Particle Shape and Laser Diffraction: A Discussion of the Particle Shape Problem

Abstract

Particle size is considered as one of the most important characteristics of particulate materials. This is because every behavior of particles depends on particle size significantly—and vice versa: particle size can be determined from any kinds of physical responses depending on the size. Kinetic or optical response maybe representative because of their easiness to determine the single particle response. Note that the response is usually modeled on an assumption of spherical particle. Of course some extensions to shapes might be available, but shape is various. How to handle the infinite sorts of shapes is an issue in powder handling with a long history, and which might still requires further studies. Laser method based on Fraunhofer diffraction is now the most widely used for particle size analysis, because of its easiness to use, speed, and reproducibility. In the method, an intensity pattern of diffraction from particles is measured with, usually, a concentric photo detector: a pattern of a diffraction image depends on the particle shape, whilst the size of the pattern depends on the particle size. Only the latter information concerning particle size is used in the normal particle size analyzer. In this respect, there are two directions of studies: one is to interpret the relationship between the diffraction pattern obtained and the equivalent spherical size distribution in the case of non‐spherical particle for a normal particle size analyzer. The other is to recognize the particle shape from the information. When an ellipsoidal particle is applied to a normal particle analyzer with concentric photo detector, it is theoretically shown that a bimodal equivalent diameter of spheres corresponding to the lengths of the major and minor axis of the ellipsoid. Contrary, there is a possibility to recognize or distinguish particle shape with a measurement of the diffraction pattern information from non‐spherical particle. As far as diffraction, the pattern corresponds to the two‐dimensional Fourier transform of the particle shape projection. The intensity pattern, however, looses phase information; therefore exact reconstruction of the shape is impossible. Nevertheless, a feature extraction maybe available not to decide nor recognize the shape but to distinguish it.

Keywords:

• Particle characterization
• Fraunhofer diffraction
• Equivalent size distribution
• Particle shape analysis
• Circular index
• Roundness factor