The particle distribution functions and applications

Abstract

The new generalized logarithmic equation defined by four parameters, called LG4, was formulated and proposed for describing particle size and shape distributions. For special choice of the parameters the LG4 was reduced to the logarithmic distribution LG2 defined by two parameters which permits the selection of mean value of the distribution as the size parameter appears explicitly in the distribution function. The LG2 has been suggested as a model for size and shape distributions of the particles (the "fourth state of matter" according to Heywood's definition) as, for example, the metallic and ceramic particles which attract a good deal of public attention as new promising high-performance materials for magnetic materials and then chemical catalysts, sintering promoting materials, sensors, etc. The shape and similarity of the particle for some purposes are very important. Total volume, total surface or any other useful property of the sample, may be related to shape and size of individual particles. If all particles are geometrically similar, all the subsequent treatment is simplified substantially in terms of shape. By introducing the shape parameter of the particle, the generalized similarity and the elliptic factor of the assembly of particles the application of the LG2 for the study of the shape distribution of the projected Nd2Fe14B particles is referred in this paper.