598 CHAPTER 20 Theories of nanoparticle and nanostructure formation in liquid phase and crystallization. In general, tiny NP "clusters" are gathered together to form NPs, and then the NPs are assembled to form nanostructures. In bottom-up approaches, cluster formation and nucleation are the first steps in NP formation, and they are the most crucial steps in controlling the crystal structure, size, shape, and surface characteristics of NPs [9]. Nucleation is the process whereby nuclei (seeds) act as templates for crystal growth. Nucleation may happen in the solution homogeneously or heterogeneously. Homogeneous nucleation occurs when nuclei form uniformly within the parent phase, whereas heterogeneous nucleation forms on a solid support (nucleating surface), such as container surfaces, impurities, grain boundaries, or dislocations [10]. In general, heterogeneous nucleation occurs much more easily than homogenous nucleation, since a stable nucleating surface is already present.The fundamental phenomena involved in crystallization from solutions via nucleation and growth is still a hot topic [11]. Recently, significant efforts have been directed to understanding the mechanism of NP formation in solutions [12][13][14]. In particular, attention has been directed to study the wide varieties of additives and their influences on prenucleation clusters, nucleation, crystallization, nanocrystal assembly, and thus morphologies.The importance of NPs and nanostructures in many fields of science and technology has spurred a high level of research activity and led to the formulation of well-established theories for nucleation and crystal growth. This chapter highlights the different theories, such as classical nucleation theory (CNT), La Mer's nucleation and growth mechanisms, the two-step nucleation and growth mechanism, and the prenucleation cluster (PNC) mechanism. Subsequently in situ experimental characterization for NP formation, including nucleation and growth processes, will be highlighted, and what occurs within the different processes outlined. ■ ■ FIGURE 20.9 (A) The processes of Au depositing on a Pt icosahedral nanocrystal is schematically demonstrated. (B) The nucleation and growth of Au on Pt nanocrystals are quantitatively analyzed. (Source: Reproduced with permission from Ref. [47]. 615 6 In situ characterization techniques ■ ■ FIGURE 20.10 Radius, concentration, and size distribution from the SAXS fitting results. (A) The results of the fit of the SAXS patterns are presented as a function of time. For the two different ligands, the concentration of particles (n/N A ), the center of the Gaussian distribution, and the σ parameter are designated. (B) SAXS patterns for the first instants of the reaction and the corresponding fits for an acid ligand are shown. (C) Corresponding size distribution is given for the SAXS patterns presented in (B). (Source: Reproduced with permission from Ref. [48].