Dynamic Inhibition of Calcite Dissolution in Flowing Acidic Pb²⁺ Solutions

Abstract

Reactions of mineral surfaces with dissolved metal ions at far-from-equilibrium conditions can deviate significantly from those in near-equilibrium systems due to steep concentration gradients, ion–surface interactions, and reactant transport effects that can lead to emergent behavior. We explored the effect of dissolved Pb²⁺ on the dissolution rate and topographic evolution of calcite (104) surfaces under far-from-equilibrium acidic conditions (pH 3.7) in a confined single-pass laminar-flow geometry. Operando measurements by digital holographic microscopy were conducted over a range of Pb²⁺ concentrations ([Pb²⁺] = 0 to 5 × 10^–2 M) and flow velocities (v = 1.67–53.3 mm s^–1). Calcite (104) surface dissolution rates decreased with increasing [Pb²⁺]. The inhibition of dissolution and the emergence of unique topographic features, including micropyramids, variable etch pit shapes, and larger scale topographic patterns, became increasingly apparent at [Pb²⁺] ≥ 5 × 10^–3 M. A better understanding of such dynamic reactivity could be crucial for constructing accurate models of geochemical transport in aqueous carbonate systems.

Short abstract

Operando observations reveal how dissolved Pb²⁺ ions can inhibit the dissolution of carbonate minerals in anthropogenically disturbed natural systems.

Introduction

Reactions of mineral surfaces with dissolved metal ions under far-from-equilibrium conditions have crucial implications for geochemical transport in environmental and engineered systems. Such reactions play a key role in nutrient cycling, contaminant transport, and carbon sequestration, thereby impacting ecosystem health, groundwater quality, and global climate change.¹⁻⁷ The interplay between chemical reactivity and transport processes under these conditions can lead to feedback mechanisms that may significantly alter system behavior.⁸⁻¹³

Carbonate minerals such as calcite play a central role in biomineralization, contaminant transport, global CO₂ cycling, long-term CO₂ sequestration, and industrial mineral processing.^{1,4−7,14−16} Despite considerable knowledge of carbonate reactivity under near-equilibrium conditions, the understanding of carbonate mineral–fluid reactions under far-from-equilibrium conditions remains limited, especially for confined fluid flow within pore spaces. The majority of (bio)geochemical reactions occur within interconnected pore spaces, where fluid advection occurs in response to gravity and hydraulic pressure gradients.^17,18 In porous media, mineral reactivity is governed by the complex balance of interfacial reactions and advective–diffusive reactive transport in the fluid phase boundary layer.¹⁸⁻²¹ Consequently, a comprehensive understanding of the coupled evolution of hydraulic and chemical properties is essential for predicting the transport and sequestration of contaminants in porous mineral-water systems.

Recent observations reported complex reactivity patterns of single-crystal calcite (104) cleavage surfaces under far-from-equilibrium conditions in a microfluidic cell.²² The experiments were performed in acidic solutions (pH = 3.5) with ∼5 × 10^–3 M dissolved Pb²⁺ in which the initial undersaturation of calcite led to calcite dissolution and the surface incorporation of 2–4 monolayers (MLs) of Pb²⁺ where 1 ML corresponds to the theoretical coverage of adsorbate cations that substitute for all Ca²⁺ atoms in one calcite unit-cell layer (∼3 Å thick). Ex situ observations with state-of-the-art micro/nanoanalytical tools showed that, at the early stages of the reaction, this confined geometry led to the formation of microscale roughness and spatially variable patterns in terms of the amount of dissolved calcite as well as the coverage of Pb²⁺ incorporated into the calcite surface. These patterns were interpreted as a manifestation of emergent behavior that occurs under the combined influence of interfacial reactivity (i.e., calcite dissolution and Pb²⁺ sorption) and advective–diffusive reactive transport within the flow channels.²² However, these experimental results were obtained by ex situ observations after extended reaction times, and therefore, little understanding was achieved concerning how these reaction patterns evolved with time. Similarly, microscale roughness and subμm-scale spatially variable dissolution have been observed during the reaction of calcite microcrystals with dissolved Pb²⁺ in droplets under far-from-equilibrium conditions.^5,6 It was speculated that this behavior resulted from the localized inhibition of calcite dissolution. However, in both cases, the specific role of dissolved Pb²⁺ in controlling this behavior was not clearly established.

It is well-known that calcite reactivity can be inhibited by the presence of dissolved metal ions, especially from observations showing that the adsorption of metal impurities to steps inhibits step flow.²³⁻²⁵ Powder-based studies have also shown that inhibition of calcite dissolution occurs for a range of metal inhibitor concentrations in which the degree of inhibition can be described with an adsorption isotherm.²⁶⁻²⁸ However, much about the inhibition process is not well understood. The high sorbed Pb coverages observed previously²² imply that the inhibition process that controls this behavior at sustained far-from-equilibrium conditions is distinct from the known inhibition of step flow at dilute ion concentrations. Notably, this inhibition of reactivity is not incorporated into current reactive transport models; the nature of how these reactions influence the evolution of interfacial topography has not been well-explored, including the nature of the dissolution process and its dependence on the inhibitor concentration.

Here, we report new operando observations that show how the presence of dissolved Pb²⁺ alters the reactivity of the calcite (104) surface under highly undersaturated conditions. Specifically, we quantify the spatial and temporal evolution of subμm-scale topography that occurs during the reaction of the calcite surface with acidic solutions with and without dissolved Pb²⁺ under confined flow conditions. These observations, performed systematically as a function of fluid flow velocity and [Pb²⁺], show that the characteristic surface topographies, including local surface roughness manifested by micropyramids and systematic changes in etch pit shapes, evolved into larger scale dissolution patterns concomitant with a decreasing calcite dissolution rate as a function of increasing [Pb²⁺]. These findings are an important step toward developing a more predictive understanding of reactive transport processes involving carbonates in the presence of dissolved metal ions.

Materials and Methods

Materials and Reaction Conditions

Optically clear calcite crystals from Brazil were cut into rectangular bars having their long axes perpendicular to the (104) plane, and these bars were cleaved with a razor blade to create fresh (104) surfaces having a cross-sectional area of approximately 6 × 4 mm². An evaporated Au film (∼100 nm thick) was deposited onto a portion of each cleavage surface, while the remainder of the surface was masked with Teflon tape. This Au film served as a chemically inert fiducial plane against which the measured height changes of the dissolving surface were referenced. The calcite (104) surfaces were then rinsed briefly with jets of ethanol and deionized (DI) water prior to the reaction with experimental solutions in the millifluidic cell. The reactant solutions (with [Pb²⁺] ranging from 5 × 10^–9 to 5 × 10^–2 M) were prepared by dissolving reagent grade Pb(NO₃)₂ salt (Sigma-Aldrich, ≥99.95% trace metals basis) in 18 MΩ·cm DI water and adjusting the pH to 3.7 by addition of dilute reagent grade HCl.

The extent of chemical disequilibrium was controlled by the initial solution composition, solution flow rate, and reaction time. Acidic input solutions (pH = 3.7), with and without dissolved Pb²⁺, were reacted with calcite (104) surfaces within millifluidic channels (0.5 mm height × 4.0 mm width; details of the millifluidic reaction cell can be found in the Supporting Information). At this pH, the rate-limiting step in calcite dissolution occurs predominantly as

1

and thereby the dissolution rate is pH-dependent.²⁹ Observations were made under continuous flow at velocities ranging from 1.67 to 53.33 mm s^–1. Some samples were reacted in a microfluidic cell mounted directly on a calcite (104) surface (details about the microfluidic reaction cell can be found in our previous report, but it differs primarily in having a vertical height of 20 μm²²). No precipitation of secondary phases was observed in these measurements, indicating that the pH was always below the value at which we expect that PbCO₃ would become saturated as predicted by equilibrium speciation calculations (e.g., pH ∼ 4.9 with [Pb²⁺] = 5 × 10^–3 M and log₁₀ pCO₂ = −2.42 atm, Figure S18).

Measurement of Surface Height Changes and Dissolution Rates

Sample height evolution was measured in operando using a DHM-R2100 (Lyncée Tec) digital holographic microscope (DHM) in reflection mode (shown schematically in Figure S1a). In this instrument, a laser beam (with λ = 666 nm) is split into reference and object beams, and the object beam is reflected by the sample and interferes with the reference beam to create a hologram. Holograms reveal both intensity and phase (ϕ) images, the latter revealing the surface height profile, h(x,y). One complication in the interpretation of the phase images is that the measured phase is uncertain to multiples of 2π (corresponding to height differences of λ/2 = 333 nm), and this can be significant when there is significant topographic variation in the sample height (either across the sample at a given time or as a function of time at a given position). We address this by treating the time-series phase images as a three-dimensional data set of ϕ(x,y,t) that is unwrapped using the Matlab “unwrap” function, along the temporal axis before converting to height: h(x,y,t) = (λ/4π) unwrap{ϕ(x,y,t) – <ϕ₁(0)>}, where <ϕ₁(0)> is the average phase within a reference area at t = 0 (e.g., corresponding to the inert gold film).³⁰⁻³²

DHM measurements were performed using a 10× lens with a field of view of 500 × 500 μm² and an effective lateral pixel size of 0.6154 μm. Operando surface-normal height images of calcite (104) surfaces were obtained near the fluid inlet and referenced to the height of an inert Au film that coated a portion of the surface. Relatively high flow rates during measurements limited the extent of the solution compositional changes. Surface-normal height images imply only minimal pH changes within the field of view (i.e., ΔpH = +0.07 at the highest dissolution rate; see the Supporting Information, Section S5 for details).

Dissolution rates for calcite were calculated from time-series height images with two different approaches. In the first approach, the average dissolution rate within a region of interest (ROI) was determined using the net change in the mean height during the whole reaction time at a single flow velocity (Figure S2). The ROIs were manually selected at a similar distance from the inlet (∼200 μm) for each experiment to avoid macroscopic features such as macrosteps and large etch pits so that reported rates represent surface-normal retreat of terrace areas. The other approach determined the “instantaneous” dissolution rate averaged over a short time (i.e., ∼10 s) as a function of position across the surface (Figure S3). The results were used to visualize spatial variations in dynamically varying surface topography during calcite dissolution. A more detailed description of the dissolution rate measurements is provided in the Supporting Information, Section S2.

Surface Characterization

Ex situ characterization of the microscopic surface roughness and surface Pb distribution was also performed. Scanning electron microscopy imaging was performed for representative samples from a set of previously described microfluidic experiments²² using the AURIGA 60 Crossbeam focused ion beam-scanning electron microscope (FIB-SEM) apparatus at the W. M. Keck Center for Advanced Microscopy and Microanalysis of the University of Delaware. X-ray fluorescence (XRF) maps of Pb distribution were made at the Advanced Photon Source (APS) microprobe beamline 13-ID-E at the Argonne National Laboratory. The XRF measurements were carried out in fly scan raster mode using a 2 × 2 μm² focused beam and a 5 μm grid spacing at the photon energy of 15 keV. The Pb surface concentration was obtained by quantitative comparison with the Pb XRF signals of an AXO (Applied X-ray Optics, Dresden GmbH) standard thin-film sample having known surface Pb coverage. Several of these samples were also imaged for surface Pb distributions by using a Cameca 50 secondary ion mass spectroscopy (nano-SIMS) instrument located at the Atmosphere and Ocean Research Institute of the University of Tokyo, Kashiwa, Japan. This instrument scanned a low ion current (∼5 nA) beam with a 40 nm spatial resolution across a 20 × 20 μm² raster area.

Results and Discussion

Effect of Pb Concentration on Microtopography and Dissolution Rate of Calcite

Topographical changes of calcite (104) surfaces during reaction with acidic solutions (at pH 3.7, with [Pb²⁺] = 0, 5 × 10^–3, and 5 × 10^–2 M), observed in situ by DHM (Figure 1a) after reaction for 15 min, illustrate the sensitivity of the dissolution process to dissolved Pb²⁺. The samples reacted in the Pb-free solution exhibited a generally flat surface with isolated rhombohedral etch pits having typical depths of ∼500 nm. In contrast, the surfaces reacted in Pb²⁺-bearing solutions dissolved more slowly, indicating that Pb inhibited calcite dissolution. These surfaces also exhibited greater heterogeneity, including substantial microscale roughness (most notably at [Pb²⁺] = 5 × 10^–3 M), and localized etch pits having depths similar to those observed in Pb-free solutions (>300 nm).

Figure 1.

(a_i–a_iii) Maps of net changes in the height of calcite (104) surfaces (shown as color, in nm) reacted for 15 min with acidic pH 3.7 solutions containing [Pb²⁺] = 0, 5 × 10^–3, and 5 × 10^–2 M, respectively (flow direction is from left to right). Note the different scales of the color bars. The squares represent regions of interest (ROI) with a size of 1600 pixels where the dissolution rate was measured. The gold film used as the height reference shows no height changes. (b) Dissolution rates of the calcite (104) terrace as a function of Pb²⁺ concentration. The average rates are measured as the changes in surface height over >300 s of reaction in the corresponding Pb²⁺-containing solutions (with uncertainty at each pixel comparable to the size of the data points). “Error bars” indicate the variability of dissolution rates within the ROIs, corresponding to the 1-σ standard deviations of rates measured within the ROIs. The dashed blue line corresponds to calculated dissolution rates using R_d [Pb²⁺] = R₀ (1 – θ[Pb²⁺]/θ_max) functional form. (c) Instantaneous dissolution rate histograms of terrace areas on calcite (104) at 15 min of reaction in acidic solution at different Pb²⁺ concentrations at a v_mean = 6.67 mm s^–1. (d) Steady-state average dissolution rates as a function of flow velocity in acidic (pH 3.7) solutions with 0 M [Pb²⁺] (red circles) and 5 × 10^–3 M [Pb²⁺] (blue triangles). (e) Ratios of the mean dissolution rates measured in acidic 0 M and 5 × 10^–3 [Pb²⁺] solutions.

The effect of dissolved Pb²⁺ on the calcite dissolution rate was quantified by systematic measurements as a function of [Pb²⁺] (5 × 10^–9 M ≤ [Pb²⁺]_tot ≤ 5 × 10^–2 M) at a constant flow velocity, v_mean = 6.67 mm s^–1 (Figure 1b). The behavior within spatially uniform regions (i.e., without visible etch pits or macrosteps) is indicated within ROIs having areas of ∼0.001 mm² (boxes, Figure 1a). The average dissolution rate within these ROIs decreased monotonically with increasing dissolved [Pb²⁺] (red circles, Figure 1b). The dissolution rate observed at the lowest [Pb²⁺], 5 × 10^–9 M, was indistinguishable from that in the Pb-free solution. The dissolution rate at the highest [Pb²⁺], 5 × 10^–2 M, was ∼34 times slower than that in the Pb-free solution. Although this analysis was focused on the behavior of nominally uniform regions of calcite surfaces, quantitatively similar behavior was also observed for larger areas that contained inherent surface heterogeneity (e.g., macrosteps and large etch pits; Supporting Information, Figure S5). These results demonstrate that the average dissolution rate is well-defined and independent of the sampling size.

As in previous studies,^26−28,33 the decreasing dissolution rate can be described by an equilibrium adsorption isotherm despite being highly undersaturated with respect to calcite and undergoing active dissolution. The degree of inhibition vs [Pb²⁺] (Figure 1b) is consistent with a functional form that is similar to the inverse of an adsorption isotherm:

2

Here, θ([Pb²⁺]) is the fractional Pb coverage with respect to maximum saturation coverage (θ_max, previously determined to be ∼2–4 Pb per calcite surface unit-cell area = ∼20 Ų),²² and R₀ is the calcite dissolution rate at [Pb²⁺] = 0 (Figure S7). The surface coverage can be expressed using a Frumkin equation:

3a

3b

where K(θ) is the effective sorption constant, K^o is the adsorption constant independent of θ, and γ is a correlation energy constant that accounts for adsorbate–adsorbate interactions. By fitting experimental data using the Frumkin equation, we obtained K^o = 10^3.64±0.12 L mol^–1 and γ = 2.11 ± 0.39 J mol^–1. This phenomenological analysis provides a measure of the effective affinity for Pb sorption on the dissolving calcite surface, although the nature of the Pb sorption mechanism remains to be explicitly defined.

Inhibition of calcite dissolution in the presence of dissolved metal ions has been previously observed and was attributed to the inhibition of step movement by dissolved cations and a relative increase of the reverse reaction rate during calcite dissolution.^{23,26−28,33} However, our previously determined amount of sorbed Pb (2–4 ML)²² indicates that a simple adsorption model cannot fully account for the observed phenomenon because the coverage is larger than the surface site density (i.e., 1 ML = 1 Pb monolayer = 1 Pb atom per surface unit cell). In situ atomic force microscopy (AFM) imaging conducted under similar continuous flow conditions showed no evidence of secondary phase precipitation at any [Pb²⁺] in this study (Figures S8–S15). Notably, AFM images in solutions containing [Pb²⁺] = 5 × 10^–3 M revealed continuous dissolution of calcite surface via lateral expansion of etch pits (although individual step movement cannot be resolved due to the lower temporal resolution of the AFM measurements; Figures S12 and S13). Observations at [Pb²⁺] = 5 × 10^–2 M showed the highest degree of inhibition (Figures S14 and S15) and revealed continuous dissolution with a significantly inhibited step velocity compared to that observed at lower [Pb²⁺]. These observations confirmed that the inhibition of dissolution was not controlled by secondary phase precipitation. While sorption of Pb was likely associated with the observed behavior, the observed Pb coverage under our experimental conditions was too large to be accounted for by sorption at surface sites alone.²² We therefore speculate that the inhibition is due to a thin Pb-incorporated calcite layer at the calcite–solution interface that developed under dynamic dissolution conditions.

Additional information is evident in the distribution of dissolution rates, calculated from histograms of surface-normal velocities (Figure 1c and Supporting Information), and referred to as “dissolution rate spectra” in previous studies.^34,35 The observed standard deviations of the dissolution rate histograms were typically ±10–20% of the mean value (indicated as error bars in Figure 1c). For example, the histogram distribution widths at [Pb²⁺] = 0 and 5 × 10^–2 M were similar although the average dissolution rates were distinct. In contrast, the distribution at [Pb²⁺] = 5 × 10^–3 M was broader and skewed toward slower rates (Figure 1c). This distribution indicated that the surface included regions with no measurable dissolution as well as an extended tail corresponding to regions having dissolution rates similar to those observed when [Pb²⁺] = 0 M (i.e., no inhibition of dissolution). This was observed as extended regions of the surface where there was apparently little inhibition of dissolution (dark blue regions in Figure 1a_ii,a_iii, at [Pb²⁺] = 5 × 10^–3 and 5 × 10^–2 M, respectively). That is, the presence of Pb not only decreased the average dissolution rate but also increased the spatial heterogeneity of the dissolution rates as reflected in the observed topographies after reaction. Notably, a large fractional variability in measured dissolution rates (Figure 1c) was observed at [Pb²⁺] = 5 × 10^–3 M where the mean dissolution rate was decreased by ∼80% (Figure 1b).

Effect of Fluid Flow on the Dissolution Rate

Fluid flow played an important role in modulating the calcite dissolution rate under the conditions investigated in this study. The calcite dissolution rate was observed as a function of fluid velocity, v_mean, from 1.67 to 53.33 mm s^–1 with two input solutions (both pH = 3.7, [Pb²⁺] = 0 M and 5 × 10^–3 M) (Figure 1d). These data revealed a monotonic increase in the average dissolution rate in both solutions as a function of flow velocity that plateaued at flow rates, v_mean > 14 mm s^–1. This behavior can be characterized using the relation:

4

where R_d0 is the maximum dissolution rate of calcite at the specified input pH = −log₁₀([H⁺]₀), and k_v is the apparent decay constant scaled to the average solution velocity in our flow cell. This expression is in good agreement with the experimental results (Pearson correlation coefficient, r = 0.98 and r = 0.96 for [Pb²⁺] = 0 M and 5 × 10^–3 M, respectively), and yields R_d0 = 2.93 ± 0.15 × 10^–6 and 6.61 ± 0.52 × 10^–7 mmoles cm^–2 s^–1 at [Pb²⁺] = 0 M and 5 × 10^–3 M, respectively. The R_d0 value at [Pb²⁺] = 0 M was consistent with the reported bulk calcite dissolution rates at this pH.^29,36 The R_d0 at [Pb²⁺] = 5 × 10^–3 M was 4.7 ± 0.3 times smaller than that in the [Pb²⁺] = 0 M solution, indicating significant inhibition of calcite dissolution by Pb in the acidic solutions. The scaling constants for the solution velocities, k_v = 1.74 ± 0.19 and 2.21 ± 0.29 mm s^–1 at [Pb] = 0 and 5 × 10^–3 M, respectively, were also obtained from these data. While these values were derived from the empirical relationship of eq 4, we provide further discussion (see the Supporting Information) on the relationship between the measured quantities and the dimensions of the cell and flow dynamics. These values were similar for the solutions with and without dissolved Pb, as evidenced by Figure 1e, where the ratio of dissolution rates is generally constant over a wide range of flow velocities.

Effect of Pb on Etch Pit Geometry

The presence of Pb significantly altered the dissolution pattern during the reaction in acidic solutions (Figures 2a–d and S8–S15). For [Pb²⁺] < 5 × 10^–5 M, the observed topography after 15 min was similar to that in Pb-free solutions as characterized by relatively smooth surfaces and rhombic etch pits with a depth of ∼100 nm or greater. The etch pit shapes evolved as a function of [Pb²⁺] (all references to the crystallographic directions are based on the macroscopic crystal shape). The corners where obtuse–obtuse and obtuse–acute steps intersect became rounded at [Pb²⁺] = 5 × 10^–4 M (Figures 2b, S10, and S11) and developed into oval shapes with the longest axes aligned to the [010] direction at [Pb²⁺] = 5 × 10^–3 M (Figures 2c, S12, and S13). At the highest [Pb²⁺] of 5 × 10^–2 M, the etch pits became highly elongated (Figures 2d, S14, and S15). We measured lateral etch pit growth velocity in directions orthogonal to the etch pit walls (e.g., [481̅]_± vs [4̅41]_±) for [Pb²⁺] < 5 × 10^–3 M and along [010] (longitudinal direction) and [421̅] (transverse direction) for elongated etch pits at [Pb²⁺] ≥ 5 × 10^–3 M. For [Pb²⁺] < 5 × 10^–3 M, there was no significant variation in lateral spread velocity in all four directions, with average lateral velocity = 72.6 ± 2.6 nm s^–1. At 5 × 10^–3 M [Pb²⁺], the primary axes of the etch pits changed and the velocities were highly asymmetric, i.e., 24.4 ± 1.8 and 7.2 ± 0.8 nm s^–1 along the [010] and [421̅] directions, respectively (Figures 2c, S12, and S13). Lateral expansion of the etch pits occurred predominantly along the [010] direction at [Pb²⁺] = 5 × 10^–2 M (Figures 2d, S14, and S15).

Figure 2.

Instantaneous dissolution rate maps (a–d) and topography maps (a_i–d_i) showing etch pits of different geometries at increasing Pb concentration, a and a_i: 5 × 10^–9 M [Pb²⁺], b and b_i: 5 × 10^–4 M [Pb²⁺], c and c_i: 5 × 10^–3 M [Pb²⁺], and d and d_i: 5 × 10^–2 M [Pb²⁺]. The reaction time is 5 min for (a–c) and 15 min for (d). The fluid flow direction is from left to right. The red, violet, dark green, and dark blue arrows correspond to the crystallographic directions orthogonal to [481̅], [4̅41], [421̅], and [010], respectively, based on the macroscopic crystal shape used for measurements of the lateral velocity of the etch pits. Arrows corresponding to the crystallographic directions are color-matched in panels (e) and (f). Schematic of an etch pit with a diagonal line corresponding to the [010] direction, and dash-dotted line corresponding to the c-glide plane is present in panels (a–d) to indicate the crystallographic orientation of each sample based on macroscopic crystal shape. (e) Lateral velocity of etch pits in nm s^–1 measured orthogonal to [481̅] (red circles) and [4̅41] (violet squares) for [Pb²⁺] < 5 × 10^–3 M. At 5 × 10^–3 M [Pb²⁺] and 5 × 10^–2 M [Pb²⁺], lateral etch pit velocity was measured along the longitudinal principal direction (parallel to [010], dark blue triangles) and the transverse principal direction (parallel to [421̅], dark green diamonds). The error is given as a standard deviation of 16 different observations along each crystallographic orientation at each [Pb²⁺]. (f) Schematic of an evolving etch pit with increasing [Pb²⁺].

These dramatic changes in the etch pit geometry with increasing [Pb²⁺] indicate that Pb²⁺–calcite interactions exert strong crystallographic control over calcite reactivity. Changes in etch pit geometry have been previously reported in the literature in the presence of Li⁺, Cd²⁺, Mg²⁺, PO₄^3–, organic acids, and solvents.^33,37−45 We note that the depths of the etch pits reported here are 2 orders of magnitude larger (hundreds of nm) compared to those reported in the literature (several nm); this was likely due to the more extreme disequilibrium caused by the more acidic conditions in our experiments.^{33,39−43,45} The previously reported changes in etch pit geometry have been attributed to step pinning due to site-specific preferential adsorption of dissolved ions, which led to curving edges of the etch pits.^33,40−43 We saw similar behavior at [Pb²⁺] ≤ 5 × 10^–4 M, but the etch pits became highly anisotropic and preferentially grew along the [010] direction at higher values of [Pb²⁺]. Highly anisotropic etch pits preferentially oriented along the [010] direction have been observed previously during calcite dissolution in Pb²⁺-bearing solutions.^46,47 Moreover, similar anisotropic structures were observed during calcite growth in the presence of Mg²⁺, where crystallographically controlled Mg²⁺ incorporation resulted in preferential inhibition at the intersection of positive and negative step types ([481̅]₋ – [4̅41]₊ and [4̅41]₋ – [481̅]₊) which resulted in formation of new steps parallel to [421̅].^48,49 Incorporation of Pb²⁺ would likely pin obtuse [481̅]₊ and [4̅41]₊ steps^50,51 that are more favorable sites to accommodate larger cations such as Pb²⁺. However, we observed that all steps dissolved more slowly in the presence of Pb²⁺, and at high Pb²⁺ concentrations, we observed strong inhibition at the intersection of alike step types [i.e., ([481̅]₊ – [4̅41]₊) and ([481̅]₋ – [4̅41]₋)], which are characterized by the intersection of k_oo – k_oo and k_aa – k_aa kink sites, where the first letter represents step orientation (i.e., o-obtuse and a-acute) and the second letter represents partial step orientation of the kink. This generated new steps with apparent orientation parallel to [010] and resulted in slower lateral velocity along the [421̅] direction.

Visualization through in situ DHM measurements allowed us to spatially resolve the effect of Pb on the anisotropic dissolution rates of the calcite (104) surface under flowing acidic aqueous solutions. Maps obtained at [Pb²⁺] = 5 × 10^–9 M (Figure 2a) showed two characteristic dissolution rates: (1) the “intrinsic” dissolution rate of the calcite (104) terrace, and (2) a higher dissolution rate at the walls of the etch pits. Note that the high apparent dissolution rates observed at the walls of the etch pits resulted from lateral expansion of the etch pits having ∼100 nm high walls and, therefore, were not directly comparable to dissolution rates of nominally flat areas. Similar behavior was observed at [Pb²⁺] = 5 × 10^–4 M. At higher [Pb²⁺], we found that the dissolution rates on the terraces were significantly lower than those at lower [Pb²⁺] conditions, while those of the etch pit floors showed almost no changes from those observed at [Pb²⁺] = 0. As indicated in Figure 1d, the slower terrace dissolution at higher [Pb²⁺] presumably resulted from the sorption of Pb at steps, whereas the consistent dissolution rate of the etch pit floors may indicate that less Pb sorption occurred at these sites.

Formation and Evolution of Calcite Micropyramids

Another characteristic observed consistently in the DHM images of calcite reacted with acidic Pb²⁺-bearing solutions was the development of μm-scale surface roughness (Figures 3a and S17). While these features were not well-resolved in the DHM images, they are reminiscent of micropyramidal topographic structures that have been observed on calcite (104) terraces during dissolution in Pb²⁺-bearing solutions both in static systems (without fluid flow) and in microfluidic channels under confined flow.^5,6,22 Furthermore, the apexes of these micropyramids approached the height of unreacted (masked) regions of the calcite (104) surface,²² demonstrating that they were due to inhibition of dissolution.

Figure 3.

(a) In situ DHM height image showing complex topographic features whose dimensions are similar to those of micropyramidal structures observed in microfluidic experiments under a similar condition reacted for 3000 min. (b) Scanning electron micrograph of micropyramidal structures formed on a calcite (104) surface during dissolution in acidic 5 mM Pb²⁺ solution flow in a microfluidic channel at v_mean = 0.37 mm s^–1. (c_i) Scanning electron micrograph displaying areas with and without microtopography with the inset showing micropyramidal geometry. (c_ii) Synchrotron microprobe XRF Pb map (where each pixel corresponds to 5 × 5 μm²) of the area shown in c_i indicating the spatial relationship of the Pb distribution with micropyramidal features. (d) Scanning electron micrograph overlaid with nano-SIMS Pb measurements of the same area showing correlation between surface Pb concentration and micropyramid distribution. The color range for the nano-SIMS Pb map is in counts per second.

The relationships between the lateral Pb distributions on the calcite surface with respect to the microtopography formed during dissolution in acidic Pb²⁺ solution were further characterized by ex situ synchrotron-based microprobe XRF mapping, nano-SIMS mapping, and scanning electron microscopy for the samples reacted in a microfluidic cell for 3000 min at v_mean = 0.37 mm s^–1 (Figure 3). Comparison of the low-resolution XRF maps and the SEM images of the same region showed a strong spatial correlation between the surface Pb coverage and the density of micropyramids, with the highest Pb coverage (6–7 ng/mm²) observed in the regions with micropyramids and the lowest coverage (1–2 ng/mm²) observed in nominally flat regions (Figure 3c). Moreover, high-resolution nano-SIMS mapping of the same sample showed higher Pb coverage associated with individual micropyramids compared with regions without micropyramids (Figure 3d). These results suggest a causal relationship between the coverage of Pb²⁺ sorption and the micropyramid formation during calcite dissolution. Previous results showed that micropyramids have four sides with edges of their bases parallel to the edge orientations of rhombohedral etch pits that formed in the absence of [Pb²⁺]^5,6 (Figure 3b). Therefore, the steps that occurred on the vicinal surfaces of the micropyramids can be attributed to obtuse ([481̅]₊, [4̅41]₊) and acute ([481̅]₋, [4̅41]₋) steps exposed along the borders of etch pits. The results shown in Figure 2e indicate that Pb²⁺ incorporation slowed the lateral spread of the etch pits in all four crystallographic directions. This suggests that micropyramids may have formed by the intersection of Pb-stabilized etch pit walls during the lateral spread of adjacent etch pits. Localized Pb incorporation on the vicinal surfaces of micropyramids apparently caused substantial decreases in their dissolution rates relative to the surrounding calcite (104) terrace areas, resulting in these characteristic topographic features.

Emergence of Complex Topographies due to Spatially Variable Dissolution Rates

As the reactant fluids flowed through the channel, they progressively dissolved calcite, resulting in increased pH (i.e., proton consumption) and bicarbonate ion concentration. This would have increased the saturation state of the solution toward equilibrium with calcite as the reaction front approached the outlet section. Therefore, we might expect a monotonic decrease in the dissolution rate and the formation of simple etching profiles along the flow path. However, the far-from-equilibrium dissolution of calcite in the presence of Pb²⁺ has been shown to result in spatially complex dissolution patterns in microfluidic channels²² including both the local coverage of Pb sorbed on the calcite (104) surface and the spatial modulation in the amount of dissolved calcite. In order to understand how such patterns evolved, we made operando observations of the development of spatially variable dissolution of calcite in the millifluidic channel during the reaction of calcite at v_mean = 3.33 mm s^–1, [Pb²⁺] = 0 and 5 × 10^–3 M at pH = 3.7. This Pb concentration, [Pb²⁺] = 5 × 10^–3 M, was chosen to maximize the impact of Pb on the fractional variation of the dissolution rates (Figure 1c). This also corresponds to the condition at which complex reactivity patterns were observed for micron-sized calcite single crystals where phenomena such as pyramid formation, and ultimately the transformation of calcite to PbCO₃, were previously observed.⁴⁻⁶

DHM topography images are shown before (Figure 4a,b) and after (Figure 4a_i,b_i) reaction of the calcite surface for 1000 s (at pH = 3.7, with [Pb²⁺] = 0 M and 5 × 10^–3 M, respectively). As shown in Figure 1, the presence of dissolved Pb significantly inhibited calcite dissolution. A time series of the net changes in the surface topography (Figure 4a_ii,b_ii) is also shown along the flow path from the regions highlighted with red boxes in parts a and b (averaged along the direction transverse to the flow direction). This time series shows that surface roughening occurred for both solution concentrations, [Pb²⁺] = 0 and 5 × 10^–3 M; however, the nature and magnitude of this roughness were distinct. For the Pb-free solutions, the roughness was mostly due to the formation of well-defined etch pits (Figure 4a_ii). In contrast, we observed three types of evolving features along the flow path at [Pb²⁺] = 5 × 10^–3 M, which included incompletely resolved peaks (<5 μm in size) that were consistent with the formation of micropyramids (as seen in Figure 3). The time-series measurements show that these micropyramids remained visible for long periods of reaction time, indicating that these features were closely related to the observed slow dissolution rates. Approximately 40 μm sized oval-shaped etch pits were also observed, whose orientations were oblique to the flow direction. Finally, there were large regions having an approximately sinusoidal height variation with ∼100 nm in amplitude and ∼50 μm in periodicity (occurring at horizontal positions between 50 and 250 μm along the flow path; indicated as dashed gray line, Figure 4b_ii). These patterns were aligned in the direction orthogonal to the flow and, therefore, can be described as reaction bands.

Figure 4.

(a, b) Topographic images of calcite (104) surfaces in a (a) calcite saturated solution, and the same regions after dissolution in acidic solutions with 0 M [Pb²⁺] (a_i) and 5 × 10^–3 M [Pb²⁺] (b_i) for 1000 s (flow direction is from left to right). Note the pattern formation along the flow path in b_i (highlighted with dashed lines) characterized by modulated dissolution. Time-series vertical profiles during dissolution in 0 M [Pb²⁺] (a_ii) and 5 × 10^–3 M [Pb²⁺] (b_ii) showing the net change in topography along the flow path averaged along the short axis within the red box shown in topography maps. Both profiles show modulated dissolution along the flow path, but rhombohedral etch pits are the primary source of height modulations in (a_ii). In contrast, a combination of micropyramids and spatially variable dissolution rates lead to an emerging pattern (highlighted by a dashed gray curve) as shown in (b_ii).

The spacing between the bands, ∼50 μm, is considerably smaller compared to the spacing of the banded structures previously observed in microfluidic experiments (∼500 μm) using similar fluid composition under similar v_mean = 3.88 mm s^–1.²² However, in microfluidic experiments, the solution was vertically well mixed by diffusion, and reactivity was controlled by the entire fluid volume and the mean flow velocity in the channel, v_mean. In contrast, we inferred that the reactivity in the millifluidic channel was controlled by the diffusion length and effective velocity near the interface (Supporting Information, Section S4) and that it scaled with differences in the effective fluid velocity. The estimated effective flow velocity near the interface in the millifluidic channel, v_effec = 0.45 mm s^–1 (see Table S2), was nearly an order magnitude slower than the v_mean = 3.33 mm s^–1. Therefore, the 10-fold smaller band spacings observed in the millifluidic channel are consistent with those observed in the microfluidic channel, when accounting for fluid boundary layer effects in the larger millifluidic cell geometry.

The temporal evolution of the surface height changes provides new insights into the possible mechanisms by which reaction bands may form. We note that each maximum in the surface topography along these bands appeared to coincide with positions where the sharp peaks (i.e., micropyramids) had appeared previously during the reaction (Figure 4b_ii). This suggests that the modulated height profiles appear to have been induced and amplified with reaction time by the earlier localization of surface micropyramids; although in many cases, these micropyramidal features subsequently became less distinct. We speculate that the specific locations of the surface micropyramids may be controlled by multiple factors. They may be seeded by pre-existing, defect-controlled topographic features and amplified by the preferential adsorption of Pb on exposed steps, especially since such site-specific adsorption would have the effect of locally hindering dissolution. Furthermore, we observed relatively defect-free regions, where the calcite dissolution rate was only minimally affected by the presence of Pb. We infer that the large-scale topographic instabilities that we observed are the result of the combined effect of these two behaviors.

The evolution of the surface topography of an initially flat surface by chemical reaction is a long-standing problem. Spontaneous pattern formations in the topography of nominally uniform surfaces have been observed over a wide range of conditions, most notably during growth^52,53 and ion sputtering of surfaces in vacuum.^54,55 The appearance of such features during dissolution is less commonly reported but has been seen under conditions of electrochemical etching⁵⁶ and dissolution under turbulent flow.⁵⁷ In these cases, patterns are recognized as surface ripples, mounds, and nanodots that have characteristic length scales (e.g., ripple period or mound spacing) that emerge dynamically during the reaction.⁵²⁻⁵⁷ The specific length scales are controlled by the balance between competing processes (e.g., the random removal of material and surface diffusion), which have opposing influences on surface roughness. The topographic structures in the present study appear to have been driven by the combination of undersaturated (i.e., acidic) solutions, which promoted calcite dissolution, and the presence of dissolved Pb²⁺, which inhibited dissolution (Figure 1c). This suggests that the formation of micropyramids and etch pits will generally evolve toward the development of longer-scale periodic banding after an extended reaction, as suggested in Figure 4.

While we have, so far, discussed the evolution of the surface topography in the context of the local mechanistic controls over reactivity, we can also consider whether the observed spatial variation of dissolved calcite may indicate a pH-driven feedback mechanism. This would evolve from a dynamic balance among surface reactions, aqueous speciation reactions, aqueous diffusion, and advective fluid flow. For example, dissolution of calcite consumes protons and generates dissolved bicarbonate species (eq 1), whereas protons are released during precipitation of carbonate secondary phases and formation of carbonate species such as PbCO₃(aq) by consuming bicarbonate species.^13,58−61 The advective flow of fluid may sustain a state of dynamic disequilibrium, whereby the system oscillates between different states of saturation along with potential changes in reaction rates with respect to calcite at the reaction front, as a result of the interplay between proton-consuming and proton-producing reactions. However, we do not observe any secondary carbonate phase, and pH estimates calculated from the changes in topography suggest that the pH changes are minimal (<0.1 pH units) within the field of view (Supporting Information, Section S5), indicating that the effect of carbonate speciation on pH would be minimal.

Environmental Implications

The importance of calcium carbonate minerals in controlling the solution composition and elemental transport in natural waters derives largely from reactions that occur while the carbonate surfaces are dynamically evolving due to dissolution and growth. The present results demonstrate that the reactivity of calcite in undersaturated solutions can be substantially inhibited by the presence of dissolved heavy metal ions in a confined fluid flow environment that represents advective transport through a porous rock formation. Notably, our in situ experimental observations showed that this behavior occurs over a wide range of hydrodynamic conditions and dissolved metal concentrations under conditions of sustained disequilibrium, and yet this type of inhibition of carbonate reactivity is not included in current reactive transport models.⁶²

Understanding this behavior will be important for enabling accurate predictions of the geochemical reactivity underlying various geological and environmental technologies. For example, the inhibition of calcite dissolution by dissolved metal cations would negatively impact the efficiency of passive remediation of mine tailings and acid mine drainages where limestone (up to 95% calcite) is used to buffer acidic waters typically characterized by elevated levels of dissolved metals.⁶³⁻⁶⁶ Specifically, the inhibited dissolution of calcite could lead to a higher-than-expected mobility of contaminants under conditions where acid mine waters pass through limestone beds. A robust understanding of these metal–carbonate interactions would help in the development of more efficient remediation strategies for metal contaminants associated with mining activities.

Supporting Information Available

The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acs.est.3c10105.

• Additional experimental details and results, including the characteristics of the millifluidic flow cell, DHM measurement of dissolution rates, the sensitivity of DHM to height variations, flow rate dependence of reactions in the flow cell, estimating pH changes, supplementary atomic force microscopy data, and equilibrium speciation calculations (PDF)

The authors declare no competing financial interest.