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Densely packed surface fractal aggregates form in systems with high local volume fractions of particles with very short diffusion lengths, which effectively means that particles have little space to move. However, there are no prior mathematical models, which would describe scattering from such surface fractal aggregates and which would allow the subdivision between inter- and intraparticle interferences of such aggregates. Here, we show that by including a form factor function of the primary particles building the aggregate, a finite size of the surface fractal interfacial sub-surfaces can be derived from a structure factor term. This formalism allows us to define both a finite specific surface area for fractal aggregates and the fraction of particle interfacial sub-surfaces at the perimeter of an aggregate. The derived surface fractal model is validated by comparing it with an ab initio approach that involves the generation of a "brick-in-a-wall" von Koch type contour fractals. Moreover, we show that this approach explains observed scattering intensities from in situ experiments that followed gypsum (CaSO4·2H2O) precipitation from highly supersaturated solutions. Our model of densely packed "brick-in-a-wall" surface fractal aggregates may well be the key precursor step in the formation of several types of mosaic- and meso-crystals. [ABSTRACT FROM AUTHOR]

The pathways of CaCO3 crystallization are manifold, often involving one or several metastable amorphous or nanocrystalline intermediate phases. The presence of such intermediates is often overlooked, because they are short-lived and/or occur at small molar fractions. However, their occurrence does not just impact the mechanisms and pathways of formation of the final stable CaCO3 phase, but also affects their crystal size, shape, and structure. Here we document the presence of a short-lived intermediate through in situ and time-resolved small and wide-angle X-ray scattering combined with high resolution electron microscope observations. When ikaite forms concomitant with the dissolution of amorphous calcium carbonate (ACC) but prior to calcite formation, fairly large glendonite-type calcite crystals grow despite the presence of citrate ligands that usually reduce crystal size. These were ideal seeding crystals for further crystallization from supersaturated ions in solution. In contrast, in the absence of ikaite the crystallization of calcite proceeds through transformation from ACC, resulting in fine-grained spherulitic calcite with sizes ~8 times smaller than when ikaite was present. Noteworthy is that the formation of the intermediate ikaite, although it consumes less than 3 mol % of the total precipitated CaCO3, still clearly affected the calcite formation mechanism. [ABSTRACT FROM AUTHOR]