Determination of pyrite particle size distribution in coal by merging analyses of size distributions at different microscopic magnificiations: Optimum allocation of number of observations to different size groups

Abstract

In the characterization of particle size distributions, it is often useful to measure the size of smaller particles using optical magnifications that are higher than the magnifications used to measure relatively large particles. This results in an examination of a smaller area in the sample specimen. This paper considers the question of how many fields should be microscopically analysed at different k magnifications to arrive at an efficient estimate of the mean particle diameter (by count). The resolution of this question depends upon the following three factors: 1, the relative sizes of areas scanned under different magnifications; 2, the expected number of particles of a given size range per optical field under a given magnification; and 3, the standard deviation within each size range scanned under the same magnification. A formula is provided for the optimum allocation of field counts at each magnification when measuring particle sizes in various size ranges. Numerical examples are also provided. The discussion in this paper is illustrated by reference to the measurement of pyrite particle sizes in a given coal. It is well known that the size distribution of pyrites in coal influences the potential amount of sulphur reduction that can be achieved by physical coal cleaning methods.