https://orcid.org/0000-0003-2365-9150
Figures
Abstract
Laser-induced breakdown spectroscopy (LIBS) appears to be a promising technique for rapid on-site assessment of precious metal concentrations in ores. However, a number of issues need to be considered for the optimal use of this technique in practical situations. This article focuses on the number of measurements (i.e., spectra or laser shots) required to assess the mean palladium concentration in drill cores from the Lac des Iles mine (Ontario, Canada). We have performed a probabilistic study of the accuracy of the mean palladium concentration obtained by LIBS as a function of the number of measurements at random locations. For this purpose, we first used the results of a detailed laser scan of the core surface and then a mathematical model of the probability density of the palladium distribution to explore the parameter space, in particular the effect of noise on the measurements. We show that for the 1-meter-long, 2-centimeter radius quarter core samples analyzed, a few thousand randomly sampled locations generally provide an assessment of the palladium concentration within useful confidence limits. For a typical laser repetition rate of 50 Hz, such an analysis is a matter of minutes compared to hours or days using conventional methods.
Citation: Vidal F, Selmani S, Elhamdaoui I, Mohamed N, Bouchard P, Constantin M, et al. (2025) Assessment of palladium concentration in drill cores using laser-induced breakdown spectroscopy (LIBS). PLoS One 20(5): e0320584. https://doi.org/10.1371/journal.pone.0320584
Editor: Amit Kumar Goyal, Manipal Academy of Higher Education, INDIA
Received: November 5, 2024; Accepted: February 20, 2025; Published: May 19, 2025
Copyright: © 2025 Vidal et al. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
Data Availability: All relevant data are within the manuscript and/or its Supporting Information files.
Funding: This work was primarily supported by the Natural Sciences and Engineering Research Council of Canada (NSERC) [grant number STPGP 521608-18]. Financial support was also provided by Impala Canada for the research.
Competing interests: The authors declare that they have no known competing financial interests or personal relationships that could appear to have influenced the work reported in this paper.
1 Introduction
Precious metals, including palladium, are commercially mined in concentrations of a few parts per million (ppm) or less. Mine samples are currently analyzed using conventional wet chemistry, fire assay, ICP [1] or atomic absorption [2] techniques after a laborious, time-consuming and energy-intensive sequence of grinding, homogenization and dissolution that typically takes more than a day. One of the desired state-of-the-art technologies would be the measurement of low average grades (a few ppm) of precious metals in real time and in situ during the various phases of mining exploration and production [3].
Laser-induced breakdown spectroscopy (LIBS) is a promising technology that can meet these requirements. LIBS is an optical analytical technique based on emission spectroscopy that uses a pulsed laser beam focused on the sample (solid, liquid or gas) to atomize a small area (typically less than 1 mm2) and create a plasma. The light emitted from the plasma is then collected and spectrally analyzed. A schematic of the LIBS setup is shown in Fig 1. Reference materials are used to establish the relationship between the intensities of the spectral lines and the content of the analyte element of interest for each laser shot. The main potential advantages of LIBS over traditional analytical techniques lie in the ability to rapidly analyze samples with minimal or no preparation, regardless of the type of sample [4]. There are several reviews on the applications of LIBS in environmental and geochemistry [5–8]. LIBS has also been adopted or is being evaluated for its potential applications in several industries, including mineral processing, food, health, and archaeology [9].
In our recent work we have measured the concentration of palladium in cores from the Lac des Iles (LDI) palladium mine in Ontario, Canada by LIBS [10] and by LIBS assisted with laser fluorescence [11]. The cores used are of gabbronorite type and come from the same zone (B3) of the LDI mine. The cores were scanned with several thousand laser shots of approximately 750 µm diameter. Ore powders spiked with various concentrations of palladium chloride were used to calibrate our measurements. Our LIBS measurements indicate that the palladium distribution on the surface of the core samples is very inhomogeneous, varying by hundreds or even thousands of ppm between adjacent locations. We then estimated the mean core concentration of palladium by averaging the concentrations for all laser shots. For the cores analyzed, the LIBS measurements were found to be in good agreement with conventional analyses performed on the transverse half of the original cylindrical cores.
Although LIBS analysis of precious metal content in cores is in principle much faster than conventional laboratory methods, it remains important to optimize the duration of the LIBS analysis by performing appropriate sampling. The duration of LIBS measurements depends on the repetition rate of the pulsed laser, the number of sites analyzed on the sample surface, and the sampling strategy used. Therefore, a trade-off must be made between the duration of the measurement (i.e., the number of laser shots) and the uncertainty in the mean concentration that is considered acceptable. An analogous issue has been discussed in [12–14] in the context of geochemical analysis of rocks containing mineral phases with concentrations in the wt% range and grain sizes comparable to the laser spot size. For such samples, it was found that as few as 10–15 [12,13] or 560 [14] laser shots at different positions were sufficient to determine their mineralogical composition.
In this paper we discuss the appropriate number of LIBS measurements to assess the palladium concentration at the ppm level in drill cores with a palladium grain size much smaller than the laser spot size. The approach we use is to take as a reference the distribution of palladium concentrations from drill cores of palladium ore from the LDI mine, scanned by LIBS at different positions, where
is of the order of 104. The measured palladium distributions in the analyzed cores are presented in Sect. 2. In Sect. 3.1, we consider subsets of
measurements from this set of
measurements and calculate the probabilities of obtaining the mean concentration
of
measurements within certain concentration limits around the reference concentration
from the set of
measurements. Then, in Sect. 3.2, we mathematically model the concentration distribution as well as the noise inherent in such measurements in a way that mimics the measured distribution for the set of
measurements. This allows us to study a wider variety of palladium and noise distributions. Sect. 4 concludes the paper.
2 Measurements
The three cores from the LDI palladium mine considered in this study, hereafter referred to as core A, B and C, are quarter cores cut longitudinally, approximately 1 m long and 2 cm in radius. Their LDI designations are listed in S1 Table. The three cores are of gabbronorite type, and the major phases identified by µ-XRF, polarized light microscopy, and electron probe microanalysis are (1) calcium-rich plagioclase feldspar (mainly bytownite), (2) amphibole (mainly hornblende), and (3) sulfides (mainly chalcopyrite, pentlandite, pyrrhotite, and pyrite) [15]. The diameter of the laser spot on the target was approximately 750 µm, and the analyzed areas were separated by 1 mm in both directions. The size of platinum group minerals in the LDI mine is known to be less than a few tens of µm [16], which is much smaller than the laser spot size. Figs 2a and 2b show examples of LDI core fragments as delivered from the mine site.
(a) and (b): Examples of core fragments as delivered from the mine site. (c): Example of a fragment face from core A after laser scanning on an 18×60 matrix (contrast enhanced). (d): Flat side of the flap, corresponding to (c), after trimming the rounded side of the fragment. The 1 cm scale applies to all 4 examples.
Details of the laser parameters and experimental conditions used for the LIBS analysis of cores A and B are given in our previous work [10]. Briefly, the laser pulses generated by a Nd:YAG laser had a duration of 8 ns and a wavelength of 1064 nm. The laser fluence on the target was approximately 18 J cm-2, the used acquisition delay and gate width were 4 and 10 µs, respectively, and the measurements were performed in ambient air. For these parameters, each laser shot was found to ablate 10–4–10–3 mm3 of material at the surface of the rock, depending on the mineral phase [17]. The palladium concentration for each laser shot was determined using 3 univariate calibration curves obtained from 3 sets of 6 reference materials each, as described in [10]. Fig 2c shows an example of a laser-scanned face of a fragment from core A, while Fig 2d shows the mirror image of this face, created by cutting the rounded side of the fragment to produce an additional flat surface. Core C was analyzed with slightly different laser parameters. The fluence was 14 J cm-2, and the acquisition delay was 3 µs. In addition, only one calibration curve obtained from a set of 6 reference samples was used.
Fig 3 shows a raw (un-normalized) spectrum obtained from a laser shot at core A, centered on the Pd I 348.12 nm line used for palladium concentration determination. The spectrum is characterized by strong emission lines from iron and nickel, both high-emission elements. Background noise is also present due to inherent fluctuations in plasma emission, electronic variations, and the ICCD camera. In this case, the palladium line is clearly distinguishable from the background noise. However, when the palladium concentration is lower, the net palladium intensity , calculated as the peak intensity minus the average background (represented by the dashed line), can approach the noise level. In some cases,
may even become negative due to random noise fluctuations around the background level. This noise limitation ultimately defines the palladium detection limit of our LIBS system, which is estimated to be about 5 ppm [10]. Since the calibration curves exhibit a linear relationship
, negative
values translate into negative
values. Although negative concentrations are physically meaningless, they are included in the analysis for statistical accuracy. These negative values compensate for the excess positive concentrations introduced by noise, ensuring an accurate evaluation of average concentrations.
The dashed line represents the average background emission.
Fig 4 shows a portion of the concentration distribution of the three cores considered in this study as determined by LIBS. The results of the LIBS analyses are summarized in Table 1, which shows the number of laser shots performed on the three cores, as well as the mean concentration and standard deviation calculated from the distributions shown in Fig 4. Due to our laboratory setup, we were only able to scan the flat surfaces of the cores. Only the two flat surfaces of quarter cores B and C were scanned. For core A, we cut the round surface to form a third flat surface, which was also laser-scanned (see Fig 2c). The number of laser shots is not the same for the three cores due to this reason and the condition of the core fragments, which allowed more or less large rectangular laser scan matrices. While the concentration range in Fig 4 is limited to 1000 ppm for better visibility, the highest concentrations reach a few thousand ppm for the three cores. The complete datasets of measurements for the three cores are provided in S2 Datasets. Note the presence of negative concentrations resulting from the extension of the calibration curve to negative values of , as discussed above. The mean palladium concentration has been calculated taking into account these negative concentrations, which are offset by the part of the positive concentrations also due to noise, as discussed in detail in Sect. 3.2.
Palladium distribution in ore from the LDI palladium mine for the three cores considered in this study. The bin size of the histograms is 5 ppm.
For all three cores, the LIBS measurements are in fairly good agreement with those determined by a certified laboratory using conventional methods for the longitudinal half of the original cylindrical cores, which are 4.9 ppm for core A, 7.7 ppm for core B and 12.8 ppm for core C. This agreement has been achieved despite the fact that LIBS performs a surface analysis, whereas wet chemical methods are applied to samples ground to grains of approximately 75 µm.
3 Probability calculations
3.1 Probability calculations using experimental measurements
In this section, we generate many random sets of values, where
ranges from 125 to 7 000, from among the
experimental measurements made on the cores, and we use them to compute the probabilities of finding the mean concentration
of any single set of
measurements within predefined limits. To generate random sets of
values among the
experimental measurements, we used the xoshiro256** pseudorandom number generator with a period of
, as implemented in the GNU Fortran compiler.
Two types of concentration bounds are considered. First, we consider the lower () and upper (
) concentrations corresponding to a 90% probability of obtaining a mean concentration between these two values, with 5% probabilities at either end of obtaining a mean concentration
outside this interval. Second, we consider the probabilities of obtaining a mean concentration
within an interval of ± 30% around the mean concentration
of the
measurements.
A key concept in this study is the Central Limit Theorem (CLT) of probability theory. Put simply, suppose the concentration distribution is characterized by a mean and a standard deviation
. According to the CLT, the mean concentration distribution of a large number of randomly and independently selected sets of
measurements will tend toward a normal (Gaussian) distribution with mean
and standard deviation
as
increases. The consequence of the CLT is that a larger number of measurements provides a greater accuracy in the mean concentration
(i.e., smaller values of
) and a larger standard deviation
requires more measurements to achieve a given accuracy. High values of
may be associated with the presence of local high concentrations (nuggets), in the case of a trace element that is predominantly present in discrete minor phase particles.
We generated the sets of elements in a completely random way, without the constraints that each element appears only once in a given set and that all sets are different. This is equivalent to extending the set of
elements by an infinite replication of itself. In this way,
sets of
elements can be formed.
Fig 5 shows the normalized distribution obtained from the mean concentrations of 106 randomly and independently generated sets of
measurements on core A. The mean of this distribution is
ppm, exactly the mean
of the set of
measurements, and its standard deviation is
ppm, the same value as
ppm expected from the CLT. As also expected from the CLT, the obtained distribution for
is close to a normal distribution, in contrast to the distribution of the
measurements (Fig 4a). However, the strong skewness of the latter does not lead to a true normal distribution for
. The concentrations
and
with 5% and 95% cumulative probability, respectively, are also shown. It follows that the mean concentration of any randomly selected
measurements has a 90% probability of being between
and
, with a 5% probability at either end of obtaining a mean concentration outside this range.
Mean concentration distribution obtained from 106 random sets of
measurements (red curve) using the experimental data for core A. The black curve is the cumulative probability (integral of the red curve as a function of the mean concentration). The concentrations
ppm and
ppm correspond to 5% and 95% of the cumulative probability, respectively.
Fig 6 shows and
for different numbers of measurements
, between 125 and 7 000, for 106 random sets of
measurements for cores A, B and C. The value of 106 was chosen here to obtain reproducible results when repeating the calculations with a different seed in the random number generator. For all values of
we find negligible differences between
and
for the three cores. It can be seen that the gap between
and
narrows as
increases due to the decrease in the standard deviation as
. In addition,
and
become increasingly symmetric about
as
increases, i.e., as the distribution becomes closer to a normal distribution. For a normal distribution,
and
slowly converge to
proportional to
. Looking at core A, for
,
ppm and
ppm which means that for any randomly distributed
measurements, there is a 90% chance that the mean concentration
has an error between +19% and –17% of the mean concentration
ppm.
and
correspond to 5% and 95% of the cumulative probability, respectively, as a function of the number of randomly selected measurements
, for 106 sets of
measurements.
is the mean palladium concentration measured by LIBS (Table 1). The dashed line
= 1 ppm represents the threshold concentration for the exploitability of the palladium ore.
An important practical parameter to consider is the lower concentration limit for ore exploitability which depends on the economics of the extraction process. For the different mineralized zones at the LDI mine, the palladium cut-off grade varies from 0.8 to 1.8 ppm [18]. In this work, we set this cut-off to = 1 ppm. By definition, the parameter
represents the threshold concentration such that there is only a 5% chance that the mean concentration
for
measurements will fall below this value. Fig 6 shows that it would take less than
randomly distributed measurements (i.e., such that
) to confirm with 95% confidence that the ore is suitable for processing.
In the event that an absolute measurement of the palladium concentration is required, we have also calculated the probability of obtaining a mean concentration
within ± 30% of
. This error value seemed to us to be a reasonable choice for obtaining a useful estimate of the mean concentration. Fig 7 shows the probability
as a function of the number of measurements
for 106 sets of
measurements. We can see that
quickly approaches 100% as the number of measurements
increases. Assuming that the distribution is close to normal for large values of
, and using the properties of the error function, we can show that
± 30% of the mean concentration vs. number of measurements. Probability within ± 30% of the mean concentration
as a function of the number of randomly selected measurements
, for 106 sets of
measurements. The dashed horizontal line represents the threshold for a probability ≥ 90%.
when , where
, the approximation improving as
increases. Therefore, a smaller value of
favors a faster convergence of
to 100% as
increases. This explains the comparative convergence rate of cores A, B, and C, since
= 9.1, 6.7, and 2.9, respectively.
3.2 Mathematical model
In this section we discuss the approach of using an analytical concentration distribution instead of a particular set of experimental data as in the previous section. This allows one to establish a conceptual framework without being restricted to a particular set of measurements, to clarify the uncertainties associated with a finite set of
measurements, to understand the effects of noise in the measurements, and to compute probabilities for arbitrary mean concentrations
. We will focus mainly on core A, since measurements were made on three faces of the core, and the number of measurements is higher than for cores B and C, and therefore likely to be more representative of the actual distribution of palladium in the core. The basic Fortran code used to generate the theoretical palladium distributions is provided in S3 File.
Measurements, such as those shown in Fig 4, suggest that this analytical concentration distribution should have a steep slope at low concentrations and a gentle slope at high concentrations. The family of two-parameter functions of the form
where is the palladium concentration and
is a scaling parameter, meets these criteria provided
. The normalized function
/
is the probability density (i.e.,
is the probability of measuring the concentration
within an interval
containing
).
The mean concentration is given by
and the variance by
Here, the concentration variable is the continuous version of the discrete variable
, which is the result of the i-th laser shot. Each laser shot performs a local averaging over the area covered by the laser spot. In a loose analogy to the CLT, one might expect that this averaging process (which makes sense if the laser spot size is much larger than the grains containing palladium) would lead to a decrease in the variance of the empirical probability density
as the laser spot size increases, but would not affect its mean value.
As discussed below, the value gives a palladium distribution of the studied core for
virtual measurements similar to the experimental result, with the right balance between the low and high concentration populations. Smaller values of
increase the probability of obtaining higher concentrations, while larger values of
emphasize the low concentration population. However, no clear differences could be found between values of
around
. For
we get the following exact results
Therefore, the ratio , which determines the rate of convergence of
to 100%, Eq. (1), is
for
. For comparison,
for
,
or
,
for
, and
for
.
Fixing the mean palladium concentration at ppm, approximately as in core A studied in the previous section, we find
ppm. This value of
is higher than that obtained from the spectra measured with
(
ppm). However, as we will see below, the value of
can vary considerably from one set of
virtual measurements to another. The probability density for these parameters is shown in Fig 8 (solid line).
Solid curve: calculated from Eq. (1) with
and
ppm (
ppm). Dashed curve: convoluted function
calculated from Eq. (9) with
ppm. The inset is an enlargement around
.
To account for the noise inherent in the experimental measurements, we assumed a Gaussian concentration noise given by the probability density
where and
is the standard deviation. Gaussian noise is generally considered a reasonable approximation for a wide variety of source noise in measurements.
is expected to be comparable to the detection limit of palladium in our experiments, which we estimated to be 5–10 ppm per laser shot for core A [10].
The probability density for the palladium distribution including noise is given by the convolution
which is shown in Fig 8 for ppm (dashed curve). It can be seen that the noise significantly smears
around
but its effect becomes negligible for
ppm.
Note that Gaussian noise does not affect the mean concentration . If we define
as the mean concentration taking into account the noise, we have
The inner integral gives , from which we conclude that
. This result justifies considering the entire experimental concentration distribution, including the negative part, when evaluating the mean palladium concentration. Similarly, we show that the variance of
is the sum of the variances of the convolved functions (i.e.,
). In the presence of noise, the standard deviation of the mean concentrations of
measurements becomes
. Note that these results hold not only for Gaussian noise, but for any function
that is symmetric about
where
is the variance of
.
To demonstrate the suitability of the probability density and its chosen parameters for modeling distributions such as those of Fig 4, we randomly performed
virtual measurements in a manner similar to that done with the experimental data in Sect. 3.1. To do this, we first solved the following equation for the noiseless palladium concentration
where is a random variable uniformly distributed in [0, 1[. For the function
with
, this equation becomes
where .
The noise for each measurement of the palladium concentration is given by
where is a random variable uniformly distributed in [0, 1]. For Gaussian noise, Eq. (8), this equation becomes
From a computational point of view, for a random number , a concentration
is calculated from Eq. (11), and then for a random number
a noise-related concentration
from Eq. (14), which can be positive or negative, is added to
, so that the concentration is
. In the following calculations we solved Eqs. (11) and (14) by the Newton-Raphson method for each set of
and
with an accuracy of less than
ppm. Another parameter used in the calculations is the range of
which we set as
to ensure the convergence of the solution of Eq. (14).
Typical examples of the palladium concentration distribution obtained using the procedure described above are shown in Fig 9. The number of virtual measurements used in Figs 9a, 9b and 9c is equal to the number of experimental measurements performed on cores A, B, and C, respectively, as described in Sect. 3.1. There is an obvious similarity with the experimental distributions of Fig 4. Of course, there is a very large number of possible realizations, since each is generated from random numbers
and
, and the limit is mostly determined by the accuracy of the solutions of Eqs. (11) and (14). In the case shown in Fig 9a,
ppm and
ppm, in the case shown in Fig 9b,
ppm and
ppm, while in the case shown in Fig 9c,
ppm and
ppm. These values differ from
and
of the analytical probability densities (
ppm and
ppm for Fig 9a,
ppm and
ppm for Fig 9b, and
ppm and
ppm for Fig 9c) due to the limited sampling of
virtual measurements.
The model uses Eq. (2) with and
and includes Gaussian noise given by Eq. (8). (a)
virtual measurements with
ppm and
ppm. (b)
,
ppm and
ppm. (c)
,
ppm and
ppm. The bin size of the histograms is 5 ppm.
We note some discrepancies between Fig 9 and Fig 4 around the zero concentration which is particularly noticeable for core C. This is the case for all realizations of virtual measurements tried. We could not find parameters within our three-parameter analytical model (
,
and
) that gave a better fit to the experimental measurements. The model could possibly be improved by using a more general distribution for the noise, such as the generalized Student’s distribution, which includes an additional parameter. A slightly higher value of
was used in Fig 9b (
ppm) than in Figs 9a and 9c (
ppm) to improve the fit to Fig 4b. Although relatively small variations in
have a noticeable effect on the concentration distribution near zero concentration, the effect of
on the parameters of interest here, namely
,
and
, is negligible as long as
since these parameters depend on
.
To have a closer look at the possible realizations of virtual measurements, we took the statistics of 106 sets of
measurements. The mean of the values of
obtained for each set of
measurements is
ppm with a standard deviation of
ppm, the latter value being close to
ppm expected from the CLT. On the other hand, the mean of the values of
obtained for each set of
measurements is
ppm with a standard deviation of 31 ppm, and the most likely value is about 46 ppm (close to the experimental value of
ppm). The distributions of
and
are shown in Fig 10. As expected from the CLT, the obtained distribution for
is close to a normal distribution in contrast to the probability density
. As suggested by additional calculations, the mean of the standard deviations
would need a much higher value of
to approach the expected value of
ppm. Fig 10 shows that different values of
and
can be obtained from certain sets of
measurements. Therefore,
measurements may not always be representative of the intrinsic probability density
of the sample. This may, of course, be the case for the experimental data shown in Fig 4.
Distributions of mean concentrations (a) and mean standard deviations
(b) for 106 sets of 25 165 virtual measurements. The model uses Eq. (2) with
and
and includes Gaussian noise given by Eq. (8) with
ppm. The bin size of the histogram is 0.05 ppm in (a) and 2 ppm in (b).
3.3 Probability calculations using the mathematical model
Fig 11 shows and
for different numbers of virtual measurements
between 125 and 7 000 for 106 sets of
measurements. In the following calculations the bin size of the distributions has been set to 0.01 ppm. The result is similar to that of Fig 6 for the set of
experimental measurements except that
is somewhat larger here for the largest values of
due to the larger value of
ppm compared to
ppm.
Palladium concentrations and
at 5% and 95% cumulative probability, respectively, as a function of the number of randomly selected measurements
, for 106 sets of
measurements. The model uses Eq. (2) with
and
and includes Gaussian noise given by Eq. (8) with
ppm. The mean concentration
is practically
ppm for all values of
.
Our analytical model can be used to explore different scenarios. Still assuming (since there is no reason to make another assumption yet) and adjusting
to obtain the desired mean concentration
using Eq. (6), Figs 12a and 12b show
and
for the cases
ppm and
ppm, respectively. In Fig 12a, we can see that
measurements are required to confirm with 95% confidence that the analyzed sample is suitable for processing (
). In Fig 12b
. In this case, more than
virtual measurements are required to confirm with 95% confidence that the ore is not suitable for processing at all (
). In the case where
, no decision can be made based on these probabilistic considerations regardless of the number of measurements. However, any analytical method will run into difficulties in assessing the economic viability of the ore when the mean concentration is close to
. In the three cores examined at
and
ppm, it appears that a few thousand randomly distributed measurements are sufficient to make a decision.
. Same as Fig 11 but for the parameter
adjusted so that
ppm (a) and
ppm (b).
Fig 13 shows the probability as a function of the number of measurements
for 106 sets of
measurements for
and
ppm. The results are similar to those in Fig 7 except that the rate of convergence of
to 100% is slower due to the higher value of
.
± 30% of the mean concentration vs. number of virtual measurements. Probability of obtaining a palladium concentration within ± 30% of the mean concentration
as a function of the number of randomly selected measurements
, for 106 sets of
measurements. Same as Fig 11 but for the parameter
adjusted so that
,
and
ppm.
4 Conclusion
In this paper a probabilistic study was carried out to estimate the number of LIBS measurements required to determine the mean palladium concentration within certain limits. Two types of limits were considered for each value of
. Firstly, the lower (
) and upper (
) concentrations corresponding to a 90% probability of obtaining a mean concentration between these two values, with a 5% probability at either end of obtaining a mean concentration outside this interval. In this case, if a given economic viability threshold (
) lies outside the interval [
then the sample can be considered suitable (
) or unsuitable (
) for palladium extraction processing with 95% confidence. Second, an interval of ± 30% around the mean concentration
in case an absolute concentration measurement is required. To perform this probabilistic study, we first used a set of
experimental measurements, assumed to be representative of the intrinsic palladium concentration probability density of the core, and then constructed an analytical probability density mimicking the
measurements of the concentration distributions. The analytical function was used to explore the parameter space and to gain insight into the LIBS measurement process, in particular to understand the effect of noise on the measurements. The two approaches were found to give similar results despite the relatively small number of actual measurements made on the samples and the fact that only a relatively small fraction of the surface (less than 25%) was scanned.
The above analysis is a case study limited in scope to one trace element (palladium) in one type of ore (gabbronorite) from one specific area (B3) of the Lac des Iles palladium mine. The conclusion we draw from the analysis presented here is that a few thousand LIBS measurements, randomly distributed over the sample, are generally sufficient to assert that the average palladium concentration is within the confidence limits of practical interest. At a typical laser repetition rate of 50 Hz, 6 000 laser shots take 2 minutes, which is much faster than wet chemical analysis. As with any analytical method, more time would be required if greater precision were required. However, it should be remembered that LIBS performance depends on how representative the surface concentration is of the bulk core concentration.
Taking random laser shots at the core should not be a problem. In fact, the cylindrical core can be translated along its axis and rotated around its axis. By combining these two movements, the laser shots will form dotted spirals on the core. This allows the laser shots to be distributed relatively evenly across the surface of the core. In principle, with a fast processor, it would be possible to control the number of laser shots by monitoring the mean concentration trend during the analysis.
In order to go beyond the case study presented in this paper and provide useful guidelines for the use of LIBS in the mining industry, a systematic investigation of many representative samples is necessary to evaluate the appropriate LIBS methodology (laser parameters, type of reference materials, etc.) to be used for a given class of samples. An analytical probability density can be used to better understand the importance of certain parameters such as noise level, mean concentration and standard deviation as a function of instrumentation and ore composition. However, a large-scale application of the results of this study was beyond the scope of this paper and is left for future work.
Supporting information
S1 Table. Lac des Iles designation of the drill cores discussed in this work.
https://doi.org/10.1371/journal.pone.0320584.s001
(DOCX)
S2 Datasets. Datasets of measurements for cores A, B and C.
https://doi.org/10.1371/journal.pone.0320584.s002
(ZIP)
S3 File. Basic Fortran code used to generate the theoretical palladium distributions.
https://doi.org/10.1371/journal.pone.0320584.s003
(TXT)
Acknowledgments
We are grateful to Lionnel Djon formerly from Impala Canada for providing us with quarter drill cores from the Lac des Iles mine and their laboratory analysis.
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