Statistical Characterization of Heterogeneous Dissolution Rates of Calcite from In situ and Real-Time AFM Imaging

Abstract

The evolution of the surface topography of a calcite crystal subject to dissolution is documented through in situ real-time imaging obtained via atomic force microscopy (AFM). The dissolution process takes place by exposing the crystal surface to deionized water. AFM data allow detection of nucleation and expansion of mono- and multilayer rhombic etch pits and are employed to estimate the spreading rate of these structures. Spatially heterogeneous distributions of local dissolution rate are evaluated from the difference between topographic measurements taken at prescribed time intervals. We rest on a stochastic framework of analysis viewing the dissolution rate as a generalized sub-Gaussian (GSG) spatially correlated random process. Our analysis yields: (i) a quantitative assessment of the temporal evolution of the statistics of the dissolution rates as well as their spatial increments; (ii) a characterization of the degree of spatial correlation of dissolution rates and of the way this is linked to the various mechanisms involved in the dissolution process and highlighted through the experimental evidences. Our results indicate that the parameters driving the statistics of the GSG distribution and the spreading rate of the multilayer pits display a similar trend in time, thus suggesting that the evolution of these structures imprints the statistical features of local dissolution rates. Article Highlights We investigate dynamics of dissolution patterns on a calcite crystal in contact with deionized water via AFM imaging Temporal behavior of parameters of our statistical model is consistent with surface pattern evolution A nested model for the spatial correlation of rates embeds multiple mechanisms driving dissolution rate.

A Gaussian-Mixture based stochastic framework for the interpretation of spatial heterogeneity in multimodal fields

“…Journal Pre-proof for several variables. For example, permeability (Painter, 1996;Riva et al, 2013), porosity (Painter, 1996;Guadagnini et al, 2014), hydraulic conductivity (Liu and Molz, 1997;Guadagnini et al, 2013;Meerschaert et al, 2004), and mineral dissolution rates observed at the microscale (Siena et al, 2021) are documented to be characterized by distributions of incremental values (∆Y ) whose moments and main traits vary with s in a way that is not consistent with the assumption that Y be modeled as a Gaussian field. With specific reference to hydrogeological settings, when considering a porous medium whose internal architecture comprises different zones (or regions), each associated with a given geomaterial, attributes such as conductivity/permeability within each region can be viewed as characterized by a unimodal distribution (see, e.g., Winter et al, 2003 and references therein).…”

“…A similar approach has been adopted by Siena et al (2020Siena et al ( , 2021 in the context of their statistical analyses of mineral dissolution rates observed at the micro-scale through the use of modern Vertical Scanning Interferometry (VSI) and Atomic Force Microscopy (AFM).…”

“…Some preliminary studies on stochastic characterizations are available. These are based, e.g., on a Generalized Extreme Value (Brand et al, 2017) or a GSG (Siena et al, 2021) model. Otherwise, further work is needed to comprehensively address the complex system behavior documented at such scales.…”

“…Prior to analysis, AFM data often require a signal processing phase, as reported by Marinello et al (2010). Following Siena et al (2021), we perform a preliminary detrend subtracting the best fitting second order polynomial function from the raw topography data. This enables us to remove the distortion induced by the AFM scanning and to obtain the fluctuation of calcite topography about its mean, i.e.…”

“…Similar to Siena et al (2021), we view the dissolution rate as a random field. We express it as the sum of an average dissolution rate, ⟨R(t)⟩ = [⟨z(x, y, t)⟩ − ⟨z(x, y, t + ∆t)⟩] /V m ∆t, which is constant…”