Particle shape thickness

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. 

Compounds crystallized directly onto the carbon grid or with a defined orientation, due to other preparation methods, normally exhibit a suitable initial zone close to 0°. Samples from insoluble compounds are almost statistically oriented only biased by the particle shape. In this case, it is difficult to find a single crystalline part of appropriate thickness oriented with a suitable zone parallel to the surface. The best flexibility, and therefore the best possibility to orient a zone correctly, is given by a recently developed rotation-double tilt holder (Gatan Inc.). Through the combination of rotation and additional tilt (beta tilt) it is possible to orient the tilt axis exactly even if the crystal is not sitting flat on the support film (see Fig. 4). The tilt range, dependent on the pole piece distance of the objective lens, should be at least 40°. 

In this respect, Kuipers made an important point (as illustrated in Fig. 3.10c), namely that layers of thickness x which cover the support to a fraction 6, have the same dispersion as hemispheres of radius 2 x, or spheres with a diameter 3x. Even more interesting is the fact that these three particle shapes with the same surface-to-volume ratio give virtually the same fp/fs intensity ratio in XPS when they are randomly oriented in a supported catalyst The authors tentatively generalized the mathematically proven result to the following statement that we quote literally For truly random samples the XPS signal of a supported phase which is present as equally sized but arbitrarily shaped convex particles is determined by the surface/volume ratio. Thus, in Kuipers model the XPS intensity ratio fp/fs is a direct measure of the dispersion, independent of the particle shape. As the mathematics of the model is beyond the scope of this book, the interested reader... 

It is evident that it is more difficult to define particle size if the particle shape is not spherical or cubic. With some other simple geometric forms, a single linear dimension, d may be used to calculate the surface area. In particular, when the particle aspect ratio is sufficiently large, dx is taken as the minimum dimension. Thus, if the particles are thin or long (i.e. plates or rods), it is the thickness which mainly determines the magnitude of the specific surface area (Gregg and Sing, 1982). 

Pearl luster pigment shape Particle size Thickness Density... 

We have studied the effea of preparation procedure, crystallite shape and size, and oxidation conditions on the oxidation behavior of silicon micro- and nanopowders. The oxidation process is shown to occur in two steps, with a transition at a certain thickness of the oxidized layer, which depends on the oxidation time, particle shape, and particle size. The composition and physicochemical properties of the oxide films have been detennined in relation to the shape and size of the silicon particles. The results indicate that the silicon micro- and nanopowdeis differ in oxidation mechanism from singlecrystal silicon. 

Considering a ratio of about 2 between Spsd and Sbet (figure 6) and the same radius R of particles measured by each technique, the contribution of each particle to Sbet is 2 ttR which, in turn, represents the surface developed by disk-shaped particles (neglecting thickness). 

FIGURE 24 An irregularly shaped particle passing through an U.S. ASTM 324 mesh sieve (45 fitn) and U.S. ASTM 400 mesh sieve (38 pm). Size obtained from sieve analysis is a function of the maximum breadth and maximum thickness, however, particle shape can affect the sieving end point. 

CCT, critical cracking thickness Boltzmann constant (1.381x10 local permeability [m ] fracture resistance [N m ] average permeability in/of compact [m ] particle shape factor compact thickness [m] initial particle number concentration [m refractive index of particle material refractive index of dispersion material number density of ion i dimensionless number dimensionless number Stokes number Peclet number capillary pressure [N-m ] dynamic pressure [N m ] local liquid pressure in the compact [N-m local solid pressure in the compact [N-m ] superficial fluid velocity [m-s q gas constant [J K ] centre to centre distance [m]... 

Armes and coworkers have investigated the structure of both PAn colloid particles [stabilized with poly(vinyl alcohol)] and electrochemically prepared PAn films. In both cases the fundamental morphology was nanoparticles of up to 20 nm in diameter. Colloid particles were rice grain shaped. Thick films showed submicronsized features that appear to be aggregates of the smaller particles. 

For l-/im particles, the inertial force is quite small relative to the drag force, and rapid formation of a particle or gel layer is predicted. However, the particle layer does not grow steadily until it plugs the channel but seems to reach a steady-state thickness. One explanation is that the high shear rate near the wall causes a tumbling motion of individual particles, which expands the layer and leads to migration away from the wall. This shear-induced dispersion and the particle movement toward regions of lower concentration can be modeled with a particle diffusivity, which is proportional to the shear rate and the square of the particle size. More work is needed to understand the effects of particle shape and surface characteristics. 

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