Spherical/spheroid particles particle size

Depending on operation conditions and metal properties, the shapes of the atomized particles may be spheroidal, flaky, acicular, or irregular, but spherical shape is predominant. The spheroidal particles are coarse. For example, roller-atomized Sn particles exhibited a mass median diameter of 220 to 680 pm. The large particle sizes and highly irregular particle shapes suggested that the disintegration process may be arrested either by the premature solidification or by the formation of a thick, viscous oxide layer on the liquid surface. The particle size distributions were found to closely follow a log-normal pattern even for non-uniform particle shapes. 

Any study of colloidal crystals requires the preparation of monodisperse colloidal particles that are uniform in size, shape, composition, and surface properties. Monodisperse spherical colloids of various sizes, composition, and surface properties have been prepared via numerous synthetic strategies [67]. However, the direct preparation of crystal phases from spherical particles usually leads to a rather limited set of close-packed structures (hexagonal close packed, face-centered cubic, or body-centered cubic structures). Relatively few studies exist on the preparation of monodisperse nonspherical colloids. In general, direct synthetic methods are restricted to particles with simple shapes such as rods, spheroids, or plates [68]. An alternative route for the preparation of uniform particles with a more complex structure might consist of the formation of discrete uniform aggregates of self-organized spherical particles. The use of colloidal clusters with a given number of particles, with controlled shape and dimension, could lead to colloidal crystals with unusual symmetries [69]. 

Spherical alumina can also be formed from commercial, low cost aluminum-oxides or even from aluminum-hydroxides. In the latter case energy of the plasma should provide not only the enthalpy of melting but that of dehydration and subsequent phase transformations of alumina as well. Under the aforementioned conditions particles below 45 pm have a good chance to be spherodized. Presumably the wide particle size distribution of starting gibbsite powder accounts for the less spheroidization rate of 70%. 

Non-porous Zr02 powders can be produced by high-temperature vapour phase condensation methods in this manner discrete spherical particles of c. 4 nm diameter have been obtained (Avery and Ramsay, 1973). It is also possible to prepare colloidal dispersions of sub-micron sized, spheroidal particles of basic salts such as Zr2(OH)6C03 and Zr2(0H)6SO4 with the aid of the carefully controlled sol-gel techniques developed by Matijevic (1988). 

An extension of the use of RF plasma for particle heating is the spheroidization of solids. By careful control of plasma enthalpy, particle size, feed rate, and feed position, it is possible to melt each particle as it passes through the plasma. The liquid droplet forms a sphere due to surface tension and, on cooling, retains its spherical shape. Spheroidized particles are commercially useful because they will flow easily. 

As far as the theoretical description is concerned, the confined acoustic phonons in an elastic sphere were first theoretically studied by Lamb [29]. He derives two types of confined acoustic modes, spheroidal and torsional modes. The frequencies of these two modes are proportional to the sound velocities in particles and inversely proportional to the particle size. The spheroidal mode is characterized by the quantum number / > 0, while the torsional modes are characterized by / > 1. From the symmetry arguments, Raman-active modes are spheroidal modes with I = 0 and 2. The I = 0 mode is purely radial with spherical symmetry and produces totally polarized spectra, while the Z = 2 mode is quadrapolar and produces partially... 

Particles derived from the evaporation of solution droplets are spheroidal. Shape (primarily in surface features), density, and size control of particles can be achieved by the appropriate selection of the compound, the concentration of the solution, the size of the droplet generated, and the conditions for the evaporation of the droplets. Fast evaporation rates tend to produce less solid and rough-surface particles, but this is tempered by the chemical properties of the compound. Smooth, spherical particles call for compounds with high solubility and slow evaporation rates. These requirements were used by Vanderpool and Rubow [48] to produce solid, smooth spheres of up to 70 pm in diameter. The different types of particles that can be produced from the evaporation of solution droplets include solid spheres with surfaces that are smooth, cracked, or wrinkled hollow spheres, shells, and spheroidal particles that have a wrinkled surface like raisins porous-type particles that are perforated with holes, and single crystals and particles composed of several crystals, which may be angular or spheroidal in shape. 

Fig. 4.6a considers a spherical core-shell particle in which the core is taken to be vacuum and the shell is silver. The particle radius is 50 nm, so when the shell thickness is 50 nm we recover the solid particle result. As the shell becomes thinner, the plasmon resonance red-shifts considerably, very much like we see for highly oblate spheroids. Fig. 4.6a assumes that the dielectric constant of silver is independent of shell thickness, so the resonance width does not change much when the shell becomes thin. However, the correct dielectric response needs to include for finite size effects (as noted above) when the shell thickness is smaller than the conduction electron mean free path. Fig. 4.6b shows what happens to the spectrum in Fig. 4.6a when the finite size effect is incorporated, and we see that it has a significant effect for shells below 10 nm thickness, leading to much broader plasmon lineshapes. 

For example, a novel, versatile technique for the synthesizing of uniform hollow capsules from a broad range of materials is based on a combination of colloidal templating and self-assembly processes [11.8]. Fig. 11.11 describes schematically the concept. Colloidal templates of different composition, size, and geometry (although spheroidal shape is preferred) can be employed. Materials range from spherical polymer particles to non-spherical biocolloids, all vdth diameters in the nano to micrometer range. The... 

The particle size is one or more linear dimensions appropriately defined to characterize an individual particle. For example, an ideal particle like a sphere is uniquely characterized by its diameter. Particles of regular shapes other than spherical can usually be characterized by two or three dimensions. Cubes can be uniquely defined by a single dimension, while cuboids require all three dimensions, length, width, and height. Two dimensions are required for regular isotropic particles such as cylinders, spheroids, and cones. 

Spherical particles proved to be superior in several applications owing to their favorable properties. Thus, they are used in thermal spraying for their excellent flowabil-ity, in powder metallurgy because of their excellent reproducibility in manufacturing parts with controlled porosity and as a filler material, as well. Metal microspheres can be easily produced by melt atomization. Similar method in the case of ceramics is impractical. Micron-sized ceramic particles, however, can be smelted by thermal plasmas that provide exceptional conditions for spheroidization due to its high temperature. In terms of purity and residence time of the particles in the hot temperature core, RF plasmas provide better conditions as compared to arc plasmas. 

For the most part, the measured size of sieved (screened) particles will be based upon a spheroidal shape since this is easiest to calculate, i.e.- V = 4/3 7T r . In the case of measurement by volume, spherical shapes are the only way to specify the apparent size of the particle. Let us now examine how we can obtain a PSD using screens to separate particles into fractions. 

Fig. 17 experimental data from Tables 1 of Refs. [83, 84]. Note that the colloidal gold particles are not spherical but can be approximated by slightly elongated spheroids or cylinders with semispherical ends [48, 83]. That is why we use the diameter of equivolume sphere as the size parameter in our... 

For the case where the particles do not have a spherical shape, various extensions of the Maxwell Garnett theory for nonspherical particles were introduced. The particles are spheroidal with the same shape (ratio of major-axis A and minor axis B), but with different sizes still in the wavelength limit. It remains only to choose between a parallel or a random orientation of the mean axis of the ellipsoids. 

The fate of nuclei is partiele eoagulation, a process in which small particles (assumed to be spherical) collide with each other and coalesce completely to form larger spherical particles. Small particles are indeed spheroidal and the assumption of spherical particles seems to be reasonable (Mitchell and Frenklach 2003, Balthasar et al. 2005). After a certain size, however, the partieles cannot coalesce completely and start to form long chains, which eventually grow into three-dimensional fractal-like structures. Fig. 4.15 shows the new partiele formation and growth pathways. A great role is played by the surface coating of primary hydrophilic soot... 

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