In our last article I re-introduced the concept of using statistics to determine if enough particle sections have been measured to produce a representative result in SEM-EDS analysis. This week I thought I’d give an example of a SEM-EDS data set to explore how the particle count impacts results and data quality. Let’s start by looking at figure 1a, which shows the cumulative quartz volume percent as a function of the number of particles measured. The data are presented in the order of particles measured.
The beginning sections on the graph, where few particles are measured, is a little crowded with data, but you should be able to make out that the quartz proportion fluctuates with high frequency (see figure 1c for more detail). This happens because in the early stages of a measurement a single particle has a significant impact on the normalised mineral proportions. In some particles quartz may present, which causes the quartz proportion to rise quickly, while in subsequent particles there may be no quartz, which causes its normalised proportion to fall. As the measurement continues we can see that the quartz proportion ‘stabilises’ and essentially converges to the ‘correct’ value for that population of particle sections. In these later stages of the measurement the addition of a single particle normally has less significant impact on the results.
The variance will be different in different parts of the curve. Figure 1b shows two regions, red and green, with high and low variance respectively. If we were to terminate the measurement while the number of particles are within the red zone the likelihood of the data being wrong is quite high, while measurement termination in the green zone is likely to produce in a reasonably accurate result. Figure 1c plots only the red portion of the curve with high variance, and it is clear that measurement termination in this zone could result in a quartz proportion anywhere between 1 and 10 vol%. Figure 1d plots only the green portion of the curve, which shows that measurement termination in this zone would result in a quartz proportion between 7 and 8 vol%, which is a much improved margin of error.
Here the graph clearly shows a stabilisation of the quartz volume proportion and indicates that the measurement results are more than adequate for further analysis and interpretation. In fact, assuming that all other phases are equally well stabilised, the graph shows that we could have saved measurement time and comfortably terminated the measurement with 2000 particles analysed, which is only 30% of the actual 6000 particles measured. Having said that, to acquire accurate data for minerals occurring in low proportions may require more particles to be measured.
Particle statistics and measurement time optimisation are particularly important in the developing area of operational mineralogy. SEM-EDS systems are increasingly being deployed at mine sites for fast turn-around information on operational efficiency and performance. It is of critical importance that statistically reliable data are collected within a reasonable timeframe to allow mine site operations to react to changes in feed ore and processing characteristics.
Retrospective investigation of data is interesting and valuable if we want to be confident about the data we use for further interpretation, however, in reality we need some idea of how many particles to measure before the measurement even starts. As I mentioned in the last article, some systems incorporate online measurement termination criteria based on statistics. I don’t know exactly how these statistical methods are implemented, but maybe we can look at this in more detail in an upcoming article.
The concepts of particle and counting statistics have been around for a long time, and a similar problem related to counting statistics exists for point counting using optical microscopy, where the number of points collected has an impact on the analytical error. For the purposes of SEM-EDS analysis the number of points collected is somewhat irrelevant because the technique normally acquires hundreds of thousands of data points; however, if measurement time is limited then the SEM-EDS system could be set up to essentially collect similar data compared to an optical point count analysis. In a response to our last article Mike Wort kindly offered a reference to a published paper by Tony Barringer, which explains the use of statistics to determine the number of points required for optical point counting of thin sections. Barringer (1953) presents a useful chart that relates the analytical error to the number of points counted as a function of the percentage of the mineral constituent in the sample (figure 4 – after the original publication).
Barringer (1953) also presents an equation for the data in the graph, which is intended for thin section pointing, but I see no immediate reason why we can’t use it to preemptively determine a target number of particles required for a given mineral grade.
where E = error (2 x standard deviation), p = percentage of each constituent in each section, and n = number of points to be counted.
Checking the number of particles and the variance of SEM-EDS results are part of the MinAssist data validation service, which can also include validating mineral identification, quantification, and sample preparation parameters. Contact us if you have data you would like us to check.
I suspect that some users may already be using this or a similar method and I am interested to hear your opinion on the use of statistics to ensure accurate and reliable SEM-EDS data. Send us an email with your comments.
Barringer, A.R., 1953. The preparation of polished sections of ores and mill products using diamond abrasives, and their quantitative study by point counting methods. Bull. Instn Min. Metall, 63, pp.21-41.