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Nanomaterials Fabrication  39

          If the suspensions are aged at an acidity where the solubility of the
        solid is very low or at a minimum, the concentration of soluble species
        in equilibrium with the solid phase does not allow an efficient transport
        of matter, and crystallization of the early amorphous material will occur
        more easily by a transformation in situ, in the solid state. The trans-
        formation involves the diffusion of ions within the solid with partial
        dehydration, and the formation of crystalline domains of very small
        size. Nanoparticles of hematite,  -Fe O , are so obtained from ferrihy-
                                             3
                                          2
        drite at 6    pH    8 [23]. Very small nanoparticles of boehmite,
                                   2   1
         -Al(O)(OH), (around 300 m   g ) are similarly obtained by aging of
        aluminate gels at the same pH range (6 to 8) [20]. Although boehmite
        is not the most thermodynamically stable phase at room temperature,
        it is probably kinetically stabilized because the system is constrained
        to evolve without heating and transforms on the lowest activation energy
        path. Between pH 2 and pH 7, where the solubility of titania is very low,
        the amorphous solid is transformed into TiO anatase nanoparticles
                                                   2
        [21]. Over this acidity range, the particle size of anatase depends on the
        pH of precipitation and aging. This effect of acidity on particle size will
        be discussed later.
          Precipitation by addition of a base at room temperature may also lead
        to stable crystalline nanoparticles without involving any transformation by
        the above mechanisms. For instance, magnetite Fe O is easily obtained by
                                                    3
                                                       4
                                3       2
        coprecipitating aqueous Fe  and Fe  ions with x   0.66 [24]. Iron ions are
        distributed into the octahedral (Oh) and tetrahedral (Td) sites of the face
                                                       3      3   2
        centered cubic (fcc) stacking of oxygen according to [(Fe ) (Fe Fe ) O ].
                                                                    Oh
                                                          Td
                                                                       4
        Magnetite is characterized by a fast electron hopping between the iron
        cations on the octahedral sublattice. Crystallization of spinel is quasi-
                                                                    2
        immediate at room temperature, and electron transfer between Fe  and
           3
        Fe   ions plays a fundamental role in the process [25, 26]. In effect,
                                3      3
        maghemite,  –Fe O , [(Fe ) (Fe   5/3 V ) O ] (where V stands for a
                                   Td
                           3
                                            1/3 Oh
                                                  4
                         2
        cationic vacancy) does not form directly in solution by precipitation of
                                              2
        ferric ions, but a small proportion of Fe  (  10 mol %) induces the
        crystallization of all the iron into spinel. Studies of the early precipitate
                           2                               2
        revealed that all Fe  ions were incorporated into a Fe -ferrihydrite,
        forming a short-range ordered, mixed valence material exhibiting fast
        electron hopping, as evidenced by Mössbauer spectroscopy [26]. Electron
        mobility brings about local structural rearrangements and drives spinel
        ordering. Besides this topotactic process, crystallization of spinel can also
        proceed by dissolution crystallization, resulting in two families of non-
                                        III    III   II
        stoichiometric spinel particles [(Fe ) (Fe 1+2z/3 Fe 1 z V ) O ] with very
                                                               4
                                                         z/3 Oh
                                          Td
        different mean size [25]. The relative importance of these two path-
                              2
        ways depends on the Fe   level in the system, and the end products of
        the coprecipitation are single phase only for 0.60   x   0.66. The com-
                                     2                   2
        parison with the cases where M  is different from Fe  emphasizes the
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