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Taylor MA (2002) has recently proposed a generalized set of particle shape parameters defined by a set of moments of the 3D particle shape. The particle shape is understood here as a 3D distribution of the particle mass. This definition of the particle shape is especially attractive for these methods of calculating optical properties of small particles which "assemble" a particle from elementary volumes, as does the discrete dipole approximation (DDA), for example. Unfortunately, this approach to the particle shape characterization requires 3D techniques of the particle shape determination, which are generally more complicated than 2D techniques.
Traditionally, stereoscopic optical microscopy (for example, Kim NH et al 1990), stereoscopic scanning electron microscopy (for example, Laird D 2001), and stereoscopic transmission microscopy (Tanji T et al 2005) were used to determine 3D particle shapes. Note that the strikingly three-dimensional appearance of particle shapes viewed with a scanning electron microscope (SEM) allows to evaluate the particle height topography by using the "shape from shades" principle and a multi-detector SEM (Drzazga W et al 2006).
More recently, the 3D particle shape determination techniques include scanning optical microscopy (for example, Nagel Y and Ay 2000), x-ray microtomography (Lin CL and Miller 2005, Vincze L et al 2001), and electron tomography (for example, van Poppel LH et al 2005).
In 3D, the sphere is a reference shape. The similarity to (or departure from) the spherical shape is frequently characterized with the sphericity parameter, S (for example, Allen T 1997):
| S = (V / Vcs )1/3 | (1) |
where V is the volume of the particle and Vcs is the volume of the circumscribed sphere. The sphericity assumes a maximum of 1 for the sphere.
Jonasz M (1987a) defined the nonsphericity parameter (NSP) as the ratio of the projected area of a particle averaged, Ap, avg, over all orientations, to the projected area, Ap, eqs of the sphere with equal volume:
| NSP = Ap, avg / Ap, eqs | (2) |
This parameter was intented to assess the effect of particle nonsphericity on light scattering by dilute dispersions of particles larger than the wavelength of light. Indeed, for such dispersions, light scattering is proportional to the total projected area of the particles per unit volume of the dispersion. This latter area is a product of the average projected area of the particle and the number concentration of particles. NSP assumes a minimum of 1 for a disk. Aas E (1984) defined a similar parameter (shape factor), Ap, avg / V 2/3, where V is the particle volume. The shape parameter equals NSP to within a constant factor.
See also: Particle shape parameters in 2D
| CITATION: Jonasz M. 2006. Particle shape parameters in 3D (www.tpdsci.com/Tpc/PtSz.php). In: Top. Part. Disp. Sci. (www.tpdsci.com). |
HISTORY: Published: 27-Aug-2007 Modified: 31-Dec-2007 Reviewed: PENDING |
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