlike instabilities. Figure 5a shows a rhombohedral etch pit imaged at supersaturation σ ) 3.1. This etch pit is one atomic layer deep, with a second layer growing along the fast steps. Although the corners of this pit are relatively sharp, the pit edges are rather jagged. After one scan at FN ) 17 nN and scan speed of 4.3 µm/s, the solution was exchanged with a more saturated solution (σ ) 3.7). An image of the resulting growth after one scan at this supersaturation is shown in Figure 5b. The advancing step in Figure 5b is wavy, reflecting a fingering instability. Despite this irregular growth, six more scans (951 s, not shown) filled the pit completely and produced a smooth surface with no obvious defects. Figure 5b also shows induced growth along the upper terrace, outside the pit in the top right corner of the image. Growth on the upper terrace includes a finger extending along the upper edge of the pit. This growth is consistent with the presence of a diffusion barrier along the edge of the pit, which would hinder material transport from the top terrace to the bottom terrace. Evidence for such barriers was first observed in studies of the

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Figure 5. AFM images of a small etch pit acquired (a) at supersaturation σ ) 3.1; (b) after raising the supersaturation to σ ) 3.7 and scanning for 414 s. Scans were acquired at FN ) 17 nN and a scan speed of 2.2 µm/s. New growth within the pit is indicated by the arrow in (b). New growth outside the pit appears in the upper right-hand corner of (b).

mobility of sorbed adatoms moving on metal surfaces at elevated surfaces by Ehrlich33 and Schwoebel.34 Ehrlich-Schwoebel barriers are a consequence of perturbed van der Waals and electronic forces along the step. Some of the material swept by the AFM tip will temporarily accumulate along this barrier. In the absence of a suitable deposition site, it will re-enter the solution and produce no visible deposit. In Figure 5b, however, the end of the finger along the upper edge of the step is a fast step. Material swept by the tip is efficiently incorporated at the tip of the finger, rapidly increasing its length. Deposition near the tip of the finger presumably reduces the amount of swept material available for deposition at the base of the finger, resulting in nonuniform growth (fingering instability). At high supersaturations (σ > 6), rapid spontaneous growth and hillock formation are typical. Figure 6a is an image of a monolayer etch pit imaged at low supersaturation. The jagged steps and the upper terrace hillock suggest that this pit has a complex history. Figure 6b shows the same pit after the solution was replaced with a fresh solution with supersaturation σ ) 6.9. Rapid spontaneous growth is observed. In addition, several new hillocks appear along the edge of the original etch pit. Nucleation at these sites again supports the presence of a Ehrlich-Schwoebel barrier. These hillocks are typically several monolayers high. In the context of this work, hillocks represent undesirable defects. Such defects are produced in especially high densities at high deposition rates and high solution supersaturations. Continuous low contact force scanning during tip-induced deposition generally prevents the formation of these defects and can also remove them after their formation. Deposition during Linear Scanning. Some control over the location of the deposited material can be exercised by drawing the tip back and forth along a line across the edge of a pit. Figure 7 shows images of a monolayer-deep etch pit acquired before and after 3072 passes of the tip along the white line in Figure 7a at a supersaturation of σ ) 1.1. Again, virtually all of the (33) Ehrlich, G.; Hudda, F. G. J. Chem. Phys. 1966, 44, 1039-1049. (34) Schwoebel, R. L.; Shipsey, E. J. J. Appl. Phys. 1966, 37, 3682-3686.

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Figure 6. Pit imaged (a) before and (b) after replacing deionized water with highly supersaturated solution (σ ) 6.9). Without continuous scanning, the pit eventually filled in, but the hillocks in (b) remained. Scans were acquired at FN ) 9.6 nN and a scan speed of 3.1 µm/s.

Figure 7. Localized growth produced by 3072 passes of the AFM tip along the white line in (a). Scanning was performed at a supersaturation σ ) 1.1, FN ) 7.2 nN, and a scan speed of 7 µm/s.

deposition occurs along the fast step on the right, although the linear scan crosses both fast and slow steps. A small, 140-nm wide deposit projects into the pit, extending about 70 nm above and below the white line. This tip-induced growth represents material swept toward the step but extends some tens of nanometers on either edge of the tip. The width of the deposit is much greater than the width of the strip of material in direct contact with the tipsless than 10 nm at these contact forces, assuming elastic contact. A careful comparison of the two images shows small amounts of deposition along the entire lengths of both fast steps; we attribute this to the diffusion of deposited material along the fast steps. As shown below, large amounts of material can be transported along fast steps under suitable conditions. Assuming that all of the material in the 140-nm wide projection in Figure 7b was provided by the AFM tip, 3072 passes of the tip have deposited about 140 000 ion pairs, which corresponds to about 40 ion pairs per pass of the tip. The total number of ions swept by the tip could be much larger since it is likely that many re-enter the solution. Similarly, at this particular solution

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Figure 9. Length of deposits (measured parallel to the scan direction) produced by 512 passes of the AFM tip across the fast step of a single etch pit as a function of scan length. Scanning was performed at a supersaturation σ ) 3.1, a scan frequency of 3.1 Hz, and FN ) 9 nN. Figure 8. Localized growth induced by 2560 passes of the AFM tip across a cleavage step along the white line in (a) at supersaturation σ ) 2.7, FN ) 22 nN, and scan speed 31 µm/s.

concentration, the length of the projection (about 120 nm) provides a lower bound on the number of ion rows nucleated at the end of the projection during scanning. In terms of elementary deposition processes, the nucleation of a new ion row corresponds to kink nucleation. The observed finger length corresponds to about one kink nucleation event (one ion row) for every 9 passes of the tip. At higher supersaturations, linear scanning can produce much larger deposits. Especially interesting deposits can be formed on noncrystallographic cleavage steps. Figure 8 shows images of a cleavage step before and after 2560 back-and-forth linear scans along the white line in Figure 8a at a supersaturation σ ) 2.7. In this case, deposition has produced two straight, intersecting fast steps above the white line, with less growth below the white line. (The step orientation was verified by subsequent scans showing nearby oriented etch pits.) Swept material accumulating along the cleavage step appears to have considerable mobility along fast steps. Here the localized nature of the deposit again rules out the solution as a direct source of material. The orientation of the original cleavage step allows deposited material to form fast steps above the scan line (the white line in Figure 8b), but not below the line. The large majority of the new material has been deposited above the line scan, which would not be the case for spontaneous deposition. Significantly, mobile material can apparently turn the convex corner (joining the two fast steps) at the upper right end of the deposit. Material traveling from the pit near the line scan to the far end of the main deposit has traveled almost 2 µm, and significant additional material appears an additional 1 µm up the cleavage step. The relatively straight sides of the main deposit show that transport is relatively efficient for at least 2 µm. The visual evidence for the diffusion of material upward along the fast step in Figure 8b is compelling. The total number of ion pairs incorporated into the new growth under these conditions is quite large. The growth in Figure 8 corresponds to at least 1 × 107 ion pairs or about 4000 ion pairs per pass of the tip across the step. Transport to the step would likely involve clusters or small mats of material, rather than individual ion pairs. Detailed comparison of the “before and after” images in Figure 8 suggests that almost 1000 new ion rows have been nucleated at the point where the scan crosses the step. This corresponds to about one kink nucleation event for every 2.5 passes of the tip.

In previous work on single crystal brushite, we showed that the amount of material deposited during linear scanning depends strongly on the length of the linear scan along the upper terrace, outside the etch pit.4 Scanning on the upper terrace, outside the etch pit, induced significantly more growth than scanning on the lower terrace, inside the etch pit. This suggests that adsorbed material inside brushite etch pits is depleted, leaving little to be swept by the AFM tip toward the step for deposition. In calcite, no significant difference in growth rates is observed between linear scanning on the upper terrace and linear scanning on the lower terrace. As discussed below, this is consistent with a lower mobility for material adsorbed on terrace sites in calcite.11,12 Figure 9 shows the length of deposits produced by linear scanning, measured parallel to the direction of the scan, as a function of scan length. Scanning was performed at a normal force of 9 nN and scan frequency of 3.1 Hz across the edge of a single, large etch pit. The length of the deposit increases monotonically with scan length, with a possible plateau at scan lengths of 500-1000 nm. Although the significance of this plateau is unclear, we note that these length scales are comparable to the experimentally accessible pit sizes employed in this work. In general, linear scanning over steps at supersaturations of σ < 1 has little effect, whereas significant enhancements are observed at supersaturations of σ > 2. As one might expect, the volume of material deposited during linear scanning is much less than during square raster scanning.

4. Discussion Fundamental Growth Processes. Crystal growth in many systems is well described by the terrace-ledge-kink model, where material deposited at terrace sites diffuses to nearby ledges (steps), and along ledges to nearby kinks. When mobile material reaches a kink site, it is incorporated into the crystal lattice.35 Calcite growth is complicated by the low mobility of material adsorbed at terrace sites, inferred from studies of step interactions. Atomic force microscope images of advancing steps during spontaneous growth by Hansma et al. show little interaction between adjacent steps at step separations greater than 0.5 nm, or about 20 lattice spacings.11,12 Step interactions are expected when the diffusion length of adsorbed material is on the order of one-fourth the step spacing.35 Thus the inferred terrace diffusion length is less than about 5 lattice spacings. Hansma et al. suggest that step advance is primarily due to adsorption of material at edge and kink sites directly from solution. (35) Hirth, J. P.; Pound, G. M. J. Chem. Phys. 1957, 26, 1216-1224.

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Since the number of terrace sites can be many orders of magnitude higher than the number of edge and kink sites, the low mobility of material at terrace sites strongly limits the rate of calcite growth. We suggest that low contact force scanning mechanically transports adsorbed material along the terraces, thereby opening this growth channel and dramatically enhancing the growth rate. Given a low surface mobility, the density of material adsorbed at terrace sites would normally depend only on material exchange with the solution. During scanning, mechanical transport of material to ledge sites would lower the concentration of adsorbed material. Evidence for this depletion appears in Figure 1, where deposition in the pit visibly accelerated over the first few scans after moving the scan area. Quantitative measurements of the pit area indicate that the deposition rate settled back to its original value after 3-4 scans. This initial depletion is not observed in most of our observations, where a sequence of images is normally preceded by a series of three or four scans of decreasing size, a procedure helpful in centering the pit of interest in a suitably sized scan. These preliminary scans likely reduce the local density of adsorbed material to something like steady-state values. The low intrinsic mobility of adsorbed ions at terrace sites helps account for an important difference between the results of linear scanning on calcite and linear scanning on brushite.4 In brushite, local deposition was much faster when most of the linear scan took place on the upper terrace, outside the pit, than when most of the linear scan took place on the lower terrace, inside the pit. This is attributed to the rapid diffusion of adsorbed material inside the pit to the pit edges, which lowers the concentration of material inside the pit relative to that outside the pit. Outside the pit, the nearest steps are typically several microns away, and surface diffusion has less effect on the density of adsorbed material. Thus, we expect a higher concentration of adsorbed material on the upper terrace than on the lower terrace. On calcite, no consistent difference in growth rates is observed between linear scanning on the upper terrace versus the lower terrace. The poor mobility of adsorbed material on the lower terrace in calcite prevents depletion by diffusion. In the absence of scanning, we expect that the areal densities of adsorbed material inside and outside the pit are roughly equal. In contrast to the low mobility of material sorbed on terraces, material sorbed along steps (ledges) appears to be quite mobiles at least along fast steps. The large deposit above the line scan in Figure 8 is presumably formed by material diffusing along a fast step edge of the pit. This transport corresponds to ledge diffusion, where loosely bound ion pairs move along the step. Given the checkerboard pattern of electrostatic charge along the surface, we propose that ledge diffusion involves ion pairs, where one ion “leapfrogs” over the other along the ledge.36 The high mobility of ion pairs at ledge sites explains the straightness of steps on calcite during growth and dissolution.16,17,37 In the case of relatively small pits, the formation of straight steps generally requires that most nucleated kinks propagate to a pit corner before other kinks are nucleated along the same step. For larger pits, this condition cannot apply. Kinetic Monte Carlo simulations suggest that the formation of straight steps takes place only for a narrow range of parameters;17 outside this range, curved or wavy steps are expected. A priori, one does not expect these material parameters to be so constrained. If loosely adsorbed material can quickly propagate along ledges before being incorporated at kinks, it will feed the kink annihilation (36) Nwe, K. H.; Langford, S. C.; Dickinson, J. T. J. Appl. Phys. 2005, 97, 043502. (37) McCoy, J. M.; LaFemina, J. P. Surf. Sci. 1997, 373, 288-299.

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events (i.e., filling in missing parts of the step) required to maintain a straight step. We expect that this high ledge mobility will constrain dissolution so that the corresponding descriptive parameters lie in the required narrow range. The high ledge mobility required to explain the extensive deposits in Figure 8 raises the question of the relative importance of kink nucleation (starting a new row of ions) versus kink propagation (deposition at the end of a preexisting ion row). Kink nucleation is required to account for the growth of finger like-protrusions during linear scanning at lower supersaturations in Figure 7. From the lengths of the projections in Figures 7 and 8, we determine that the number of kinks nucleated at σ ) 2.7 is four times the number nucleated at σ ) 1.1. In contrast, the total amount of deposited material is one hundred times greater at the higher supersaturation. Although other factors may play a role, it appears that the rate of kink nucleation (new rows) during linear scanning is much less sensitive to solution concentration than the rate of material deposition (new area). At high supersaturations, the nucleation of new terraces is a fundamental growth process on ideal crystal surfaces. (On typical crystals, dislocation spirals allow for continuous growth without terrace nucleation.) In this work, terrace nucleation is a relatively unstable process, resulting in the formation of hillocks some nanometers thick. This suggests that hillock formation is similar to droplet nucleation, where the minimum stable droplet may contain many ion pairs. Hillocks are not observed during tipinduced growth, presumably due to the mild abrasive action of the tip. Significantly, hillocks most often appear on the upper terraces of previously existing pits, as in Figure 6. This is consistent with the presence of a potential barrier along the pit edge (EhrlichSchwoebel barrier), which in many systems hinders diffusion of adsorbed material from the upper terrace into the pit. The constraint provided by this potential barrier would favor nucleation at these sites. We expect that nucleation on ideal terrace sites is much more difficult. The low mobility of material adsorbed at terrace sites, relative to the high mobility of material absorbed at ledge sites, presents a dilemma. Ions adsorbed at terrace sites have fewer near neighbors than ions at ledge sites, leading one to expect higher mobilities at terrace sites. The data appear to indicate just the opposite. The average residence time of ion pairs at terrace sites may in fact be too short to allow for significant diffusion. At terrace sites, larger molecular units, such as molecular squares or cubes, would be much more stable and relatively immobile. Larger units would help account for the very high deposition rates observed at high supersaturations, e.g., the 4000 ions per pass of the AFM tip inferred from the line scan image of Figure 8. These larger units would also serve as nuclei for the relatively large hillocks observed at even higher solution concentrations. Asymmetry of Growth Processes. As noted above, the rhombohedral pits observed in undersaturated aqueous solutions display two pairs of distinct crystallographic steps. Under the conditions of this work, deposition is especially rapid along one pair, here denoted fast steps,11,16,17,29 and correspondingly slow along the other pair, here denoted slow steps. The asymmetry between fast and slow steps is attributed to deposition of the carbonate unit. For instance, Paquette and Reeder show that growth asymmetry is reduced at higher CO32- concentrations, and greater at higher Ca2+ concentrations.38 The role of the carbonate ion is consistent with its large size and planar geometry. The role of crystallographic orientation is illustrated along in Figure 10, where the atomic positions are taken from Wyckoff.39 (38) Paquette, J.; Reeder, R. J. Geochim. Cosmochim. Acta 1995, 59, 735749.

Scanning-Induced Growth on Calcite

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material outside the pit is swept into the pit during preliminary scanning, we expect R < β. Equation 1 has solutions of the form

(

A(t) ) A0 +

Figure 10. Schematic diagram of the ideal atomic positions for Ca2+ and CO32- around the perimeter of an etch pit. Shown in lighter color are ion pairs shown in the positions required for deposition along a fast step (upper row of ions) and along a slow step (lower row of ions).

The diagram shows the ion positions along the perimeter of an ideal etch pit, with fast steps along the top and right edges, and slow steps along the lower and left edges. Shown in lighter color are CaCO3 ion pairs oriented for incorporation into the lattice, one along the upper fast step and one along the lower slow step. Along the fast step, the new carbonate ion lies on top of preexisting material, where it is not significantly constrained. In contrast, the edge of the new carbonate ion along the slow step fits underneath a preexisting carbonate ion, a strong steric constraint. The orientation of solvated carbonate ions being incorporated into slow steps must lie in a relatively narrow range. However, once in position, carbonate ions adsorbed along slow steps are bound more tightly than carbonate ions along slow steps.29 The steric and energetic constraints illustrated in Figure 10 are the cause for relatively rapid growth along fast steps versus slow steps in this work. In pure water at room temperature (dissolution), Liang et al. found that the velocities of fast steps were typically 2.3 times that of slow steps.29 This asymmetry is especially important for tip-induced growth, where a relatively large number of ions must be incorporated into the lattice in a short time, as many as 4000 ion pairs per pass of the tip in Figure 8. At these high rates, the deposition process may be best viewed as the formation and transport of particle clusters or mats along the step. This would help account for the smoothly continuous change in pit area versus time in Figure 4b, despite the spatial nonuniformity of deposition in the corresponding images of Figure 3. Kinetics of Scanning-Induced Growth. A simple model for scanning enhanced deposition can be constructed, assuming that the AFM tip sweeps adsorbed material from terraces sites and deposits it along fast steps. Some of the swept material is from sites within the pit. On the time scale of our observations (individual scans), the amount of this material swept to fast steps per unit time is reasonably assumed to be proportional to the pit area, A. Other material is swept from terraces sites outside the pit, which we take to be proportional to the scan area, S, minus the pit area. Then the change in pit area per unit time becomes

RS RS exp[-(β - R)t] β-R β-R

)

(3)

This solution is well approximated by a simple exponential, with a time constant τ ) (β - R)-1, as long as A(t) . RS/(β - R). Eventually, A(t) becomes comparable to RS/(β - R) and A(t) drops dramatically, in a superexponential fashion. A least-squares fit of eq 3 to pit areas from Figures 2 and 3, using the measured values of A0, are shown in Figure 4. The data of Figure 4 show that pits within pits (the middle pit in each case) fill in faster than the outermost pits. One could construct more complex models incorporating three terrace levels, but it is sufficient to note that material swept from the upper terraces tends to accumulate on the lower terraces, thus raising both R and β for the inner pits. Thus, the time constants for the decay of the middle pit areas are shorter than the time constants for the outer pits. This model neglects several aspects of tip-enhanced deposition that are important in some cases. For instance, the constants R and β would be affected by any change in the density of adsorbed material during the early stages of scanning. Such a change is evident when the imaged area was shifted in Figure 1. As noted above, much of this depletion in our other measurements would normally take place during preliminary scans, while the pit of interest is being centered in the image. Induced Growth in Biological and Industrial Settings. Several important industrial and biological processes involve mechanical stimuli in supersaturated solution. Fluids in the human body, for instance, are supersaturated with respect to several calcium-containing compounds; the deposition of calcium pyrophosphate dihydrate, hydroxyapatite, and octacalcium phosphate in the joints can play an important role in arthritic conditions.40 In the absence of pathology, one can envision that material deposition (biomineralization) along articulating surfaces would produce the highly smooth surfaces desired for joints through mechanisms described here. Although chemical mechanical polishing of semiconductor wafers and optical components typically involve material removal, it is likely that mechanical material deposition in shallow structures could play an important role in producing surfaces with near-atomic smoothness. The filling in of small pits would be energetically favored over the removal of entire surface layers to achieve a smooth surface. With care, the mild abrasive action of the polishing particles would prevent the growth of unwelcome deposits, even in somewhat supersaturated solutions. In future planarization technologies, mechanically stimulated crystal growth may prove a promising technique.

5. Conclusion

where R and β are constants. These constants would be proportional to the density of material adsorbed outside the pit, R, and inside the pit, β, respectively. Since some of the adsorbed

Continuous, low contact-force scanning can dramatically accelerate deposition along fast steps on calcite surfaces under supersaturated conditions. We provide evidence that this acceleration is due to the tip-induced transport of loosely bound material from terrace sites to nearby steps, followed by ledge diffusion and subsequent incorporation into the crystal. The amount of material deposited, as well as the apparently low mobility of the loosely bound material, indicate that the swept material involves clusters of many ions, rather than isolated ions or ion pairs.

(39) Wyckoff, R. W. G. Crystal Structures: Inorganic Compounds RXn, RnMX2, RnMX3, 2nd ed.; Interscience: New York, 1964; Vol. 2.

(40) Lomotan, E. R.; Zimmermann, B.; Lally, E. V. Rheumatol. Musculoskeletal Med. Primary Care 1999, 1, 1-10.

dA ) -R(S - A) - βA ) -RS - (β - R)A dt

(2)

6938 Langmuir, Vol. 22, No. 16, 2006

Images of deposition along fast steps during linear scanning show significant deposits hundreds of nanometers from the line scan. The simplest explanation for these deposits invokes diffusion along the step, corresponding to ledge diffusion in terrace-ledgekink models of crystal growth. These images are compelling evidence for the importance of ledge diffusion in the calcite system. Facile ledge diffusion explains why etch pits on calcite surfaces remain relatively straight over a large range of solution concentrations; otherwise, this would seem to require rather special material properties.17 Our studies may be relevant to new methods of planarization of surfaces as well as to biomineral-

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ization in supersaturated solutions, especially along articulating surfaces (e.g., joints), where both wear and deposition could occur. Acknowledgment. This work was supported by the National Science Foundation under Grant CMS-0409861 and by NIH under Contract No. HG-002647-01A1. Some of the equipment employed in this work was acquired under NSF Grant CHE-02-34726. LA0608359