X-ray–driven reaction front dynamics at calcite-water interfaces

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Science  18 Sep 2015:
Vol. 349, Issue 6254, pp. 1330-1334
DOI: 10.1126/science.aab3272

Driving dissolution with x-rays

Carbonate minerals are important for Earth's carbon cycle. They precipitate directly from solution into diverse materials, depending on their physical or biological source. Whether carbonate minerals grow or dissolve is controlled by the thermodynamic drivers of the mineral/water interface. To control and observe the reactions, Lanaait et al. developed a synchrotron x-ray technique that images calcium carbonate surfaces in water and selectively tunes the solution saturation state (see the Perspective by Wolthers). The x-ray beam drives fast-moving reaction fronts far from equilibrium that are more limited by solution-ion transport than by surface processes.

Science, this issue p. 1330; see also p. 1288


The interface between minerals and aqueous solutions hosts globally important biogeochemical processes such as the growth and dissolution of carbonate minerals. Understanding such processes requires spatially and temporally resolved observations and experimental controls that precisely manipulate the interfacial thermodynamic state. Using the intense radiation fields of a focused synchrotron x-ray beam, we drove dissolution at the calcite/water interface and simultaneously probed the dynamics of the propagating reaction fronts using surface x-ray microscopy. Evolving surface structures were controlled by the time-dependent solution composition, as characterized by a kinetic reaction model. At extreme disequilibria, we observed the onset of reaction front instabilities with velocities of > 30 nanometers per second. These instabilities serve as a signature of transport-limited dissolution of calcite under extreme disequilibrium.

Calcium carbonate precipitates abiotically and is synthesized by living organisms into complex and functional biomineral architectures (1). Combined, calcium carbonate minerals constitute a major fraction of Earth’s upper crust in the form of carbonate rocks (2). Characterizing the rapidly evolving morphology of calcium carbonate during growth (3, 4) and dissolution (5, 6) is central to both a fundamental understanding of its reactivity and manipulation of its versatile functionality. The morphology of calcium carbonate phases can be imaged in situ with electron (7, 8) and x-ray microscopies; however, the large radiation doses deposited by these probes can substantially alter the state of the system (9).

We used a focused x-ray beam to both observe and drive dissolution in a quantifiable manner (10). The synchrotron x-ray beam induces acidification and depletion of carbonate ions within the solution, which controlled the interfacial saturation state of solutions with respect to calcite. Simultaneously, we imaged the evolution of the calcite/water interface topography with lateral resolution below 100 nm and <1 nm height sensitivity by using x-ray reflection interface microscopy (XRIM) (11, 12). We interpreted the driven morphological changes by calculating the solution saturation within a reaction kinetics model, explaining both the observed rates of mineral reaction and the dissolution mechanisms.

XRIM captured the evolving surface topography of a calcite(104) surface in contact with a thin film of calcite-equilibrated solution (about 2 μm thick) (Fig. 1). The initial surface topography (Fig. 1A and figs. S1 and S2) was a nominally flat surface with widely spaced steps. In situ imaging was enabled by the high penetration depth of 10-keV x-rays and their scattering from the mineral/water interface (the Thomson cross-section, σT). The absorption of x-rays by the photoelectric effect (σpe) resulted in acidification and substantial (almost 100,000-fold) undersaturation of the solution with respect to calcite, driving calcite to dissolve by multiple modes, such as etch pit development and step retreat (Fig. 1C and figs. S2 and S3). The degree of undersaturation subsequently decreased to near ~10-fold undersaturation as the system approached a steady state.

Fig. 1 Imaging the calcite/water interface while simultaneously driving it far from equilibrium.

(A) Optical configuration of the x-ray reflection interface microscope. (Inset) XRIM image of steps on a pristine calcite surface. (B) (Top) Photoelectron (eph) generated by absorption of an incident x-ray photon in the calcite crystal. The photoelectron propagates to the mineral/water interface and disrupts the local equilibrium through the formation of short-lived radicals and hydrated electrons (eaq). (Bottom) Elastically reflected x-rays image the calcite surface topography, with an angle of incidence α and wave vector kin. The imaging was performed at a scattering condition, Q = 2 |kin| sin(α) = 2.1 Å−1. (C) Images of etch pits formed in response to solution undersaturation. All XRIM images were flat-field–corrected and scaled to correct for distortions due to the viewing angle of the lens with respect to the crystal surface (10). Scale bars, 2 μm.

The onset of x-ray­–induced dissolution was localized to the illuminated surface area. The initial unperturbed calcite surface was largely devoid of topographical features [time (t) = 0 s in Fig. 2A]. After irradiation, topographic changes began near a preexisting inhomogeneity (site 1). Subsequently, this region served as a nucleation center of a rhombic pit (site 2, t = 156 s), indicating the possible presence of a strain field in the crystal. At longer exposures, dissolution pits formed in apparently defect-free areas (homogenously nucleated pits) (sites 3 and 3′), and etch pits driven by extended defects that displayed anisotropic shapes occurred throughout the surface. Pit interactions such as annihilation due to surface retreat (site 5) and coalescence (site 4) were pronounced. Area measurements of sites 3 and 4 over time (movie S1) show the initial rapid lateral expansion of both pits and their subsequent stagnation at t >1500 s (Fig. 2B). The functional variation in pit area over time for these two sites was nearly identical except for an overall scale factor.

Fig. 2 Calcite dissolution driven by a pulsed x-ray beam.

(A) X-ray images acquired during the 3-s irradiation pulse (t, experimental time; τ, total time under irradiation). Sites 1, 2, and 4, dislocation etch pit; site 3, homogeneously nucleated pit; site 5, pit annihilation by surface retreat. arb., arbitrary. Scale bars, 3 μm. (B) Time-dependent area measurements of sites 3 and 4. (Inset) Final shape of site 4. (C) The homogeneously nucleated pit of site 3 assumes the shape of a conical frustum at the indicated time. (D) Velocity field analysis of the reaction fronts that drive the lateral expansion of the pit in site 3. The arrows indicate the front direction, whereas their length and color give the magnitude of the front velocity in nanometers per second. The times when the reaction front vector fields were extracted are indicated in the figures.

The occurrence of calcite etch pits is interpreted within the pit nucleation model as indicative of mineral dissolution far from equilibrium (2). The pit nucleation free energy, ΔG (6), is Embedded Image(1)where a is the size of the pit, Vuc is the volume of a calcite unit cell, kBT is the thermal energy, cCaCO3 is the solution concentration of calcium carbonate, ceq is the equilibrium concentration, γ is the surface energy of the crystal/water interface, and Uelastic is the elastic energy associated with a preexisting strain field in the crystal lattice. Pit formation results as a competition between the energy cost to create new surface area (the second term in Eq. 1) and the energy gain due to crystal dissolution (first term) and lattice strain (third term). When the system is far from equilibrium (cCaCO3ceq), pit formation is expected to occur by homogeneous nucleation at point defects, as exemplified by sites 3 and 3′ (Fig. 2A). Strain distribution associated with an extended dislocation, Uelastic, lowers the nucleation barrier of pits such as sites 2 and 4, and induces the anisotropic dissolution morphology. The appearance of the bright region in the image (Fig. 2C) indicates the formation of a flat bottom, consistent with the energetics associated with dissolution at point defects, as predicted by the pit nucleation model (2).

Front velocity field analysis of the entire data sequence reveals the propagation of surface reaction fronts and their dependence on the dissolution mode (10). Velocities of ~5 nm/s are reached within the first few hundred seconds (Fig. 2C). Reaction fronts of the homogeneously nucleated pit are largely isotropic both in shape and velocity distributions, in agreement with the pit nucleation model. The spatial distribution of the etch pit front velocity for site 4, however, shows pronounced asymmetry and directional preference (fig. S4). The role of elastic strain in the formation of such dislocation etch pits is well established (6). A time-averaged and area-normalized calcite dissolution rate of 2.24 monolayers per second was calculated from the depth and lateral extent of pits in sites 3 and 3′ [fig. S3 (10)]. This rate is nearly 10 times faster than the separate dissolution and growth rates at equilibrium (13), indicating that the perturb-image procedure drives the system far from equilibrium.

The equilibrium state of the calcite surface, determined by the aqueous concentrations of carbonate species [CO32–, HCO3–, CO2(aq), and H2CO3] and Ca2+, is disrupted by radiolysis via photoelectrons, generating highly reactive species such as hydroxyl radicals (OH) and hydrated electrons (14). We used a chemical kinetics model to predict the time evolution of the above processes and their magnitudes (10). This model includes a network of interdependent reaction pathways including (i) radiolysis, (ii) carbonate equilibria, and (iii) calcite surface reactions (table S1). The production of radicals is described within the spur diffusion model (9, 15, 16). In the absence of radiolysis, the model correctly predicts the far–from-equilibrium calcite dissolution rate versus pH and was validated against standard geochemical reaction modeling software (figs. S6 and S7 and table S2).

Upon irradiation with the pulse sequence, the solution conditions are predicted to change through two primary mechanisms: (i) acidification of the solution by generation of H+, with the solution pH dropping precipitously from the equilibrium initial value of 8.3 to 5.2 (Fig. 3, A and B); and (ii) scavenging of OH by the carbonate and bicarbonate ions to yield the carbonate radical CO3 (Fig. 3B; see fig. S8 for the time-dependent concentrations of all 25 chemical species in the system). As the acidity of the solution increases, the carbonate ion also reacts with H+ to form bicarbonate. These factors prompt a substantial decrease of the saturation index of the solution, Embedded Image, where a(t) are predicted time-dependent ionic activities, and Kcalcite (=10−8.48) is the equilibrium constant of calcite (Fig. 3D). At such a large undersaturation (Ω ~ –5), ccarbonate (t) << ceq, and homogeneous nucleation of pits is favored; we observed this dissolution behavior in sites 3 and 3′ (Fig. 2A). The ensuing dissolution of calcite releases Ca2+ and CO32– into the solution, stabilizing the solution pH by consumption of H+ to produce HCO3, and increases the bulk concentration of dissolved carbonate (Fig. 3C). After 1700 s, the saturation index approaches its initial (equilibrium) value, and there is no longer an energetic driving force to promote further calcite dissolution. This is observed in the data, where the expansion of all dissolution modes stagnates at similar times (Fig. 2B). The average rate of calcite dissolution predicted by the kinetic model, 1.5 × 10−9 mol cm−2 s−1 or 1.8 calcite monolayers per second (Fig. 3C), is in good agreement with the observed average dissolution rate of 2.2 monolayers per second. Moreover, both of these values are in agreement with previously measured calcite dissolution rates at pH ~ 5 by other methods (13, 17, 18).

Fig. 3 The predicted evolution of the composition and saturation state of a calcite equilibrated solution due to irradiation.

(A) Evolution of pH for continuous (dashed blue lines) and pulsed (red line) irradiation [and similarly in (D) and (E)]. (Inset) Irradiation sequences begin at t = 0 s. Dashed blue line, continuous exposure; solid red line, pulsed irradiation. (B) Time-dependent concentrations of solution species in response to a single x-ray square-wave pulse (off at t = 3 s). (C) Oscillations of solution concentrations irradiated by square-wave pulses. (D) Variation of the calcite solution saturation index under irradiation. (E) Calcite dissolution (instantaneous) rates predicted by the model (10). (F) Temporal evolution of calcite saturation index, Ω, as a function of absorbed radiation dose. XRIM subjects the system to a dose of 4 × 105 Gy/s under constant illumination (dashed curve) and an average of 105 Gy/s under pulsed illumination, whereas a typical in situ transmission electron microscope (TEM) subjects the system to ~108 Gy/s (9). At continuous doses higher than 104 Gy/s, the system reaches a steady state but not equilibrium.

Constant irradiation led to a substantially higher degree of undersaturation (dashed lines, Fig. 3), with a predicted calcite dissolution rate that is larger by a factor of 2 (Fig. 3E). The reaction fronts of homogeneously nucleated pits (sites 1 and 2 in Fig. 4A) reached velocities of ~25 nm s−1 (Fig. 4B), which is five times higher than observed in the pulsed irradiation experiments (Fig. 2D). Furthermore, these conditions led to a distinct anisotropy in the spatial distribution of front velocities. Upon further time evolution, a homogeneously nucleated pit at t = 123 s (site 3), began to exhibit distortions in its reaction front (Fig. 4A). At later times (t = 240 s), the configuration of this front was reminiscent of “wormhole” instabilities (19). Within the first 100 s of site 3 nucleation, the distorted front propagated with a large average velocity of ~100 nm s−1, eventually annihilating sites 1 and 2 by surface retreat (Fig. 4C) and covering the entire image field of view (movie S2). This mode of calcite dissolution was found to be reproducible under similar irradiation conditions and only present when the system was constantly driven by the beam probe (movies S3 to S6), corresponding to extended periods with substantial undersaturation (Ω < –2). The lack of any preferred direction for the reaction fronts (Fig. 4A) and the highly anisotropic spatial distribution of the front velocities (Fig. 4B) indicate that this front undergoes an instability at these extreme undersaturations. This dissolution mode is neither controlled by preexisting strain fields of extended defects (e.g., site 4 in Fig. 2A) nor displays the isotropic front velocity field expected from pits originating at point defects (e.g., site 3 in Fig. 2A).

Fig. 4 Calcite reaction front instabilities under constant irradiation.

(A) Time sequence showing the homogeneous nucleation of pits (sites 1 and 2). At later times, the appearance of a pit (site 3), whose reaction front undergoes a distortion that resembles a “wormhole” or fingering instability, is shown. Scale bars, 3 μm. (B) Reaction front velocity field analysis of site 2 at different times during its evolution, showing a clear asymmetry in velocity distribution without a distinct preferential direction. (C) Area measurements of the dissolution modes in (A).

Instabilities are a hallmark of systems undergoing reaction-diffusion processes (20). Numerous studies, however, have established that calcite dissolution is surface-controlled (i.e., not mass transport–limited) at pH > 4 (17, 21), a condition that was nominally satisfied in our experiments. The prevalence of front instabilities when the system is constantly driven by the beam probe suggests that they represent a mode of mineral/water interface reaction dynamics at conditions far from equilibrium (19). These instabilities therefore represent a dynamical signature of the onset of transport limitations and other dissipative processes at mineral/water interfaces.

Supplementary Materials

Materials and Methods

Figs. S1 to S9

Tables S1 and S2

References (2237)

Movies S1 to S6 (compressed video files)


  1. Materials and methods are available as supplementary materials on Science Online.
  2. ACKNOWLEDGMENTS: This work was supported by the Geosciences Research Program of the Office of Basic Energy Sciences, U.S. Department of Energy (DOE), at Argonne National Laboratory (ANL), the University of Illinois at Chicago, and the University of Delaware. The x-ray data were collected at the Advanced Photon Source (33-ID-D), a U.S. DOE Office of Science User Facility at ANL. A portion of this research was performed by N.L. as a staff member at the Center for Nanophase Materials Sciences, a U.S DOE Office of Science User Facility at Oak Ridge National Laboratory. Primary data for this report are uncompressed video files that are available upon request from N.L and P.F. N.L. and P.F. designed the research and wrote the manuscript with input from all authors. N.L. analyzed the x-ray data and performed modeling and computations. E.B.C. and P.F. prepared the samples. All authors participated in x-ray imaging experiments.
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