Autor: Alberto Guadagnini (Vice rector de investigación en el politécnico de Milán)
In-situ observation of calcite dissolution rates via Atomic Force Microscopy.
We analyze the dissolution process taking place at the surface of a calcite crystal in contact with deionized water. We document the heterogeneous pattern of surface topography and ensuing reaction rates through in-situ real-time imaging obtained via atomic force microscopy (AFM). The experiments enable one to document the occurrence of various mechanisms driving the evolution of the crystal surface. These include nucleation and expansion of mono- and multilayer etch pits as well as terraces. Local dissolution rates are evaluated from the diﬀerence between measurements of the crystal surface at various times. Observations are then interpreted within a stochastic framework. We analyze jointly the probability distribution of reaction rates and their associated spatial increments, taken between locations separated by any given distance (or lag). We rely on a bi-modal Gaussian mixture model to characterize the spatial distribution of reaction rates. The modes of the mixture correspond to an indicator random variable. The latter is in turn related to the processes taking place across the domain of observation. Our formulations for the probability density function of spatial increments of the rate enables us to embed a joint analysis of the PDF of data and their increments within a unique theoretical framework that ensures consistency between these two types of information. Our results (a) support our ability to obtain direct observation at the microscale of such dissolution processes, (b) reveal a remarkable agreement between sample and modeled statistics of dissolution rates and their spatial increments, and (b) show that one can effectively infer distributions of quantities of interest through a joint analysis of observed values and their increments.