Stereological Error in Particle Sections - The Solution

The volumetric distribution of valuable mineral, or phase, within a set of particles is called the liberation distribution. To optimise a mineral processing plant it is necessary to know the liberation distribution in most of the streams, especially those adjacent to separation devices. Possibly the most common method of analysing ore particles is to section sets of similarly-sized particles. However, the observed sections can appear liberated even if the particle is composite. This means that the 'apparent' liberation distribution can be very different to the 'actual' liberation distribution. This discrepancy is called stereological error. One must then somehow estimate the actual liberation distribution using the apparent liberation distribution. This problem is called the liberation distribution problem and its solution is the subject of this paper. The solution is based on a sorting algorithm which uses geometric probability equations. These equations are based on the assumption that sectioning is isotropic and uniform. Apart from these assumptions the equations are completely independent of particle shape or texture. The algorithm is verified by numerical simulation and experimental methods. For the numerical simulations the correspondence between the actual and estimated liberation distributions is excellent. For the experimental methods, the agreement is not as good and appears to be due to experimental errors.