Cubical particle shape

Many uses of aggregates require cubical particle shapes (see sections 8.3.3 and 8.5.4). Products which are excessively flaky may be brought within specification by the use of de-flaking screens. These may have transverse, elongated or slotted apertures, and may incorporate weirs or baffles to improve the presentation of slabby particles. In some cases, such screens simply remove a size fraction which has been found to be particularly flaky. 

Regarding the historic explanations, the students were neither convinced by the idea of hooks and eyes (Lenkipp, Demokrit), nor by the idea of cubic particles (Hairy). However, the historic arguments were used by the students to discuss their own ideas of bonds between the particles and to discuss the cubic shape of some crystals. 

One can do the same for a cubic particle, in fact for any shape factor. Since the chemical potential, p, is related to AG, we use the following equations ... 

The three most important characteristics of an individual particle are its composition, its size and its shape. Composition determines such properties as density and conductivity, provided that the particle is completely uniform. In many cases, however, the particle is porous or it may consist of a continuous matrix in which small particles of a second material are distributed. Particle size is important in that this affects properties such as the surface per unit volume and the rate at which a particle will settle in a fluid. A particle shape may be regular, such as spherical or cubic, or it may be irregular as, for example, with a piece of broken glass. Regular shapes are capable of precise definition by mathematical equations. Irregular shapes are not and the properties of irregular particles are usually expressed in terms of some particular characteristics of a regular shaped particle. 

Fortunately, the particle shape has little effect in the resolved parameter values when using solute concentration and obscuration measurements to identify the model. The parameters shown in Table 5 are estimated assuming spherical crystals. Comparing these values to those for cubic particles (Table 4) shows little difference between the two sets of parameters. 

When particles of irregular shape are involved, the particle diameter corresponding to a sphere of the same volume dsph is used in many equations. For instance, a cubic particle with a side of 5 mm has a volume of 53, and thus the dsph is... 

FIG. 1.14 Model particles of different shapes with the same or different chemical compositions (a) rodlike particles of akageneite (/3-FeOOH) (b) ellipsoidal particles of hematite (a-Fe203) (c) cubic particles of hematite and (d) rodlike particles of mixed chemical composition (a-Fe203 and /3-FeOOH). All are TEM pictures. (Reprinted with permission of Matijevic 1993.)... 

Fig. 7. Detailed models of surface free energies based on quasi-chemical metal-metal interactions allow detailed Wulff plots, and hence particle shapes, to be predicted as a function of temperature, (a) Interfacial phase diagram for simple cubic lattice model with nearest-neighbor and next-nearest-neighbor attraction, (b) Representative Wulff plots and equilibrium crystal shape of (a) (103).

There is a consensus from both theoretical and experimental studies that small particles may have unusual physical, chemical, and catalytic properties. Both in terms of numbers of sites of different co-ordination and with regard to electronic effects small means particles having diameters less than about 2 nm. For very small particles, sites having a particular co-ordination may be important, but the calculation of the number and distribution of such sites is subject to serious errors and requires assumptions about particle shapes, etc., which are difficult to confirm, and which may vary from one system to another. Although particles having unusual five-fold symmetry have been detected in certain circumstances, the large majority of small metal particles have conventional cubic symmetry. However, the difference in energy between two alternative structures is small - much smaller than typical heats of... 

For reliable application of the free volume concept of disperse systems one must have dependable methods of determination of the maximum packing fraction of the filler tpmax. Unfortunately, the possibility of a reliable theoretical calculation of its value, even for narrow filler fractions, seems to be problematic since there are practically no methods available for calculations for filler particles of arbitrary shape. The most reliable data are those obtained by computer simulation of the maximum packing fraction for spherical particles which give the value associated with possible particle aggregation, so that they are probable for fractions of small particle size. Deviations of particle shape is nearly cubic. At present the most reliable method of determination of [Pg.142]

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). 

The size of a cubic particle is uniquely defined by its edge length. The size of a spherical particle is uniquely defined by its diameter. Other regular shapes have equally appropriate dimensions. With some r ular particles more than one dimension is necessaiy to specify the geometiy of the particle as, for example, a cylinder, which has a diameter and a length. With irregulariy shaped particles, many dimensions... 

Oc is the geometric constant for the shape of the ceramic particles and [1 + (Lg/a f] is the volume fraction correction for the adsorbed layer on the ceramic particles. Again, this equation is only good for colloidally stable suspensions. Fleer et al. [19] verified this equation for cubic particles with polytvinyl alcohol) adsorbed at the surface. For polymer solution concentrations (i.e., p) that give essentially monolayer coverage of the particle surface, the value of [1 + (LJaf] is nearly constant for a wide range of ceramic powder concentrations (Le., d>c)-... 

Most pigments and extenders used in paints are crystalline in nature. Particles may be tetragonal, rhombic, cubic, nodular, rod-like, or platelike. Noncrystalline pigments such as the carbon blacks are also used in the paint industry. As particle shape affects pigment packing, it also affects its hiding power. 

Narayanan and El-Sayed investigated the effect of the electron-transfer reaction between ferricyanide and thiosulfate on the stability of particle shape [39,40]. The change in shape of the nanoparticle was time-dependent this change was in the form of a thermodynamic rounding of the particle into a sphere due to the dissolution of platinum atoms from the comers and edges of the tetrahedral and cubic platinum nanoparticles. Figure 18.3 demonstrates that the tetrahedral particle evolves into a distorted tetrahedral particle after one reaction cycle (Fig. 18.3a and b). For the cubic platinum nanoparticles (Fig. 18.3c), the rate of dissolution of platinum atoms was slower, and distorted cubic platinum nanoparticles (Fig. 18.3d) were dominant after two reaction cycles. 

Particle shape can also affect blending processes. Spherical and cubic shaped particles typically exhibit good flow properties and therefore promote blending. However, readily flowing materials may also be more prone to segregation. Plates and needle shaped particles have poor flow properties, are harder to dilate/expand, and are more likely to agglomerate. As a result, it may be more difficult to achieve uniformity when blending plate and needle shaped particles. Conversely, a benefit to this decreased mobility is that once blended, these are more likely to stay blended. 

If the expansion level is very low and maintained at THP, i.e., if expansion is carried out via Curve A addition shown in Figures 5 and 6, larger particles would be expected to form. Figure 15 shows such large particles formed by very slow addition to the threshold pressure with expansion subsequently maintained at this value. Large, dense, regular particles, i.e., spherical or cubical in shape, are desired for the explosive formulations. 

Particle shape flat, spherical Crystal structure cubic Particle size, pm 10-23 (powder)... 

Particle shape spherical or flake Crystal structure cubic... 

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