Powder shape factors

Shape. Metal powder particles are produced in a variety of shapes, as shown in Figure 4. The desked shape usually depends to a large extent on the method of fabrication. Shape can be expressed as a deviation from a sphere of identical volume, or as the ratio between length, width, and thickness of a particle, as weU as in terms of some shape factors. 

This can be done via Eqs. (29) through (32). From the dissolution data, the coefficient B2 is obtained and through the results from microscopy the moments r2 and p3 can be evaluated. By knowing N, the initial number of particles, and the density of the solid, the average initial volume shape factor for a polydisperse powder can be estimated. 

A more detailed analysis using multivariable regression of the ibuprofen data demonstrated that a three-parameter model accurately fit the data (Table 7). The Bonding Index and the Heywood shape factor, a, alone explained 86% of the variation, while the best three-variable model, described in what follows, explained 97% of the variation and included the Bonding Index, the Heywood shape factor, and the powder bed density. All three parameters were statistically significant, as seen in Table 7. Furthermore, the coefficients are qualitatively as... 

The range of specific surface area can vary widely depending upon the particle s size and shape and also the porosity.t The influence of pores can often overwhelm the size and external shape factors. For example, a powder consisting of spherical particles exhibits a total surface area, S, as described by equation (1.6) ... 

Podczek F. 1997. Shape factor to assess the shape of particles using image analysis. Powder Technol. 93(1) 47-53. 

Solid Dissolution. The dissolution rate of a solid, whether it be a nondisintegrating compact or a powder, generally decreases with time because of the reduction in surface area as the dissolution proceeds. The familiar cube-root law for dissolution of solids was derived by Hixson and Crowell (1 on the basis of diffusion away from the surface of a spherically-shaped solid. The convex surface of a sphere decreases in area as solid mass is lost from the surface so that the dissolution rate decreases in proportion to the decrease in area until the solid is completely dissolved. By including shape factors, this model has been extended to describe the dissolution of various prismatic forms (2). As in the case of spherical particles, the dissolution rates decrease with time as the dissolution process progresses because of the decrease in area. 

The fineness of the powder is characterized by a number (e.g., a diameter d). Particles, of course, will have different shapes so that there are different ways of defining a diameter. The technique for obtaining d, given above has been used microscopically. More conventional is the so-called surface mean diameter, which, is the diameter of a sphere that has the same surface area as the particle. The so-called single-particle volume mean diameter is possible if there are instruments that can measure the volume of an odd-shaped particle. If the shape factor is indepen-... 

Shape Coefficients and Shape Factors There are various types of shape factors, the majority based on statistical considerations. In essence this translates to the use of shape factors that do refer not to the shape of an individual particle but rather to the average shape of all the particles in a mass of powder. However, a method developed by Hausner [38] that uses three factors—elongation factor, bulkiness factor, and surface factor—may be used to characterize the shape of individual particles (Table 5). 

Once the average shape of the particles in a powder has been established by one of several means and its ramifications on shape factors, fractal dimensions, surface area, and porosity are determined, the distribution of particle sizes is the next piece of information necessary to characterize the powder. 

Tsubaki et. al. [44,45] argue that many of the proposed shape factors have little practical relevance to the analysis of real powders until the advent of electronic equipment and the computer. They define six shape indices based on the following diameters (see Table 2.1) d, d dp, dp. The shape... 

Wallace et al. (20) correlated GC retention volumes of several poly(vinyl chloride) powders with their uptake of plasticizer. Since the diffusion of plasticizers into polymer powders is controlled by the external surface area, the diffusion coefficient of the plasticizer and some shape factor, a correlation with GC measurements could be expected. It was found that plasticizer absorption ( drying ) took place only when the polymer was heated to a temperature immediately above the glass transition temperature as defined by the minimum of the experimental retention diagram. 

Particle sizes combined with shape factors have been the subject of many of the recent studies regarding flow of solids. Sphericity, circularity, surface-shape coefficient, volume-shape coefficient, and surface-volume-shape coefficient are some of the most commonly used shape factors. It is generally accepted that the flowability of powders decreases as the shapes of particles become more irregular. Efforts to relate various shape factors to powder bulk behavior have become more successful recently, primarily because of the fact that shape characterization techniques and methods for physically sorting particles of different shapes are... 

Some work has shown a direct correlation between shape factor and the flow properties of powders. The flowability of fine powders, as measured by a shear-cell as well as by Carr s method, was found to increase with increasing sphericity, where the sphericity is indicated by a shape index approaching one, as measured by an image analyzer. Huber and co-workers derived an equuation in which flow rate was correlated to the volume specific surface as measured by laser diffractometry. Reasonable predictions were made for individual powders as well as binary and ternary mixtures. 

Bouwman AM, Bosma JC, Vonk P, et al. Which shape factor( ) best describe granules Powder Technol 2004 I46(l-2) 66-72. 

K is known as the shape factor or Scherrer constant which varies in the range 0.89 < XT < 1, and usually K = 0.9 [H.P. Klug and L.E. Alexander, X-ray diffraction procedures for polycrystalline and amorphous materials, Second edition, John Wiley, NY (1974) p. 656]. L.W. Finger, D.E. Cox, A.P. Jephcoat. A correction for powder diffraction peak asymmetry due to axial divergence, J. Appl. Cryst. 27, 892 (1994). 

If the particle-size distribution of a powder composed of hard, smooth spheres is measured by any of the techniques, the measured values should be identical. However, many different size distributions can be defined for any powder made up of nonspherical particles. For example, if a rod-shaped particle is placed on a sieve, then its diameter, not its length, determines the size of aperture through which it will pass. If however, the particle is allowed to settle in a viscous fluid, then the calculated diameter of a sphere of the same substance that would have the same falling speed in the same fluid (i.e., the Stokes diameter) is taken as the appropriate size parameter of the particle. Since the Stokes diameter for the rod-shaped particle will obviously differ from the rod diameter, this difference represents added information concerning particle shape. The ratio of the diameters measured by two different techniques is called the shape factor. 

Particle sphericity, ip aerodynamic shape factor, x- crystal density, p aerosolized powder bulk density, pg volume mean diameter, dy aerodynamic mean volume diameter, d total (Hildebrand) solubility parameters of the cohesive (drug-drug), 6c, and adhesive (drug carrier), 6a, interactions. 

Very few, if any, practical particulate systems are mono-sized. Most show a distribution of sizes and, depending on the quantity measured, the distribution can be by number, surface or mass. Conversion from one type of distribution to another is theoretically possible but it assumes a constant shape factor throughout the distribution which often is not true and such conversion is in error. The conversions are therefore to be avoided whenever possible by choosing a measurement method which measures the desired type of distribution directly. Except for a few specialized applications like rating of filter media, the most relevant types in powder handling are usually the mass or the surface distributions. 

A number of methods have been proposed for particle shape analysis these include verbal description, various shape coefficients and shape factors, curvature signatures, moment invariants, solid shape descriptors, the octal chain code and mathematical functions like Fourier series expansion or fractal dimensions. As in particle size analysis, here one can also detect intense preoccupation with very detailed and accurate description of particle shape, and yet efforts to relate the shape-describing parameters to powder bulk behaviour are relatively scarce.10... 

While the position and intensity of peaks in a powder pattern are determined by the unit cell size and contents, their shapes and widths are determined by instrumental effects (which can be coiTected for or modeled) and sample properties, such as the sizes and strains of crystallites and stacking faults.The simplest expression for peak broadening due to sample size (the Scherrer formula) predicts that peak width and particle size are related hy fwhm = A,/ /z cos0, where K is a shape factor (often 0.9), fivhm the peak full width at half maximum. and X the wavelength absolute numbers from this expression should be treated with caution. A sample strain leads to a peak width dependence on tanO. In more sophisticated treatments, hkl-dependent peak widths can be used to obtain information on the anisotropies of size and strain in a sample. More details on the interpretation of peak shapes are given elsewhere. ... 

The retention volumes on poly(vinyl chloride) powders were correlated with their capacity for incorporating the plasticizer [153]. The diffusion of plasticizer in the polymer powder being controlled by the external smface, by the plasticizer diffusion coefficient and by a shape factor, some connection with gas chromatographic measurements is to be expected. The plasticizer adsorption was found to take place only at a temperature slightly above T,. 

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