Improving Quantitative Analysis of Lithium in Brines Using Laser-Induced Breakdown Spectroscopy with τ–Algorithm (τLIBS)

Abstract

In this work, a quantitative analysis of Li in natural brines was carried out by laser-induced breakdown spectroscopy (LIBS) assisted by the τ–algorithm for detailed analysis of the experimental line shapes (τLIBS). Brine samples were collected from different salars located in the Puna plateau (Northwest Argentina) and analyzed by LIBS in the form of solid pressed pellets. The emission intensities of Li I, H_α, and Mg I–II lines were measured and spatially integrated along the line of sight with temporal resolution by using a high-spectral-resolution spectrometer equipped with an intensified charge-coupled device (iCCD) detector. The plasma was characterized through the determination of the electron density and the temperature. The τ–algorithm calculated the optical thicknesses of the Li I lines to generate synthetic intensity profiles that were subsequently fitted to the experimental spectra. By applying the developed τLIBS approach, valuable spectroscopic insight was recovered about the physical processes occurring in the plasma, such as self-absorption. The analytical process involved an univariate external calibration process using the resonant Li I line at 6707.7 Å measured from a series of Li standard samples. Self-absorption effects were evaluated and subsequently compensated. The final LIBS results, with an enhanced accuracy of 15%, were validated by crosschecking them against those obtained with the standard AAS method.

1. Introduction

Laser-induced breakdown spectroscopy (LIBS) is a useful atomic emission spectroscopic technique that can supplement conventional methods for the quantitative analysis of lithium (Li) in brines [1]. The LIBS technique is not competitive but complementary to the other existing analytical techniques, such as atomic absorption spectroscopy (AAS) and inductively coupled plasma–atomic emission spectroscopy (ICP–AES). Li is a light element that is often difficult to detect with AAS and ICP–AES methods but can be readily detected with LIBS [2]. Li’s perceived value has risen over the last years, primarily due to both its limited availability and the increasing demand for Li salts in the battery industry for devices like computers and electric vehicles [3]. Approximately 58% of the global Li resources are found in continental brines located in salt flats, known as “salars” [4]. Continental brines are highly saline solutions with a high sodium (Na) content and varying amounts of other elements, including Li, potassium (K), magnesium (Mg), and calcium (Ca). In South America, the “Lithium Triangle”, comprising Argentina, Bolivia, and Chile, is an extensive area rich in Li brine salars [5]. These salars hold together about 80% of the world’s Li resources in brines. Argentina’s primary Li deposits are found in the Puna region, a high-altitude plateau with an average elevation of 3600 m above sea level. This region, located in the provinces of Jujuy, Salta, and Catamarca, makes Argentina the third-largest producer of Li from brines globally [6]. The concentration of Li in salar brines varies (e.g., from 10 to 1000 ppm) due to the unique geological characteristics of each salar [3,5]. However, reliable data on the availability of Li salts in these salars remains limited. Therefore, a better understanding of the Andean salars and their Li resources is essential to ensure effective and sustainable Li recovery [7,8,9,10,11,12].

LIBS works by analyzing the characteristic spectral lines emitted from a plasma created by a laser-ablated material from the sample being interrogated. LIBS methodology is simple, versatile, and allows for rapid, in situ, multi-element measurements with minimal sample preparation [13]. The LIBS technique has been mainly used for geochemical studies to analyze Li in various solid geological materials like rocks and minerals, including muscovite and other Li-bearing minerals [14,15,16]. However, its application for analyzing Li in liquid samples, such as brines, has not been widely explored. This is mainly because LIBS analysis of liquid samples has known drawbacks (i.e., splashing, bubbles, surface ripples, and lower emitted intensity) that diminish its performance compared to the analysis of solid samples [17]. For instance, Erbetta et al. used a handheld LIBS system to analyze natural brines from Chile’s Atacama Desert, which has a Li content of 0.5–1.75% by weight [18]. Additionally, Xing et al. combined LIBS with a Convolutional Neural Network to perform quantitative analysis of natural brines with a Li concentration ranging from 5 to 40 ppm [19]. Understanding the physical processes of the plasma that influence its behavior, such as self-absorption, is crucial for enhancing the accuracy of LIBS analysis. In a recent work of our group, the LIBS technique was successfully assessed for the determination of Li in continental brines using a compact LIBS equipment [20]. Although in this study, the obtained results showed an acceptable average quantification error of 25%, a deeper investigation into these processes is expected to further improve the technique’s accuracy. In a previous work, we evaluated a self-designed algorithm, called the τ–algorithm, for providing spectroscopic information that is particularly effective for studying emission lines, measured with good spectral resolution, from plasmas generated with LIBS [21]. In the present work, we developed a novel approach that is based on the LIBS technique incorporating the τ–algorithm (τLIBS) for the analysis of the measured line shapes. τLIBS is a variant of the traditional LIBS method for the detailed analysis of line shapes. The τLIBS approach was applied to determine the Li elemental content in natural brines. The analytical process involved the spectral analysis of the resonant Li I line at 6707.7 Å and univariate external calibration using a series of Li standard samples. The plasma was characterized through the determination of the electron density and the temperature. To improve the accuracy of the quantitative results, self-absorption effects were evaluated and subsequently compensated. The final LIBS results were validated by cross-checking them against those obtained with the standard AAS method.

2. Theoretical Section

We consider a cylinder-symmetrical homogeneous plasma in local thermodynamic equilibrium (LTE), where the emission and absorption of radiation are described by an emission coefficient ε_λ (J s⁻¹ m⁻³ sr⁻¹ Å⁻¹) and an absorption coefficient κ(λ) (m⁻¹). The spectral intensity $I_{\lambda }$ (J s⁻¹ m⁻² sr⁻¹ Å⁻¹) radiated along the line of sight is given by

$$I_{\lambda }=C{U}_{\lambda }\left(T\right)\left(1-e^{-{\tau }_{\lambda }\left(T\right)}\right),$$

(1)

where C (a.u.) is a factor that unifies units and depends on the instrumental setup, U_λ (T) (W m⁻² sr⁻¹ Å⁻¹) is Plank’s distribution for blackbody radiation, T (K) is the plasma temperature, and τ_λ (dimensionless) is the optical thickness [22]. The optical thickness can be separated into different factors:

$${\tau }_{\lambda }\left(T\right)=\kappa \left(\lambda \right)\left(T\right)l={\kappa }_e\left(T\right)NlP\left(\lambda \right),$$

(2)

where κ_e (T) (m³) is a coefficient that depends on the temperature and the atomic parameters of the transition, N (m⁻³) is the density of the emitting element in the plasma, l (m) is the length of the plasma along the line of sight, and P (λ) (m⁻¹) is the normalized line shape, generally given by a Voigt function. The optical thickness (τ_λ) determines self-absorption of the spectral emission lines within the plasma. If τ_λ is known, a self-absorption correction factor R_λ (dimensionless) can be obtained,

$$R_{\lambda }={\displaystyle \frac{I_{\lambda }^{thin}}{I_{\lambda }}}={\displaystyle \frac{{\tau }_{\lambda }}{1-e^{-{\tau }_{\lambda }}}}.$$

(3)

The correction factor R_λ can be applied to the experimental lines (I_λ) to compensate for self-absorption effects, thus retrieving the optically thin line profiles (I_λ^thin) for the same number density of emitters [23]. Namely,

$$I_{\lambda }^{thin}=R_{\lambda }{I}_{\lambda }.$$

(4)

For a given emission line, self-absorption can be quantitatively assessed by the line self-absorption coefficient:

$${SA}_l\equiv \left(1-{\displaystyle \frac{I^{exp}}{I^{thin}}}\right)\times 100,$$

(5)

where I^exp (a.u.) and I^thin (a.u.) are the wavelength-integrated intensities of the experimental and optically thin lines, respectively. The SA_l coefficient is expressed as a percentage, in such a way that SA_l = 0% if the line is optically thin, and it increases up to SA_l = 100% as the line becomes completely self-absorbed.

3. Materials and Methods

3.1. Brine Samples

In this study, 11 natural brines collected from different salars (designated #1–11), located in the Puna region of Argentina, were analyzed in the laboratory for Li determination. To overcome the drawbacks of LIBS measurement of liquid matrices, the samples were prepared in the form of pellets employing a liquid-to-solid matrix conversion [20,24]. For each brine sample, a volume of 12 mL was mixed with 6 g of pure calcium oxide (CaO, Aldrich Powder 98%). Then, the mixture was stirred under controlled, contamination-free conditions to ensure homogeneity. Subsequently, the mixture was dried in an oven at 70 °C until constant weight was achieved. The resulting solid was ground to a fine powder using an agate mortar and pestle before being pressed at 35 MPa using a stainless steel die. The final pellets measured 3 cm in diameter, 1 cm in thickness, and had a mass of 8 g. For calibration purposes, 8 pellets with known Li concentrations ranging from 0 to 1300 ppm, and including a blank, were also prepared. These Li standards were prepared by diluting a stock lithium carbonate solution (Li₂CO₃, Agilent) with suitable volumes of doubly distilled water (σ < 5 μS/cm). The accuracy of the quantitative LIBS analysis was assessed by comparing the results obtained for the Li concentrations in the brines with those determined by atomic absorption spectroscopy (AAS) according to standard procedures [25].

3.2. LIBS Setup

The employed LIBS setup is shown in Figure 1. A Nd: YAG laser (wavelength 1064 nm, pulse width 4.5 ns, pulse energy 30 mJ, repetition rate 20 Hz) was used to generate the plasmas in air at atmospheric pressure. The laser beam was focused at right angles to the sample surface using a plano-convex lens (126 mm focal length) placed at a lens-to-sample distance of 122 mm from the sample surface. The samples rotated at 300 rev min⁻¹ to avoid the formation of a deep crater by the ablation process. A plastic nozzle (4 mm in diameter) was used to blow air (pressure < 7 kPa) over the ablation spot to remove the dust released by laser shots and prevent the spark of the breakdown in the air above the samples’ surface. The whole plasma emission was collected by using a fiber optics (100 μm core diameter), placed at a 1 cm distance from the laser spot on the target at a 45–degree angle, and transmitted to the entrance of a Czerny–Turner spectrometer (focal length 0.5 m, gratings of 2400 and 3600 lines mm⁻¹, slit width 20 μm) equipped with an intensified charge-coupled device (iCCD) detector (1200 × 256 effective pixels). The experimental setup had a high spectral resolution (50 pm at 3000 Å), providing an instrumental broadening comparable to or less than the experimental line widths, which allowed the detailed measurement of the true line profiles.

Emission line spectra of Li I, H_α, and Mg I–II (spatially integrated along the line of sight) were recorded using suitable delay times (1–10 μs) with a gate width of 1 μs. An additional spectrum was measured at a late time window (delay 15 μs, width 1 μs) where the electron density had decreased to a negligible value. This latter spectrum was used as a reference for the estimation of the instrumental width. Each recorded spectrum was the result of the in-software accumulation of individual spectra generated from 300 consecutive laser shots to improve the signal-to-noise ratio, after discarding the first 100 cleaning shots delivered to avoid any possible superficial contamination due to handling of the samples. The recorded raw spectral data (i.e., 1024 pixels vs. emission intensity) were pre-processed in software through automated routines that removed the “dark” background (i.e., spectrum without laser firing), and carried out the wavelength calibration (i.e., pixel-to-wavelength relationship).

4. Results and Discussion

Figure 2 shows the temporal behavior of the line profiles of spectral emission intensity for the resonant Li line at 6707.7 Å measured from the reference sample with a Li concentration of 62.5 ppm. It was observed that the emission intensity of the Li I line decreased with time as the plasma cooled down. Moreover, a central dip was present at the Li I line profiles for delay times larger than 2 μs. The presence of such a dip is an unequivocal sign that the Li emission is being self-absorbed in a non-uniform plasma regarding the Li concentration, with a large temperature gradient between the inner and outer parts of the plume [26]. For larger Li concentrations, a similar trend was observed. For a Li concentration of 1346 ppm, the dip was present at an early time of 1 μs. Self-reversal of the resonant Li line measured at atmospheric pressure has already been reported by Tanra et al. [27]. The authors attributed this to the very light mass of Li atoms (m_Li = 6.941 g/mol), which are “blown” by the plasma shock wave to the periphery. This can be realized with a simple picture of a plasma composed of two regions: a hot core surrounded by a cold periphery, which are populated mainly by ions (Li II) and neutral atoms (Li I), respectively [28]. Hence, the relatively high density of neutral atoms in the plasma periphery increases the self-absorption of the spectral lines, thus leading to an optically thick inhomogeneous plasma. Following this observation, a delay time of 1–2 μs (i.e., delay time 1 μs, gate width 1 μs) was selected for the LIBS analysis, where suitable conditions of an approximately homogeneous plasma were achieved. In the following, we describe the plasma characterization (Section 4.1), the analysis of the recorded spectral lines (Section 4.2), and the quantitative analysis of Li in the natural brine samples, together with the evaluation of its accuracy (Section 4.3).

4.1. Plasma Characterization: Electron Density and Temperature

The plasma was characterized by the determination of the electron density and the temperature. The electron density was determined from the Stark broadening of the H_α line at 6563.0 Å. As reported in our previous works [20,21], the H_α line features a very small optical thickness (i.e., the maximum value at the line center being τ₀^Hα << 1) due to its large Stark broadening. This low τ_λ^Hα ensures that self-absorption is minimal, accounting for less than 1%, and thus its effects in the line profile are negligible. The measured Hα profiles were fitted with a Lorentzian function, as shown in the example of Figure 3. The obtained Stark widths were in the range w_Stark = 11–12 Å. The electron density (N_e [m⁻³]) was then calculated through the empirical expression given by Gigosos and Cardeñoso [29]:

$$N_e={10}^{23}{\left({\displaystyle \frac{w_{Stark}}{1.098}}\right)}^{1.47},$$

(6)

The obtained mean value of electron density was N_e = (1.0 ± 0.1) × 10¹⁷ cm⁻³. This value is well above the minimum density of N_e,0 = (1.4 ± 0.1) × 10¹⁶ cm⁻³ required by McWhirter’s criterion for LTE conditions [30]. It should be mentioned that, despite McWhirter’s criterion being satisfied for all the measured transitions, suggesting that LTE may exist, it is a necessary but not sufficient condition. The plasma temperature (kT [eV]) was obtained through a Saha–Boltzmann plot constructed with a set of selected Mg I–II emission lines having wavelengths in the range 2775–2855 Å (Figure 4) and with available spectroscopic data in the NIST Atomic Spectra Database [31] (

Table 1. Spectral lines used for plasma characterization (Mg I–II and H I) and compositional analysis (Li I). Spectroscopic data from NIST Database [31].

Species	λ0 (Å)	Aki (108 s−1)	Ei (eV)	Ek (eV)	gi	gk
Mg I	2776.5	1.32	2.712	7.175	3	5
Mg I	2778.5	1.82	2.709	7.170	1	3
Mg I	2779.7	1.36	2.712	7.170	3	3
Mg I	2781.0	5.43	2.717	7.173	5	3
Mg I	2782.8	2.14	2.717	7.170	5	3
Mg I	2852.1	4.91	0.000	4.345	1	3
Mg II	2790.8	4.01	4.422	8.864	2	4
Mg II	2795.5	2.60	0.000	4.434	2	4
Mg II	2798.0	4.79	4.434	8.863	4	6
Mg II	2802.7	2.57	0.000	4.422	2	2
H I	6563.0	0.44	10.199	12.087	8	18
Li I	6707.7	0.37	0.000	1.848	2	4

). Self-absorption of these Mg I–II lines is low to moderate, thus they can be used to perform a reliable plasma characterization [20]. An example of a Saha–Boltzmann plot is shown in Figure 5. The obtained mean value for the plasma temperature was kT = (0.75 ± 0.03) eV. The kT and N_e parameters obtained for the different samples were the same within the experimental error; hence, matrix effects were negligible in our experiment. The electron density and temperature values were derived from the measurement of spectral lines integrated along a time interval as well as along the line of sight from a near-homogeneous plasma. Hence, these plasma parameters corresponded to apparent values, as a result of population-averaged values over the real spatial-temporal distribution of the species emissivity [32].

4.2. Plasma Analysis of Li Spectral Emission with τ–Algorithm

The experimental line profiles (pre-processed) were analyzed by the τ–algorithm, a self-designed computational algorithm developed in Python^® (Version 3.13.1). In the following, we review briefly the theory supporting the τ–algorithm framework, which has been described in more detail in a previous work [21]. The τ–algorithm is based on the framework of a homogeneous plasma in LTE. It is aimed at extracting the spectroscopic information saved in the optical thickness of the line of interest, such as self-absorption evaluation/compensation. The retrieved information is very useful for plasma characterization and to achieve quantitative results. Basically, it models the emission line shapes and matches them to the experimental lines through an iterative fitting procedure. The fitting routine runs until the deviation of the synthetic from the experimental spectrum is minimized. Hence, a modeled line profile that reproduces the measurements is obtained along with its wavelength-dependent optical thickness τ_λ (τ₀, w_V), where τ₀ is the maximum and w_V is the full width at half maximum (FWHM). The coefficient SA_l (Equation (5)) is evaluated, and the experimental profile is subsequently compensated for self-absorption, retrieving the optically thin line profile. The calculation time is less than 10 s for each individual line.

The normalized line profile P(λ) in Equation (2) is represented by a Voigt function with Gaussian and Lorentzian widths corresponding to the Doppler and Stark effects, respectively. The Doppler width, being a fixed parameter, was estimated from the plasma temperature (w_Doppler = 0.17 Å). The Stark width (w_Stark) is a free-fitting parameter. The true line shape I_λ (Equation (1)) is convolved with the instrumental function to compute the experimental line profile. Due to the Li I line being self-reversed at the late time window, the instrumental width (FWHM) was estimated from the adjacent Ca I spectral line at 6717.7 Å (w_Instr = 0.66 ± 0.03 Å). In the τLIBS approach, the intensities of all the Li I lines from both the reference and brine samples were computed with the τ–algorithm and matched to their experimental profiles. A representative example of a modeled Li I line is shown in Figure 6. The results obtained from the analysis of the Li I lines are reported in

Table A1. Calculated spectroscopic parameters for 6707.7 Å Li I line with τ–algorithm: Experimental intensity (I^tot), optically thin intensity (I^thin), maximum optical thickness (τ₀), line self-absorption coefficient expressed as a percentage (SA_l), and Stark width (w_Stark).

Li	Sample	Itot (a.u.)	Ithin (a.u.)	t0 (adim.)	SAl (%)	wStark (Å)
Calibration	30.83 ppm	6950 ± 530	7575 ± 580	1 ± 1	26 ± 2	0.39 ± 0.05
	62.4 ppm	8110 ± 620	9253 ± 700	2 ± 1	39 ± 3	0.35 ± 0.03
	62.5 ppm	10,440 ± 790	11,073 ± 840	2 ± 1	44 ± 4	0.35 ± 0.03
	125 ppm	9311 ± 700	14,365 ± 1000	4 ± 1	54 ± 4	0.35 ± 0.03
	250 ppm	12,760 ± 970	21,110 ± 1600	7 ± 2	65 ± 5	0.35 ± 0.03
	500 ppm	20,030 ± 1500	33,788 ± 2500	8 ± 2	69 ± 6	0.33 ± 0.03
	1000 ppm	29,420 ± 2200	53,409 ± 4000	27 ± 5	84 ± 7	0.35 ± 0.03
	1346 ppm	42,260 ± 3200	76,444 ± 5800	21 ± 4	82 ± 7	0.33 ± 0.03
Brines	# 1	4756 ± 360	4768 ± 370	1 ± 1	1 ± 1	0.35 ± 0.03
	# 2	5942 ± 450	6952 ± 530	1 ± 1	18 ± 1	0.40 ± 0.05
	# 3	13,640 ± 1000	15,005 ± 1100	4 ± 1	54 ± 4	0.35 ± 0.03
	# 4	13,990 ± 1000	17,451 ± 1300	3 ± 1	24 ± 2	0.39 ± 0.05
	# 5	21,410 ± 1600	32,115 ± 2440	3 ± 1	50 ± 4	0.39 ± 0.05
	# 6	23,630 ± 1800	41,109 ± 3100	11 ± 3	74 ± 6	0.35 ± 0.03
	# 7	23,500 ± 1800	40,861 ± 3100	11 ± 3	74 ± 6	0.35 ± 0.03
	# 8	23,580 ± 1800	38,824 ± 2900	7 ± 2	65 ± 5	0.39 ± 0.05
	# 9	28,400 ± 2200	46,851 ± 3600	7 ± 2	65 ± 5	0.39 ± 0.05
	# 10	30,160 ± 2300	50,958 ± 3900	9 ± 3	69 ± 5	0.39 ± 0.05
	# 11	41,040 ± 3100	71,610 ± 5400	13 ± 3	74 ± 6	0.39 ± 0.05

(Appendix A).

4.3. Quantitative Li Analysis

The determination of the Li elemental content in the brines was carried out by the univariate calibration method with the Li I line at Li I 6707.7 Å. In Figure 7, the Li I net intensities (wavelength-integrated) measured from the calibration samples are plotted against the corresponding Li concentrations. A linear growth of the emitted intensity is observed at low concentrations, while saturation is observed at higher concentrations, suggesting that self-absorption effects become more important. The experimental data were fitted with the non-linear function:

$$y=a+bc\left(1-e^{-{\displaystyle \frac{x}{c}}}\right),$$

(7)

where x is the Li concentration; y is the line net intensity; and a, b, and c are the constant fitting parameters [33]. For low concentrations (x ≪ c), Equation (7) is reduced to the linear form:

$$y=a+bx.$$

(8)

Physically, a is the line intensity related to zero concentration of the analyte (i.e., a ≈ 0); b is the sensitivity, given by the slope of Equation (7) in the low concentration region; and c refers to the concentration at which self-absorption of the line becomes noticeable. In our experiment, a linear growth is observed for low Li concentrations (x ≤ 700 ppm), where the plasma is optically thin. After that, self-absorption starts to increase at Li concentrations close to x_c = 770 ppm. Then, self-absorption is clearly evident for higher Li concentrations (x ≥ 800 ppm) as the plasma becomes optically thick. The negative value obtained at the x-axis (i.e., y = 0 and x₀ = − a/b) indicated that an initial concentration of Li (x₀^Li = 16.4 ± 0.2 ppm) was measured in the sample matrix as an impurity and taken into account in the calibration samples.

The limit of Li detection (LoD), defined as the concentration that results in a net line intensity equivalent to three times the standard deviation of the background, was calculated with the following expression:

$$LoD={\displaystyle \frac{3{\sigma }_B}{b}},$$

(9)

with ${\sigma }_B$ being the standard deviation of the background signal measured close to the line for low concentrations, and b being the slope of the linear fit [34]. In our experimental conditions, the limit of detection determined for Li was LoD = 5.8 ± 0.3 ppm. The Li emission intensities were compensated for self-absorption through Equation (4) to obtain the intensities emitted in optically thin plasma conditions (I^thin), as shown in Figure 7. It is observed that the compensated intensities fit well with the predictions of Equation (8), within the experimental error. Nevertheless, for Li concentrations higher than about ≥1000 ppm, the optically thin intensities are lower than the values predicted by the model. As already described in our previous work [21] and also by Aragón and Aguilera [35], this establishes a limit of validity for the model of a homogeneous plasma. In fact, the model is not able to account satisfactorily for the high concentration region of calibration curves where the plasma cannot be considered as homogeneous.

The Li concentrations (ppm) determined with LIBS in the natural brines with and without self-absorption (SA) compensation of the intensity data, together with the reference AAS values, are presented in

Table 2. Li concentrations determined in brines by LIBS (without/with self-absorption (SA) compensation) and AAS techniques.

Brine Samples	Li Concentration (ppm)
	LIBS		AAS
	Without SA Compensation	With SA Compensation
1	42 ± 3	41 ± 3	45 ± 2
2	62 ± 5	77 ± 6	83 ± 4
3	213 ± 17	214 ± 18	141 ± 7
4	220 ± 18	248 ± 20	240 ± 12
5	402 ± 32	489 ± 39	477 ± 24
6	466 ± 37	636 ± 51	593 ± 30
7	462 ± 37	632 ± 51	626 ± 31
8	464 ± 38	599 ± 47	660 ± 33
9	625 ± 50	731 ± 58	710 ± 36
10	692 ± 55	798 ± 63	837 ± 42
11	1342 ± 107	1136 ± 91	852 ± 43

and compared in Figure 8. It can be seen that all the results are qualitatively similar for the different brine samples, evidencing a consistency between the different approaches.

The overall accuracy of the LIBS methodology both with and without self-absorption compensation was evaluated by the averaged quantification error calculated as the normalized standard deviation σ_N (%),

$${\sigma }_N=\sqrt{{\displaystyle \frac{\sum {\left(\frac{q_{LIBS}-q_{AAS}}{q_{LIBS}}\right)}^2}{n-1}}}·100,$$

(10)

where q_LIBS and q_AAS are the Li concentration values calculated with LIBS and AAS techniques, respectively, and n is the number of samples (i.e., n = 11) [36]. The accuracy of σ_N = 29% (Figure 9a) obtained for the LIBS data without compensation was enhanced to σ_N^c = 15% (Figure 9b) after applying the self-absorption compensation, thus improving the quantitative results.

5. Conclusions

The synergy between LIBS and the τ–algorithm (τLIBS) enabled the successful application of this spectroscopic technique for the quantitative elemental analysis of Li in natural brines collected from the Lithium Triangle. The samples were prepared as solid pellets to overcome the inherent challenges associated with liquid samples in LIBS. An optimal time of measurement was selected, ensuring that self-reversal was not observed in the experimental line shapes, i.e., a dip in the line center, and thus a near-homogeneous plasma was achieved. In these conditions, the influence of spatial gradients in temperature and species densities on the line profiles was minimized. The laser-induced plasma was characterized by calculating its temperature and electron density. High-spectral-resolution measurements were performed on the emission intensity profiles of the Li I line at 6707.7 Å for both calibration and analytical brines. Individual analysis of the Li line shapes allowed the evaluation and subsequent compensation of self-absorption. A univariate calibration procedure was applied to the experimental data. The resulting calibration curve exhibited a linear behavior at low Li concentrations, where the plasma was optically thin with a minimal self-absorption of 26%. As Li concentrations increased, the curve reached saturation due to the plasma becoming optically thick, with strong self-absorption reaching 84%. The initial quantitative results, without self-absorption compensation, demonstrated a general accuracy of 29% when compared to the conventional AAS technique. For the highest Li concentrations, the homogeneous plasma model proved inadequate for accurately describing the self-absorption-compensated data. However, incorporating self-absorption compensation provided by the τ–algorithm significantly improved the analytical accuracy of the LIBS results to 15%. This demonstrated the critical importance of self-absorption compensation for achieving precise and accurate quantitative analysis in LIBS, particularly at high analyte concentrations. In future work, additional analytical evaluations with a larger number of samples should compare external calibration with standard addition and matrix-matched synthetic brines, perform more relevant statistical tests, and apply machine learning methods.