Two-Dimensional Crystal Growth from Undersaturated Solutions

autophobic, never advancing over a lower terrace of the same material and never nucleating a second layer in undersaturated solutions (Figures 1C and ...
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Langmuir 2007, 23, 5852-5856

Two-Dimensional Crystal Growth from Undersaturated Solutions Anne E. Murdaugh,† Mary Liddelow,‡ Anneliese M. Schmidt,§ and Srinivas Manne*,† Department of Physics and Department of Materials Science & Engineering, UniVersity of Arizona, Tucson, Arizona 85721 ReceiVed December 7, 2006. In Final Form: March 21, 2007 The solubility of a substance is commonly understood as the minimum concentration necessary for the condensation of a solid phase from solution. Here we report the nucleation and growth of ionic compounds from aqueous concentrations on the order of 0.1 times the solubility. The condensation is catalyzed by a foreign substrate, and the new phase grows as a crystalline monolayer. Undersaturated growth is observed only in cases where the dissolved compound is isomorphic with the substrate and the interaction strength between a dissolved-ion/substrate-ion pair exceeds that between the two dissolved ions. These results are consistent with a simple model in which favorable ion-surface interactions lead to ion enrichment and supersaturation in the two-dimensional interfacial zone.

A solid cluster nucleating from a metastable solution must overcome a kinetic barrier arising from its unfavorable interfacial energy, and the size of this barrier determines the degree of supersaturation required for condensation to occur within an experimental time frame. If the solution is already in contact with a crystal of the solute material, then the energy barrier is eliminated and any solute in excess of solubility begins to condense immediately onto the crystal surface. A solution in contact with a foreign substrate is usually considered to be an intermediate system in which the interfacial energy barrier is reduced but not eliminated. Here, some supersaturation is commonly considered to be a requirement for epitaxial growth, with the amount depending on the chemical and physical compatibility between the substrate and solute. This model has been challenged by recent reports1,2 of semiconductor films grown from undersaturated solutions on certain foreign substrates (Ge on Si and Al0.8Ga0.2As on GaAs). These observations have so far been indirect (via calorimetry) and limited to semiconductor films in metallic solvents at concentrations near (>0.8×) the solubility. The results have been interpreted in terms of a global reduction of interfacial energy,1 but the molecular-level driving forces and the 2D growth mechanisms are not well understood. Although semiconductor heterostructures drive the technological interest in epitaxy, ionic crystals offer a scientifically accessible model system because they possess a wider variety of well-known lattice structures and spacings and their aqueous solution chemistry can be visualized at room temperature by atomic force microscopy (AFM).3-16 The adsorption of metal * Corresponding author. E-mail: [email protected]. † Department of Physics. ‡ Department of Materials Science & Engineering. § Now at Antares Group, Inc., Landover, MD 20785. (1) Hansson, P. O.; Albrecht, M.; Dorsch, W.; Strunk, H. P.; Bauser, E. Phys. ReV. Lett. 1994, 73, 444. (2) Jeganathan, K.; Qhalid Fareed, R. S.; Baskar, K.; Ramasamy, P.; Kumar, J. J. Cryst. Growth 2000, 212, 29. (3) Hillner, P. E.; Gratz, A. J.; Manne, S.; Hansma, P. K. Geology 1992, 20, 359. (4) Hay, M. B.; Workman, R. K.; Manne, S. Langmuir 2003, 19, 3727. (5) Dove, P. M.; Hochella, M. F. Geochim. Cosmochim. Acta 1993, 57, 705. (6) Teng, H. H.; Dove, P. M.; Orme, C. A.; De Yoreo, J. J. Science 1998, 282, 724. (7) Davis, K. J.; Dove, P. M.; De Yoreo, J. J. Science 2000, 290, 1134. (8) Hoffmann, U.; Stipp, S. L. S. Geochim. Cosmochim. Acta 2001, 65, 4131. (9) Liang, Y.; Baer, D. R. Surf. Sci. 1997, 373, 275. (10) Lea, A. S.; Hurt, T. T.; El-Azab, A.; Amonette, J. E.; Baer, D. R. Surf. Sci. 2003, 524, 63. (11) Jun, Y. S.; Kendall, T. A.; Martin, S. T.; Friend, C. M.; Vlassak, J. J. EnViron. Sci. Technol. 2005, 39, 1239.

ions on mineral lattices also plays an important role in geochemical weathering models17,18 and can lead to new strategies for freshwater remediation.19 Whereas previous AFM studies of epitaxial growth have usually focused on individual overgrowth/ substrate systems in supersaturated solutions, here we have investigated a wide variety of systems in undersaturated solutions (Table 1) in an effort to find the general conditions for film growth in subcritical environments. The substrates used were perfectly cleavable, sparingly soluble minerals that resulted in well-defined terrace-step structures on which growth could be monitored on imaging time scales. The most reproducible results were obtained on celestite (SrSO4), barite (BaSO4), and calcite (CaCO3) substrates, although some experiments were also performed on other carbonates and sulfates.20 The aqueous solute compounds were chosen across a range of parameters (e.g., lattice symmetry, spacing, and ion size) related to solute-substrate compatibility. Solutions of these sparingly soluble salts were prepared by mixing aliquots of soluble salt solutions (chloride or nitrate salts of the cation and sodium salts of the anion). The departure from solubility was calculated using the parameter β ≡ [C][A]/Ksp, with [C] and [A] being the molar cation and anion concentrations, respectively, and Ksp being the known solubility product. Carbonate solutions were handled differently because of the strong pH dependence of [CO32-], as described earlier;4 briefly, aliquots of the cation solutions were mixed with those of NaHCO3, the pH was adjusted using NaOH (usually in the pH range of 8.4 to 8.8), and β was calculated using the (12) Astilleros, J. M.; Pina, C. M.; Ferna´ndez-Dı´az, L.; Putnis, A. Geochim. Cosmochim. Acta 2000, 64, 2965. (13) Sa´nchez-Pastor, N.; Pina, C. M.; Astilleros, J. M.; Ferna´ndez-Dı´az, L.; Putnis, A. Surf. Sci. 2005, 581, 225. (14) Shtukenberg, A. G.; Astilleros, J. M.; Putnis, A. Surf. Sci. 2005, 590, 212. (15) Pina, C. M.; Becker, U.; Risthaus, P.; Bosbach, D.; Putnis, A. Nature 1998, 395, 483. (16) Becker, U.; Gasharova, B. Phys. Chem. Miner. 2001, 28, 545. (17) Krauskopf, K. B. Geochim. Cosmochim. Acta 1956, 10, 1. (18) Brown, G. E.; Parks, G. A. Int. Geol. ReV. 2001, 43, 963. (19) Sturchio, N. C.; Antonio, M. R.; Soderholm, L.; Sutton, S. R.; Brannon, J. C. Science 1998, 281, 971. (20) Only clear and colorless natural crystals were chosen for experiments. Crystals were cleaved using a sharp blade and a hammer and then glued to the sample puck and imaged in water within 1 h of cleaving. (The water used in these experiments was distilled and deionized with a minimum resistivity of 17.8 MΩ cm. All ionic salts were used as received from Sigma-Aldrich and had a minimum purity of 99%.) Only surfaces showing broad terraces (>500 nm) and faceted, monomolecular steps were used for growth experiments. All AFM images were captured in static solutions at room temperature by a Digital Instruments AFM (Nanoscope III or Dimension 3000) using cantilever spring constants of ∼0.6 N/m, imaging forces of ∼1-10 nN, and scan rates of 5-20 Hz at a scan angle of 90°. All images shown are unfiltered except for slope removal along each scan line.

10.1021/la063548d CCC: $37.00 © 2007 American Chemical Society Published on Web 04/25/2007

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Langmuir, Vol. 23, No. 11, 2007 5853 Table 1. Summary of Ionic Crystal Growth Resultsa

substrate

solute

(∆Gi-s - ∆Gi-i)/kT

CaCO3

BaCO3 CaC2O4‚H2O CaF2 CaMoO4 CaSO4‚2H2O CaWO4 SrCO3 CaSO4‚2H2O SrC2O4‚H2O BaMoO4 BaC2O4‚H2O BaCO3

-0.26 -0.37 +0.46 +1.47 +9.14 +0.95 -1.79 +4.51 -0.77 +5.79 +5.36 +3.17

CdCO3 MnCO3 BaSO4 PbSO4 PbSO4 SrSO4

-8.12 -5.01 -8.07 -2.61 +5.46 +8.07

SrSO4 BaSO4

CaCO3 SrSO4 BaSO4

Si GaAs

Ge Al0.8Ga0.2As

undersaturated growth?

Anisomorphic

description of observed growth

no no no no no no no no no no no no

3D growth at steps at β ) 950 wetting growth at β ) 2.9 no growth up to β ) 3.1 no growth up to β ) 6800 wetting growth at β ) 15 no growth up to β ) 14 000 wetting growth at β ) 7.9 no growth up to β ) 320 no growth up to β ) 2.4 no growth up to β ) 110 no growth up to β ) 63 no growth up to β ) 12

no no no no yes yes

wetting growth at β ) 5.4 wetting growth at β ) 380 3d growth at steps at β ) 93 wetting growth at β ) 2.5 wetting growth at β ) 0.06 wetting growth at β ) 0.03

Isomorphic

From Previous Work1,2 (+12.2)b yes yes (+14.6)b,c

film growth at ∼80% of solubility film growth at slightly undersaturated conditions

a Results are divided into the anisomorphic and isomorphic cases. ∆Gi-i is the dissociation free energy of the two solute ions, and ∆Gi-s is the dissociation free energy of the common ion (ion common to substrate and solute) and its complimentary substrate ion. ∆G values are determined from ∆G ) -ln Ksp, where Ksp values are taken from ref 27. (The compound forms were assumed to be those most favorable to form under aqueous conditions.) For the observed cases of undersaturated growth, the solute Ksp values were also checked against primary references.37,38 Note that anisomorphic systems never exhibit undersaturated growth, and isomorphic systems exhibit undersaturated growth only when ∆Gi-s > ∆Gi-i. b For these cases, because the Ksp values are not known in the particular liquid metal solvents used in the experiments, bond strengths in vacuum (also from ref 27) were used for comparison. When corrected for the presence of the solvent, the dissociation free energy values will decrease. c For this case, the average bond strengths were determined by weighting the interactions according to the reported stoichiometry.2 (See Supporting Information.)

corresponding value of [CO32-] for a solution equilibrated with the atmosphere21 (Supporting Information). Each substrate typically was first imaged in water to check for normal dissolution behavior before exchanging the fluid cell volume (>10×) with the foreign solution. Concentration effects were explored by exchanging dilute solutions with progressively higher concentrations, up to and including supersaturated solutions (β > 1). Each substrate compound was also imaged in solutions of the same compound to confirm that homoepitaxial crystal growth began near β ) 1 as expected. The growth results for foreign overlayers are summarized in Table 1. For most substrate/solute combinations, the condensation of a solute film occurred only in supersaturated solutions, if at all. However, for two cases, SrSO4 on BaSO4 (Figure 1) and PbSO4 on BaSO4 (Figure 2), film growth was observed at concentrations far below the solubility.22 Both systems showed wetting growth at very low threshold concentrations (β ) 0.03 for SrSO4 and β ) 0.06 for PbSO4), beginning at steps on the BaSO4 substrate. The speed of the growing step increased with concentration, with the PbSO4 growth exhibiting much faster step speeds than the SrSO4.23 At higher concentrations, step flow was accompanied by the nucleation and spread of islands on substrate terraces, (21) Stumm, W.; Morgan, J. J. Aquatic Chemistry: An Introduction Emphasizing Chemical Equilibria in Natural Waters; John Wiley & Sons: New York, 1981. (22) These observations survived several control experiments. Each case of undersaturated growth was repeated over at least four independent experiments using different substrates, cantilevers, and stock solutions. Simultaneous lateral force microscopy (shown in Figures 1D and 2D) confirmed that the growing films were chemically distinct from the substrate. Conversely, we also confirmed that the corresponding homoepitaxial systems, namely, SrSO4 on SrSO4 and BaSO4 on BaSO4, showed no film growth in undersaturated solutions. We minimized tip scanning effects on the growing film by using low imaging forces, and we also confirmed the similarity in images between scanned and previously unscanned areas.

beginning at β ) 0.2 for PbSO4 solutions (still undersaturated) and β ≈ 2 for SrSO4 solutions. For both compounds, step flow and/or island spread continued until the substrate was covered by a single molecular layer. This 2D overgrowth was perfectly autophobic, never advancing over a lower terrace of the same material and never nucleating a second layer in undersaturated solutions (Figures 1C and 2C). Atomic scans (not shown) revealed no statistically significant differences between the film and substrate lattices. After the 2D film was complete, additional layers could be grown only at high supersaturations (β > ∼30), in agreement with previous work.13 We now consider how a solute film can grow over a foreign substrate (where it must overcome lattice strain) under conditions where the solute fails to grow over its own crystal lattice. Two trends are noteworthy here (Table 1). First, undersaturated growth is never observed unless the substrate and solute are isomorphic. Second, among isomorphic cases, undersaturated growth is observed only in cases where the association of an aqueous ion and its substrate counterion is more favorable than that between the two aqueous species themselves. For instance, in the case of the SrSO4 solute on the BaSO4 substrate, the dissociation free energy of the aqueous SO42- species and the substrate Ba2+ species (9.43 × 10-20 J) exceeds that of the two dissolved species (6.12 × 10-20 J). These trends are also broadly consistent with previous semiconductor results (Table 1). In the undersaturated growth of Ge on Si, for example, the solute lattice is also isomorphic with the substrate, and the Ge-Si bond strength (5.00 × 10-19 J) exceeds that of Ge-Ge (4.54 × 10-19 J). (23) For a given sample and step orientation, measured step speeds ranged from ∼0.3 nm/s at β ) 0.06 to ∼0.8 nm/s at β ) 0.2 for PbSO4 and from ∼0.02 nm/s at β ) 0.03 to ∼0.1 nm/s at β ) 1.9 for SrSO4. Step speeds varied somewhat between samples and depended strongly on step orientation.

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Figure 1. AFM images of SrSO4 monolayer growth on a BaSO4 (001) cleavage plane. (All images show the same area.) (A) BaSO4 substrate in water. (B) Sample 68 min after exchanging with undersaturated SrSO4 solution at β ) 0.03. A crystalline monolayer of SrSO4 grows outward from the step edges at a rate of ∼0.02 nm/s. The measured step height (∼0.4 nm) is half the SrSO4 unit cell height, consistent with the known spacing of near-equivalent (002) planes.15,39 (C) Height and (D) LFM images of a sample 168 min after exchanging with SrSO4 solution at β ) 1.9. The step speed increases to ∼0.1 nm/s, and island nucleation begins with a perimeter growth rate of ∼0.3 nm/s. Note that islands growing near step edges never advance over the previously grown SrSO4 layer, indicating that the film is autophobic. No dissolution of the substrate was observed on the time scale of the experiment.

We propose that a strong interaction between a substrate species and a solubilized species creates a surface excess of the latter, leading to a local supersaturation that drives 2D condensation (Figure 3). This model is consistent with several observations. First, previous experiments have shown that conventional crystal growth (e.g., SrSO4 on SrSO4)24 occurs by step flow at low supersaturations, followed by island nucleation at higher supersaturations. This is exactly the growth progression observed here for the epitaxial films (at much lower bulk concentrations), suggesting that the interfacial solution layer is similarly supersaturated in both cases. Second, the observed autophobicity of the growing film is consistent with the comparatively weak attraction between solute ions and their own solid phase, leading to a smaller adsorption density over the film region. Thus, whereas a supercritical 2D solution above the substrate “feeds” the initial monolayer film, the 2D solution above the growing film remains subcritical, preventing the nucleation of further layers (compare left vs right halves of Figure 3B). Third, lateral force microscopy (LFM, Figures 1D and 2D) shows that the imaging tip experiences significantly lower friction over the growing film, which is consistent with the expected lower concentrations and weaker binding of adsorbed ions on top of the film region. The friction contrast is especially revealing here because in previous epitaxial systems requiring supersaturated solutions4 the overgrowth has always exhibited higher friction than the substrate (an observation then attributed to strain-induced defects in the overlayer). (24) Pina, C. M.; Enders, M.; Putnis, A. Chem. Geol. 2000, 168, 195.

Letters

Figure 2. AFM images of PbSO4 monolayer growth on a BaSO4 (001) cleavage plane. (All images show the same area.) (A) BaSO4 substrate in water. (B) Sample 22 min after exchanging with undersaturated PbSO4 solution at β ) 0.06. A crystalline monolayer of PbSO4 grows outward from the step edges at a rate of ∼0.3 nm/s. The PbSO4 step height (∼0.3 nm) is half a unit cell height, as in Figure 1.15,39 (C) Height and (D) LFM images of a sample 11 min after exchanging with PbSO4 solution at β ) 0.2. The step speed increases to ∼0.8 nm/s, and island nucleation begins with a perimeter growth rate of ∼3.8 nm/s. Note that islands growing near step edges never advance over the previously grown PbSO4 layer, indicating that the film is autophobic. No dissolution of the substrate was observed on the time scale of the experiment.

The above model is also consistent with two separate control experiments. Whereas SrSO4 solutions on the BaSO4 substrate showed undersaturated growth at β ) 0.03, the reverse system (BaSO4 solution on a SrSO4 substrate, Figure 4) showed no growth at all until high supersaturation (β ) 93). Here, the common anion (SO42-) has a less favorable interaction with the substrate counterion (Sr2+) than with the dissolved counterion (Ba2+), so no interfacial enrichment is expected. Moreover, when a BaSO4 substrate with pregrown SrSO4 islands was exposed to PbSO4 solution (result not shown), undersaturated growth of a PbSO4 monolayer was observed only over the substrate (BaSO4) region, where interfacial enrichment is expected, and not over the SrSO4 islands. Rough estimates of ion concentrations lend additional support to the interfacial enrichment model. Assuming Boltzmann statistics, the surface concentration of an adsorbed ion is inversely proportional to its desorption probability e-∆G/kT, where ∆G is the free energy cost of desorption, k is the Boltzmann constant and T is the temperature. We define the surface excess S of a dissolved ion as the ratio of its interfacial concentration on a foreign (f) substrate to that on a hypothetical reference (r) substrate of the solute crystal (e.g., for the cation, SC ≡ [C]f/[C]r ≈ e(∆Gf-∆Gr)/kT, where ∆Gf and ∆Gr are the dissociation free energies on the two substrates). Thus the interfacial concentration product is βf ≡ [C]f[A]f/Ksp ) SCSAβ, where SC and SA are the cation and anion surface excesses, respectively. For the SrSO4 solute on the BaSO4 substrate, the surface excesses SSO42- ≈ e(∆GBaSO4-∆GSrSO4)/kT ≈ 3000 and SSr2+ ≈ 1 (because Sr2+ interacts with the same ionic species in solution and at the surface), yielding βf ≈ 3000β. Thus, at the observed onset of 2D growth of SrSO4 on BaSO4

Letters

Langmuir, Vol. 23, No. 11, 2007 5855

Figure 4. AFM deflection images of BaSO4 growth on a SrSO4 (001) cleavage plane. (Both images show the same area.) (A) SrSO4 substrate in water. (B) Sample 14 min after exchanging with supersaturated SrSO4 solution at β ) 93. BaSO4 overgrowth is pebblelike and anchored at step edges. Unlike the reverse system (Figure 1), here the overgrowth is nonwetting, and the SrSO4 substrate continues to dissolve throughout the experiment, as seen by the movement of steps 1 and 2.

Figure 3. Schematic of proposed interfacial enrichment at a foreign substrate. (Arrows signify the surface diffusion of adsorbed ions.) (A) Adsorption of Sr2+ and SO42- onto a (hypothetical) reference SrSO4 substrate. When the solution is undersaturated, the interfacial concentration of Sr2+ and SO42- ions is insufficient for crystal growth. (B) Adsorption of Sr2+ and SO42- onto a foreign BaSO4 substrate. The strong attraction between solution SO42- and substrate Ba2+ species increases the interfacial concentration of SO42-. Even in undersaturated solution, the interfacial concentration product of SO42and Sr2+ exceeds the Ksp, leading to the condensation and growth of a monolayer step (right half). (A similar mechanism holds for Pb2+ PbSO4 condensation.)

(Figure 1B), β ) 0.03 w βf ≈ 90. Similar calculations yield βf ≈ 230β for PbSO4 on BaSO4, giving βf ≈ 14 at the onset of 2D growth for this case. In both cases, the condition for 2D nucleation (βf >1) is fulfilled in undersaturated solutions as long as the interfacial liquid is understood to be a unique region with its own distinct ion concentrations. (A more realistic calculation for βf would take into account electrostatic interactions within the adsorbed layer. However, this will not drastically change βf because whereas electrostatic repulsion within the anion layer would tend to reduce the anion surface excess, electrostatic attraction would tend to increase the cation excess to a similar degree.) The quantitative difference between SrSO4 and PbSO4 growth rates probably reflects differences in compatibility with the BaSO4 substrate. The Pb2+ ion (118 pm) is closer in size to the Ba2+ ion (136 pm) than is the Sr2+ ion (113 pm),25 and the rectangular PbSO4 unit cell on the cleavage plane (0.847 nm × 0.539 nm) is a closer match to BaSO4 (0.887 nm × 0.545 nm) than is SrSO4 (0.838 nm × 0.537 nm).26 Similarly, ∆GPbSO4(17.5kT) is closer to ∆GBaSO4(22.9kT) than is ∆GSrSO4(14.9kT).27 The unit cell and ion size comparisons suggest that PbSO4 should be more compatible with the substrate than SrSO4, consistent with the observations of faster step speeds for PbSO4 and smaller βf at the onset of PbSO4 nucleation. The free-energy comparisons indicate that the interfacial enrichment effect will be smaller for (25) Marcus, Y. Biophys. Chem. 1994, 51, 111. (26) Klein, C.; Hurlbut, C. S. Manual of Mineralogy, 20th ed.; John Wiley & Sons: New York, 1977; pp 349-350. (27) Lange’s Handbook of Chemistry, 16th ed.; Speight, J. G., Ed.; McGraw Hill: New York, 2005.

PbSO4 and that 2D growth will start at a slightly higher bulk concentration than for SrSO4, exactly as observed. Whereas βf >1 is necessary for undersaturated growth, it is not a sufficient condition, as evidenced by several anisomorphic systems showing no undersaturated growth despite favorable ion-substrate interactions (Table 1). In the case of BaMoO4 on BaSO4, for example, the attraction between Ba2+ (aq) and SO42(substrate) ions should lead to an interfacial product of βf ≈ 330β, yet epitaxial growth of BaMoO4 was never observed for any concentration tested up to β ) 110. Lattice strain likely places an additional constraint on growth, especially for anisomorphic systems, where steric constraints prevent the lowenergy planes of the film lattice from adopting the same symmetry as the substrate lattice. Although strain is difficult to quantify for anisomorphic lattices, rough estimates for isomorphic lattices show that the two systems exhibiting undersaturated growth satisfy the energy requirement for spontaneous wetting growth.28 The above analysis assumes that the 2D condensate in undersaturated growth is a pure phase of the original solute material. Although mixed phases (containing significant fractions of substrate Ba2+ ions) cannot be ruled out, several observations indicate that a pure phase is far likelier. First, the observed dissolution of the BaSO4 substrate was infinitesimal even in pure water, as reported previously.29 We estimate an upper limit of ∼10-5 monolayers of BaSO4 solubilized in the first 10 min of exposure, yielding a [Ba2+]/[Sr2+,Pb2+] ratio of at most ∼10-7 in the fluid cell volume before the onset of 2D undersaturated growth. Second, these tiny BaSO4 dissolution rates observed in water are likely further suppressed by the presence of Sr2+ or Pb2+ ions in the growth solution because these ions adsorb preferentially to substrate steps (Figures 1 and 2), where (28) A 2D film forms spontaneously when (γfilm + γstrain) < γsubstrate, where γfilm and γsubstrate are the aqueous interfacial tensions of the film and substrate materials, respectively, and γstrain is the lattice strain energy per unit area. Assuming that the strain is limited to the film lattice (which distorts to match the substrate lattice), the strain energy in vacuum γvac is B∆V/A ) Bh(∆A/A), where B is the bulk modulus of the film material, ∆V is the volume change in the unit cell, h is the height of the film, and ∆A/A is the fractional area change of the film lattice. This energy cost originates from Coulomb interactions between ions, which in an aqueous environment are reduced by the dielectric constant  of water, giving γstrain ) (Bh/)(∆A/A). Using published values (sources below) gives the following estimates: for SrSO4 on BaSO4, γfilm ) 87 mJ/m2, γstrain ) 8.4 mJ/m2, and γsubstrate ) 140 mJ/m2; for PbSO4 on BaSO4, γfilm ) 100 mJ/m2, γstrain ) 24 mJ/m2, and γsubstrate ) 140 mJ/m2. In both cases (γfilm + γstrain) < γsubstrate, consistent with the observation of wetting growth. (Sources: Klein, C.; Hurlbut, C. S. Manual of Mineralogy, 20th ed.; John Wiley & Sons: New York, 1977; pp 349-350. Smithells Metals Reference Book, 6th ed.; Brandes, E., Ed.; Butterworths: London, 1983. So¨hnel, O. J. Cryst. Growth 1982, 57, 101.) (29) Higgins, S. R.; Jordan, G.; Eggleston, C. M.; Knauss, K. G. Langmuir 1998, 14, 4967.

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dissolution normally occurs. Third, we observed no undersaturated growth in the reverse system of BaSO4 on the SrSO4 substrate (Figure 4), where the substrate dissolved continuously, creating a significant source of Sr2+ coexisting in solution with the original Ba2+ and SO42- species. In this case, even an impurity mole fraction of order 1 (estimated Sr2+/Ba2+) did not result in 2D film condensation until high supersaturations of BaSO4 were reached (∼10×). It therefore seems unlikely that solid solutions could account for 2D condensation from highly undersaturated solutions of SrSO4 in Figure 1. These observations are also consistent with the known rarity of Sr-Ba-SO4 solid solutions in natural crystals and with the strong compositional zoning of artificially cocrystallized samples observed previously.30 The current results on undersaturated film growth compliment other reports of subcritical condensation observed in markedly different interfacial systems. For example, surfactant solutions in contact with a solid surface can exhibit quasi-2D lyotropic phases of close-packed micelles at solution concentrations far below the 3D mesophase transition.31-33 These interfacial phases occur either when a hydrophobic surface interacts with surfactant tails via hydrophobic interaction31 or when a polar surface interacts with surfactant heads via electrostatic interactions.32,33 Another example of subcritical condensation is the underpotential deposition (UPD) of foreign metals on an electrode surface34 (i.e., the condensation of an initial 2D monolayer at electrode potentials positive of the bulk electroplating potential). Although (30) Prieto, M.; Frena´ndez-Gonza´lez, A.; Putnis, A.; Frena´ndez-Dı´az, L. Geochim. Cosmochim. Acta 1997, 61, 3383. (31) Manne, S.; Cleveland, J. P.; Gaub, H. E.; Stucky, G. D.; Hansma, P. K. Langmuir 1994, 10, 4409.

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the mechanism is not completely understood, results35,36 have shown that strong anion-electrode interactions play a central (and sometimes decisive) role in the occurrence of UPD. Taken together, these phenomena suggest that a 2D liquid layer mediating between a surface and the bulk solution is a feature common to all immersed solids and that favorable substrate-solute interactions can create supercritical interfacial zones in subcritical solutions. The simple guidelines for undersaturated growth reported here can serve as a useful starting point in the design of organic interfaces for biomimetic materials synthesis or for the sequestering of metal ions from aqueous systems. Acknowledgment. This research is based upon work supported by the National Science Foundation under grant no. 0094385 and University of Arizona TRIF Program funding. Supporting Information Available: Calculations of the interaction strength and β values. pH calculations and a plot of the ionic composition of pure water in equilibrium with atmospheric CO2 as a function of pH. Glossary of terms. This material is available free of charge via the Internet at http://pub.acs.org LA063548D (32) Manne, S.; Gaub, H. E. Science 1995, 270, 1480. (33) Lamont, R. E.; Ducker, W. A. J. Am. Chem. Soc. 1998, 120, 7602. (34) Herrero, E.; Buller, L. J.; Abruna, H. D. Chem. ReV. 2001, 101, 1897. (35) Magnussen, O. M. Chem. ReV. 2002, 102, 679. (36) Leiva, E. Electrochim. Acta 1996, 41, 2185. (37) Pina, C. M.; Putnis, A.; Astilleros, J. M. Chem. Geol. 2004, 204, 145. (38) Liu, H.; Papangelakis, V. Ind. Eng. Chem. Res. 2006, 45, 39. (39) James, R. W.; Wood, W. A. Proc. R. Soc. London, Ser. A. 1925, 109, 598.