Dissolution Kinetics of Cubic Tricalcium Aluminate Measured by Digital Holographic Microscopy

In situ digital holographic microscopy is used to characterize the dissolution flux of polycrystalline cubic tricalcium aluminate (C₃A-c). The surface dissolves at rates that vary considerably with time and spatial location. This implies a statistical distribution of fluxes, but an approximately steady-state median rate was obtained by using flowing solutions and by reducing the water activity in the solution. The dissolution flux from highly crystalline C₃A-c depends on the water activity raised to an empirically derived exponent of 5.2 and extrapolates to a median flux of - 2.1 μmol m^-2 s^-1 in pure water with an interquartile range of 3.2 μmol m^-2 s^-1. The flux from a less crystalline source of C₃A-c has an empirical water activity exponent of 4.6 and an extrapolated median flux of only -1.4 μmol m^-2 s^-1 in pure water with an interquartile range of 1.9 μmol m^-2 s^-1. These data suggest that the bulk dissolution rate of C₃A-c can vary by at least 30% from one source to another and that variability in the local rate within a single material is even greater because of the heterogeneous spatial distribution of structural characteristics (i.e., degree of crystallinity, chemical impurities, and defects).

Calcite dissolution rate spectra measured by in situ digital holographic microscopy

Digital holographic microscopy in reflection mode is used to track in situ, real-time nanoscale topography evolution of cleaved (104) calcite surfaces exposed to flowing or static deionized water. The method captures full-field holograms of the surface at frame rates of up to 12.5 s-1. Numerical reconstruction provides 3D surface topography with vertical resolution of a few nanometers and enables measurement of time-dependent local dissolution fluxes. A statistical distribution, or spectrum, of dissolution rates is generated by sampling multiple area domains on multiple crystals. The data show, as has been demonstrated by Fischer et al. (2012), that dissolution is most fully described by a rate spectrum, although the modal dissolution rate agrees well with published mean dissolution rates (e.g., 0.1 µmol m-2 s-1 to 0.3 µmol m-2 s-1). Rhombohedral etch pits and other morphological features resulting from rapid local dissolution appear at different times and are heterogeneously distributed across the surface and through the depth. This makes the distribution in rates measured on a single crystal dependent both on the sample observation field size and on time, even at nominally constant undersaturation. Statistical analysis of the inherent noise in the DHM measurements indicates that the technique is robust and that it likely can be applied to quantify and interpret rate spectra for the dissolution or growth of other minerals.

In situ nanoscale observations of gypsum dissolution by digital holographic microscopy

Recent topography measurements of gypsum dissolution have not reported the absolute dissolution rates, but instead focus on the rates of formation and growth of etch pits. In this study, the in situ absolute retreat rates of gypsum (010) cleavage surfaces at etch pits, at cleavage steps, and at apparently defect-free portions of the surface are measured in flowing water by reflection digital holographic microscopy. Observations made on randomly sampled fields of view on seven different cleavage surfaces reveal a range of local dissolution rates, the local rate being determined by the topographical features at which material is removed. Four characteristic types of topographical activity are observed: 1) smooth regions, free of etch pits or other noticeable defects, where dissolution rates are relatively low; 2) shallow, wide etch pits bounded by faceted walls which grow gradually at rates somewhat greater than in smooth regions; 3) narrow, deep etch pits which form and grow throughout the observation period at rates that exceed those at the shallow etch pits; and 4) relatively few, submicrometer cleavage steps which move in a wave-like manner and yield local dissolution fluxes that are about five times greater than at etch pits. Molar dissolution rates at all topographical features except submicrometer steps can be aggregated into a continuous, mildly bimodal distribution with a mean of 3.0 µmolm-2 s-1 and a standard deviation of 0.7 µmolm-2 s-1.

Phase Uncertainty in Digital Holographic Microscopy Measurements in the Presence of Solution Flow Conditions

Digital holographic microscopy (DHM) is a surface topography measurement technique with reported sub-nanometer vertical resolution. Although it has been made commercially available recently, few studies have evaluated the uncertainty or noise in the phase measurement by the DHM. As current research is using the DHM to monitor surface topography changes of dissolving materials under flowing water conditions, it is necessary to evaluate the effect of water and flow rate on the uncertainty in the measurement. Uncertainty in this study was concerned with the temporal standard deviation per pixel of the reconstructed phase. Considering the effects of solution flow rate, magnification, objective lens type (air or immersion), and experimental configuration, measurements under static conditions in air and in water with an immersion lens yielded the smallest amount of uncertainty (mean of ≤ 0.5 nm up to 40× magnification). Increasing the water flow rate resulted in an increase in mean uncertainty to ≤ 0.6 nm up to 40× with an immersion lens. Observations of a sample through a glass window at 20× magnification in flowing water also yielded increasing uncertainty, with mean values of ≤ 0.5 nm, ≤ 0.8 nm, and ≤ 1.1 nm for flow rates of 0 mL min^-1, 15 mL min^-1, and 33 mL min^-1. Different hologram acquisition rates (12.5 s^-1 and 25 s^-1) did not significantly impact the uncertainty in the phase. Collecting holograms in single-wavelength versus dual-wavelength modes did impact the uncertainty, with the mean uncertainty at 10× magnification for the same wavelength being ≤ 0.5 nm from the single-wavelength mode compared to ≤ 1.5 nm from the dual-wavelength mode. When the quantified uncertainty was applied to simulated dissolution data, lower limits of measured dissolution rates were found below which the measured data may not be distinguishable from the uncertainty in the measurement. The limiting surface-normal dissolution velocity is -10^-11.7 m s^-1 for experiments with an immersion lens in flowing water conditions and -10^-11.7 m s^-1, -10^-11.4 m s^-1, and -10^-11.0 m s^-1 for static (0 mL min^-1), slow (≤ 15 mL min^-1), and fast (≤ 109 mL min^-1) flowing water conditions in experiments with a glass window, respectively. The data presented by this study will allow for better experimental design and methodology for future dissolution or precipitation studies using DHM and will provide confidence in the data produced in postprocessing.