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Nanomaterials Fabrication  37

           and growth rates (Figure 3.2a). In order to obtain particles of homoge-
           neous size, it is necessary that the nucleation and growth steps be sep-
           arated to ensure that a single nucleation stage takes place, and that
           growth, via accumulation of all remaining matter, be controlled. This
           implies that the nucleation rate should be much greater than the rate
           at which the precursor is generated. Under these conditions, nucle-
           ation is very brief and clearly decoupled from the growth phase. If the
           nucleation rate is not high enough compared to the rate of generation
           of the precursor, precursor concentration remains higher than C min
           throughout the reaction, and nucleation and growth are simultaneous.
           The growth of the first nuclei is much larger than that of the younger
           ones, which leads to a large particle size distribution.
        4. Nucleation and growth steps form particles under kinetic control fol-
           lowing a reaction path of minimum activation energy under condi-
           tions imposed to the system (acidity, concentration, temperature), but
           the products are not necessarily thermodynamically stable. Aging of
           the suspensions, which may take place over a very large time scale
           (hours, days, or months), allows the system to tend toward or reach
           stability, and it is often associated with modifications of some phys-
           ical or chemical characteristics of the particles. “Ostwald ripening”
           leads to an increase in the average particle size and possible aggre-
           gation (zone IV, Figure 3.2a). Aging may also trigger a change in
           morphology and crystalline structure or even cause crystallization of
           amorphous particles. In fact, aging is one of the most important phe-
           nomena that must be considered, because it determines the charac-
           teristics of the particles after precipitation.

        Control of particle size, crystalline structure, and morphology. There are
        different techniques to form the complex of zero charge and to obtain a
        solid. The most common method consists of introducing a base into the
        acid solution of a metal salt at room temperature. When solutions such
        as these are mixed, a high concentration of hydroxylated complexes
        rapidly forms along with induced local pH gradients. Inhomogeneities
        in the hydrolysis products often present during such a missing procedure
        may result in random condensation and the formation of an amor-
        phous solid with an ill-defined chemical composition. Such a result
        is exemplified by the case of ferric ions. They precipitate quasi-
        instantaneously at pH 
 3 into a poorly defined, highly hydrated phase,
        called 2-line ferrihydrite [19]. (This phase takes its name from its X-ray
        diffraction pattern, which exhibits only two broad bands.) In similar con-
        ditions, Al 3   ions form a transparent amorphous gel [20]. At pH 
 2,
        Ti 4   ions form an amorphous oxyhydroxide with a composition near to
        TiO 0.3 (OH) 3.4  [21]. These solids are formed of very small size particles,
        around 2–3 nm in diameter, and are strongly metastable. They evolve
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