Precipitation nucleation kinetics

The reactor has been successfully used in the case of forced precipitation of copper and calcium oxalates (Jongen etal., 1996 Vacassy etal., 1998 Donnet etal., 1999), calcium carbonate (Vacassy etal., 1998) and mixed yttrium-barium oxalates (Jongen etal., 1999). This process is also well adapted for studying the effects of the mixing conditions on the chemical selectivity in precipitation (Donnet etal., 2000). When using forced precipitation, the mixing step is of key importance (Schenk etal., 2001), since it affects the initial supersaturation level and hence the nucleation kinetics. A typical micromixer is shown in Figure 8.35. 

The Ostwald step rule, or the mle of stages, postulates that the precipitate with the highest solubility (i.e., the least stable solid phase) will form first in a consecutive precipitation reaction. This mle is very well documented mineral formation via precursors and intermediates can be explained by the kinetics of the nucleation process. The precipitation sequence results because the nucleation of a more soluble phase is kinetically favored over that of a less soluble phase because the more soluble phase has the lower solid-solution interfacial tension (7cw) than the less soluble phase (equation 50). In other words, a supersaturated solution will nucleate first the least stable phase (often an amorphous solid phase) because its nucleation rate is larger than that of the more stable phase (Figure 13.26). While the Ostwald step mle can be explained on the basis of nucleation kinetics, there is no thermodynamic contradiction in the initial formation of a finely divided precursor. 

The presence of other chemical species can also influence the nucleation kinetics, crystal growth and aggregation characteristics, resulting in a modified crystal morphology due to complexation of some precipitant species and/or obstruction of some active growth sites [57,60]. 

Following the approach proposed by Nielsen (1964), Tanaka and Iwasaki (1985) used Eqs. (6.14) and (6.15) to estimate the nucleation kinetic order, n, at the onset of nucleation. For the initial precipitation conditions characterized by the supersaturation ratio, So, they obtained... 

Experimental techniques used in the assessment of kinetics of precipitation and sizing of precipitate must address the specificity of this process. In particular, they need to be concerned with rapid chemical reactions, high initial supersaturation, high-order nucleation kinetics, very short time-scale of concurrently occurring component-phenomena, and small size of the crystals. 

The classic example of precipitate nucleation in metals is the formation of GP zones in Al-Cu alloys. In ceramics, analogous examples include spinel in NiO, rutile in sapphire, or platelets of nitrogen in diamond. When particles are very small, the surface energy dominates. The calculation in Eqs. Box 15.1-Box 15.4 is instructive. Remember that the calculation is for a spherical nucleus and it ignores kinetics kinetics are actually important as we saw in Figure 15.5. 

As a solute-rich P alloy, Ti-15-3 uudez oes a phase separation into a solute-rich phase O) and a solute-lean phase (PO prior to the formation of uniform, needle-like a within the P. This uniformly dispersed a provides strengthening, but its formation requires longer aging times because of slower nucleation kinetics (compared to solute-lean p alloys). The refinement of the size and spacing of a precipitates can be achieved by minimizing the amount of recovery and recrystaUization after deformation. Stored eneigy (deformation) alters the... 

An accelerated rate of intragramdar a formation also reduces the extent of grain boundary a formation. like other solute-rich P alloys, Ii-15-3 is also susceptible to the formation of grain boundary a. The tendengrain boundary a is more pronounced because the nucleation kinetics of grain boimdaiy a is not as solute sensitive as the kinetics of homogeneous a precipitation. 

Similarly, several authors have presented MSMPR methods for kinetics determination from continuous crystallizer operation (Chapter 3), which have become widely adopted. In an early study, Bransom etal. (1949) anticipated Randolph and Larson (1962) and derived a crystal population balance to analyse the CSD from the steady state continuous MSMPR crystallizer for growth and nucleation kinetics. Han (1968) proposed a method of kinetics determination from the moments of the CSD from a cascade of continuous crystallizers and assessed the effect of sample position. Timm and Larson (1968) suggested the use of the extra information present in transient response data to determine kinetics, followed by Sowul and Epstein (1981), Daudey and de Jong (1984) and Jager etal. (1991). Tavare (1986) applied the j-plane analysis to the precipitation of calcium oxalate, again assuming nucleation and growth only. 

Figure 7 illustrates the relative rates of precipitation of y in y and y in y observed in a dendritic region of the alloy containing 22.0 % A1 aged for 48 h at 700 C. It is quite evident that the precipitation of y in y is much slower than the precipitation ofy iny. This is most likely due to the faster coarsening kinetics of y in y, but the slower nucleation kinetics ofy iny undoubtedly contribute as well. According to Calderon et al., A canbe expressed by the equation... 

This type of phase-change reaction is distinct from the dissolution-precipitation reaction which occurs in the Pb, PbOg, Ag, and Cd electrodes. In a dissolution-precipitation reaction, one soUd phase ie.g. Pb) dissolves electrochemically e.g. to form Pb " ), combines with an ion in solution, and the product precipitates e.g. PbS04). Methods for modeling mass transfer and nucleation kinetics in dissolution-precipitation reactions have been described [18,50,51,52,53,8]. 

The failure of conventional criteria may be due to the fact that it is not only one mixing process which can be limiting, rather for example an interplay of micromixing and mesomixing can influence the kinetic rates. Thus, by scaling up with constant micromixing times on different scales, the mesomixing times cannot be kept constant but will differ, and consequently the precipitation rates (e.g. nucleation rates) will tend to deviate with scale-up. 

The model is able to predict the influence of mixing on particle properties and kinetic rates on different scales for a continuously operated reactor and a semibatch reactor with different types of impellers and under a wide range of operational conditions. From laboratory-scale experiments, the precipitation kinetics for nucleation, growth, agglomeration and disruption have to be determined (Zauner and Jones, 2000a). The fluid dynamic parameters, i.e. the local specific energy dissipation around the feed point, can be obtained either from CFD or from FDA measurements. In the compartmental SFM, the population balance is solved and the particle properties of the final product are predicted. As the model contains only physical and no phenomenological parameters, it can be used for scale-up. 

Zauner, R. and Jones, A.G., 2000a. DeteiTnination of nucleation, growth, agglomeration and disruption kinetics from experimental precipitation data The calcium oxalate system. Chemical Engineering Science, 55, 4219-4232. 

Principles The reduction reaction is controlled essentially by the usual kinetic factors such as concentration of reactants, temperature, agitation, catalysts, etc. Where the reaction is vigorous, as, for example, when a powerful reducing agent like hydrazine is used, wasteful precipitation of A/, may occur throughout the whole plating solution followed by deposition on all exposed metallic and non-metallic surfaces which can provide favourable nucleation sites. In order to restrict deposition and aid adhesion, the selected areas are pre-sensitised after cleaning the sensitisers used are often based on noble metal salts. 

We might take a purist s approach and attempt to use kinetic theory to describe the dissolution and precipitation of each mineral that might appear in the calculation. Such an approach, although appealing and conceptually correct, is seldom practical. The database required to support the calculation would have to include rate laws for every possible reaction mechanism for each of perhaps hundreds of minerals. Even unstable minerals that can be neglected in equilibrium models would have to be included in the database, since they might well form in a kinetic model (see Section 26.4, Ostwald s Step Rule). If we are to allow new minerals to form, furthermore, it will be necessary to describe how quickly each mineral can nucleate on each possible substrate. 

Lebron, I. Suarez, D.L. 1996. Calcite nucleation and precipitation kinetics as affected by dissolved organic matter at 25°C and pH > 7.5. Geochimica et Cosmochimica Acta, 60(15), 2765-2776. 

A better insight into the mechanisms of the individual steps in the formation of crystals would be of great help in explaining the creation and transformation of sedimentary deposits and biological precipitates. Valuable reviews are available on the principles of nucleation of crystals and the kinetics of precipitation and crystal growth (Zhang and Nancollas, 1990 Steefel and Van Cappellen, 1990 Van Cappellen, 1991). Only a few important considerations are summarized here to illustrate the wide scope of questions to be answered in order to predict rates and mechanisms of precipitation in natural systems. 

The Ostwald Step Rule, or the rule of stages postulates that the precipitate with the highest solubility, i.e., the least stable solid phase will form first in a consecutive precipitation reaction. This rule is very well documented mineral formation via precursors and intermediates can be explained by the kinetics of the nucleation process. The precipitation sequence results because the nucleation of a more soluble... 

An interesting difference between the samples is found in the behaviour of the samples during destabilisation. While for the sample under a deuterium pressure, LiBD4 is not destabilised until both phases are molten, in the vacuum sample LiD is destabilised in the solid phase, and at much lower temperatures (ca. 360°C). This is primarily due to the improved diffusion kinetics of Li species over that of LiBD4. There is also the possibility that LiD precipitation out of the liquid phase at nucleation sites on the Mg particles allows improved mixing over the solid Mg and liquid LiBD4 observed in the sealed sample. 

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