Experimental Procedure

Laboratory dissolution experiments were conducted using the pH-stat technique developed by Morse (1974a), which allows calcite dissolution to occur under a constant-saturation state (Ω_calcite). Keeping Ω_calcite constant can be attained by considering the dissolution of calcium carbonate according to the following equations:

Where Ω = saturation state, a = activity, K_eq = equilibrium constant for reaction (1), pCO₂ = partial pressure of CO₂, and K₀₁₂ = the activity equilibrium constant for the following reaction:

Rearranging Equation 2 and using , gives,

Equation 4 shows that in order to keep Ω_calcite constant during dissolution, a_Ca²⁺, pCO₂, and a_H⁺ must remain constant (Morse 1974a). In our dissolution experiments, pCO₂ was held constant by bubbling gas-CO₂ mixture of known composition through the solution. The pH of the solution, and thus a_H⁺, was fixed by continuous addition of acid to compensate the H⁺ ions consumed during calcite dissolution. The a_Ca²⁺ is assumed to be nearly constant given that a negligibly small amount of Ca is added to the solution through calcite dissolution compared to the high amount of Ca originally present in the solution (Morse 1974a).

A schematic diagram of the pH-stat system is shown in Figure 1. The dissolution reaction of calcite takes place in a 900 mL Pyrex reaction vessel placed in a temperature bath set to a constant temperature. An overhead electric stirrer is used to continuously stir the reaction solution with a constant stirring rate that is fast enough to keep the calcite solid suspended in the solution. A gas bubbler is used to bubble air through the solution. The pH of the solution is monitored using an electrode attached to a pH controller. Before each experimental series, a three-point pH calibration was performed at pH 4, 7, and 10, using buffers traceable to NIST standards.

A predetermined pH value is set on the pH controller with a small hysteresis (dead band) to prevent oscillation around the set pH value. The pH of the solution is then brought as close as possible (within ∼ 0.2 pH units) to the set pH value on the low end by adding either Na₂CO₃ or HCl. A known mass of calcite is then added, marking the beginning of the dissolution experiment. When a predetermined value of pH is exceeded (due to calcite dissolution), the controller activates an automated syringe which injects HCl acid of known normality into the reaction vessel. The amount of acid injected is monitored and automatically recorded in real time, and is then used to calculate the dissolution rate based on the stoichiometry of Equation 1, and Equation 5 (Walter and Morse 1984):

Where R = dissolution rate (mol.g^–1.s^–1), N = normality of acid (eq.L^–1), V_t = volume of acid added per second (L.s^–1), and w = initial weight of calcite (g). The dissolution rate can be normalized by the calcite reactant surface area according to the following equation:

Where s = surface area (cm².g^–1). When normalized by surface area, the dissolution rate unit is mol.s^–1.cm^–2. The percent calcite dissolved as a function of reaction time was then calculated using the following equation:

Where D = calcite dissolved (%), and M = molecular weight of calcite (g. mol^–1).

All experiments were conducted at constant temperature of 25 °C, and pCO₂ of 10^–3.4. A 600 ± 10 mL of NaCl–CaCl₂ containing the same [Ca] and ionic strength as seawater of average salinity was used as a reaction solution (Millero 2016), and 1 g of calcite reactant. A pipette was used to sample approximately 10 ± 2 mL of the reaction solution. The mixed fluid–solid sample was immediately separated using a vacuum flask, rinsed with distilled water, filtered, and the solid materials were dried in a vacuum desiccator at room temperature.

In total, eight experimental series were conducted, and each series was replicated at least once (Table 1). Ω_calcite in each series was set by fixing the pH at a specific value. The pH values used were 4 ± 0.2, 6 ± 0.1, 7 ± 0.05, and 7.5 ± 0.05, which correspond to Ω_calcite of 10^–7.89, 10^–3.90, 10^–1.85, and 10^–0.85, respectively. Note that under our experimental conditions, the pH value at which calcite is at equilibrium with the solution (Ω_calcite = 1) was 7.92. In all the series, sampling was done at 5%, 10%, and 30% calcite dissolved. This was possible because % calcite dissolved was calculated in real time (i.e., as dissolution was occurring) and was displayed on a computer screen. This was done through a computer program which uses as input (before the start of each experiment) acid normality and calcite reactant weight. The program receives the volume of acid added continuously from the automated syringe, and it uses Equation 7 to calculate % calcite dissolved.

It should be pointed out that the terminology used to describe the distance from equilibrium is relative. It has been previously established that below a pH of approximately 4–5, dissolution rate is linearly dependent on solution pH and independent of pCO₂ (Plummer et al. 1979; Morse and Arvidson 2002). Above this pH range, dissolution rate becomes progressively independent on solution pH, and dissolution mechanisms vary in a complex manner as equilibrium is approached (Morse et al. 2007). The exact pH values separating these regions are poorly defined (Morse et al. 2007). Accordingly, we consider experiments conducted at pH = 4 to be far-from-equilibrium or high degree of undersaturation. In contrast, experiments conducted at both pH = 7 and 7.5 are considered near-equilibrium or low degree of undersaturation.

Surface Area, XRD, and SEM

A three-point BET (Brunauer et al. 1938) specific-surface-area analysis for the synthetic calcite was performed using Micromeritics TriStar II 3020 instrument equipped with a nitrogen gas purge. Standard powder XRD techniques were used to determine the mineralogy of the solid reactants. Powders were prepared with an agate mortar and pestle. Powders were then mounted on a boron-doped silicon P-type zero background diffraction plates and placed in a Bruker D2 Phaser Diffractometer with a CuKα anode. Relative abundances of aragonite and calcite were determined using the ratio of calcite 104 and aragonite 111 peak heights (h) after subtracting the background intensity (Milliman 1974):

SEM imaging was performed on a Field Emission JEOL 7500 using an accelerating voltage of 5 kV and a working distance of 6 ± 0.2 mm. Samples were coated with 10 nm of osmium to avoid charging effects. Crystals were described in terms of their overall morphology (e.g., rhombic, polyhedral, rounded), edges and corners (sharp vs. smooth, curved, or rounded), crystal surface features (dissolution pits, layers, and roughness), and inter-crystal boundaries. “Crystal” and “microcrystal” are used interchangeably to refer to micrometer-size calcite crystals measuring ≤ 10 μm consistent with the definition of Kaczmarek et al. (2015). This terminology will be consistently used throughout the article.

Dissolution Rates

Experimentally determined dissolution rates are summarized in Table 1 and are plotted as a function of pH in Figure 3A. The amount of calcite dissolved (%) as a function of reaction time for Series 1–4 is shown in Figure 3B. These data show that dissolution rates exhibit a strong inverse covariance with solution pH and a normal covariance with the degree of solution undersaturation with respect to calcite (Fig. 3A). Dissolution rate in Series 1 (pH = 4) is approximately two orders of magnitude faster than dissolution rate in Series 4 (pH = 7.5). Experiments conducted at the same pH but with different calcite reactants show considerable variability in dissolution rate, particularly at lower pH values (Fig. 3A).

While dissolution rates reported here are not normalized to reactant surface area, we measured the surface area of the synthetic calcite reactant used in Series 1–4 so that a direct comparison between our rates and those reported in previous studies is possible. The dissolution rate in Series 1 is 0.0018 mol.min^–1.g^–1. Normalizing by the synthetic calcite surface area of 3800 cm².g^–1 and converting the units yields a log dissolution rate of 4.40 mg.cm^–2.yr^–1, which is in a good agreement with the log dissolution rate of 4.36 mg.cm^–2.yr^–1 reported by Berner and Morse (1974) for a comparable reactant and dissolution conditions. The calculated log dissolution rate is also within the range of log dissolution rates of 3.48–4.48 mg.cm^–2.yr^–1 reported by Arvidson et al. (2003) based on a compilation of published data. It should be noted that the dissolution rate measured in our study, like all other bulk-chemistry studies, is a macroscopic rate. This rate represents an average of varied region-specific rates (different crystal faces, edges, corners, pits, etc.) (Noiriel et al. 2020).

Calcite Crystal Morphology

Some of the dissolution features described below are shown at high magnification in Figure 4. Series 1 (synthetic calcite, pH = 4) results show that after 5% calcite dissolution, the initially rhombic calcite microcrystals develop smooth edges and corners (Fig. 5A), but the crystals retain their original overall shape and do not become spherical. Inter-crystal boundaries are characterized by gulfs (sensu Lambert et al. 2006), which are defined as narrow grooves or channels between adjacent, touching crystals. In some cases, dissolution accentuates inter-crystal boundaries with the appearance of gulfs. In other cases, however, dissolution preferentially occurs at edges and corners as evidenced by the rounding, which tends to obscure the boundaries between touching crystals. As dissolution proceeds to 10%, crystals are still characterized by smooth edges and corners, and inter-crystal gulfs, and some crystal faces develop flat-bottomed, smooth-sided etch pits with shapes that vary between rectangular to irregular (Fig. 5B). At 30% dissolution, crystals are still characterized by smooth edges and corners, inter-crystal gulfs, and pits, but now some crystal edges and corners are characterized by narrow ledges (sensu Berner 1980) oriented parallel to one another in a stair-stepping fashion (Fig. 5C). Crystal surfaces are also rougher and bumpy in appearance due to what appears to be fine particles attached to the surfaces (Fig. 5C).

Series 2 (synthetic calcite, pH = 6) results show that after 5% calcite dissolution, crystals retain their original rhombic shape but are characterized by distinct layers on crystal surfaces that are either oriented parallel to the crystal faces or appear irregular in nature (Fig. 5D). Some crystals develop slightly smooth edges and corners, but the general morphology of these crystals remains rhombic (Fig. 5D). Etch pits similar to those observed in Series 1 are more common in Series 2. After 10% and 30% dissolution, ledges become increasingly pronounced (Fig. 5E, F). Similar to Series 1, crystal surfaces become rougher after 30% dissolution.

Series 3 and 4 (synthetic calcite, pH = 7 and 7.5, respectively) results show that after 5% calcite dissolution, crystals retain their rhombic shape with sharp edges and corners and crystal faces characterized by distinct layers (Fig. 5G, J). After 10 and 30% dissolution, layers become deeper and spaced farther apart (Fig. 5H, I, K). Smaller crystals are partially embedded in larger ones (Fig. 5H, I, K, L), which is more common in Series 4 than in Series 3. Etch pits are common in all Series 3 and 4 experiments after 5% dissolution. Some etch pits are rectangular in shape with some edges oriented parallel to the crystal faces (Fig. 5G, H), but with most appearing more randomly oriented (Fig. 5K). In both series, crystals commonly occur in clusters but the boundaries between individual crystals remain sharp and gulfs are not observed.

Collectively, the observations from Series 1–4 show that smooth edges and corners and inter-crystal gulfs are most developed in Series 1 and become progressively less pronounced and less common towards Series 4. Furthermore, smooth edges and corners and inter-crystal gulfs develop after 5% dissolution and continue to exist after 10% and 30% dissolution, but they do not become more common with further dissolution (Fig. 5). In contrast, etch pits, dissolution layers, and ledges are least developed in Series 1 and become progressively more common towards Series 4. These features typically appear after 5% dissolution and become increasingly more common and more visible with further dissolution (Fig. 5).

Series 5 (stabilized coral, pH = 4) results indicate that after 5% calcite dissolution, most of the initially polyhedral calcite crystals constituting the stabilized coral reactant (Fig. 2B) develop smooth, curved edges and corners, and etch pits similar to those observed in Series 1 (Fig. 6A). After 10% and 30% dissolution, crystals are still characterized by a few etch pits as well as crystal edges and corners that are smooth and curved, but inter-crystal boundaries are characterized by gulfs (Fig. 6B). Surface roughness also becomes more noticeable, though it does not appear to reflect the presence of etch pits or depressions but rather the occurrence of fine particles that make the surface bumpy (Fig. 6C). Some compromise boundaries between crystals remain sharp (Fig. 6A, C), similar to those observed in the undissolved reactants (Fig. 2B). Lacy, web, and strand-like structures are observed on and between some crystals (Fig. 6B).

Series 6 (stabilized single crystal aragonite, pH = 4) results show that after 5% calcite dissolution, crystals remain euhedral with well-developed faces and sharp edges and corners, and some crystal surfaces develop sharp and irregular pits (Fig 6D). Some of the pits observed in Series 6 (Fig. 6E) are similar to those observed in other experiments (e.g., Fig. 6A), while some others differ significantly in their irregular shapes, larger sizes, pointed bottoms, and the fact that some of them occur in clusters (Fig. 6D). Aggregates of equant and elongated nanocrystals are also observed (Fig. 6D). After 10% calcite dissolution, crystal edges, corners, and surfaces develop layers (Fig. 6E). In most cases, the layers are broadly subparallel to one another, but the orientations of the steps between layers are highly irregular. A few small (< 0.2 μm in diameter) and irregular pits are observed on crystal surfaces (Fig. 6E). After 30% calcite dissolution, crystal surfaces become rough and some crystal corners become slightly curved, meaning that crystals themselves become less euhedral (Fig. 6F).

Series 7 (natural calcite, pH = 4) results indicate only subtle textural modifications are observed after 5% calcite dissolution (Fig. 2D). Calcite crystals remain polyhedral with flat faces, but some crystal edges and corners become slightly rounded and other edges develop fine ledges (Fig. 6G). After 10% calcite dissolution, the ledges become wider and thus more easily discernible, and crystal surfaces become rougher and uneven (Fig. 6H). Further dissolution to 30% yields crystals with smoother edges and corners, but the crystals largely remain polyhedral (Fig. 6I).

Series 8 (natural calcite, pH = 7.5) results show that after 5% calcite dissolution, crystal edges exhibit sharp and discrete ledges (Fig. 6J). In most cases, the ledges are parallel to one another and to crystal faces. After 10% dissolution, crystals remain generally polyhedral, but the ledges are more widely spaced (Fig. 6K). After 30% dissolution, ledges become even more widely spaced, and some crystal faces develop dissolution pits (Fig. 6L). Most of the pits are shallow and small, sharp-sided, and irregular in shape, and their orientation is highly variable.

High-resolution SEM images provide a more detailed look at the effects of dissolution. These images show that both synthetic and natural calcite dissolved under far-from-equilibrium conditions (Series 1 and 7, respectively) develop smooth and rounded crystal edges and corners (Fig. 7A, B) compared to synthetic and natural calcite dissolved under near-equilibrium conditions (Series 4 and 8, respectively), which develop ledges on crystal edges and corners (Fig. 7C, D). In the dissolution experiments conducted under far-from-equilibrium conditions, the edges and corners of the synthetic calcite crystals are smoother than those on natural calcite crystals (Fig. 7A, B). Additionally, the far-from-equilibrium dissolution experiments of the natural calcite reactant shows that the initially polyhedral crystals develop smooth edges and corners and the overall crystal morphology becomes more spherical, but the crystals retain their straight faces even after 30% calcite dissolution (Fig. 8).

Transport-Controlled vs. Surface-Controlled Dissolution

How we interpret our data is ultimately guided by our conceptual understanding of mineral dissolution in aqueous solutions, which assumes the following processes: i) diffusion of reactants to the mineral surface, ii) physicochemical reactions at the mineral–fluid interface (i.e., ion exchange, surface diffusion, hydration, desorption, etc.) that ultimately lead to the detachment of ions, and iii) transport of products from the mineral surface to the bulk solution (Berner 1980; Rickard and Sjöberg 1983; Murphy et al. 1989; Morse and Arvidson 2002). Typically, one of these processes is slower than the others, and is thus referred to as the rate-limiting step because it governs the overall dissolution rate (Morse and Arvidson 2002). When reactions at the mineral surface are slower than diffusion of reactants or products, a reaction is considered surface-controlled. In contrast, reaction rates limited by diffusion are called transport-controlled reactions (Berner 1978, 1980). Which dissolution mechanism dominates depends on several factors, including the degree of undersaturation, hydrodynamic conditions, mineral solubility and reactivity, temperature, and the presence of kinetic inhibitors (Berner 1978; Morse and Berner 1979; Sjöberg and Rickard 1984; Svensson and Dreybrodt 1992; Morse et al. 2007). Whether dissolution is transport-controlled or surface-controlled dictates the type of dissolution features on the dissolving mineral (Berner 1980). It has previously been demonstrated that when dissolution occurs under high degrees of undersaturation (i.e., far-from-equilibrium), ion detachment is likely to be faster than ion transport, and thus dissolution is expected to be transport-controlled, whereas when dissolution occurs under low degrees of undersaturation (i.e., near-equilibrium), ion detachment is likely to be slower than ion transport, and thus dissolution is expected to be surface-controlled (Berner 1980; Sjöberg and Rickard 1983; Morse and Arvidson 2002). At intermediate degrees of undersaturation, a transition region has been inferred where dissolution is jointly controlled by ion transport and surface reactions (Sjöberg and Rickard 1983).

The experimental design of our study explicitly controls for several of the factors described above. First, all experiments were conducted at the same temperature. Second, the hydrodynamic component (diffusion and advection) is assumed to be constant across all dissolution experiments because the stirring rate is an experimental control. Third, our solutions are devoid of all known calcite dissolution inhibitors, such as magnesium (e.g., Arvidson et al. 2006), orthophosphate (e.g., Walter and Hanor 1979; Svensson and Dreybrodt 1992), strontium (e.g., Gutjahr et al. 1996), and organic compounds (e.g., Compton and Sanders 1993). Therefore, the observed differences in reaction rate and crystal texture can be confidently attributed to the only two experimental variables investigated: the degree of undersaturation and/or reactant type (Table 1).

Evolution of Crystal Morphology during Dissolution

Our data show that dissolution at high degree of undersaturation (Series 1, 5, 6, and 7) results in crystals with smooth and rounded edges and corners (Figs. 5A–C, 6A–C, G–I), implying that dissolution is mainly transport-controlled. High degrees of undersaturation lead to dissolution that occurs evenly across the crystal surface and preferentially along edges and corners because these features have more exposed reactive surface area compared to flat crystal faces (Berner 1978; Lasaga 2014). In contrast, dissolution at lower degrees of undersaturation (Series 3, 4, and 8) yields crystal surfaces characterized by etch pits, dissolution layers, and ledges (Figs. 5D–L, 6J–L), suggesting that dissolution is surface-controlled. Low degrees of undersaturation promote selective dissolution at excess energy sites such as point defects, dislocations (edge and screw), and steps and kinks (Berner 1978; Morse and Arvidson 2002; Lasaga 2014). Note that in Series 1 (pH = 4), where dissolution occurred at high degree of undersaturation, few dissolution pits were observed (Fig. 5B, C), implying that dissolution was perhaps not purely transport-controlled, but is more likely jointly controlled by transport and surface processes (Sjöberg and Rickard 1983). Dissolution in Series 2 (pH = 6) also led to the formation of pits and ledges as well as slightly smooth edges and corners on the dissolving crystals (Fig. 5D–F), suggestive of dissolution controlled by both transport and surface reactions.

The results from Series 6 are inconsistent with this interpretation in that the solution was highly undersaturated, yet calcite crystals did not initially develop rounded edges and corners (Fig. 6D–F) as they did in Series 1, 6, and 7, which had the same solution chemistry but different reactant types. We attribute this discrepancy to the possible presence of small remnants of aragonite with the calcite stabilized from single-crystal aragonite (SCA) that was used as a reactant in Series 6. XRD diffractograms confirm that the stabilized SCA used in Series 6 contained a small amount of aragonite. Given that aragonite is more soluble than calcite (Morse et al. 1980) and generally has faster dissolution kinetics (Walter and Morse 1985), aragonite would have reacted faster, and after 5% dissolution, only very little of the calcite may have dissolved. In fact, SEM observations suggest the presence of finely crystalline material that differs in appearance from calcite (Fig. 6D) that could be small remnants of partially dissolved aragonite, though this could not be confirmed with XRD due to the lack of sufficient sample size following the dissolution experiments. Aragonite remnants in the stabilized SCA calcite can also explain the irregular pits observed on calcite crystal surfaces (Fig. 6D), which are similar to the aragonite relics reported in diagenetic calcite crystals in natural settings interpreted to have been stabilized from aragonite (e.g., Sandberg et al. 1973; Steinen 1982; Lasemi and Sandberg 1993; Munnecke et al. 1997). This explanation is also consistent with the observation that Series 6 samples taken from the 10% and 30% dissolution experiments had calcite crystals that were more rounded with slightly curved edges and corners, which is predicted from transport-controlled dissolution expected at higher degrees of undersaturation (Fig. 6F).

Comparison between synthetic and natural calcites dissolved at the same high degree of undersaturation (Series 1 and 7, respectively) shows that dissolved natural calcite crystals are less rounded and have more ledges (Fig. 6C, G–I,) compared to dissolved synthetic calcite crystals (Fig. 5A–C, 6A). This observation suggests that surface reactions were slower during dissolution and that natural calcite is less reactive than the synthetic calcite. Numerous factors, such as crystallinity, texture, defect density, and the presence of organic compounds and chemical inhibitors, have been shown to influence mineral reactivity and thus dissolution rates in natural calcites (e.g., Morse 1974b; Naviaux et al. 2019). The observation that natural calcite dissolved slower than synthetic calcite (Fig. 3A) also supports the claim that the natural calcite is less reactive. The fact that natural calcite reactants were coarser than the synthetic calcite reactants (and thus had lower reactive surface area), however, could also explain the lower dissolution rate for natural calcite. An inverse relationship between reactant size and dissolution rate is well established in the literature (e.g., Walter and Morse 1985; Morse and Arvidson 2002; Subhas et al. 2015).

Do Rounded Calcite Microcrystals in Natural Limestones Indicate Dissolution?

Based on textural evidence from a microporous Cretaceous limestone from Iraq (Mishrif Fm.), Lambert et al. (2006) proposed that rounded calcite microcrystals with inter-crystal gulfs reflect partial dissolution of rhombic and polyhedral crystals during burial diagenesis, an explanation consistent with some of our experimental observations. For example, our experiments show that partial dissolution of rhombic and polyhedral calcite crystals under a high degree of undersaturation yields crystals with rounded edges and corners, as well as inter-crystal gulfs (Figs. 5A–C, 6A–C, G–I).

Despite this agreement, multiple lines of evidence suggest that rounded crystals should not be used alone as evidence for post-stabilization dissolution of calcite. First, Kaczmarek et al. (2015) noted that many of the microcrystals described by others as rounded do not actually exhibit strong evidence of roundness at crystal edges and corners. Rather, many of the microcrystals appear polyhedral (i.e., multi-faceted) with sharp edges and flat crystal faces. Second, Hashim and Kaczmarek (2020) recently demonstrated in laboratory experiments that polyhedral crystals with rounded edges and corners can form directly during mineralogical stabilization from aragonite to calcite. Given that the chemical conditions of these experiments did not permit dissolution of calcite to occur, rounded calcite microcrystal shape does not appear to be conclusive evidence for dissolution of a euhedral calcite precursor. Based on observations from natural limestones by Lambert et al. (2006) and our own experiments on calcite microcrystal dissolution (Figs. 5A–C, 6A–C), inter-crystal gulfs may serve as better evidence for dissolution because they are the one textural feature that develops only during dissolution.

If we accept that calcite microcrystals with rounded edges and corners and inter-crystal gulfs, like those reported by Lambert et al. (2006), are produced during dissolution, what was the shape or texture of the calcite precursor? If one assumes that fitted textures that are characterized by a dense mosaic of closely packed crystals (Moshier 1989; Kaczmarek et al. 2015) are unlikely to produce a loose framework of rounded crystals upon dissolution, the two remaining candidate textures are granular euhedral and granular subhedral (Kaczmarek et al. 2015). The most abundant (35% relative abundance) calcite microcrystal texture in Phanerozoic limestones is the granular subhedral, which is characterized by polyhedral and rounded microcrystals, whereas the granular euhedral, which is characterized by rhombic microcrystals, is less abundant (10%) (Kaczmarek et al. 2015). Perhaps the reason rhombic microcrystals are less abundant in ancient limestones is that many have experienced partial dissolution and became polyhedral, which implies that dissolution is much more common than generally thought. However, our data show that when dissolved under a high degree of undersaturation, the synthetic calcite rhombic crystals (Series 1), developed rounded edges and corners as well as inter-crystal gulfs. But the microcrystals themselves did not become spherical (Fig. 5A–C). In contrast, when dissolved under a high degree of undersaturation, the natural calcite polyhedral crystals (Series 7), and to a lesser degree, the coral polyhedral crystals (Series 5), not only developed rounded edges and corners, but the microcrystals became nearly spherical (Figs. 6G–I, A–C, 8). These reactants likely became more spherical with progressive dissolution because their initial equidimensional shape (Figs. 2B, D, 8A) already approximates a spherical form. The synthetic calcite microcrystals, in contrast, are initially rhombic with a longer c-axis dimension (Fig. 2A), which upon dissolution is more likely to produce elongate crystals with rounded edges and corners as was observed here (Fig. 5A–C). Lastly, as noted in Kaczmarek et al. (2015), the calcite microcrystals shown in Lambert et al. (2006) are polyhedral with well-developed crystal faces rather than rounded, an observation that may provide strong evidence of the precursor shape: that the co-occurrence of polyhedral and rounded calcite in the rock record may represent a direct link between the two textures, demonstrating that calcite with rounded edges and corners, and inter-crystal gulfs most likely formed via partial dissolution of a polyhedral precursor. This is supported by the observation that, upon dissolution, the natural polyhedral crystals developed smooth edges and corners and become more spherical, but they retained their well-developed, straight edges (Fig. 8). Taken collectively, these observations suggest that the precursor of rounded crystals is more likely to be equant polyhedral crystals, and not euhedral (micro-rhombic) calcite microcrystals as proposed by Lambert et al. (2006).

The Burial-dissolution Model

To explain their observations of rounded calcite microcrystals with inter-crystal gulfs in a Cretaceous limestone, Lambert et al. (2006) invoked corrosive fluids associated with oil migration during burial diagenesis. Many other studies following Lambert et al. (2006) have invoked the dissolution hypothesis based mainly on petrographic data and paragenetic relationships (e.g., Feng et al. 2013; Rosales et al. 2018; Tavakoli and Jamalian 2018; Valencia and Laya 2020). Whereas our data broadly support the hypothesis that rounded crystal shape and inter-crystal gulfs may indicate dissolution, the specific conditions, mechanisms, and timing of large-scale dissolution in nature are highly debated (Ehrenberg et al. 2012, 2019). Although a discussion on all aspects of the burial-dissolution model is beyond the scope of the current study, an examination of potential dissolution mechanisms can provide some constraints on the burial-dissolution model.

The observation that rounded crystals with inter-crystal gulfs only formed in experiments where dissolution was transport-controlled, which was obtained by using high degrees of undersaturation (Series 1, 5, and 7) suggest that, in natural settings, a specific set of chemical conditions, namely highly acidic pore fluids, may be required to produce rounded microcrystals. The presence of kinetic inhibitors in natural waters has also been shown to exert control on dissolution reactions (Morse 1974b, Morse and Arvidson 2002). More specifically, kinetic inhibitors, such as magnesium (e.g., Arvidson et al. 2006), orthophosphate (e.g., Walter and Hanor 1979; Svensson and Dreybrodt 1992), strontium (e.g., Gutjahr et al. 1996), and organic compounds (e.g., Compton and Sanders 1993), may retard surface reactions during dissolution. This suggests that, in natural settings, where kinetic inhibitors are abundant, an even higher degree of undersaturation would be required to promote transport-controlled dissolution.

Hydrodynamic conditions also play a crucial role in determining the minimum degree of undersaturation required for transport-controlled dissolution (Berner 1978). The simplest way to promote transport-controlled dissolution is with a high degree of undersaturation so that surface reactions are faster than ion transport. Transport-controlled reactions can also be promoted with a slow stirring rate, so that ion transport is slower than surface reactions. In all our experiments, we employed a much higher stirring rate than expected in most geologic environments, which meant that to achieve transport-controlled dissolution, a very high degree of undersaturation (pH = 4) was required. We speculate that if calcite crystal dissolution occurred under slower stirring rates, a lower degree of undersaturation (i.e., closer to equilibrium) would be sufficient to achieve transport-controlled dissolution, and thus produce crystals with rounded edges and corners. If dissolution in natural environments occurred during deep-burial diagenesis, as suggested by Lambert et al. (2006), one would expect the microporous limestone to have a relatively low permeability, and thus limited fluid flow (stirring rate in the laboratory is a proxy to fluid flow in nature). This means that the degree of undersaturation required for transport-controlled dissolution, and thus production of crystals with rounded edges and corners, would be lower than what was required in our experiments. It is worth mentioning here that numerous studies have investigated calcite dissolution under near-equilibrium conditions (e.g., Stipp et al. 1994; Liang et al. 1996; Friis et al. 2003; Arvidson et al. 2006). Yet, most of these studies employ fast enough stirring rates so that dissolution is controlled by surface reactions (e.g., Arvidson et al. 2006; Xu and Higgins 2011).

Our ability to predict reaction mechanisms is extremely limited because dissolution, diffusion, and advection rates in natural settings are rarely known (e.g., Berner 1978). That being said, the presence of rounded crystals with inter-crystal gulfs, and the lack of dissolution pits and ledges (Lambert et al. 2006), suggest that dissolution was transport-controlled.

The claim that dissolution can lead to significant porosity generation in burial settings (e.g., Lambert et al. 2006; Swart et al. 2016; Rosales et al. 2018) also requires additional evaluation. For example, Lambert et al. (2006) suggested that approximately 8–13% porosity is generated as a result of burial dissolution based on, i) difference in average porosity between samples characterized by rounded crystals and those characterized by rhombic crystals, and ii) an inverse relationship between porosity and average crystal diameter. This claim was criticized by Ehrenberg et al. (2012) based on mass-balance considerations and geochemical constraints. First, Ehrenberg et al. demonstrated that a reduction in crystal diameter from 4.5 μm to 3 μm, as implied by the data of Lambert et al. (2006), would result in a 71% loss of solid material, which is unrealistic. Second, they showed that the trend of porosity vs. crystal diameter from Lambert et al. (2006), when extrapolated, would result in only 64% porosity when crystal size is equal to zero, which implies that cementation must have taken place in other parts of the reservoir. Accordingly, Ehrenberg et al. (2012) concluded that an 8–13% increase in porosity is too high. Our data show that after only 5% dissolution, calcite crystals developed rounded edges and corners and inter-crystal gulfs (Figs. 5A, 6A). This means that burial dissolution in natural limestones need not mean extensive porosity generation because crystals exhibiting evidence of dissolution (i.e., rounded edges and corners and inter-crystal gulfs) may occur after only minor dissolution. This conclusion is also supported by the observation that most of the crystals reported by Lambert et al. (2006) are not rounded but rather polyhedral, which suggests that the rock has probably experienced slight dissolution only.

Textural Criteria for Recognizing Dissolution

Carbonate dissolution is common in a wide range of natural environments, and it is significant in numerous critical topics, including the fate of anthropogenic CO₂, global geochemical cycles, and carbonate-reservoir properties (Morse and Arvidson 2002). Although the discussion above focuses on calcite microcrystal dissolution in burial settings, our experimental results are broadly applicable to other natural environments where calcite dissolution may take place. For example, calcite dissolution may occur within the water column (Milliman et al. 1999), at the sediment–water interface (Subhas et al. 2019), within sediments during early diagenesis (Malone et al. 2001), burial diagenesis (Lambert et al. 2006), and potentially as a result of CO₂ sequestration in deep carbonate reservoirs (Pokrovsky et al. 2009). Additionally, and perhaps most importantly, carbonate dissolution in the ocean is expected to become more pervasive due to the falling saturation state with respect to carbonate minerals as a result of rising CO₂ concentrations (i.e., ocean acidification) (Kleypas et al. 1999; Morse et al. 2006). While calcite microcrystals are not a major component of marine carbonate sediments in modern environments (e.g., Gischler et al. 2013; Hashim and Kaczmarek 2019), the dissolution features described here (pits, ledges, rounding, etc.) are not unique to calcite microcrystals, and have been shown to develop during the dissolution of other carbonate components (Berner 1978; Hover et al. 2001; Arvidson et al. 2003; Noiriel et al. 2020). For example, Hover et al. (2001) examined Holocene carbonates using high-resolution imaging and observed pits on high-Mg calcite crystals and rounded terminations on aragonite needles, which they ascribed to dissolution.

As demonstrated here, dissolution features on partially dissolved calcite microcrystals may help identify the occurrence of dissolution in natural environments and assess whether dissolution is surface controlled or transport controlled. This is particularly important when sampling of pore fluids is not possible or in open systems where fluid chemistry is continuously evolving. While carbonate dissolution has been extensively studied in the laboratory (e.g., Morse 1974b; Arvidson et al. 2003; Naviaux et al. 2019), textural changes of the dissolving material have received little attention. Future work is needed to document textural evolution during dissolution of common carbonate components in modern sediments, which will help us constrain carbonate dissolution in natural environments, particularly as a consequence of ocean acidification.