Dissolution kinetics and topographic relaxation on celestite (0 0 1) surfaces: The effect of solution saturation state studied using Atomic Force Microscopy

Abstract

Dissolution of celestite (0 0 1) was studied by atomic force microscopy as a function of solution undersaturation. In solutions near saturation with respect to celestite, dissolution of the mineral took place exclusively by removal of ions from existing step edges. The onset of etch pit nucleation was observed at a critical saturation state of ${\Omega }_{\text{crit}}\sim 0.1(=[{\text{Sr}}^{2+}][\text{SO}_4{}^{2-}]/K_{\text{sp}})$. Below this saturation state, dissolution took place both at existing step edges and via the creation of new steps surrounding the etch pits. The dissolution rates of celestite exhibited a non-linear dependence on saturation state. Basic crystal dissolution/growth models were inadequate to describe the non-linearity, but a model that incorporates a critical undersaturation provided an improved fit to data collected at high undersaturation. A simple model for dissolution at low undersaturation also fit the rate data well, but in light of the conditions necessary to produce new step edges, the rate coefficient in this model is poorly constrained due to the effects of sample surface history. Consideration of the process of topographic relaxation, consisting of changes in the surface microtopography (i.e., step density) resulting from changes in solution conditions, led to predicted relaxation times on the order of days for the celestite–water interface.

Introduction

Mineral dissolution processes have significant geochemical, environmental and biological impacts; and thus exert essential controls over geochemical cycles. Of all minerals, reactions at the interfaces of naturally occurring sulfate minerals and water control important aspects of the sulfur geochemical cycle. Geochemical transformations of sulfur in sediments impact processes like early sedimentary diagenesis, conditions for mineral deposition and the global cycling of sulfur (Goldhaber, 2004). Celestite (SrSO₄), a naturally occurring sulfate mineral, is usually found in marine sedimentary deposits and sometimes in groundwater aquifers (Hanor, 2000, Chapelle, 2004). Celestite is highly reactive at room temperature compared to the isostructural mineral barite (e.g., Dove and Czank, 1995) and dissolution and precipitation of celestite likely plays an important role in determining the Sr composition in natural waters.

Understanding the kinetics of dissolution of minerals at different experimental conditions permits a description of mineral–water interactions in natural systems, for example, in ground and surface water, or in soils and sediments. The general form of the rate equation used in most mineral dissolution studies is (Lasaga, 1981):

$$\text{Rate}=k(1-\Omega {)}^n$$

where rate is typically in units of mol cm⁻² s⁻¹ and Ω in Eq. (1) represents the solution saturation state:

$$\Omega =\frac{[{\text{Sr}}^{2+}][\text{SO}_4{}^{2-}]}{K_{\text{sp}}}$$

In the above expressions, k is the rate coefficient with units depending on the reaction order, n, a constant which may relate to the reaction mechanism if appropriate constraints are placed on the system of interest (Teng et al., 2000). [Sr²⁺] and $[\text{SO}_4{}^{2-}]$ are the activities of Sr²⁺ and $\text{SO}_4{}^{2-}$ ions, respectively, and K_sp represents the solubility product of the celestite. In Eq. (1), the kinetic behavior of a mineral reaction with n = 1 describes either adsorption-controlled or transport-controlled growth and dissolution (Nielsen, 1983). With n = 2, the rate equation may be indicative of spiral growth and dissolution at screw dislocations (Brantley, 2004). From a fundamental mechanistic perspective, simple integer power laws such as Eq. (1) provide a test for experimental consistency with certain proposed mechanisms (Nancollas et al., 1973), however, n has often been used as an adjustable parameter for empirical fitting of data (Reddy and Nancollas, 1973, Reddy, 1977, House, 1981, Blum and Lasaga, 1987, Shiraki and Brantley, 1995).

To model trends in dissolution rate as a function of saturation state in which Eq. (1) models do not apply, Lasaga and Lüttge (2001) proposed a different rate equation on the basis of dissolution of steps originating from dissolution etch pits. The model features non-linear variation in the reaction rate with chemical potential and is expressed as:

$$\text{Rate}=A(1-\Omega )\tanh \left(\frac{B}{f(\Omega )}\right)f(\Omega )$$

$$f(\Omega )=\left(\frac{{\Omega }_{\text{crit}}-\Omega }{1-\Omega }\right)$$

Three parameters, A, B and Ω_crit describe the relationship between dissolution rate and Ω where Ω_crit is the critical saturation state below which etch pit formation at linear defects is spontaneous, A is the dissolution rate far from equilibrium, and B is related to the surface diffusion distance, x_s, expressed in molecular or lattice units (Lasaga and Lüttge, 2001).

$$B=\frac{1}{2x_{\text{s}}}$$

Dissolution generally occurs on mineral surfaces by the nucleation of dissolution etch pits and by the retreat of surface steps. Previous studies show that formation of etch pits promoting mineral dissolution occurs on the exposed mineral surfaces at discrete active sites (Helgeson et al., 1984, Brantley et al., 1986). The “active sites” include cleavage fractures, dislocations and grain boundaries (Helgeson et al., 1984). Studies of celestite dissolution have characterized both the mineral’s microscopic and macroscopic dissolution characteristics. The rate of celestite (0 0 1) dissolution was measured by AFM (6.3 × 10⁻¹² mol cm⁻² s⁻¹) in deionized water at ∼30 °C (Dove and Platt, 1996). Related studies on sulfate powder specimens by Dove and Czank (1995) described the dissolution kinetics of celestite, barite (BaSO₄) and anglesite (PbSO₄) over a wide range of pH and temperatures. Because AFM-based rates are typically sampled from surface areas of order 100 μm² whereas powder-based rates result from areas often exceeding 100 cm², and mineral surfaces may possess a wide range of heterogeneities such as microfacets, grain boundaries, dislocations and microfractures (Schott et al., 1989), comparison of rates in the two methods is not immediately valid.

Mineral surface behavior and reaction kinetics are influenced by solution saturation state, affecting both nucleation of etch pits and dissolution at step edges. A recent study on calcite demonstrated the effect of saturation state on the generation of etch pits (Teng, 2004), however, prior studies on celestite dissolution have not explored this effect. In the calcite study, in nearly saturated solutions (Ω > 0.54), no etch pit formation was observed and dissolution proceeded at the existing steps. Further from equilibrium (Ω  ≅ 0.50), etch pits were generated at presumed linear defect sites. A dramatic rise in etch pit density was noted at Ω ≅ 0.007 where random two-dimensional etch pit nucleation was observed. The findings presented above in light of the theoretical dissolution kinetics models indicate a need to examine effects on dissolution kinetics of other minerals to eventually formulate more generally applicable rate equations describing dissolution in natural systems (Teng, 2004).

Here, the investigations are aimed at addressing the basic hypothesis that dissolution models based on step edge dissolution do not adequately predict behavior under conditions where defect-driven etch pit nucleation is significant. To test the applicability of the models discussed above in the dissolution of celestite, a series of experiments were conducted using fluid cell AFM as a means to simultaneously measure dissolution rates and observe the surface microtopography at varying degrees of solution undersaturation.