Particle morphology fractal shapes

The effects on the particle shape of particle formation from partially hydrolyzed monomers were also investigated. By choosing certain mixtures of monomers, Schaefer and Keefer generated all kinds of particle morphologies, from porous clusters to surface and mass fractals. 

Particle property any property of a particle that is not (only) a bulk property of the dispersed phase there are several, not necessarily excluding categories (geometric properties, dynamic properties, interactions with electromagnetic or sound fields) these properties are related to particle size or, more generally, to the particle morphology, which also includes the particle shape (e.g. sphericity) and structural composition (e.g. fractal dimension). 

The parameters mentioned above for shape analysis are straightforward to obtain. As computing technology has advanced, so have the descriptors that have been used to describe particles. Kaye proposed the use of fractal dimensions in describing particulate solids.27 Leurkins proposed the application of the morphological variational principle to describe particle shape that states 25... 

As for the linear properties, numerous approaches have been proposed to predict and explain the nonlinear optical response of nanocomposite materials beyond the hypothesis leading to the simple model presented above ( 3.2.2). Especially, Eq. (27) does not hold as soon as metal concentration is large and, a fortiori, reaches the percolation threshold. Several EMT or topological methods have then been developed to account for such regimes and for different types of material morphology, using different calculation methods [38, 81, 83, 88, 96-116]. Let us mention works devoted to ellipsoidal [99, 100, 109] or cylindrical [97] inclusions, effect of a shape distribution [110, 115], core-shell particles [114, 116], layered composites [103], nonlinear inclusions in a nonlinear host medium [88], linear inclusions in a nonlinear host medium [108], percolated media and fractals [101, 104-106, 108]. Attempts to simulate in a nonlinear EMT the influence of temperature have also been reported [107, 113]. 

Reaction-bonded titanium nitride (RBTN) ceramics are like RBSN made from a porous green shape of titanium powder that is reacted with nitrogen to titanium nitride (TiN) at temperatures up to 1000°C. Here the titanium hardly increases in molar volume when nitrided and the initial porosity remains the same but the gas permeability of a pressed titanium tablet is increased after it has been converted to titanium nitride. If the titanium powder particles are too large, the reaction stops after passivation of the metal surfaces the TiN formed at the surface is a diffusion barrier that stops the reaction. A fractal powder morphology of the starting metal (such as can be obtained from gas-phase preparation) is a very suitable reactant for complete reaction at modest temperatures. 

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