Partial matrix matching multi-energy calibration for direct quantification of Al, Fe, Li and Si in spodumene by laser-induced breakdown spectroscopy

Abstract

The increasing demand for new energy sources, such as lithium batteries, has driven exploration of lithium sources like brines and pegmatites, with spodumene being the only mineral with an economically viable extraction route. In 2020, the European Commission listed lithium as a critical raw material. To ensure the quality of spodumene, rapid and accurate analytical methods are essential. Laser-induced breakdown spectroscopy (LIBS) is a promising technique for direct, rapid multi-element analysis, but it usually suffers from intense matrix effects. This study proposes a partial matrix matching multi-energy calibration approach (PMM-MEC) for the determination of Al, Fe, Li and Si in spodumene samples from different locations in Minas Gerais, Brazil, using LIBS. A mixture of spodumene samples, previously characterized by XRF and ICP OES, was used as the standard. The PMM-MEC method was validated by determining Al, Fe, and Ti in bauxite (CRM BXMG-2); Ca, Si and Mn in manganese ore (CRM NCS47009); and Al, Ca and Si in portland cement (CRM 1889a). Sodium and boron, or lithium and boron, were used as internal standards to mitigate matrix effects and improve the method's accuracy. The method provided relative errors between −12% and 10% and relative standard deviations (RSD) ranging from 0.2% to 2.5%. The limits of detection for all analytes were in the 0.0003–0.7% range.

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1 Introduction

Global lithium consumption significantly increased in recent years due to its intensive use in rechargeable batteries. Global production of lithium in 2022 was approximately 130 000 tons, a 41% increase compared with 2021.^1–4 The demand for lithium is expected to grow further, up to 89 times by 2050, due to an accelerating digital transition.⁵ For this reason, lithium has been part of the European Commission's list of critical raw materials since 2020. Although 70% of the world's lithium reserves are found in brines, especially in Chile and Argentina, most of the lithium used in industry today comes from pegmatite deposits mainly from Australia, followed by Canada, Zimbabwe, Portugal, and Brazil.^4,6

Pegmatites are economically important sources of minerals such as feldspar, quartz, petalite, and spodumene, which has high technological significance. Its added value heavily relies on its quality, making quality control processes associated with spodumene production essential.^1,2,7

Rocks and mineral characterization are usually carried out by X-ray fluorescence spectroscopy (XRF), which is of simple application, as it requires little to no sample preparation, and has multi-element capability. On the other hand, XRF is limited to analytes with atomic numbers between 9 and 92, i.e. from fluorine (Z = 9) to uranium (Z = 92). For lighter (Z < 9) elements like lithium (Z = 3), XRF is not recommended due to the low intensity of characteristic X-rays. In such cases, inductively coupled plasma optical emission spectrometry (ICP OES) or inductively coupled plasma mass spectrometry (ICP-MS) are typically used. The main drawback of these methods, however, is the need for converting solid samples into aqueous solutions before instrumental analysis. The total digestion of samples such as rocks and minerals is particularly challenging due to their refractory nature. Their quantitative dissolution cannot be achieved even using a mixture of concentrated acids, high pressure, and high temperature.^6,8,9 Direct analysis of solids is also possible with ICP OES and ICP-MS by using a sample introduction system based on laser ablation or electrothermal vaporization rather than the usual pneumatic nebulization. Another interesting alternative that has been gaining prominence due to its flexibility and potential portability is laser-induced breakdown spectroscopy (LIBS). LIBS is a multielement method with microanalytical capability that employs a high-energy laser pulse to promote the ablation of the sample and atomization and excitation of analytes and uses optical emission spectrometry for signal detection. The method's relative instrumental simplicity allows its use in situ and remote analysis applications.^10–12

Although LIBS has been well established for qualitative analysis, its use for quantitative applications is still challenging, especially due to the intense matrix effects caused by the complex nature of laser–sample interactions.¹⁰ Therefore, the use of appropriate calibration strategies is imperative to ensure the accuracy of quantitative LIBS analyses.^9,13 Among the traditional calibration approaches, external standard calibration (EC) using certified reference materials (CRM) with composition similar to the sample's is the most usual. The main difficulty associated with this approach is finding at least 3 CRMs with similar composition and increasing amounts of the analytes. Furthermore, most of the commercially available CRMs guarantee representative sampling (which is associated with sample homogeneity) only for sample masses higher than 100 or 500 mg, which are much higher than the amount of material ablated in LIBS (ca. 0.1 mg). Such low mass of sample significantly contributes to LIBS’ poor precision in many applications. Matrix matching calibration (MMC) has also been used in LIBS analysis by employing CRMs of the same matrix, or by preparing standards with increasing amounts of analyte added to the sample or other solid support.^14,15 This approach, however, is laborious and time-consuming and, therefore, rarely used in routine applications. Internal standard calibration (ISC) has also been used in LIBS analysis, especially to correct for physical interferences. Typical examples of ISC applications in LIBS include monitoring C¹⁶ and Si¹⁷ for correcting physical interferences in the analysis of organic- and inorganic-matrix samples, respectively.

Some non-traditional calibration alternatives are commonly used in LIBS. The slope ratio calibration (SRC) method, for example, is based on monitoring analytical signals from increasing masses of standard and sample. In LIBS, the variation in sample mass is easily achieved by changing the number of laser pulses, which is directly related to the amount of sample ablated. The analyte concentration in the sample can then be calculated by comparing the slopes obtained from the standard and sample plots. Other calibration strategies include two-point transfer calibration (TPC), which is similar to SRC, but uses only two standard and sample masses for calibration,^15,18,19 and single-sample calibration (SSC), which employs a nonlinear model based on the Lomakin–Scherb equation and correlates the intensity of the analytical signal recorded for the sample and the standard with the amount of analyte in the standard.^15,20 Methods based on multivariate calibration have also been used in LIBS. As the name suggests, multiple variables are simultaneously monitored for a given set of samples when applying these methods. Referred to as first-order calibration, in which a vector is determined for each sample, multivariate calibration methods use chemometric tools to find relationships between these vectors (scores) and their variables (loadings).^15,21

Among non-traditional approaches, multi-energy calibration (MEC) stands out.²² The main advantages of this calibration strategy are its general accuracy and the use of only one standard and two sub-samples for calibration:¹ a mixture of standard and sample (signals plotted on the X axis), and² a mixture of standard and blank (signals plotted on the Y axis). In MEC, the instrument response for each sub-sample is simultaneously monitored at least at three wavelengths for the same analyte. The matrix matching nature of MEC (the same amount of sample is present in each of the sub-samples used for calibration) significantly minimizes matrix effects, which has allowed its application to several types of liquid and solid samples and accurate determinations by ICP OES, microwave-induced plasma optical emission spectrometry (MIP OES), high-resolution continuum source atomic absorption spectrometry (HR CS AAS),²² and LIBS.^23,24

In the present study, we describe an adaptation to MEC for which samples and standard are separately analyzed, with no need to prepare two sub-samples for calibration. In partial matrix matching MEC (PMM-MEC), the analytical signals recorded for the sample at several wavelengths are plotted on the Y-axis (e.g., Li I 323.266 nm, Li I 610.354 nm, and Li I 670.776 nm), while the corresponding signals recorded for the standard are plotted on the X-axis. It is important to highlight that the signals for the sample and the standard, recorded at the same emission lines, are plotted on the Y- and X-axes, respectively, and at least three emission lines are required. The analyte concentration in the sample is then calculated from the slope (m) of the resulting calibration plot. Because spodumene is the sample being evaluated in this study, a mixture of spodumene samples previously analyzed by XRF and ICP OES is adopted as the standard. The relationship between instrument response and analyte concentration in both the sample and the standard can be represented by eqn (1) and (2), where I_(λi)^Sam and I_(λi)^Std are instrument responses for an analyte at a given wavelength (λ_i) for the sample and the standard, respectively; k is a proportionality constant that incorporates all physical variables related to the instrument response (including potential matrix effects); and C^Sam and C^Std are the concentration of analyte in the sample and the standard, respectively.

I_(λi)^Sam = k·C^Sam (1)

I_(λi)^Std = k·C^Std (2)

Let us consider the same instrumental conditions and the same sample matrix, in which case k assumes the same value in eqn (1) and (2) and allows for their combination and rearrangement, resulting in eqn (3) and (4):

When I_(λi)^Sam and I_(λi)^Std are plot on the Y and X axis, respectively, the slope (m) of the PMM-MEC calibration plot is represented by eqn (5), and the analyte concentration in the sample can be determined by eqn (6):

C^Sam = m·C^Std (6)

The main advantage of PMM-MEC compared to MEC is a significant increase in sample throughput. MEC requires two calibration solutions per sample, while PMM-MEC only uses one calibration solution/solid standard for all samples. Furthermore, because no sample/standard and sample/blank solid mixture is required in PMM-MEC, it is less prone to homogeneity issues that may occur in MEC-LIBS applications. On the other hand, PMM-MEC is unable to completely correct for matrix effects. Although both samples and standard contain a similar matrix, the specific constitution of the standard (a mixture of several spodumene samples) may be slightly different from each individual spodumene sample. In the present study, matrix effects were minimized by employing internal standard species (IS) in combination with PMM-MEC. The method was evaluated for the direct determination of Al, Fe, Li and Si in spodumene glass beads by LIBS and the results were compared with values obtained for the same samples by XRF (for Al, Fe, and Si) and ICP OES (for Al, Fe, Si, and Li), given the known limitations of XRF for lithium determination. Additionally, to demonstrate the effectiveness of the calibration procedure the method was evaluated for the direct determination of Al, Fe, and Ti in bauxite (CRM BXMG-2); Ca, Si and Mn in manganese ore (CRM NCS47009); and Al, Ca and Si in portland cement (CRM 1889a).

2 Experimental

2.1 Instrumentation

All measurements were carried out with a commercial J 200 Tandem LIBS system (Applied Spectra, West Sacramento, CA, USA), which has a Q-switched Nd:YAG laser operating at 266 nm and at a 10 Hz repetition rate, with a maximum energy of 25 mJ per pulse, and a CCD-based spectrometer that covers the 186–1044 nm spectral range. Beam shaping (spot size) was achieved using a combination of a motorized beam expander and aperture imaging. The Axion 2.0 software (Applied Spectra) was used for data processing, including the monitoring of emission spectra, identification of emission peaks, correction of background signals, and integration of peak areas. ICP OES (ICAP 6300, Thermo Fisher Scientific, Waltham, MA, USA) and XRF (Zetium, Malvern Panalytical, Malvern, UK) instruments were used for method comparison and evaluation. Closed-vessel microwave-assisted digestion was used for sample preparation before ICP OES analysis. A MARS 6 (CEM, Matthews, NC, USA) microwave system was used for sample decomposition. An automated hydraulic press (Xpress 3635, Spex SamplePrep, Metuchen, NJ, USA) was used to prepare sample pressed pellets employed in XRF analyses. Fused glass disks were prepared in an automated fusion furnace (Katanax, SpexSamplePrep, Metuchen, NJ, USA) equipped with platinum-gold 95–5% crucibles and molds.

2.2 Sample preparation

Spodumene samples were collected at different locations in the state of Minas Gerais, Brazil. A mixture of spodumene samples, also from various regions within the state of Minas Gerais, Brazil, was used as the standard. These samples had been previously chemically characterized by XRF and ICP OES. For other mineral matrices, reference materials were used as standards and samples, respectively: bauxite (BXMG-1 and BXMG-2 – CETEM, Rio de Janeiro, Brazil), manganese ore (NCS47008 and NCS47009 – NACIS, Beijing, China), and portland cement (SRM 1886a and SRM 1889a – NIST, Gaithersburg, USA). Fused glass disk of each sample was prepared by mixing 1 g of sample with 7 g of lithium borate flux (49.75% Li₂B₄O₇ + 49.75% LiBO₂ + 0.5% LiBr) and submitting them to the following heating program in the automated fusion furnace (temperature/°C; ramp/°C min⁻¹; hold/min): step 1 (1000; 30, 6), and step 2 (1100; 50; 2). For spodumene samples sodium borate flux (Na₂B₄O₇) was used instead since Li was the analyte to be investigated. The standards were prepared in the same way.

Reference values for spodumene were established for Al, Fe, Li and Si by analyzing the samples by ICP OES after microwave-assisted acid decomposition using the “Spodumene (Lithium Feldspar)” method.²⁵ Briefly, the digestion procedure requires the mixture of 250 mg of sample, 1 mL of concentrated nitric acid, 3 mL of concentrated hydrochloric acid, and 4 mL of concentrated hydrofluoric acid, which is heated at 200 °C for 20 min. After the solution cools to room temperature, 30 mL of distilled-deionized water and 2 g of boric acid are added to it, and the system is once again heated at 170 °C for 10 min. For ICP OES analysis, the following instrumental parameters were adopted: radio frequency applied power of 1150 W, peristaltic pump rate of 30 rpm using a phthalate free PVC pump tube (0.64 mm inner diameter, orange/white), auxiliary gas flow rate of 0.5 L min⁻¹, nebulization gas flow rate of 0.5 L min⁻¹, and coolant gas flow rate of 12 L min⁻¹.

Additionally, reference values were established for Al, Fe and Si by XRF. Pressed pellets used in XRF analysis were prepared using approximately 17% paraffin (Oregon) as a binding agent, and the measurements were performed in scanning mode, which renders them semi-quantitative. Additionally, loss on ignition (LOI) tests were conducted in a muffle furnace at 1020 °C for 2 hours, and the concentrations obtained by XRF were normalized to 100%. Although a product of scanning mode measurements, the values determined by XRF presented no statistical difference from those determined by ICP OES.

2.3 LIBS measurements

Fused glass disks were inserted into a LIBS ablation chamber equipped with an automatic x–y–z position adjustment system, and three equally spaced sampling lines per sample were scanned using a rastering speed of 0.15 mm s⁻¹. The most intense emission lines (nm) presenting no evidence of spectral interference or self-absorption according to the LIBS instrument's controlling software were monitored: Al I 308.215, Al I 309.284, Al I 394.400, Al I 396.152, Li I 323.266, Li I 610.354, Li I 670.776, Si I 212.412, Si I 288.158, Si I 390.552, Fe II 259.939, Fe II 258.587, Fe II 274.712, Fe II 275.574 (for spodumene); Al I 327.577, Al I 308.215, Al I 309.284, Al I 394.400, Al I 396.152, Fe II 238.204, Fe II 239.924, Fe II 258.587, Fe II 260.709, Fe II 275.574, Ti II 307.297, Ti II 316.852, Ti II 325.425, Ti II 334.940 (for bauxite); Ca II 393.366, Ca II 396.847, Ca I 422.673, Ca I 430.253, Si I 250.690, Si I 252.851, Si I 288.158, Mn II 260.568, Mn II 293.305, Mn II 294.920, Mn I 353.212, Mn I 354.803 (for manganese ore), and Al I 237.312, Al I 308.215, Al I 309.284, Al I 394.400, Al I 396.152, Si I 250.690, Si I 251.611, Si I 252.411, Si I 263.129, Si I 288.158, Ca II 393.366, Ca II 396.847, Ca I 422.673 (for portland cement) (here, I and II represent atomic and ionic lines, respectively). Measurements were based on the peak area of the corresponding emission lines after averaging background subtraction. The results are presented as mean ± 1 standard deviation (n = 3) of the three individual accumulated spectra obtained. The analyte emission signals were normalized using the signal intensities from B I 249.677 nm, Li I 670.766 nm and Na I 589.592 nm as internal standards (IS) to circumvent potential matrix effects caused by variation in instrumental conditions and different laser–matrix interactions.

It is important to highlight that the LIBS instrument's controlling software (Axion 2.0) is based on the NIST Atomic Spectra Database.²⁵ Therefore, the selection criterion for the emission lines was based on a comparison between potential spectral interferences indicated by the Axion 2.0 software and the minor elements detected by XRF for spodumene (K, Mg, P, Ca, Cr, Mn, Ni, and Sn, all at concentrations below 0.1%) or present in the CRM certificates. No relevant spectral interferences were identified for the selected lines.

The evaluation of self-absorption was based on the graphical behavior observed in the PMM-MEC approach. In other words, PMM-MEC explores the principle that the instrumental response (atomic emission) at a given wavelength is directly proportional to both the analyte concentration and the excited-state transition energy. Therefore, different emission lines (free from spectral interference or self-absorption) are expected to show a linear relationship, that is, a calibration curve. Any spectral interference or self-absorption would be detected as a deviation from linearity. For the selected lines, no such deviations were observed, indicating the absence of both spectral interference and self-absorption.

Instrumental operational parameters, such as laser fluence (optimized by varying the laser energy and spot size), delay time, and argon flow rate, were optimized using a univariate approach aiming at higher sensitivity and signal-to-background ratio (SBR) for the main emission lines selected for each spodumene element. Laser energy values evaluated were in the 5–20 mJ range, laser spot diameter, delay time, number of accumulated pulses, and argon flow rate were evaluated in the 35–140 μm, 0.25–1.0 μs, 135–400 pulses, and 0–2.0 L min⁻¹ ranges, respectively.

2.4 Analyte concentration uncertainty and limit of detection calculations

For PMM-MEC, the uncertainty of the analyte concentration in the sample (S_C^Sam) depends on the errors associated with the slope of the calibration curve (S_m) and the analyte concentration in the standard (S_C^Std). Liquid standard solutions, used in MEC, for example, present negligible values for S_C^Std. However, C^Std errors are not negligible for a solid standard prepared from a mixture of spodumene samples for which reference analyte values were determined by XRF and ICP OES. Thus, the uncertainty of the analyte concentration in the sample determined by PMM-MEC is estimated using the error propagation method, as shown in eqn (7).

The limits of detection (LOD) and quantification (LOQ) were calculated according to IUPAC's recommendations as LOD = 3 S_CBlk and LOQ = 10 S_CBlk, where S_CBlk is the standard deviation of the analyte concentration found for the blank (n = 10) 22. A fused glass disk of sodium borate flux (Na₂B₄O₇) was used as the blank for LOD and LOQ calculations.

3 Results and discussion

3.1 LIBS instrument optimization

Instrumental parameters directly influence laser–sample interactions affecting the analytical signals obtained with LIBS. To achieve accurate quantitative results, univariate optimization of instrumental parameters was carried out to determine a compromise condition with the best signal-to-background ratio (SBR) possible for the main emission lines selected for each spodumene analyte. The instrumental parameters evaluated were laser fluence (optimized by varying the laser energy and spot size), delay time, and argon flow rate.

The effect of the number of accumulated pulses on the analytical signal intensity was evaluated for values in the 135–400 pulse range. In this study, the other instrumental parameters were fixed: spot size of 50 μm, 0.50 μs of delay time, 20 mJ of laser energy per pulse, and absence of argon as purge gas in the chamber. Results showed that the integrated area of the emission signals increased linearly with the number of laser pulses. Since variations in the SBR were not significant, the highest number of tested pulses was chosen for the following studies.

Fixing the other parameters and using 400 accumulated pulses, laser fluence was evaluated in the 2079–130 J cm⁻² range by varying laser spot size in the 35–140 μm range. A larger spot size is expected to result in a larger ablated area, a larger plasma volume, and a lower laser fluence (J cm⁻²).²⁶ On the other hand, emission and excitation processes are usually favored by smaller laser spot sizes, as it can be seen in Fig. 1. The effects of spot size on the analytical signals and SBR values for (A) Al I 396.152 nm, (B) Li I 670.776 nm, (C) Si I 288.158 nm, and (D) Fe II 259.939 nm were similar. The analytical signal is improved when spot size is increased from 35 μm (2049 J cm⁻²) to 65 μm (603 J cm⁻²), probably due to an increase in the ablated area. For spot sizes larger than 65 μm, a decrease in analytical signal is observed, probably due to a decrease in laser fluence, self-absorption, and the shielding effect.²⁷ Considering a compromise condition among the analytes and between ablated area and fluence, 65 μm (603 J cm⁻²) was chosen for further studies.

Fig. 1 Influence of the laser spot size on the analytical signal integrated area (●) and signal-to-background ratio, SBR (▲) for (A) Al I 396.152 nm, (B) Li I 670.776 nm, (C) Si I 288.158 nm, and (D) Fe II 259.939 nm (I and II represent atomic and ionic lines, respectively).

Laser fluence was evaluated again, this time in the range of 151–603 J cm⁻², by varying the laser energy from 5 to 20 mJ per pulse. Since higher energies increase ablation efficiency and favor atomization and excitation processes,¹⁰ higher analytical signals and SBR were observed using the highest energy tested. Thus, a 20 mJ per pulse (603 J cm⁻²) was chosen as the best condition. It is important to note that the same fluence (603 J cm⁻²) was achieved by adjusting either the laser spot size or the laser energy.

With the number of accumulated pulses and laser spot size fixed at 400 and 65 μm, respectively, and using a laser energy of 20 mJ per pulse, in absence of argon in the chamber, the influence of delay time on the analytical results was evaluated for values in the 0.25–1.0 μs. As shown in Fig. 2, both the analytical signals integrated areas and the plasma continuum background decreased with an increasing delay time, which contributed to improved SBRs. Considering a compromise condition for all analytes, a delay time of 0.5 μs was chosen for further studies.

Fig. 2 Influence of delay time on the analytical signal integrated area (●), signal-to-background ratio, SBR (▲), and spectral emission profiles for (A) Al I 396.152 nm, (B) Li I 670.776 nm, (C) Si I 288.158 nm, and (D) Fe II 259.939 nm (I and II represent atomic and ionic lines, respectively).

Using the previously optimized conditions for all the other parameters, the effects of introducing argon into the ablation/atomization/excitation chamber were evaluated. An argon atmosphere promotes the generation of hotter plasmas compared with those generated in the absence of argon.²⁸

Considering argon flow rates in the 0–2.0 L min⁻¹ range, analytical signal improvements were observed when argon flowing at 0.5 L min⁻¹ was used. Compared to air atmosphere, signal enhancements by 1.6-fold for Li and Al, 2.5-fold for Si, and 125.7-fold for Fe (based on integrated area in a.u.) were observed. No significant increases in SBR were observed for higher argon flow rates, so 0.5 L min⁻¹ was adopted as the optimal condition.

The optimized compromise condition for LIBS measurements on spodumene adopted in the present study can be summarized as laser fluence of 603 J cm⁻² (laser energy of 20 mJ per pulse and laser spot size of 65 μm), delay time of 0.5 μs, 400 accumulated laser pulses per site, and argon flowing at 0.5 L min⁻¹ into the ablation/atomization/excitation chamber. These parameters were applied for all the subsequent experiments, and the CRMs were analyzed under the same conditions.

3.2 Quantitative analysis

The PMM-MEC method was applied to the analysis of spodumene samples, bauxite (CRM BXMG-2), manganese ore (CRM NCS47009) and portland cement (CRM 1889a) using the optimized LIBS instrumental parameters. Analyte mass fraction values were calculated using eqn (6), and concentration uncertainties were determined using eqn (7). Results for two spodumene samples and three mineral CRMs evaluated are shown in Table 1. As expected for a method based on partially matched matrices, relatively high biases (up to 35%) were observed when comparing PMM-MEC results with reference values. To minimize matrix effects and improve the method's accuracy, B (B I 249.677 nm), Li (Li I 670.766 nm, for all samples except for spodumene), and Na (Na I 589.592 nm, only for spodumene analysis), which were present in all sub-samples at the same mass fraction, were used as internal standards (IS). The effectiveness of an IS species usually depends on its ionization and excitation energies similarity with those of the analytes.²⁹ Thus, considering ionization energy values, for spodumene, Na (5.14 eV) was used as internal standard in Li (5.39 eV) and Al (5.99 eV) determinations, while B (8.30 eV) was used as IS in Si (8.15 eV) and Fe (7.90 eV) determinations; for bauxite, the best results was achieved using only B (8.30 eV) as internal standard in Al (5.99 eV), Fe (7.90 eV) and Ti (6.83 eV) determinations; for manganese ore, in the same way, the best results was achieved using only B (8.30 eV) as internal standard in Mn (7.43 eV), Si (8.15 eV) and Ca (6.11 eV) determinations; and, for portland cement, Li (5.39 eV) was used as internal standard in Al (5.99 eV) and Ca (6.11 eV) determinations, while B (8.30 eV) was used as internal standard in Si (8.15 eV).³⁰ Normalizing analytical signals based on the IS signals significantly contributed to improving both linearity and accuracy, as shown in Fig. 3 and 4, and Table 1. These improvements are probably associated with the correction of possible physical interfering effects taking place during the ablation process.

Table 1 Quantitative determination by LIBS using PMM-MEC and internal standardization. Values correspond to the mean ± 1 standard deviation (n = 3 averaged spectra from 400 laser pulses) mass fractions

	Analyte	Expected value (%)	Without internal standardization			With internal standardization^a^b^c^d
			Found (%)	Relative error (%)	Slope	Found (%)	Relative error (%)	Slope
a Spodumene (Sample 1 and Sample 2): Na as IS for Al and Li, and B for Fe and Si determination. b Bauxite (BXMG-2): B as IS for Al, Fe, and Ti determination. c Manganese ore (NCS47009): B as IS for Ca, Si, and Mn determination. d Portland cement (SRM 1889a): Li as IS for Al and Ca, and B for Si determination. e Reference values are based on XRF and ICP OES analyses.
Sample 1^e	Al	16.4 ± 0.1	12.4 ± 0.1	−24	0.8621	14.5 ± 0.2	−12	1.0071
	Li	3.52 ± 0.02	3.05 ± 0.21	−14	0.8673	3.37 ± 0.03	−4	0.9603
	Si	27.6 ± 0.4	21.3 ± 1.6	−23	0.7388	28.4 ± 3.0	+3	0.9852
	Fe	0.875 ± 0.013	0.735 ± 0.019	−16	0.6837	0.959 ± 0.025	+10	0.8923
Sample 2^e	Al	16.5 ± 0.1	14.4 ± 2.8	−13	0.9991	15.4 ± 2.3	−6	1.0695
	Li	2.93 ± 0.01	2.52 ± 0.38	−14	0.7167	2.69 ± 0.41	−8	0.7672
	Si	27.3 ± 0.4	31.1 ± 0.5	+14	1.0806	29.7 ± 0.3	+9	1.0287
	Fe	0.861 ± 0.013	0.928 ± 0.021	+8	0.8634	0.884 ± 0.020	+3	0.8220
BXMG-2	Al	26.7 ± 0.2	34.3 ± 0.9	+29	1.2947	26.1 ± 0.7	−2	0.9864
	Fe	9.62 ± 0.11	12.3 ± 0.2	+28	1.0084	9.36 ± 0.15	−3	0.7683
	Ti	0.984 ± 0.02	1.34 ± 0.03	+36	1.0570	1.02 ± 0.03	+4	0.8053
NCS47009	Ca	14.2 ± 0.07	12.5 ± 0.5	−12	1.1918	12.9 ± 0.9	−9	1.2258
	Si	7.38 ± 0.04	7.09 ± 0.69	−4	1.0772	7.30 ± 0.71	−1	1.1079
	Mn	15.7 ± 0.1	15.7 ± 0.7	0	0.6961	16.2 ± 0.7	+3	0.7160
1889a	Al	2.06 ± 0.05	1.99 ± 0.02	−3	0.9730	1.94 ± 0.02	−6	0.9474
	Si	9.67 ± 0.07	10.7 ± 0.1	+11	1.0266	10.4 ± 0.1	+7	0.9924
	Ca	46.7 ± 0.2	42.3 ± 6.0	−9	0.8708	41.2 ± 5.8	−11	0.8479

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Fig. 3 PMM-MEC determination of Al, Li, Si and Fe in sample 1 without (A–D, respectively) and with the use of Na I 589.592 nm (E and F for Al and Li, respectively) and B I 249.677 nm (G and H for Si and Fe, respectively) as internal standards (I represents an atomic line).

Fig. 4 PMM-MEC determination of Al, Li, Si and Fe in sample 2 without (A–D, respectively) and with the use of Na I 589.592 nm (E and F for Al and Li, respectively) and B I 249.677 nm (G and H for Si and Fe, respectively) as internal standards (I represents an atomic line).

Analytical parameters, such as the coefficient of determination (R²), precision (expressed as RSD), limit of detection (LOD) and limit of quantification (LOQ) are presented in Table 2. Considering the low sample mass ablated in LIBS (<100 μg), the relatively low RSD values obtained (RSD < 2.5%) indicate adequate sample homogeneity and method precision.²³

Table 2 Analytical parameters evaluated for quantitative determination by LIBS, PMM-MEC, and internal standardization

	Analyte	R ^2	RSD^a (%)	LOD (% m m^−1)	LOQ (% m m^−1)
a n = 10.
Sample 1	Al	0.99973	1.3	0.03	0.09
	Li	0.99995	1.3	0.0003	0.001
	Si	0.98894	0.2	0.0004	0.001
	Fe	0.99918	2.2	0.001	0.003
Sample 2	Al	0.93107	0.8	0.02	0.07
	Li	0.97746	0.6	0.001	0.002
	Si	0.99999	0.4	0.002	0.01
	Fe	0.99948	2.3	0.001	0.003
BXMG-2	Al	0.99798	0.5	0.03	0.1
	Fe	0.99974	2.1	0.01	0.04
	Ti	0.99912	2.1	0.004	0.01
NCS47009	Ca	0.99750	0.2	0.002	0.01
	Si	0.99059	2.1	0.1	0.4
	Mn	0.99480	1.9	0.03	0.1
1889a	Al	0.99996	1.0	0.003	0.01
	Si	0.99999	1.9	0.003	0.01
	Ca	0.98034	2.5	0.7	2

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The results shown in Tables 1 and 2 confirm the feasibility of applying the PMM-MEC method in combination with internal standardization for the quantitative determination of Al, Fe, Li and Si in spodumene; Al, Fe, and Ti in bauxite; Ca, Si and Mn in manganese ore; and, Al, Ca and Si in portland cement by LIBS.

4 Conclusions

The PMM-MEC method has proven to be a simple calibration strategy for the quantification of Al, Fe, Li and Si in spodumene; Al, Fe, and Ti in bauxite; Ca, Si and Mn in manganese ore; and Al, Ca and Si in portland cement. The method described in this study allows for using a single calibration standard, which increases sample throughput and reduces waste generation. Sample preparation by fusion proved to be important for this mineral application, as the homogeneous pellet produced minimizes variations associated with differences in particle size, thus enhancing the precision of the analytical results. Strong matrix effects associated with LIBS analysis remain a significant drawback for a broader application of this method; however, employing sodium and boron or lithium and boron (which are present in the flux used to prepare the sample pellets and have ionization and excitation energies that are similar to those of the analytes) as internal standard species contributed to overcoming this issue. It is important to note that, in some cases, internal standardization has limitations, as observed in the determination of Mn in manganese ore and of Al and Ca in portland cement. In these cases, the concentrations obtained without internal standardization were already satisfactory, and applying internal standardization resulted in poorer agreement with the expected values. This probably occurred because internal standardization was unnecessary. For Mn in manganese ore and Ca in Portland cement, the results obtained with and without internal standardization were statistically equivalent according to the t-test. It is important to highlight that, as with the originally described MEC method, PMM-MEC requires at least three analytical lines that are free from spectral interference to be effectively employed.

Author contributions

João Manoel de Lima Júnior: conceptualization, methodology, data curation, formal analysis, writing – review & editing. Nícolas Pico de Azeredo: data curation, formal analysis, writing – review & editing. Juliana Naozuka: data curation, formal analysis, writing – review & editing. Carina Ulsen: data curation, formal analysis, writing – review & editing. George L. Donati: data curation, formal analysis, writing – review & editing. Cassiana Seimi Nomura: supervision, writing – review & editing, project administration, funding acquisition.

Conflicts of interest

There are no conflicts to declare.

Data availability

The data that support the findings of this study are openly available JMLJ personal cloud file. The authors confirm that the data supporting the findings of this study are available within the article.

Acknowledgements

The authors are grateful to the Fundação de Amparo à Pesquisa do Estado de São Paulo (2021/14125-6, 2023/16168-0) for the financial support, and to Micro Service - Tecnológica em Micronização, Produtos e Processos Industriais for the technical support.

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