Transformations initiated heterogeneous nucleation

Phase transformations in heterogeneous catalysis have been described recently by topochemical kinetic models [111-115]. These models were taken from solid chemistry, where they had been developed for "gas-solid reactions. The products of such reactions are solids. When gas is in contact with the initial solid, the reaction rate is negligible. But as nucleates of the phase... 

At Ms temperature TiNi initiates a uniform (inhomogeneous) distortion of its lattice — through a collective atomic shear movement. The lower the temperature, the greater the magnitude of shear movements. As a result, between Ms and Mr temperature the crystal structure is not definable. In sharp contrast, other known martensitic transformations initiate a nonuniform (heterogeneous) nucleation at Ms and thereafter the growth of martensite is achieved by shifting of a two dimensional plane known as invariant plane [28] at a time. Thus, between Ms and Mr temperature the crystal structure is that of austenite and/or martensite . 

Figure 13.29. Schematic sorption isotherms of a metal ion (Me) on an oxide (XO ) at constant pH (a) adsorption only (H) adsorption and surface precipitation via ideal solid solution (c) adsorption and heterogeneous nucleation in the absence of a free energy nucleation barrier (AG 0) adsorption and heterogeneous nucleation of a metastable precursor (e) same as in (3) but with transformation of the precursor into the stable phase. The arrows show the isotherm evolution for continual addition of dissolved Me. The initial isotherm with the slope of 1 (in the double logarithmic plot) corresponds to a Langmuir isotherm (surface complex formation equilibrium). [Me]s , = solubility concentration of Me for the stable metal oxide [Me]p = solubility concentration of Me for a metastable precursor (e.g., a hydrated Me oxide phase). (From Van Cappellen, 1991.)...

In a phase transformation such as crystallization, the two basic processes are the initiation or nucleation process by which a new phase is initiated within a parent phase, and the subsequent growth of the new phase at the expense of the previous one (Gedde, 1995). The former may occur homogeneously, by statistical fluctuations in the parent phase, or by formation of nuclei catalysed by heterogeneity... 

Most systems in everyday life are not perfectly clean, and dusts, particulates or several substrates provide a template for initial growth of a new phase. If the value of the interfacial tension between the new condensing phase and the particle (or the substrate) surface is low, then this property considerably decreases the energy requirement of nuclei formation (AGT)max so that heterogeneous nucleation occurs as an easier and preferable path for phase transformations. In addition, phase transformations take place at or very close to the equilibrium temperature. 

The existence of three populations in a macroemulsion process (i) (monomer-swollen) micelles, (ii) polymer particles, and (iii) large monomer droplets only heterogeneous nucleation leading to transformation of micelles into polymer particles is considered (shown here with the entry of R2 formed after two propagation steps with I) I2, water soluble initiator large arrow represents monomer diffusion towards polymer particle. 

Tobin (53) has treated the impingement problem in a somewhat different manner from that of Avrami. The premise that impingement is the cause of the cessation of growth and the termination of the crystallization is still the underlying principle involved. This analysis was initially developed for a constant homogeneous nucleation rate accompanied by either two- or three-dimensional growth. It was subsequently extended to heterogeneous nucleation. For the two-dimensional problem, the transformed area at time t, A(t), can be represented as... 

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