Lattice incorporation

In summary, Pingitore and Eastman (31) presented a model of lattice and non-lattice incorporation of Sr2+ into calcite, the contribution of each mode of coprecipitation to the overall calculated value of kcSr depending on the specific conditions of the experimental run. 

When the charge-transfer step in an electrodeposition reaction is fast, the rate of growth of nuclei (crystallites) is determined by either of two steps (I) the lattice incorporation step or (2) the diffusion of electrodepositing ions into the nucleus (diffusion in the solution). We start with the first case. Four simple models of nuclei are usually considered (a) a two-dimensional (2D) cylinder, (b) a three-dimensional (3D) hemisphere, (c) a right-circular cone, and (d) a truncated four-sided pyramid (Fig. 7.2). 

La is of interest in its relationship to biological hydroxyapatite because of their inhibitory effect on the demineralization of dental enamel. The form of La was not clear, namely surface adsorption or lattice incorporation. In an attempt to clarify it, laser-induced luminescence has been used (Mayer et al. 1999). La " is not luminescent, Gd-containing samples were prepared and studied. Figure 11.1 demonstrates Gd luminescence spectra with 266 nm laser excitation before and after heating at 800 °C. It is clearly seen that luminescence intensity is drastically stronger after thermal treatment. Thus precipitated samples must be heated to 800 °C to enable Gd " " to replace Ca and become luminescent and its incorporation form is surface adsorption. 

Fig. 7.120. The path taken by ions undergoing deposition and lattice incorporation to form a new row of atoms.

Fig. 7. 122. Representation of a hydrated ion at the OHP awaiting deposition and lattice incorporation.

Fig. 7.132. Following surface diffusion to a step site, the adion diffuses along the step to a kink site and to final lattice incorporation.

Fig. 7.133. Consecutive steps (charge transfer, surface diffusion, and lattice incorporation) involving several ions and showing the advancement of a step by lattice building.

The steps by which ions from solution are incorporated into the lattice have been described. The next question is obvious. What happens when many ions travel the deposition path, i.e., the path of charge transfer to a plane, surface diffusion to steps, then movement to kinks, and finally lattice incorporation ... 

The relevance of crystal faces to the subject of electrociystalhzation comes up as follows Each of the crystal faces just described contains all the microfeatures that have been described in previous sections, steps, kinks, etc. Further, the same phenomena of deposition—the ions crossing the electrified interface to form adions, the surface diffusion, lattice incorporation of adions, screw dislocation, growth spirals, etc.—occur on all the facets. 

These authors assume that lattice incorporation occurs with the participation of metal ions... 

In any event, extensive purification in the laboratory by any applicable method, including preparative high-performance liquid chromatography, is recommended as part of growth potential determination studies. The importance of this effort cannot be over-stated since a particular compound may not grow only because of the presence of impurities and not because of inherent crystal lattice incorporation restrictions. 

At low Ti02 contents (0-15 mol % Ti02), there is a pronounced interaction between two oxides resulting in the formation of Al-Ti mixed oxide. In this oxide, a part of Ti ions appears to occupy tetrahedral positions of the AI2O3 lattice. Incorporation of Ti ions lowers the crystallinity of AI2O3, which, in turn, results in an increase in the specific surface area of the mixed oxide. As a result of Ti-Al interaction, formation of the Ti02 phase is negligible and Ti is uniformly distributed in the oxide particles. 

Investigations into the possibility of incorporation of chromium or copper into the tin(IV) oxide were made by indexing and refining the XRD patterns by the Rietveld method. No lattice incorporation is induced by thermal treatment. 

In the case of crystal growth from the vapour phase, the energy change involved in lattice incorporation can be related approximately to the enthalpy of subli-... 

Fig. 9.9 - The formation of a screw dislocation by the displacement of atoms shown in the figure creates an edge at which lattice incorporation can occur. The edge then propagates, allowing further growth without the need for the formation of new growth centres by nucleation.

NUCLEATION AND GROWTH OF THREE-DIMENSIONAL CENTRES 9.4.1 Rate determining step—lattice incorporation... 

Lattice incorporation Resemblance of molecular Sweating, fractional... 

The total amount of impurities in the crystalline product, is the sum of all potential impurities as depicted in Figure 7.1, that is, the contributions of the surface adsorption, mi, of bulk phase inclusion of mother liquor, m2, the liquid inclusions in the crystal, m3, and the lattice incorporation, (Equation 7.1) ... 

As already stated, the crystallization conditions have a significant influence on the product purity achieved. For example, the crystallization conditions that control the growth rate particularly affect the content of impurities originating from liquid inclusions and lattice incorporation. 

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