Analytical Techniques for Detecting Rare Earth Elements in Geological Ores: Laser-Induced Breakdown Spectroscopy (LIBS), MFA-LIBS, Thermal LIBS, Laser Ablation Time-of-Flight Mass Spectrometry, Energy-Dispersive X-ray Spectroscopy, Energy-Dispersive X-ray Fluorescence Spectrometer, and Inductively Coupled Plasma Optical Emission Spectroscopy

Abstract

Rare earth elements (REEs) hold significant industrial, scientific, and modern technological worth. This study focused on detecting and quantifying REEs in various geological ore samples. These samples were collected from different REE-bearing locations recommended by geological experts. The analysis was conducted using laser-induced breakdown spectroscopy (LIBS) and laser ablation time-of-flight mass spectrometry (LA-TOF-MS). In this work, LIBS methodology was employed using three different configurations: standard LIBS, LIBS with an applied magnetic field, and LIBS with both an applied magnetic field and target sample heating within an optimal temperature range. Elements from the REE group, specifically lanthanum (La), cerium (Ce), and neodymium (Nd), were identified and quantified. To detect, quantify, and validate the results from LIBS and LA-TOF-MS, we utilized an array of analytical techniques—Energy-Dispersive X-ray Spectroscopy (EDX), Energy-Dispersive X-ray Fluorescence Spectrometer (ED-XRF), and Inductively Coupled Plasma Optical Emission Spectroscopy (ICP-OES). Interestingly, the quantitative results for REEs (La, Ce, and Nd) in the ore samples obtained using the LIBS technique with various configurations were found to be in agreement with those from LA-TOF-MS, EDX, XRF, and ICP-OES. In addition, LIBS enables detailed microchemical imaging, allowing the map of the spatial distribution of elements within the mineral–ore matrix. The high-resolution microscale elemental mapping of REEs was accomplished using the emission lines Ce (II) at 446.0 nm, La (II) at 492.1 nm, and Nd (II) at 388.8 nm. By integrating multiple analytical techniques, our study enabled the construction of a complete elemental distribution map, providing new insights into the geochemical processes and mineral composition of rare earth ores, while advancing geochemistry and contributing valuable data for rare earth resource exploration.

1. Introduction

Rare earth elements (REEs) are a group of metals such as cerium (Ce), dysprosium (Dy), erbium (Er), europium (Eu), gadolinium (Gd), holmium (Ho), lanthanum (La), lutetium (Lu), neodymium (Nd), promethium (Pm), praseodymium (Pr), scandium (Sc), samarium (Sm), terbium (Tb), thulium (Tm), yttrium (Y), and ytterbium (Yb) [1,2,3]. The metals Sc and Y are considered REEs but not part of the lanthanide series. REEs have been the subject of significant economic and scientific interest, due to the chemical, optical, and magnetic properties that make them useful in the production of magnets, emission control devices, rechargeable batteries, computer memory, digital optical discs, tube lights, smartphones, and much more [1,4]. A key phenomenon affecting these elements is the lanthanide contraction effect [2], namely, the fact that the atomic radius decreases as the atomic number rises, attributed to imperfect shielding of f-orbitals [5]. In comparison with other metals such as Ag, Au, and Cu, REEs do not occur in native form, due to their reactivity [1,6,7]; instead, they occur as minor or major constituent minerals such as bastnaesite, eudialyte, fergusonite, loparite, monazite, xenotime, and zircon [1,6,7]. It is estimated that more than 250 minerals contain REEs [6,7].

The worldwide production of REEs is primarily derived from several deposit types: carbonatite-related deposits (e.g., Bayan Obo in China), ion-adsorption clays (mainly in southern China and Myanmar), monazite-bearing placer deposits (India, Brazil, and Australia), pegmatite deposits (notably in the United States and Brazil), and phosphorite deposits (e.g., in the United States). Several ores hold economically extractable beneficial minerals that contain REEs [8]. The creation of ores involves the concentration and enrichment of specific minerals and metal oxides through geological occurrences like hydrothermal activity [9], seasoning, and deposition. Rapid, accurate, and precise quantitative determination of REEs is important because it allows the assessment of abundance and distribution in geological samples, providing information for resource evaluation and determination of economic viability. Quantitative analyses in industrial and commercial processes enable the assessment of contamination levels, identification of pollution sources, implementation of effective remediation strategies, and maintenance of efficient and sustainable operations.

Analytical techniques for quantitatively determining REEs are essential in most mining activities, as well as in industrial and manufacturing processes [1,10,11,12]. Chemical analyses are required for quality control, continuous monitoring for improved efficiency, and waste reduction. Each industry aims to develop and employ analytical techniques that deliver precise and consistent results within tight timeframes and budget constraints. In general, REEs are mined as a co-product or by-product of other materials [1] and their chemical analysis requires the analytes to be separated from the sample matrix through chemical separation and preconcentration processes [1]. Analyzing REEs is particularly challenging due to their similar physical and chemical properties, their presence in low concentrations, the wide range of complex matrices they are found in, and the lack of standardized reference materials. A large variety of analytical methods are utilized for the determination of REEs in various samples, including inductively coupled plasma mass spectrometry (ICP-MS), energy-dispersive X-ray (EDX), laser-induced breakdown spectroscopy (LIBS), laser ablation time-of-flight mass spectrometry (LA-TOF-MS), X-ray fluorescence (XRF), gravimetry, titration, mass atomic absorption spectroscopy, and neutron activation analysis (NAA) [1,12]. Techniques such as LIBS, XRF, EDX, and LA-TOF-MS stand out, as they typically do not necessitate sample preparation and can be easily utilized in the field. Nonetheless, for geological materials, certain preparatory steps are advisable.

Quantitative analysis of REEs is more complex than qualitative analysis, especially when dealing with different matrices and mineral deposits. This complexity stems partly from the similarity in ionic radii of REEs, which allows them to substitute for one another in the host matrix, and partly from the refractory nature of the matrices themselves, which makes separation and quantification difficult [7]. LIBS is an analytical technique that can provide the qualitative and quantitative elemental composition of almost any type of material [13,14,15,16,17,18]. Atomic [19,20], molecular [21], and isotopic [22] LIBS analyses are possible. It operates by focusing a high-energy laser pulse onto a sample, resulting in the formation of a localized plasma that emits light characteristic of the sample composition. Time and spectral resolution allow elemental identification and calibration. LIBS is extensively utilized across various fields such as materials science, environmental monitoring, geological research, and forensic investigations. In particular, LIBS has proven to be well-suited for analyzing REEs in heterogeneous samples such as ores [23,24,25,26]. Its advantages lie in its ability to provide fast, non-destructive, and on-site elemental analysis, rendering it a valuable tool for mineral exploration and mining operations. However, due to the discrete (i.e., small sampling volume) and superficial analysis, many challenges remain for the analysis of geomaterials and discrete analytes [27]. The most common method for chemical quantification requires calibration curves, that is, establishing a mathematical correlation between the analyte concentration and the corresponding analytical LIBS signal, usually the emission intensity of a specific spectral line. Through calibration, quantification of unknown samples is possible. Other methodologies such as calibration-free LIBS also exist; however, a set of strict assumptions and conditions must be met for validity [28,29].

Figueiredo et al. [30] recently used a portable ED-XRF spectrometer to conduct semi-quantitative screenings of rare earth elements (REEs) in CRT phosphors and NdFeB magnet residues. They have devised a calibration model for the portable ED-XRF equipment to enable quantitative analysis of REEs in WEEE solid samples, which is especially valuable for industrial use. Fu et al. [31] employed EDX for the semi-quantitative analysis of minerals containing rare earth elements (REEs) in coal. They categorized rare earth and yttrium (REY) minerals by examining particle morphology and chemical characteristics. For mineral grains that were difficult to identify based solely on their chemical composition, further analysis was conducted using point analysis, line scans, and mapping techniques to accurately determine the particle mineralogy. Baghaliannejad et al. [32] developed a rapid analytical process to detect trace amounts of REEs including Ce, Dy, Er, Eu, Gd, Ho, La, Lu, Nd, Pr, Sm, Tb, Tm, and Yb in a primary uranium matrix using ICP-MS and ICP-OES methodologies.

LIBS is an analytical technique that uses a high-energy laser pulse to create plasma on a sample’s surface. The plasma emits light, which is then analyzed to determine the elemental composition of the material. Quantification in LIBS can be achieved through several methods. (1) The calibration curve method involves creating calibration curves using known standards to compare emission intensities and determine element concentrations. (2) Internal standardization uses a known internal standard element within the sample for comparison, eliminating the need for external standards. (3) Calibration-free LIBS operates under the assumption of optically thin and locally thermodynamically equilibrium plasma, eliminating the need for calibration curves or external standards. The evaluation of LIBS for geological ore applications has been performed by various authors. For instance, Abedin et al. [25] examined various REEs including Ce, La, Pr, Nd, Y, Yb, Gd, Dy, and Er, along with the associated metallic elements in raw monazite sands, using LIBS. The purpose was to assess LIBS as a rapid and efficient technique for detecting multiple REEs in natural mineral samples, despite the presence of interfering elements (Fe and Ti). Bhatt et al. [13] studied the detection and quantification of REEs, such as Ce, La, and Nd, in natural geological samples, using LIBS. The study aimed to assess LIBS as a rapid and efficient technique for both qualitative and quantitative analysis of REEs, demonstrating its potential for producing results comparable to ICP-MS analysis. Rethfeldt et al. [14] used LIBS combined with iPLS regression to detect REEs in minerals and soils. They found iPLS more effective than univariate regression for analyzing heterogeneous field samples, improving accuracy despite matrix effects. This approach enhances LIBS’s potential for on-site REE exploration. Harikrishnan et al. [15] used LIBS to analyze REEs in meteorites, including iron and lunar samples. LIBS, along with PCA, effectively detected trace REEs and classified meteorite samples based on elemental composition. This method validated the presence of REEs in stony meteorites and highlighted LIBS utility in studying meteorite origins. Phuoc et al. [17] utilized LIBS to detect REEs in Powder River Basin sub-bituminous coal ash. Using a Q-switched Nd-YAG laser with pulse energy of 25 mJ and wavelengths of 1064 nm and 532 nm, they analyzed emission spectra from 200 to 980 nm. Key elements identified include Ce with emission lines at 522.34 nm, 524.59 nm, and 571.90 nm; Eu with lines at 462.72 nm and 583.09 nm; and U with lines at 348.93 nm and 381.19 nm. The study focused on LIBS capability for rapid analysis of trace elements in coal ash.

The present work focuses on analyzing REEs in geological ore samples using a range of advanced analytical techniques. These include standard LIBS optimized at 100 mJ, LIBS combined with a magnetic field (using 510 mT and 40 mJ as optimal parameters for magnetic field strength and laser energy), and a target heating setup with temperatures ranging from 25 °C to 125 °C. For a comparative analytical study, LA-TOF-MS, ICP-OES, XRF, and EDX were employed. While various samples were analyzed, a detailed analysis is provided for one representative sample set, which includes seven samples with different matrix and mineralization characteristics. The elements of interest—La, Ce, and Nd—were identified and quantified within this representative sample set. The integration of LIBS with magnetic field assistance and target heating demonstrated promising results. Integrating these two methods enhances LIBS sensitivity and accuracy by improving plasma efficiency. Pre-heating the sample boosts vaporization, leading to improved detection limits, while the magnetic field refines plasma dynamics, enhancing the signal-to-noise ratio (SNR) and spectral resolution. Furthermore, microscale elemental mapping was performed to achieve high spatial resolution in the distribution analysis of REEs, allowing for the precise localization and quantification of these elements on a fine scale. Microscale elemental mapping of the REEs was achieved using the emission lines for Ce (II) at 446.0 nm, La (II) at 492.1 nm, and Nd (II) at 388.8 nm.

2. Materials and Methodology

2.1. Sample Preparation

The geological ore samples containing REEs were collected from three distinct deposits located in the Neelam Valley, Azad Kashmir. The source of these REE deposits was extensively studied by Malkani et al. [33]. With the assistance of the local geology department, each sample was meticulously labeled with its location, matrix, and mineralization. To ensure purity, samples were initially cleaned using distilled water and brushes to remove surface contaminants. The rock samples were then crushed into smaller pieces and sieved to obtain uniform particle sizes, followed by grinding into a fine powder using a mortar and pestle for homogeneity. These prepared samples were stored in airtight containers to prevent contamination. Preliminary tests, including mineralogical and chemical analyses, were conducted to determine the composition and properties of the samples.

For the analytical spectroscopic study, a total of 7 samples with varying matrix and mineralization characteristics (as shown in

Table 1. Elements, matrix composition, and mineralization types for various ore samples.

Sample	Mineralization	Matrix	Elements
S1	Gadolinite	Silicate	Y, Ce, La, Nd, Gd, Be, Fe, Al, Si
S2	Eudialyte		Ce, La, Nd, Pr, Na, Zr, Fe, Mn, Ca
S3	Cerite		Ce, La, Nd, Y, Fe, Ca, Al, Si, Mg
S4	Allanite		Ce, La, Nd, Pr, Y, Fe, Al, Ca, Th, Si
S5	Xenotime	Phosphate	Y, Ce, La, Nd, Gd, P, (Zr), Hf, Fe
S6	Bastnäsite	Fluorocarbonate	Ce, La, Nd, Pr, Sm, F, C, O, Ca, Fe
S7	Monazite	Phosphate	La, Ce, Nd, Pr, Sm, Gd, Th, U, P, Ca, Fe

) were prepared into pelletized forms, each with a thickness of 5 mm and a diameter of 15 mm, using a pellet presser operated with a pressure force of ~98 kN. Seven samples (labeled S1, S2, S3, S4, S5, S6, and S7) were selected, based on their REE content, mineralization characteristics, and matrix composition. The elements of interest were La, Ce, and Nd. These samples present distinct characteristics with regard to their matrix and mineralization. Figure 1a shows the full-length periodic table, highlighting the elements of interest, La, Ce, and Nd, from the REEs identified in this study. These elements belong to the group of light REEs from the lanthanoids. Light REEs are easier to detect in ores, due to their higher abundance in the Earth’s crust compared to heavy lanthanides. Their distinct geochemical behavior leads to recognizable mineral phases, aiding in detection. Light REEs also exhibit higher solubility and mobility in hydrothermal fluids, concentrating in certain geological settings. Additionally, the economic demand for these elements drives extensive exploration and research, improving detection methods. Figure 1b shows the representative 7 rock samples containing REEs, while Figure 1c shows the representative pellets of these samples used in this study.

2.2. Experimental Details

For the LIBS spectroscopic analysis, a Q-switched Nd: YAG laser (2nd harmonic (2ω), Brilliant, Quantel, Lannion, France) was utilized. This laser produced 800 mJ of energy at a wavelength of 1064 nm and 400 mJ at 532 nm, with a 5 ns pulse width and a repetition rate of 10 Hz. The laser energy was fine-tuned to 100 mJ for standard LIBS experiments, resulting in an average power density of ~0.1 GW/cm². A lens with a focal length of 10 cm was employed to focus the beam, creating a spot size of ~50 μm on the sample surface. The diffraction-limited diameter of the focused laser beam was determined by using the following relation [34].

$$d~2.44\left({\displaystyle \raisebox{1ex}{$\lambda \times f$}\!\left/ \!\raisebox{-1ex}{$D$}\right.}\right)$$

(1)

where f is the focal length of the lens, λ denotes the laser wavelength, and D shows the diameter of the collimated laser beam. The sample was mounted on a holder rotating at about 15 rpm, ensuring a fresh surface was presented for each laser shot. The emission spectra were captured using an optical fiber with a core diameter of 600 μm and high OH content, paired with a collimating lens that provided a field of view ranging from 0 to 45°. This setup was integrated into the LIBS system, which included four miniature spectrometers. Each spectrometer had a slit width of 10 μm and covered a wavelength range of 220 to 970 nm. These spectrometers were equipped with a 2048-element linear CCD array, offering a spectral resolution of ~(0.06 ± 0.01) nm. The delay timing for the laser firing, the activation of the detection system, and the integration period for capturing spectrally resolved light were set to 2 μs and 10 ms, respectively, to minimize the influence of background emission.

The schematic diagrams for the LIBS setup with a magnetic field and the LIBS setup with target heating are presented in Figure 2. The laser energy was optimized specifically for each configuration of the LIBS setup. Initially, the laser energy was optimized for the standard LIBS setup without the magnetic field, where 100 mJ was found to provide suitable results for the baseline experiments. Subsequently, once the magnetic field-assisted LIBS (MFA-LIBS) setup was implemented, the laser energy was re-optimized to ensure the best possible performance under the influence of the magnetic field. Through this re-optimization, the laser energy was adjusted, and it was found that 40 mJ provided the best SNR under the MFA-LIBS conditions. The SNR was determined by comparing the signal amplitude with the background noise, ensuring that 40 mJ offered the most consistent and clear spectral data. Furthermore, in the configuration where both the magnetic field and target heating (thermal LIBS) were combined (MFA-LIBS with target heating), the laser energy was again evaluated, and the same energy level of 40 mJ was maintained, as it continued to provide the optimal SNR. The target sample was placed on a high-temperature plate, and the temperature was gradually raised from 25 °C to 125 °C, at specific intervals. For each LIBS configuration, 20 laser shots were used to acquire a spectrum. To minimize uncertainty and account for energy fluctuations, the spectra from these shots were averaged over 20 repetitions. This consistency across the MFA-LIBS setups ensured reliable comparisons between the different configurations.

For the LA-TOF-MS spectrometric studies, a locally fabricated system based on the Wiley–McLaren design was utilized. This laboratory setup includes a stainless steel vacuum chamber with a diameter of 30 cm, which contains the ionization region, extraction region, and a flight tube measuring 8 cm by 200 cm. The ionization and extraction regions feature three metallic electrodes, each with a circular shape and a diameter of 3 cm, spaced 15 mm apart. Two of the electrodes have 1 cm diameter openings, covered with fine tungsten mesh. To block scattered ion signals, a magnetic lens was positioned in the ion beam’s path near the metallic electrodes. Additionally, an aluminum disc with a 1 mm hole was placed in the magnetic lens to refine the ion beam. The vacuum in the chamber maintained at ~10⁻⁶ mbar was achieved using a turbo molecular pump. The same laser system used in the LIBS setup was also integrated with the LA-TOF-MS for this experiment. A laser energy of 5 mJ, optimized based on the material’s threshold values to generate plasma, was employed to ablate the target sample within the vacuum chamber. The focused beam diameter at the target surface was about 150 μm, achieved using a quartz lens with a focal length of 60 cm. Ion signals were detected by a CEM (USA) detector operating at around 2–3 kV. These signals were then analyzed using a Tektronix (Tektronix, Beaverton, OR, USA) oscilloscope with a 500 MHz digital storage capacity, which was triggered by a fast photodiode intercepting a fraction of the laser light.

For EDX spectroscopic analytical studies, the EDX system using an X-MaxN-20 detector was used in this study. The EDX system is integrated into an electron microscope, such as a scanning electron microscope (SEM) and transmission electron microscope (TEM), enabling high-magnification elemental composition analysis. The EDX detector features a 20 mm² Silicon Drift Detector (SDD) with an energy resolution of ~130 eV at Mn K_α, providing precise elemental distinction. The detector operates at an optimal acceleration voltage and tilt angle tailored to the sample material and elements of interest. Equipped with specialized software, the system facilitates data acquisition, peak identification, quantitative analysis, and elemental mapping, ensuring accurate results through calibration with standards. Sample preparation involves conductive coating and appropriate mounting, to prevent charging and ensure stability. The setup was operated under high vacuum conditions to minimize electron and X-ray scattering, enhancing spectral quality.

The energy-dispersive X-ray fluorescence spectrometer (ED-XRF) system (JSX-3202M, JEOL, Tokyo, Japan) was employed to record the spectrum for the same REE sample set. The system operated within a voltage range of 5 to 50 kV and a current range of 0.01 to 1.0 mA, allowing for flexible adjustments based on the sample requirements. It achieved an energy resolution of 135 eV at 5.9 keV (Mn K_α), ensuring precise elemental analysis. The system included an SDD detector for high-count rate capabilities and a rhodium (Rh) anode X-ray tube to provide consistent excitation. The limit of detection of the system ranges from 10–100 ppm, varying inversely with the atomic weight of the element. The samples were placed in a chamber under vacuum conditions to minimize air absorption and scattering effects, enhancing the detection sensitivity and accuracy. Data acquisition was managed through commercially available software (XRF.FP Software), enabling detailed spectrum analysis and elemental quantification. Elemental quantification involves converting the net peak intensities observed in the XRF spectrum into the concentrations of each element within the sample. The quantification process begins with identifying all the elements present in the ED-XRF spectrum. This initial step is crucial for accurate qualitative analysis, which relies on precisely determining the position of each peak in the spectrum. Peaks in the spectrum are converted into energy channels using a linear energy-calibration curve [35].

$$E \left(\mathrm{k}\mathrm{e}\mathrm{V}\right)=p+qX$$

(2)

where p and q are the fitting coefficients measured in keV per channel, and X represents the number of channels. For this energy calibration, standard reference elements with known K_α and K_β emission lines are used. The calibration process involves utilizing the least squares fitting method to accurately establish the relationship between energy and channel number. This is achieved by analyzing the spectrum obtained for each standard reference line through specialized software. Once this calibration is complete, a linear relationship between energy and channel number is established, which is essential for estimating the energy levels corresponding to each peak in the spectrum. This approach ensures precise identification and quantification of the elements present in the sample.

To confirm the results obtained from various spectroscopic techniques, ICP-OES was used for elemental quantification of the samples. The measurements were conducted using an ICP system (Thermo Jarrell Ash, model IRIS, SpectraLab Scientific Inc, Markham, ON, Canada) equipped with a peristaltic pump and a cross-flow nebulizer connected to a cyclone spray chamber. This device features an echelle diffraction grating and a solid-state charge-injection device detector with 262,144 light-sensitive pixels arranged in a 512 × 512 array, utilizing radial torch configurations. The IRIS spectrometer includes two slits, with the integration time set to 15 s, and the system is operated using Thermo-Spec software. The wavelengths used for measuring element concentrations were Ca (I) = 616.2 nm, C (I) = 247.8 nm, Ce (II) = 446.0 nm, Fe (I) = 373.5 nm, K (I) = 766.5 nm, La (II) = 492.1 nm, Mg (II) = 279.6 nm, Na (I) = 588.9 nm, Nd (II) = 388.8 nm, Si (I) = 288.2 nm, and Ti (I) = 334.9 nm. The samples used for ICP-OES measurements were prepared through a wet chemical-digestion process, utilizing a mixture of hydrochloric acid (HCl) and hydrofluoric acid (HF) to ensure complete dissolution of the samples. To verify complete dissolution, the solutions were visually inspected, and filtration confirmed the absence of any solid residues. The digested samples were diluted with ultrapure deionized water at a 10:1 dilution factor, using a 2% HNO₃ matrix for stability. Additionally, certified reference materials with similar compositions were analyzed using the same procedure to validate the accuracy and reliability of the ICP-OES measurements.

3. Results and Discussion

3.1. Qualitative Analysis: Laser-Induced Breakdown Spectroscopy (LIBS)

In standard LIBS analysis, a good SNR is crucial for accurate and reliable results. Generally, an SNR of at least 10:1 is recommended for qualitative analysis, meaning the signal should be ten times greater than the noise. For more precise quantitative analysis, an SNR of 50:1 or higher is often desired. Higher SNR improves the detection limits and accuracy of elemental concentrations, allowing for clearer and more reliable spectral data. To estimate the SNR for the emission lines in our LIBS experiments, we focused on La (II) at 492.1 nm, Ce (II) at 551.2 nm, and Nd (II) at 410.9 nm, analyzing these lines for different laser energies in mJ. For each line, a featureless region around the peak was selected, with a length equal to the peak broadening at its base position, determined by the full width at half maximum (FWHM) of the emission peak. The noise was estimated by calculating the standard deviation (σ) of the signal in this region, which was chosen to avoid significant contributions from the emission line itself. The signal amplitude (A) was measured as the difference between the maximum intensity of the emission line and the baseline noise level. The SNR was then calculated as the ratio of the signal amplitude (A) to the standard deviation of the noise (σ). Before SNR estimation, the spectra underwent baseline correction, but no further normalization or filtering was applied. For precise peak parameter extraction, a Voigt profile fitting was employed, as it effectively accounts for both Gaussian and Lorentzian broadening effects. This procedure was consistently applied across the selected emission lines, to ensure reliable SNR comparisons.

The impact of laser energy ranging from 10 mJ to 140 mJ on SNR, and the results for the La, Ce, and Nd lines are shown in Figure 3. Based on the optimal SNR, we selected 100 mJ for standard LIBS as the most suitable laser pulse energy for this study, resulting in a corresponding laser fluence of ~51 J/cm².

In the present LIBS studies, reducing spectral interference and self-absorption effects is crucial for accurate analysis. To address spectral interference, we have adjusted the choice of wavelengths and employed advanced procedures to distinguish between overlapping spectral lines, including mathematical deconvolution methods. For self-absorption effects, we minimized their influence by adjusting laser pulse energy, optimizing laser focus, and using appropriate plasma conditions to reduce the impact of the plasma on emission lines. To check for self-absorption, we analyze the peak shape and compare it with reference spectra, observing any signs of distortion. We then vary experimental parameters such as laser pulse energy and gate width to assess changes in peak intensity and shape; stable peaks across these variations indicate minimal self-absorption.

In Figure 4, we show the comparative spectrum of a representative sample S7 obtained from LIBS analysis. The spectra cover the wavelength range from 464 nm to 646 nm. This region was selected because of the relatively good SNR of the emission peaks, as REEs have abundant emission lines in the 400-to-600 nm wavelength range. The high density of these emission lines in this region makes it particularly suitable for detecting and analyzing REEs with greater accuracy. In the ore sample, various emission lines of La with a relatively smaller magnitude of intensity are detected within five line clusters, highlighted with elliptical loops in the figure, showing common lines between the pure lanthanum (La₂O₃) spectrum and the ore sample. In this wavelength region, La lines are detected at 465.0, 470.3, 489.9, 492.1, 510.6, 514.5, 515.9, 517.7, 521.2, 523.9, 624.9, 628.9, and 639.4 nm. In the sample spectrum, elements other than rare earths are also identified, including calcium (Ca) with a major peak at 616.2 nm, carbon (C) at 247.8 nm, iron (Fe) at 373.5 nm, potassium (K) at 766.5 nm, magnesium (Mg) at 279.6 nm, sodium (Na) at 588.9 nm, silicon (Si) at 288.2 nm, and titanium (Ti) at 334.9 nm.

Table 2. The main detected emission lines in the representative ore sample S7.

Element		Detected Emission Lines at Central Wavelengths (nm)
Carbon (I)		247.8
Calcium (I) Calcium (II)		422.7, 428.3, 428.9, 429.9, 430.3, 430.8, 431.9, 442.5, 443.5, 445.5, 527.0, 534.9, 558.2, 558.9, 559.0, 559.5, 559.9, 612.2, 616.1, 616.2, 643.9, 646.2, 649.4 315.9, 317.9, 370.6, 373.7, 393.4, 396.9
Potassium (I)		691.1, 693.8, 766.5, 769.9
Magnesium (I) Magnesium (II)		277.7, 277.9, 278.3, 285.2, 383.2, 383.8, 516.7, 517.3, 518.4 279.1, 279.6, 279.8, 280.3
Sodium (I)		568.8, 588.9, 589.6
Titanium (I) Titanium (II)		319.2, 320.0, 320.4, 321.8, 321.9, 322.1, 322.4, 322.6 301.7, 302.4, 303.0, 304.4, 304.7, 304.9, 305.7, 305.8, 306.4, 306.6, 306.6, 306.7, 307.3, 307.5, 307.9, 308.2, 308.8, 308.9, 334.9, 334.9, 336.1, 337.3, 338.4
Silicon (I)		250.7, 251.4, 251.6, 251.9, 252.4, 252.9, 263.1, 288.2
Iron (I) Iron (II)		271.9, 272.1, 296.7, 302.1 258.6, 259.9, 260.7, 261.2, 263.1, 274.0, 275.6
Rare earth elements	La (I) La (II)	465.0, 470.3, 510.6, 514.5, 515.9, 517.7, 521.2, 523.9, 624.9, 628.9, 639.4 433.4, 452.2, 466.3, 466.9, 472.8, 474.0, 489.9, 492.1, 492.2, 497.0, 498.7, 500.0, 626.2
	Ce (I) Ce (II)	544.9, 556.6, 559.6, 560.1, 567.8, 569.3, 569.7, 571.9, 577.3, 578.8, 581.3, 594.1 456.2, 462.8, 526.6, 527.4, 533.1, 535.4, 551.2, 439.9, 441.8, 442.9, 444.9, 446.0, 447.9
	Nd (I) Nd (II)	463.4, 488.4, 489.7, 492.5, 494.5, 495.5 371.5, 373.8, 375.3, 377.6, 378.4, 380.2, 380.5, 383.9, 384.8, 386.3, 389.0, 389.2, 395.2, 397.3, 399.0, 399.2, 399.5, 401.2, 402.1, 404.1, 410.9

shows the detected emission lines for C, Na, Mg, Si, K, Ca, Ti, Fe, La, Ce, and Nd, each at different wavelengths. The spectral lines were identified by comparing spectroscopic data such as central wavelength, transition probability (s⁻¹), statistical weight (g), upper- and lower-level energy (cm⁻¹), and theoretical intensity (arb. unit) from the NIST atomic spectral database [36]. Initially, only lanthanum (La) was detected with low-intensity peaks. However, upon applying a magnetic field and heating the target, additional emission lines corresponding to cerium and neodymium also appeared. This suggests that these elements were probably present as trace elements in the sample, and the signal enhancement techniques allowed their detection.

3.1.1. Magnetic Field-Assisted LIBS Enhancement

We employed magnetic field-assisted LIBS (MFA-LIBS) to enhance the detection of cerium (Ce) and neodymium (Nd) in ore samples, which were not detectable using standard LIBS plasma emission spectra. MFA-LIBS enhances elemental detection by applying a magnetic field during the LIBS process, which slows down the ablated plume’s velocity and confines the plasma. Although the magnetic field does not completely stop the high-velocity plume, it increases the rates of recombination, collision excitation, electron generation, and ionization, by shielding the plasma’s interior with its outer layer. This confinement leads to significantly stronger emission intensities. The increased plasma confinement provided by the magnetic field results in more distinct and intense emission lines, thus improving the sensitivity and accuracy of elemental analysis. This is particularly beneficial for detecting trace elements that may otherwise remain undetected due to low concentrations or weak signals. In this study, MFA-LIBS was conducted with magnetic field strengths of 430, 450, 470, 490, 510, 530, and 550 mT. The optimal magnetic field strength of 510 mT was chosen for recording MFA-LIBS spectra. The selection of the 510 mT field strength as optimal was not arbitrary, but based on a complete analysis of the SNR values obtained for each sample. A comparative investigation of the LIBS spectra revealed that 510 mT consistently yielded the highest SNR for the majority of the samples tested, especially when focusing on the emission lines of the REEs, such as Ce, Nd, and La. This enhancement in SNR at 510 mT indicates more efficient plasma confinement and prolonged plasma lifetime, which is a direct consequence of the magnetic field’s influence on charged-particle trajectories within the laser-induced plasma. Although slight variations in SNR were observed for certain samples at higher or lower magnetic-field strengths, the 510 mT value provided the best overall performance across all tested elements. The trade-off between field strength and plasma characteristics such as electron density and temperature also supported 510 mT as a balanced choice for maximizing spectral intensity without introducing excessive plasma instabilities, which were more noticeable at higher magnetic fields (e.g., 550 mT). Thus, 510 mT was selected as the optimal magnetic field strength for all subsequent MFA-LIBS measurements, to ensure consistent and reproducible data acquisition with better spectral quality.

A comparative analysis of the emission spectra for sample S7, covering the wavelength range of 448 to 497 nm is shown in Figure 5. The figure highlights the prominent and well-isolated ionic emission lines of element La as detected by MFA-LIBS. These La emission lines are distinctly visible and well-separated in the spectrum obtained using MFA-LIBS. The main emission lines of La in this optical range are observed at wavelengths 489.9, 492.1, 465.0, and 470.3 nm. However, when comparing this with the standard LIBS spectrum, represented in black (color), these emission lines appear less prominent, and are not as clearly isolated. This demonstrates the enhanced spectral clarity achieved through the MFA-LIBS technique, which improves the visibility and distinction of specific ionic lines that may otherwise be less discernible with standard LIBS.

The optical emission spectrum in the range of 440 to 447 nm, comparing the standard LIBS technique with MFA-LIBS, is displayed in Figure 6. The emission lines corresponding to Ce that were either nearly undetectable or exhibited radically diminished SNR using standard LIBS were, however, detected with much higher SNR when MFA-LIBS was employed. These enhanced SNRs of the emission lines are crucial for plasma characterization. The primary emission lines within this spectral range are observed at central wavelengths of 439.9, 441.8, 442.9, 444.9, 446.0, and 447.9 nm. Remarkably, significant SNR enhancement was observed; for instance, the intensity amplitude of the 441.8 nm spectral line was recorded at 4300 arbitrary units (a.u.) without the application of a magnetic field. With the MFA-LIBS technique, the intensity of this same line increased substantially to 39,900 a.u. The enhancement factor, calculated using the ratio $I^{enhanced}/I^{standard}$, was estimated to be ~9. The significant increase in these Ce II transitions possibly indicates an increase in plasma temperature. Therefore, this demonstrates the effectiveness of MFA-LIBS in detecting trace REEs such as Ce and Nd, making it a valuable technique for the analysis conducted in this study.

Figure 7 exhibits the comparative emission spectra of Nd within the wavelength range of 364 to 418 nm, using both standard LIBS and MFA-LIBS. The spectrum represented in blue corresponds to the standard LIBS technique, where the emission peaks of Nd are observed with very low intensity, with some peaks barely visible, or absent. In contrast, the spectrum depicted in black, obtained through MFA-LIBS, reveals well-isolated and significantly more-intense Nd peaks. This enhancement highlights the efficiency of MFA-LIBS in detecting trace amounts of REEs such as Ce and Nd, which might otherwise be missed using standard LIBS. Overall, the application of MFA-LIBS enabled the successful detection of three rare earth metals in the sample: La, Ce, and Nd.

Using the same methodology, with consistent experimental conditions and procedures, elemental analysis was conducted on the remaining samples. In sample S1, a few emission lines of La were observed in the 400-to-495 nm optical region, accompanied by signals from C, Na, Mg, Al, Si, K, Ca, Ti, Fe, and Zn. For sample S2, the REEs, including La and Ce, were detected, together with elements such as Li, Na, Mg, Si, Ca, Ti, and Fe. In sample S3, La, Ce, and Nd were identified along with C, Na, Mg, Al, Si, Ca, Ti, and Fe within the 350-to-550 nm wavelength range. Sample S4 showed the presence of La and Nd in the 400-to-450 nm wavelength region, along with C, Al, Si, Na, K, Ca, Ti, Fe, and Mg. In sample S5, only Ce was detected, characterized by a few strong-resonance emission lines within the 350-to-450 nm wavelength range. Finally, in sample S6, La, Ce, and Nd were identified with well-isolated and intense emission lines covering the 400-to-600 nm wavelength range.

In addition to the application of a magnetic field, sequential target heating (thermal LIBS) with a controlled increase in temperature during the LIBS experiment leads to a noticeable enhancement in the intensity of emission lines. This increase in intensity not only improves the overall signal strength, but also plays a crucial role in the detection and confirmation of trace elements. By amplifying the weaker signals typically associated with these elements, the enhanced-emission lines provide a more reliable and sensitive analysis, making it easier to identify and quantify trace elements that might otherwise be missed in standard conditions.

3.1.2. Thermal LIBS: Impact of Temperature on REE Emission Intensity

The emission line intensity ($I_e$) in a laser-produced plasma is related to the number density ${(n}^{*})$ of the excited-state population ($I_e\propto n^{*}$). For various elements in thermal equilibrium at less than ~5000 K temperature, the number density and spectral emission intensity of the excited atoms can be estimated using the Boltzmann distribution.

$$n^{*}=n\left({\displaystyle \frac{g_k}{g_i}}\right)e^{{\displaystyle \frac{{-E}_k}{kT}}}$$

(3)

$$I\propto n\left({\displaystyle \frac{A_k{g}_k}{\lambda }}\right)e^{{\displaystyle \frac{{-E}_k}{kT}}}$$

(4)

where g_k and g_i are the statistical weights of the upper- and lower-energy levels, respectively, E_k is the upper-level energy, k is Boltzmann’s constant, λ is the central wavelength, A_k is the transition probability, n is the total number density and T is the excitation temperature. Equation (4) suggests that emission intensity may rise with increasing sample temperature. However, in practice, as plasma temperature increases, enhanced ionization leads to a higher concentration of ionic species at the expense of neutral atoms. This change in plasma composition can reduce emission intensities for neutral species, even though the overall temperature is higher. Therefore, the observed decrease in intensity for some ionic states at elevated temperatures might be due to increased ionization, requiring a more nuanced interpretation of the emission data.

Among the various LIBS techniques, such as MFA-LIBS, double-pulse, spatially confined, nanoparticle-enhanced, and target heating, the target-heating method is the simplest technique used in LIBS. The figure of merit for this method includes the low energy required from the pulsed laser to ablate the material, as the heat transferred to the sample weakens the bonds between lattice structures. When materials are heated close to their melting point and then ablated with low-energy pulses, they typically show poor enhancement [37]. However, using high-energy pulses results in a good SNR. Numerous studies have investigated the impact of target temperature on the emission intensity of elements in silicon (Si), lead (Pb), and aluminum (Al) plasma [38,39,40,41]. However, the use of target heating with a sequential increase in temperature to enhance spectral intensity for the detection of trace REEs in geological ore samples using LIBS has yet to be thoroughly explored. In this section, we examine the impact of target temperature on the spectral emission intensity of REEs using the LIBS technique. Specifically, the emission lines of La, Ce, and Nd were analyzed at various sample temperatures ranging from 25–125 °C. The experiments were conducted with optimized parameters: a laser energy of 100 mJ, a time delay of 2 μs, and an integration time of 10 ms.

An increase in temperature is typically associated with a greater ablated mass [39,40], leading to an overall enhancement in the intensity of both ionic and neutral emission lines. Therefore, the well-isolated, weak optical emission lines of REEs with good SNR, including La (I) at 521.2 nm, Ce (II) at 551.2 nm, and Nd (II) at 410.9 nm, were selected to study signal enhancement due to sample temperature rise. The variation in intensities of these emission lines as a function of sample temperature ranging from 25 to 125 °C is shown in Figure 8a–c. A systematic increase in the intensities of La, Ce, and Nd is observed at specific wavelengths as the sample temperature rises. At lower temperatures, around 25 °C (room temperature), the REEs exhibit broadened peaks and relatively weak intensities, making it difficult to detect and confirm their presence in the sample. However, as the temperature increases, the optical peaks become narrower and significantly more intense. Figure 8d illustrates the linear increase in the intensities of La and Nd emission lines at 521.2 nm and 410.9 nm, respectively, with rising sample temperatures (R² ~ 0.999). However, the linear trend for Ce at 551.2 nm showed a slight deviation compared to La and Nd. This deviation in Ce emission intensity with increasing temperature may be due to its lower ionization potential, leading to easier ionization at higher temperatures, which reduces the neutral atom population available for emission. Additionally, Ce may experience self-absorption or spectral interference, impacting both the intensity and stability of its emission signal. These findings suggest that while preheating the sample can enhance the LIBS optical signal, maintaining stability at elevated temperatures is crucial for accurate REE detection.

3.2. LIBS Quantitative Analyses

Quantitative analyses for LIBS, MFA-LIBS, and thermal LIBS were performed using a calibration-free approach. In this method, the plasma was assumed to be in local thermodynamic equilibrium (LTE), optically thin, and free from self-absorption and spectral interference. The optically thin condition was validated by comparing the theoretical and experimental intensity ratios of two emission lines with the same charge state. For this study, La emission lines at 514 nm and 517 nm were used, showing agreement within 5% relative error. With the optically thin condition confirmed, the plasma excitation temperature was calculated using the Boltzmann plot method [26]. Spectroscopic data for La emission lines, obtained from the NIST database [36], were carefully selected from a narrow spectral region, to minimize detector efficiency errors. The calculated excitation temperatures were 8900 ± 350 K for standard LIBS, 9400 ± 150 K for MFA-LIBS, and 9500 ± 250 K for thermal LIBS. The electron number density (N_e) was estimated from the Stark-broadened line profile of titanium at a central wavelength of 368 nm, yielding a value of ~10¹⁷ cm⁻³. McWhirter’s criterion [26] was used to check the LTE condition, and it was found that the plasma met the required critical density limits. With the plasma confirmed as optically thin and in LTE, plasma parameters were used to estimate the concentration (wt.%) using the calibration-free LIBS technique [28]. To estimate the concentration of atomic species, the Boltzmann equation was applied [28]:

$$F{C}^{\gamma }=I_{ki}{\displaystyle \frac{P^{\gamma }\left(T\right)}{A_{ki}{g}_k}}\exp \left[{\displaystyle \frac{E_k}{k_{B}T}}\right]$$

(5)

Here, factor F is an experimental parameter, $C^{\gamma }$ is the concentration of the neutral atom, $I_{ki}$ is the integrated line intensity, $P^{\gamma }\left(T\right)$ is partition function dependent on temperature, $g_k$ is the statistical weight of the upper level, $A_{ki}({\mathrm{s}}^{-1}$) is the transition probability, E_k (eV) is the energy of the upper level, $T$ is the plasma temperature, and k_B is the Boltzmann constant. For the concentration of the ionized species, the Saha–Boltzmann equation was used [28]:

$$N_e{\displaystyle \frac{C^{\alpha ,\gamma +1}}{C^{\alpha ,\gamma }}}=6.04\times {10}^{21}{\left(k_{B}T\right)}^{{\displaystyle \frac{3}{2}}}{\displaystyle \frac{P_{\alpha ,\gamma +1}}{P_{\alpha ,\gamma }}}\exp [-{\displaystyle \frac{E_{\alpha ,\gamma }}{k_{B}T}}]$$

(6)

Here, $E_{\alpha ,\gamma }\left(\mathrm{e}\mathrm{V}\right)$ is the ionization energy, $C^{\alpha ,\gamma +1}$ is the concentration of the ionized species, $N_e$ is the electron number density, $P_{\alpha ,\gamma +1}$ and $P_{\alpha ,\gamma }$ are the partition functions. The total concentration (wt.%) of all elements in the sample was estimated by summing the neutral and ionic contributions [29].

3.3. LA-TOF-MS and EDX

For comparative analyses, LA-TOF-MS, EDX, ED-XRF, and ICP-OES techniques are employed for both qualitative and quantitative analysis of the rare-earth geological ore samples. A detailed analysis is provided exclusively for sample S7. The LA-TOF-MS and EDX are analytical techniques used to identify and quantify elemental compositions, but they operate on different principles. LA-TOF-MS involves using a low-energy laser pulse to ablate a small amount of material from a sample, which is then ionized. The resulting ions are accelerated through a TOF mass spectrometer, where their mass-to-charge ratios are determined, based on the time they take to reach the detector. This technique is highly sensitive, and can analyze trace elements and isotopes. In contrast, EDX relies on the principle of electron-induced emissions (of K_α, K_β, L_α, and L_γ, etc., lines), where a sample is bombarded with high-energy electrons, causing the emission of characteristic X-rays from the elements within the sample. These X-rays are detected and used to determine the elemental composition. A similarity between the two methods is their ability to analyze solid samples with minimal preparation and their use in multi-elemental analysis. However, while LA-TOF-MS provides detailed isotopic information, EDX is generally used for qualitative and semi-quantitative elemental analysis.

A comparative analysis of the distinct peaks for each element found in a sample of rare-earth geological ores is shown in Figure 9. The mass spectrum obtained using the LA-TOF-MS system is depicted in Figure 9a, while Figure 9b presents the emission spectrum recorded by the EDX spectrometer. In both methods, the y-axis depicts the relative intensity of the signals detected, indicating the abundance of the detected elements. For the LA-TOF-MS spectrum, the x-axis represents time in microseconds (μs), corresponding to the time it takes for ions to travel through the spectrometer, which is used to determine their mass-to-charge ratios. In contrast, the x-axis of the EDX spectrum represents energy in kilo-electron volts (keV), which corresponds to the characteristic X-ray energies emitted by the elements within the sample when they are excited by an electron beam. The spectra from EDX and LA-TOF-MS consistently identify most elements, although oxygen (O) is an exception. To assist comparison, we have synchronized the x-axis to match the mass peaks from LA-TOF-MS with the energy peaks from EDX for Si and La. This alignment reveals a strong agreement between the results of the two methods. Both techniques prominently identify Si as the major component, followed by C, Ca, Ti, Na, Mg, and Fe.

In the LA-TOF-MS analysis, a broad contour was observed from 34 to 37 μs time interval, as shown in the inset of Figure 9a. This contour corresponds to the presence of the REEs La, Ce, and Nd in the sample. While La does not have any naturally occurring stable isotopes, Ce has four isotopes, and Nd has five. As a result, the signals from these elements and their isotopes overlap, creating a single, broad contour in the spectrum. To accurately determine the composition of these elements within the sample, a multi-peak fitting procedure was employed. This method involves deconvoluting the overlapping signals to isolate and identify the individual peaks of La, Ce, and Nd, allowing for a complete analysis of their concentrations. In EDX, the cluster of peaks observed in the energy range of 4 to 6 keV is indicative of the characteristic X-ray emission (L_α and L_γ) lines of certain REEs. Specifically, the Lα lines are attributed to La at ~4.7 keV, Ce at ~4.8 keV, and Nd at ~5.2 keV. Additionally, the Lγ lines are identified with La at ~5.8 keV and Ce at ~6.1 keV. These lines result from the transitions of electrons between the inner-shell levels of these elements and are crucial for their identification and analysis using spectroscopic techniques.

The EDX spectrum displays distinct and well-separated peaks for the REEs La, Ce, and Nd, which were not as clearly distinguished in the LA-TOF-MS spectrum. This difference arises because EDX detects characteristic X-ray emissions at specific energy levels corresponding to the Lα and Lγ lines of these elements. In contrast, LA-TOF-MS measures the time it takes for ions to reach the detector. Despite the differences in detection methods, both EDX and LA-TOF-MS provide complementary information that confirms the presence of REEs in the analyzed sample. These techniques together offer a more comprehensive understanding of the elemental composition.

3.4. Energy-Dispersive X-ray Fluorescence Spectrometer (ED-XRF)

Energy-dispersive X-ray fluorescence spectrometer (ED-XRF) is an analytical technique used to determine the bulk chemical composition of a sample. This non-destructive method is widely used in various fields, including geology [42], mineralogy [43], archaeology [44], the cement industry [45], and botanical materials [46], for its ability to provide rapid and accurate elemental analysis. It works by directing X-rays onto a sample, which causes the atoms in the sample to become excited and emit secondary X-rays. The emitted X-rays have energies characteristic of the elements present in the sample, allowing for their identification and quantification. In this study, the emission spectra were captured under specific acquisition parameters: a tube voltage of approximately 30.0 kV, a current of 1.0 mA, and a real-time measurement duration of 80 s. The live time was set to 58.88 s, with a dead time of 26%, and the counting rate was 16,617 counts per second. The energy range was from 0 to 41 keV, and a collimator with a diameter of 4.0 mm was used. Additionally, the fitting coefficient was approximately 0.4024. These parameters ensured the accurate and precise recording of the emission spectra for the study.

Figure 10 demonstrates the spectrum for sample S7, indicating the presence of elements such as Na, Mg, Si, P, Ca, K, Fe, and Ti. Furthermore, the spectrum also reveals the detection of REEs such as La, Ce, and Nd, each with distinct emission lines at varying energies. The estimated weight percentages of the detected components in their oxide forms are as follows: Na₂O = 1.94%, MgO = 2.28%, SiO₂ = 37.61%, P₂O₅ = 2.53%, K₂O = 2.98%, CaO = 9.65%, Fe₂O₃ = 22.45%, and TiO₂ = 16.25%. The estimated concentrations of REEs are La₂O₃ = 9.72%, CeO₂ = 5.85%, and Nd₂O₃ = 4.66%. This technique effectively detected the REEs, and the results are consistent with those obtained using LIBS, LA-TOF-MS, and EDX. However, light elements such as C and Li were not identified by ED-XRF, due to its limitations in detecting these elements.

3.5. Inductively Coupled Plasma Optical Emission Spectrometry

The analytical technique ICP-OES is used for elemental analysis [47,48], where a sample is atomized in a high-temperature argon plasma. The energy from the plasma excites the electrons in the atoms of the sample, causing them to move to higher energy levels. As these electrons return to their ground states, they emit light at characteristic wavelengths specific to each element. This emitted light is then measured to determine the concentration of elements within the sample, with each element having a unique spectral fingerprint, due to its specific electronic transitions. This method is renowned for its high sensitivity and accuracy, and ability to analyze multiple elements simultaneously, making it a popular choice in environmental, geological, mineralogical, and industrial applications.

In this study, representative samples S3, S5, and S7 were analyzed using the ICP-OES technique. Various elements, including the REEs La, Ce, and Nd, were detected, and their concentrations were estimated. The concentrations of elements such as C, Na, Mg, Si, K, Ti, Ca, Fe, La, Ce, and Nd were determined by measuring the intensity of their characteristic emission lines. The emission lines used for each element were Ca (I) = 616.2 nm, C (I) = 247.8 nm, Ce (II) = 446.0 nm, Fe (I) = 373.5 nm, K (I) = 766.5 nm, La (II) = 492.1 nm, Mg (II) = 279.6 nm, Na (I) = 588.9 nm, Nd (II) = 388.8 nm, Si (I) = 288.2 nm, and Ti (I) = 334.9 nm.

Table 3. Elemental concentration (%) estimated using ICP-OES.

Element	S3	S5	S7
Non-REEs, Concentrations (%) ± RSD%
C	1.87 ± 0.83	0.77 ± 0.02	2.04 ± 0.17
Na	4.19 ± 1.02	3.19 ± 0.92	2.11 ± 0.08
Mg	1.63 ± 0.51	2.68 ± 0.77	1.33 ± 0.01
Si	25.28 ± 2.71	21.41 ± 3.17	20.01 ± 2.53
K	0.91 ± 0.06	1.02 ± 0.05	1.24 ± 0.19
Ti	10.45 ± 1.09	13.01 ± 1.88	15.73 ± 1.32
Ca	7.03 ± 0.58	9.52 ± 1.57	5.22 ± 0.19
Fe	17.68 ± 1.28	15.68 ± 2.88	13.88 ± 2.23
REEs, Concentrations (%) ± RSD%
La	7.31 ± 1.43	4.01 ± 0.03	5.66 ± 0.89
Ce	2.41 ± 0.13	1.43 ± 0.16	3.01 ± 0.64
Nd	3.58 ± 0.33	2.19 ± 0.20	2.51 ± 0.79

shows the estimated concentrations (%) of elements C, Na, Mg, Si, K, Ti, Ca, Fe, La, Ce, and Nd, along with their standard deviations, for samples S3, S5, and S7. The relative standard deviation (RSD%) was calculated to assess the precision of the measurements, with lower RSD% values indicating higher precision. In this analysis, the RSD% was found to be a maximum of ~3%, ensuring reliable quantification of these elements in the samples.

Interestingly, the sum of the molecular composition obtained from ED-XRF is ~116%. This slight excess can be attributed to potential errors or uncertainties in the elemental determinations, which are common in such techniques. Additionally, the 2% carbon content found in the same sample through ICP-OES further supports the results and suggests that the overall composition remains consistent within acceptable analytical margins. We have thoroughly reviewed the results obtained from both techniques, XRF and ICP. Furthermore, the observed variation in the concentration of elements, such as titanium (9.7% in XRF vs. 16% in ICP), can be figured from factors such as instrumental sensitivity, calibration standards, sample homogeneity, and the distinct detection limits and capabilities of each technique. Additionally, instrumental noise and matrix effects may further contribute to these variations.

To verify the accuracy of element detection and concentration measurements obtained through LIBS with a magnetic field and LIBS with a magnetic field applied to a target on a high-temperature plate, we compared the results with those from ICP-OES. Figure 11 demonstrates this comparison, showing good agreement among the MFA-LIBS, MFA-LIBS with temperature, and ICP-OES results. The correlation between these LIBS methods and ICP-OES is indicated by a coefficient of determination R² ≈ 0.998 for MFA-LIBS and R² ≈ 0.999 for MFA-LIBS with target heating. This suggests that both LIBS techniques provide consistent quantitative measurements for major elements (Si, Fe, Ti, and Ca) and minor elements (C, Na, Mg, K, La, Ce, and Nd). In particular, the results from MFA-LIBS with target heating are particularly good, as shown in the figure, with a slope of 1, compared to MFA-LIBS which has a slope greater than 1.

In Figure 12, we compare the qualitative and quantitative results for sample S7 obtained using LIBS, TOF, EDX, and XRF with ICP-OES as the reference. Qualitatively, all techniques successfully detect REEs; however, XRF shows differences in the quantitative detection of Ce, where its results are less consistent. All methods identify nearly the same elements, except XRF, which fails to detect carbon, due to its detection limitations. Interestingly, XRF detects phosphorus (P), which is missed by the other techniques.

XRF is particularly effective in identifying phosphorus (P) as a trace element in ores, because it directly excites the inner-shell electrons of atoms using high-energy X-rays. When these electrons are ejected, outer-shell electrons transition into the vacancies, emitting secondary X-rays at energies specific to each element, including phosphorus. XRF’s sensitivity to phosphorus (P) is due to the detectability of its distinct K_α and K_β lines. In contrast to LIBS, TOF-MS, EDX, or ICP-OES, which may face challenges due to energy transfer limitations or matrix effects, XRF is less influenced by these factors. This enables XRF to achieve more accurate detection of phosphorus, even in complex sample matrices.

As shown in the figure, the elements such as Si, Fe, and Ti are estimated using XRF at higher weight percentages. This is attributed to its greater penetration depth and stronger interaction with heavier elements, providing improved sensitivity compared to LIBS, TOF, or EDX, which are typically constrained by surface effects and shallower analysis depths. The error bars in the weight percentages represent the standard deviation in the measurements.

3.6. Advantages and Disadvantages of Analytical Techniques

LIBS offers high sensitivity, with detection limits generally ranging from 1 to 100 ppm, making it effective for analyzing trace elements. It requires minimal sample preparation and allows for direct analysis of solid samples. LIBS can detect a wide range of elements, from lithium (Li) to uranium (U), and simultaneously identify multiple elements with high speed. However, it is influenced by matrix effects, which can impact accuracy and reproducibility, and calibration can be challenging due to variability in the laser-induced plasma.

ICP-OES offers excellent sensitivity and precision, with detection limits for REEs typically in the range of 0.1 to 10 ppm, and has a wide dynamic range for analyzing elements across broad concentration ranges. It is efficient for high sample throughput. The drawbacks include the need for extensive sample preparation, such as dissolution and digestion, which can be time-consuming, and the potential for spectral and chemical interferences from complex matrices.

LA-TOF-MS is distinguished by its high spatial resolution, making it ideal for detailed sample characterization. It enables both elemental and isotopic analysis with minimal sample destruction. However, data interpretation can be complex due to the intricacy of mass spectra, and matrix effects can affect the accuracy of quantitative results.

EDX excels in providing elemental mapping and studying the distribution of elements in heterogeneous samples. It can analyze elements from boron (B) to uranium (U), with detection limits for REEs typically in the range of 100 to 1000 ppm. Minimal sample preparation is required, making it convenient for bulk or thin-section analysis. Its limitations include higher detection limits, typically in the ppm range, and sensitivity, mainly to surface layers, which may not reflect the bulk composition accurately.

ED-XRF is advantageous for the non-destructive analysis of solid samples, powders, and liquids, offering quick results with minimal sample preparation. It can detect elements from sodium (Na) to uranium (U), with detection limits for REEs generally in the range of 10 to 1000 ppm. However, it generally has higher detection limits, ranging from ppm to percentage levels, and is affected by matrix effects and sample heterogeneity, which can impact accuracy and precision.

3.7. Spatial Distribution of Elements

In addition to analytical techniques such as LIBS, LA-TOF-MS, EDX, XRF, and ICP-OES, microscale elemental mapping is performed on various samples. For this study, a detailed mapping analysis is provided for the representative sample S7. LIBS surface mapping is an innovative technique that provides detailed, spatially resolved chemical information across a sample’s surface [49,50]. By focusing the laser beam to a small spot size, LIBS achieves high spatial resolution, enabling the analysis of heterogeneous samples and the identification of localized elemental concentrations. This method offers rapid and direct analysis with minimal sample preparation, making it minimally destructive and ideal for valuable or sensitive materials from geological or mineralogical sites. Furthermore, LIBS systems can be made portable for in-field analysis, benefiting environmental monitoring and planetary exploration. These innovations make LIBS surface mapping a powerful tool for material characterization, offering insights into the distribution and concentration of elements with high precision and speed.

In this study, elemental mapping of each sample surface was performed using spectral data collected across a 15 × 15 array, with individual laser shots spaced 25 µm apart. Each spectrum was acquired from a single shot, and the scanning was automated using a displacement program that controlled both the shot frequency and stage movement. This process generated two-dimensional maps at a fine spatial scale, illustrating the relative emission intensities of various elements and revealing their geochemical behaviors. Separate panels of different sizes were created, to display the spatial distributions of elements such as Si, C, Na, Ca, Ti, K, Mg, Fe, and REEs including La, Ce, and Nd. The maps cover an area of 5 × 5 mm², with features labeled to indicate the distribution of these elements, as shown in Figure 13. Scanning was performed at 10 different locations using an automated revolving stage operating at 50 rpm, and the data obtained from these scans were averaged to produce the final results. The spectral lines used for microscale elemental mapping were Ca (I) = 616.2 nm, C (I) = 247.8 nm, Ce (II) = 446.0 nm, Fe (I) = 373.5 nm, K (I) = 766.5 nm, La (II) = 492.1 nm, Mg (II) = 279.6 nm, Na (I) = 588.9 nm, Nd (II) = 388.8 nm, Si (I) = 288.2 nm, and Ti (I) = 334.9 nm.

Comparative analysis of the eleven spatial maps, dominated by shades of dark and light red, yellow, and green, exhibits a full range of color variations from green-to-yellowish dark, with dotted contours indicating concentration variations. Specifically, Si is represented by green-to-yellowish dark gradients with dotted contours, while C is depicted in magenta with black gradient contours, and Na shows a step variation. Ca, Fe, and La feature cyan to green, with yellow centers and dotted contours. Ti is marked by red spatial variations, whereas K and Mg show cyan-to-green, with a red-center pattern and dotted-white contours for K. Ce displays cyan-to-greenish hues without contour variation, and Nd is indicated by cyan with black-dotted variations. These variations are detailed within the 5 × 5 mm² spatial scale.

4. Conclusions

In this study, the focus was on utilizing LIBS to detect and quantify rare earth elements (REEs) in geological ores. LIBS analysis was performed on a representative set of samples selected from various REE-bearing locations under identical experimental conditions. Rare earth elements, including lanthanum (La) (within the wavelength range of 464 to 646 nm), cerium (Ce) (within 440 to 447 nm), and neodymium (Nd) (within 364 to 418 nm) were identified. To improve the signal-to-noise ratio of these elements, magnetic field-assisted LIBS was employed, with magnetic field strengths of 430, 450, 470, 490, 510, 530, and 550 mT. This technique was compared with standard LIBS, showing an enhancement factor estimated to be ~9. The impact of temperature, ranging from 25 to 125 °C, on the emission intensity of REEs was also studied, demonstrating significant enhancement. To validate the analytical performance, LIBS results were compared with those obtained from LA-TOF-MS, EDX, ED-XRF, and ICP-OES. Additionally, LIBS allowed for detailed microchemical mapping, providing a map of the spatial-scale distribution of elements within the mineral–ore matrix. High-resolution microscale elemental mapping of REEs was achieved using the emission lines Ce (II) at 446.0 nm, La (II) at 492.1 nm, and Nd (II) at 388.8 nm. Therefore, the results highlight the application of combined manifold analytical techniques to obtain accurate and inclusive elemental analysis of REEs in geological ores.