pubs.acs.org/Langmuir © 2009 American Chemical Society
Friction Dependence on Growth Conditions in Epitaxial Films Anne E. Murdaugh and Srinivas Manne* Department of Physics, University of Arizona, Tucson, Arizona 85721 Received March 9, 2009. Revised Manuscript Received May 18, 2009 In investigating the growth kinetics of epitaxial films in situ by force microscopy, we have observed several instances where the lateral force contrast on the growing monolayer exhibits a strong dependence on the driving force for growth (i.e., solute concentration). We present results for three epitaxial growth systems in aqueous solutions: CaSO3 on CaCO3, PbSO4 on BaSO4, and BaSO3 on BaSO4. In each system, material grown at higher solute concentrations exhibits a friction higher than that of material grown at lower concentrations. These observations suggest a link between defect density and friction contrast in growing epitaxial films. An additional time-dependent behavior is observed in the CaSO3/CaCO3 system, indicating an annealing process.
Introduction Friction is a poorly understood and nonfundamental force, better described as a collection of forces, which has been estimated to cause an over $100 billion loss of gross domestic product annually due to a reduction in device efficiencies and lifetimes.1 For two macroscopic surfaces sliding against each other, the friction force is often approximately proportional to the normal force (Amontons’ law), as long as the surfaces are dry, rough, and wear by plastic deformation.2 At the atomic scale, sliding consists of successive stick-slip motions between the lattices of the opposing surfaces. Modeling this motion as a spring-loaded particle in a periodic potential, Tomlinson3 derived an average lateral force proportional to the normal force, providing a theoretical justification for Amontons’ law under certain conditions. The advent of atomic force microscopy (AFM) and frictional or lateral force microscopy (LFM) has led to direct investigations of friction and motion at the atomic level.4,5 The AFM/LFM tip is often modeled as a single asperity moving over a surface, thus reducing the complications inherent to large interacting surfaces. Lateral forces have been shown to depend on many factors, including cantilever stiffness, temperature, scan parameters, tipsample interaction, and tip and sample wear.2,6,7 Recent simulations have also shown that an atomic vacancy defect can trap a single-asperity tip, causing a considerable increase in the lateral force near the defect;8 larger defect densities are, therefore, expected to correlate to higher frictional forces. The quantitative interpretation of friction contrast on heterogeneous surfaces directly depends on which of the above factors are considered the dominant sources of friction. Ionic crystals offer an appealing platform for studying nanoscale frictional forces. Their physical and chemical properties are *Corresponding author. E-mail:
[email protected]. (1) Krim, J. Surf. Sci. 2002, 500, 741–758. (2) Gnecco, E.; Bennewitz, R.; Gyalog, T.; Meyer, E. J. Phys.: Condens. Matter 2001, 13, R619–R642. (3) Tomlinson, G. A. Philos. Mag. 1929, 7, 905. (4) Binnig, G.; Quate, C. F.; Gerber, C. Phys. Rev. Lett. 1986, 56, 930–933. (5) Mate, C. M.; McClelland, G. M.; Erlandsson, R.; Chiang, S. Phys. Rev. Lett. 1987, 59, 1942–1945. (6) Harrison, J. A.; White, C. T.; Colton, R. J.; Brenner, D. W. Phys. Rev. B 1992, 46, 9700. (7) Carpick, R. W.; Salmeron, M. Chem. Rev. 1997, 97, 1163–1194. (8) Sokolov, I. Y. Tribol. Lett. 2002, 12, 131–134.
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well-known, and their aqueous solution chemistry can be monitored in situ by AFM;9-22 recent work has shown that LFM can distinguish between the substrate and a foreign monolayer film during epitaxial growth.18 Various explanations have been offered for this friction contrast, including strain-induced defects from lattice mismatch,18 differences between the adsorbed-ion atmospheres over the substrate and overgrowth,23 and differences in dehydration enthalpy between the two materials.24 Here, we show that the lateral force contrast of an overgrowth region can also depend on the growth conditions, specifically, the solute concentration during growth. Even on a chemically homogeneous overgrowth layer, regions grown at higher concentrations (larger driving force) show a friction greater than that of those grown at lower concentrations. Although this phenomenon was observed in several systems, we choose to focus the discussion on three specific ones: (1) CaSO3 on CaCO3, (2) PbSO4 on BaSO4, and (3) BaSO3 on BaSO4. The three cases include anisomorphic lattices (systems 1 and 3) and isomorphic lattices (system 2), anion substitutions (systems 1 and 3) and cation substitutions (system 2), and growth from supersaturated solutions (system 1) and from undersaturated solutions (systems 2 and 3). The apparent generality of friction dependence on growth concentration leads us to hypothesize that this phenomenon is linked to defect density in the growing epitaxial films. (9) Hillner, P. E.; Gratz, A. J.; Manne, S.; Hansma, P. K. Geology 1992, 20, 359. (10) Dove, P. M.; Hochella, M. F. Geochim. Cosmochim. Acta 1993, 57, 705. (11) Liang, Y.; Baer, D. R. Surf. Sci. 1997, 373, 275. (12) Teng, H. H.; Dove, P. M.; Orme, C. A.; De Yoreo, J. J. Science 1998, 282, 724. (13) Pina, C. M.; Becker, U.; Risthaus, P.; Bosbach, D.; Putnis, A. Nature 1998, 395, 483. (14) Astilleros, J. M.; Pina, C. M.; Fernandez-Dı´ az, L.; Putnis, A. Geochim. Cosmochim. Acta 2000, 64, 2965. (15) Davis, K. J.; Dove, P. M.; De Yoreo, J. J. Science 2000, 290, 1134. (16) Hoffmann, U.; Stipp, S. L. S. Geochim. Cosmochim. Acta 2001, 65, 4131. (17) Becker, U.; Gasharova, B. Phys. Chem. Miner. 2001, 28, 545. (18) Hay, M. B.; Workman, R. K.; Manne, S. Langmuir 2003, 19, 3727. (19) Lea, A. S.; Hurt, T. T.; El-Azab, A.; Amonette, J. E.; Baer, D. R. Surf. Sci. 2003, 524, 63. (20) Jun, Y. S.; Kendall, T. A.; Martin, S. T.; Friend, C. M.; Vlassak, J. J. Environ. Sci. Technol. 2005, 39, 1239. (21) Sanchez-Pastor, N.; Pina, C. M.; Astilleros, J. M.; Fernandez-Dı´ az, L.; Putnis, A. Surf. Sci. 2005, 581, 225. (22) Shtukenberg, A. G.; Astilleros, J. M.; Putnis, A. Surf. Sci. 2005, 590, 212. (23) Murdaugh, A. E.; Liddelow, M.; Schmidt, A. M.; Manne, S. Langmuir 2007, 23, 5852–5856. (24) Higgins, S. R.; Hu, X. M.; Fenter, P. Langmuir 2007, 23, 8909–8915.
Published on Web 08/10/2009
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Experimental Details Only clear and colorless natural BaSO4 and CaCO3 crystals were chosen for the experiments. Crystals were cleaved using a sharp blade and a hammer, then glued to a sample puck covered with freshly cleaved mica. These were then cured for ∼40 min at ∼350 K and exposed to UV light (1 μm) and faceted, monomolecular steps were used, allowing for growth to be monitored at imaging time scales. Solutions of the sparingly soluble salts CaSO3, PbSO4, and BaSO3 were prepared by mixing aliquots of soluble salt solutions (chloride or nitrate salts of the cation and sodium salts of the anion). All ionic salts were used as received from Sigma-Aldrich and had a minimum purity of 99%. The departure from solubility was calculated using the parameter β [C][A]/Ksp, where [C] and [A] are the molar cation and anion concentrations, respectively, and Ksp is the known solubility product.26,27 All AFM images were captured in static solutions at room temperature by a Digital Instruments Nanoscope III AFM, using triangular cantilevers with a spring constant of ∼0.6 N/m, with imaging forces of ∼1 to 10 nN, scan rates of 5-15 Hz, and a scan angle of 90. Imaging forces and scan rates were kept constant throughout each individual experiment. All images shown are unfiltered except for slope removal along each scan line and background polynomial removal. Each substrate was, first, imaged in water to check for normal, faceted dissolution behavior. The fluid cell volume was then exchanged liberally (>10 times) with the foreign solution over an exchange time of ∼10 to 30 s. It was often essential to continue imaging throughout the exchange process, to capture the rapid surface changes that resulted. Imaging was continued in standing solution thereafter.
Results and Discussion Each epitaxial system was imaged continuously over a period of hours, first, in pure water and then in solutions of increasing solute concentration. Representative height and friction images are shown for the systems CaSO3 on CaCO3 (Figure 1), PbSO4 on BaSO4 (Figure 2), and BaSO3 on BaSO4 (Figure 3). Despite differences in detail, these epitaxial growth sequences share some common features summarized below. (i) At low solute concentrations (just above those needed for growth), epitaxial growth begins at preexisting substrate steps and advances as a monomolecular wetting film along the lower terrace (e.g., Figures 1C, 2C, and 3C). The onset of growth occurs at drastically different concentrations, namely, β = 6 for CaSO3 on CaCO3, β = 0.06 for PbSO4 on BaSO4, and β = 0.001 for BaSO3 on BaSO4. The under(25) The dissolution and growth behavior of samples exposed to ultraviolet light showed no difference from earlier experiments in which the samples were not cured. The practice was put in place after occasional trouble with contaminated samples. (26) The Ksp values used were 6.8 10-8 for CaSO3, 8.0 10-7 for BaSO3, and 2.53 10-8 for PbSO4. See: Masson, M. R.; Lutz, H. D.; Engelen, B. In Sulfites, Selenites and Tellurites; Kertes, A. S., Ed.; Solubility Data Series; Pergamon Press: Oxford, U.K., 1986; Vol. 26, pp 187 and 241. Clever, H. L.; Johnston, F. J. J. Phys. Chem. Ref. Data 1980, 9, 751. (27) The hydrated phase of CaSO3 creates some ambiguity in the calculation of β. Although CaSO3 3 1/2H2O is the most thermodynamically stable phase, the CaCO3 substrate may create a templating effect that favors anhydrous CaSO3. For consistency in the β calculations, we will assume the anhydrous form. See: Arai, Y.; Yasue, T.; Nagata, N.; Shino, H. Bull. Chem. Soc. Jpn. 1982, 55, 738–741.
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saturated growth in the latter two cases is explained by an interfacial enrichment effect, as described elsewhere.23,28 (ii) LFM images reveal a marked friction contrast between the substrate and the epitaxial film (e.g., Figures 1D, 2D, and 3D). Consistent with previous observations,18,23 the epitaxial film requiring β > 1 shows a friction higher than that of the substrate (Figure 1D), whereas the two films that can grow in undersaturated solutions show a friction lower than that of the substrate (Figures 2D and 3D). The contrast mechanism is discussed in detail below. (iii) LFM also reveals friction contrast within the monolayer films themselves, with regions grown at higher concentration exhibiting a friction higher than that of those grown at lower concentration (Figures 1H, 2F, and 3F). This holds true regardless of the friction contrast between the film and substrate. Growth at higher β generally occurs by the birth and spread of monomolecular islands over regions of the substrate left uncovered by the step flow at low β. In Figures 1H and 3F, the islands coalesce too quickly to image. In Figure 2E,F, the islands are fewer and larger (visible near the bottom) and are accompanied by faster step flow. These trends were tested by several control experiments. Each epitaxial system was observed in at least three independent experiments using different samples and cantilevers, ruling out cantilever variations as the source of the trends. Friction contrast between the film and substrate was never observed when the two materials were identical, that is, for CaCO3 on CaCO3 or for BaSO4 on BaSO4. Friction contrast within a growing epitaxial monolayer was never observed when the existing growth solution was exchanged with a solution of the same concentration. Throughout each experiment, tip velocity, normal force, and temperature were kept constant. The observation of friction dependence on the growth conditions imposes new constraints on the contrast mechanism, which is, at present, poorly understood. Early work suggested that the (then universally observed) higher friction on epitaxial films was caused by strain-induced defects during growth, although effects due to the ionic solution environment were not ruled out.18 Subsequent work showed that certain epitaxial films could grow in undersaturated solutions and exhibited a friction lower than that of the substrate, and both effects were attributed to ionic enrichment over the substrate phase.23 Others have presented evidence for friction contrast dependent on the normal force6 and on compositional variations in mixed epitaxial films29 and have argued for friction contrast based on the surface dehydration enthalpy.24 These mechanisms are not mutually exclusive, and the friction contrast may be a combination of these factors. Although the present work does not give a definitive answer, the correlation of increased film friction with increased driving force for nucleation implicates film defects as the mechanism underlying the friction change. The low-β and high-β regions of (28) Briefly, the PbSO4/BaSO4 interface becomes enriched due to the large association free energy between the aqueous SO42- and substrate Ba2þ ions. (For BaSO3 on BaSO4, the corresponding pair is aqueous Ba2þ and substrate SO42ions.) This lowers the bulk threshold concentration for nucleation in these systems, by a factor of 230 for PbSO4/BaSO4 and 7400 for BaSO3/BaSO4, estimated from the differences in association free energies of the relevant ion pairs. In both systems, solutions undersaturated with respect to the solute material behave like supersaturated solutions at the foreign surface. (29) Higgins, S. R.; He, X. M. Geochim. Cosmochim. Acta 2005, 69, 2085–2094.
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Figure 1. AFM images showing the same area of a CaCO3 (1014) cleavage plane in the presence of CaSO3 solutions of varying concentrations. The horizontal scale bar represents 1 μm. The vertical color bar represents 0-5 nm for height and 0-0.1 V for friction images. (A) Height and (B) friction images of CaCO3 in pure H2O. Dotted lines show representative steps, and the circle indicates a mesa of interest. (C) Height and (D) friction images 5 min after introduction of the β= 6.0 CaSO3 solution. A CaSO3 monolayer nucleates at the “obtuse” steps18 and grows anisotropically along the Æ441æþ and Æ481æþ directions (arrows, step speed ∼ 1.3 nm/s). The smaller etch pits are now completely filled with CaSO3 overgrowth, making them effectively invisible in (C). However, these pits are observable in (D). (E) Height and (F) friction images 32 min after introducing the β=6.0 solution, showing a nearly complete monolayer of CaSO3. The dark areas in (F) reveal patches of substrate (e.g., the circled mesa) left permanently bare either by solution conditions insufficient for island nucleation or by the anisotropic step flow at β=6.0. All other areas accessible to the step flow from the obtuse steps are covered with CaSO3. (G) Height and (H) friction images of the sample immediately upon introduction of the β=62 CaSO3 solution (indicated by scan noise). CaSO3 island nucleation and coalescence quickly cover the exposed substrate in (F). The new CaSO3 growth at β=62 shows a friction higher than that of the earlier growth at β = 6.0. (I) Height and (J) friction images of the sample 6 min after introduction of β = 62 CaSO3. Overgrowth returns to uniform friction contrast for all areas. The CaSO3 topography in (I) is a perfect mask of the initial substrate topography in (A). 9794 DOI: 10.1021/la9008448
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Figure 2. AFM images showing the same area of a BaSO4 (001) cleavage plane in the presence of PbSO4 solutions of varying concentrations. The horizontal scale bar represents 1 μm, and the vertical color bar represents 0-3 nm for height and 0-0.2 V for friction images. (A) Height and (B) friction images of the BaSO4 substrate in pure H2O. (C) Height and (D) friction images of the sample 29 min after introduction of β = 0.06 PbSO4. The PbSO4 overgrowth (bars, step velocity ∼ 0.3 nm/s) has a friction lower than that of the substrate, as described in previous work.23 (E) Height and (F) friction images of the sample 16 min after exchange with β = 0.3 PbSO4, showing an increased step velocity (∼0.8 nm/ s) and island nucleation. The new PbSO4 growth at β = 0.3 shows a friction higher than that of the earlier growth at β = 0.06 (although both still show a friction lower than that of the substrate). (G) Height and (H) friction images of the sample 3 min after exchange with pure H2O. Growth from the β = 0.06 solution remains on the substrate, whereas growth from β = 0.3 was dissolved immediately and completely. Some pitting of the remaining overgrowth is visible in (G). See Figure 4 for profiles of areas indicated by lines 1, 2, and 3. (A portion of this growth sequence has been published previously.23)
the film have nominally identical topography and surface chemistry, so they should have similar dehydration enthalpies and similar adsorbed-ion atmospheres in a given solution environment. The chief distinction between the low-β and high-β regions is the faster growth rate of the high-β regions and their switch Langmuir 2009, 25(17), 9792–9796
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Figure 4. Section profiles of areas indicated by lines drawn in Figure 2D,H. Friction contrast between the overgrowth and substrate reduces significantly from area 1 (solid line) to areas 2 and 3 (dotted and dashed lines, respectively), indicating an increase in overgrowth friction correlated with the degree of dissolution. Compared with the friction contrast of section 1, the contrast of section 2 is reduced by 50% and that of section 3 by 65%.
Figure 3. AFM images showing the same area of a BaSO4 (001) cleavage plane in the presence of BaSO3 solutions of varying concentrations. The horizontal scale bar represents 1 μm. The vertical color bar represents 0-2 nm for height and 0-0.02 V for friction images. (A) Height and (B) friction images of the BaSO4 substrate in pure H2O. The circle indicates a mesa of interest. (C) Height and (D) friction images of the sample 60 min after introduction of the β = 0.001 BaSO3 solution. A BaSO3 monolayer grows outward from substrate steps (dotted lines), eventually surrounding the mesa in (A). The BaSO3 layer has a friction lower than that of the substrate, so the original mesa is still visible in (D). Arrows indicate the current growth edge of BaSO3 at β = 0.001 (step velocity ∼ 0.2 nm/s). (E) Height and (F) friction images of the sample 30 min after introduction of β = 0.005 BaSO3. Growth occurred as island nucleation and coalescence on the remaining substrate (not shown), and the BaSO3 topography in (E) is a perfect mask of the initial substrate in (A). The new growth at β = 0.005 shows a friction slightly higher than that of the earlier growth at β = 0.001 (edge shown by arrows). The mesa, now covered with the overgrowth, is again visible in the topography images.
from step flow to island nucleation and coalescence. In threedimensional crystallization, increased supersaturation and increased nucleation density are known to lead to a greater density of kinetically trapped defects,30 and we expect an analogous phenomenon for two-dimensional growth. Two other observations give circumstantial evidence for the role of defects in the friction contrast between low-β and high-β films. First, the friction contrast in the CaSO3 film fades over a period of minutes (compare images H and J in Figure 1), indicating a slower annealing process after the fast initial condensation. (To a smaller degree, this was also evident in the BaSO3 film of Figure 3.) A similar annealing process has been observed in self-assembled monolayers, in which 2D Ostwald ripening (30) Strickland-Constable, R. F. AIChE Symp. Ser. 1972, 68, 1–7.
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converts an initially polycrystalline film into a dominant epitaxial orientation over a period of minutes to hours.31-33 The second observation linking defect density with growth conditions comes from the subsequent dissolution behavior of the epitaxial film. A comparison of images F and H in Figure 2 shows that the PbSO4 film grown at high β dissolves immediately upon exchange with pure water, whereas the film grown at low β dissolves more slowly over several minutes. Defects act as nucleation sites for etch pits, so areas with higher defect densities are expected to dissolve more quickly.18 In the time it takes for the high-β region to dissolve completely, etch pits only just begin to appear in the low-β region (see Figure 2G). Figure 4 displays friction profiles across the low-β overgrowth in the growth solution (section 1) and in water (sections 2 and 3), showing that the pitting in Figure 2G,H clearly correlates with an increase in overgrowth friction (i.e., a decrease in LFM contrast between the overgrowth and substrate). This correlation is apparent even within a single image because regions scanned near the end of a scan have been exposed to solvent longer than those near the beginning. In Figure 2H, which is raster-scanned from bottom to top in 70 s, the overgrowth region encountered later in the scan (section 3 in Figure 4) is more extensively pitted and shows a friction higher than that of the one encountered earlier in the scan (section 2). Repeated attempts to quantify the defect density met with little success. Uncertainties in the tip shape and wear characteristics gave inconsistent measurements of absolute friction forces.34 Moreover, we know of no theoretical framework that directly relates defect density and friction coefficient, although the correlation between the two has been noted.8 The nature of the defects is also open to question. Some authors report evidence of mixed films (due to codissolution of the substrate) whose exact (31) Gong, J. R.; Lei, S. B.; Pan, G. B.; Wan, L. J.; Fan, Q. H.; Bai, C. L. Colloids Surf., A 2005, 257-58, 9–13. (32) Stabel, A.; Heinz, R.; Deschryver, F. C.; Rabe, J. P. J. Phys. Chem. 1995, 99, 505–507. (33) Samori, P.; Mullen, K.; Rabe, H. P. Adv. Mater. 2004, 16, 1761. (34) Tip wear sometimes led to a slow drift of the friction contrast over tens of minutes. However, this drift cannot explain the observed sudden changes in the overgrowth friction that correlate with the introduction of a more concentrated growth solution. Similarly, any sample wear effects would show a dependence on the time of exposure to scanning, leading to gradual changes within a single overgrowth zone. The observed results are, therefore, not consistent with wearrelated artifacts.
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composition changes with solution conditions.29 Although substitutional defects are possible, we do not believe they are dominant in the experiments reported here. The BaSO4 substrate dissolves very little even in pure, static water (we estimate
