In the years since automated mineralogy has become a mainstream tool there has been debate over whether it is necessary to used screened fractions. I often get asked whether we can reduce costs on a project by analysing unsized material, effectively reducing the total number of blocks required to generate an answer. The general question is that there is capability in all the analysis software for automated mineralogy to produce a synthetic particle or grain size distribution so why not use it? My response is always that it is fine for analysis of modal mineralogy or elemental deportment but to generate a meaningful grain size distribution or locking/liberation analysis screened fractions should be a requirement. This isn’t the answer that we generally want to hear but I will attempt to explain why it adds significant risk to cut corners by eliminating screened fractions.
The use of screened fractions at the simplest level is done to provide cleaner data by helping to reduce touching particles and the bias that can be introduced through stereological effects. There are well documented reasons based on the mathematics of converting 2d section images into 3d particles (stereology), which show that if we want to generate a meaningful grain size distribution it should be required that screened fractions are analysed. Stereological corrections work well because they calculate 3d parameters based on a statistically random distribution of particle orientations.
If we consider figures 1 and 2 you can see that in 2 dimensions a single particle can be presented in section in a myriad of different ways. It is only when these are considered in a statistically random distribution that a mean diameter (size) can be calculated. Taking figure 1 into account you can see that if the same particle is ‘cut’ at different points it will look like significant different particles in 2 dimensions. While orientation 2 best represents the actual mean diameter of that particle, both of the other other orientations present much smaller particles.
If we take this one step further in figure 2 and group very small particles with big particles you can see that the section for a corner of a large particle can look exactly like the section for a small particle, giving us no way to differentiate between them.
So why does this mean screened fractions are better than unscreened fractions? If we look at the particle size distribution generated from 2d section information in comparison with an actual screened particle size distribution we would see that the calculated distribution has a very long ‘tail’ of fine particles. Considering what we just learned about stereology this makes absolute sense. What is happening in the calculated distribution is that portions of larger particles are being sectioned and measured as smaller particles, which contribute to the distribution. So, if we generate a calculated particle size distribution from the unscreened information you should be able to see that the finer size bins will contain a disproportionate amount of the mass. This can have implications when assessing things like flotation circuits where particles may be designated as unfloatable for being too fine, when in fact they are simply artefacts of the data.
On the other hand, if we used screened fractions we can utilise the ‘mean particle diameter’ that is calculated for each population of mineral grains and use that to define the mean size of the target mineral grains for a given total particle size. This can tell us a lot of information about the effectiveness of grinding and likelihood of liberation. This can be taken one step further by eliminating particles that are below the size of the screen fraction, allowing us to build a more accurate grain size distribution.
There is definitely a time and place for use of unscreened samples in automated mineralogy but it is important that we understand the data that can be generated from these samples and not try to report results that stretch the corrections beyond what they should be used for. It is tempting to try and extract as much as we possibly can from each analysis but this shouldn’t be at the cost of generating quality results.
If you would like more detailed information on stereological effects in automated mineralogy check out articles by Stephen Gay, Mineralogical modelling: rule of thumb vs probability methods, Part 1 and Part 2. If you are feeling more adventurous feel free to look at the theoretical side of stereology at Stereology.info.