Multi-element determination in soil using laser-induced breakdown spectroscopy with only one internal reference element by one-point calibration

Abstract

Soil elemental analysis is vital for assessing nutrient availability and contamination. For soil analysis, conventional calibration-free LIBS (CF-LIBS) methods suffer from unavoidable uncertainty of the Einstein coefficients and optical coefficients. Although one-point calibration LIBS (OPC-LIBS) can tackle these problems to some degree, it is still limited by the self-absorption effect and strict requirement of accuracy of all-elemental content. In this work, a modified OPC-LIBS method was proposed, which combines an internal reference element strategy with self-absorption correction and columnar-density Saha–Boltzmann (CD-SB) plotting. Only one major element, silicon, needed to be certified in the reference soil sample. All other elements across diverse soils were deduced. Moreover, self-absorption and plasma parameters (temperature and electron density) were corrected via CD-SB plots, providing a more reliable basis for elemental determination. The results demonstrated that mean relative errors (MRE) were reduced to 16.324–42.358% in the proposed method, much lower than in conventional CF-LIBS and in CF-LIBS with self-absorption correction. The analytical accuracy also matched or outperformed conventional OPC-LIBS (requiring certification of all elements in the reference sample). This work provided a more convenient and accurate method for multi-element soil analysis.

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1. Introduction

The species composition and elemental composition of soil provide essential agricultural information regarding nutrient availability and contamination levels. Elemental analysis forms the basis for soil generation, fertility evolution, and improvement. Conventional methods, including inductively coupled plasma mass spectrometry (ICP-MS), inductively coupled plasma atomic emission spectrometry (ICP-AES), and atomic fluorescence spectroscopy (AFS), require complex operation and significant time, thus limiting their use to laboratories rather than field applications. Laser-induced breakdown spectroscopy (LIBS) is a promising technique for soil analyses. As the excitation source, a pulsed laser is focused on the soil sample surface to generate a tiny plasma with optical emission for spectral analysis. The elemental species and concentration in soil can be deduced by analyzing the plasma spectra, making LIBS a real-time, on-line technique. The minimal sample preparation and remote sensing are significant advantages for fast analysis in farmlands.

LIBS has attracted considerable research interest as a tool for soil analysis. Ciucci et al. used a standard curve approach to analyze trace contaminants in certified soil samples (elemental concentration <500 ppm), demonstrating the practical feasibility of the LIBS technique in sensitive diagnosis of soil contaminants.¹ Bublitz et al. quantified metal ions on the surface of two natural soils, demonstrating LIBS’s capability for the spatially resolved analysis of ion transport in soil.² LIBS matrix effects in sand and soil samples were reported by Eppler et al.,³ greatly influencing the analytical accuracy. The applications of LIBS in the analysis of geological samples such as soils were reviewed by Harmon et al. and McMillan et al.^4,5 These previous studies demonstrated that the matrix effect is one of the biggest challenges encountered in the quantitative analysis of soil samples using LIBS. In addition, it is difficult to obtain similar reference soil samples, where matrix effects are difficult to avoid.⁶

As a solution to the matrix effect and reference sample limitations, a method called calibration-free LIBS (CF-LIBS) was proposed by Ciucci et al. in 1999.⁷ The elemental concentration information is determined by describing the physical states of the laser-induced plasmas with mathematical models. However, the accuracy of CF-LIBS has been limited by the challenge of meeting several fundamental assumptions in CF-LIBS,⁸ uncertainty of the atomic Einstein coefficients, measurement error of the optical coefficient curve, and the inevitable self-absorption effect of the plasma.

To improve precision, in 2013, a modification of CF-LIBS called the one-point calibration (OPC) method was proposed by Cavalcanti et al.⁹ as a means to enhance reliability and accuracy. Notably, the OPC method effectively addresses errors arising from the uncertainty of the Einstein coefficients and the measurement error of the optical coefficient curve.¹⁰ This method is favored for its unique advantages and characteristics.¹¹ Fu et al. conducted an analysis on three stainless steel samples and five heat-resistant steel samples by employing the OPC method in combination with a standard reference line.¹² Hai et al. utilized OPC-LIBS to analyze titanium alloys, resulting in significantly improved quantitative results compared to conventional methods.¹³ Gomes, G. et al. utilized OPC-LIBS to determine the calcium–phosphorus ratio in hydroxyapatite. Their results were compared with established techniques such as X-ray fluorescence (XRF) and atomic absorption spectroscopy, yielding a relative error within 5%.¹⁴ However, the OPC-LIBS method imposes stringent requirements on the calibration samples: the concentrations of all elements under investigation must be accurately certified, and the samples must share highly similar matrix compositions. Moreover, OPC-LIBS still faces the same normalization-related challenges as CF-LIBS, such as, atmospheric interferences during spectral acquisition, difficulty in detecting certain elements in soil samples, and the presence of elements in multiple oxide forms.

In this work, we have proposed a modified OPC-LIBS method that overcomes these limitations by:

(1) Internal-reference-element strategy: only one element (Si) in the reference sample need be certified, drastically reducing calibration requirements.

(2) Self-absorption correction plus CD-SB plotting: avoids the need for optically thin lines, more accurate characteristic line intensities are obtained, and plasma temperature and electron density are derived more precisely.

(3) Non-normalized processing: avoids oxide-based normalization, improving accuracy in elemental determination for complex matrix soil samples.

This work aims to provide a robust, cost-effective solution for real-time, on-site soil analysis where reference samples are scarce and matrix effects are severe.

2. Experimental setup and theoretical methods

2.1. Experimental setup and samples

The experimental setup used in this study is illustrated in Fig. 1. The samples were ablated with a Q-switched Nd: YAG laser (Q-Smart 450), with adjustable pulse energy ranging from 0.5 to 208 mJ at a wavelength of 532 nm, a pulse width of 5 ns, and a repetition rate of 10 Hz. The laser beam was focused 1 mm below the sample surface using a quartz lens with a focal length of 150 mm. An x–y–z motorized stage was used to position the samples, ensuring that each laser pulse targeted a new spot on the surface, thus preventing deep crater formation. The experiments were performed under ambient atmospheric conditions. Plasma emissions were collected through an optical fiber and subsequently analyzed using an echelle spectrometer (LTB, Aryelle 200). The spectrometer, equipped with an ICCD (iStarDH-334T, Andor), has a detectable spectral range of 200 to 850 nm and a spectral resolution between 23 and 84 pm. The spectral relative efficiency of the entire experimental system was calibrated using a radiation-certified deuterium-halogen light source (Ocean Optics). To optimize the signal-to-noise ratio (SNR) of the spectra, the pulse energy and delay time were set to 35 mJ and 1.5 μs, respectively.

Fig. 1 Schematic diagram of the experimental setup.³²

Eleven soil samples were certified by the Institute of Geophysical and Geochemical Exploration, Chinese Academy of Geological Sciences. The elemental information is listed in Table S1 of the SI.

2.2. Self-absorption correction

Under the assumption of local thermal equilibrium (LTE) and spatially homogeneous plasma, the emission intensity I(λ) of the spectral lines can be described using the Boltzmann distribution:¹⁵where j and i denote the upper and lower energy levels of the atomic transition, respectively; h is the Planck constant (erg s); c is the speed of light (cm s⁻¹); λ₀ is the central wavelength (nm); n is the number density (cm⁻³); g is the degeneracy of the energy level (dimensionless); k(λ) is the absorption coefficient (cm⁻¹); and l is the absorption path length (cm). The extent of self-absorption is determined by the optical thickness and is expressed as:where m_e and e are the mass (g) and charge (C) of the electron, respectively; f is the oscillator intensity of the transition; and L(λ) is a normalized Lorentzian line shape function with wavelength dependence.

The self-absorption coefficient SA quantitatively characterizes the magnitude of the self-absorption effect, where SA ranges from 0 (complete self-absorption) to 1 (no self-absorption):

I(λ₀) is the observed maximum peak intensity; I₀(λ₀) is the ideal peak intensity under optical thinness without self-absorption. The SA value equals one if the observed line is optically thin and tends to zero under significant self-absorption conditions. The self-absorption effect not only reduces the spectral intensity but also enlarges the line width. To quantify the self-absorption effect through spectral broadening, the self-absorption coefficient can be expressed as:¹⁶where α = −0.54; the Stark broadening in Δλ can be separated by the deconvolution or approximate subtraction¹⁷ method; Δλ₀ can be calculated from , where ω_s is the Stark broadening coefficient;^18–20N_ref is the reference electron number density, typically in the magnitude of 10¹⁶ or 10¹⁷ cm⁻³; N_e is the electron number density.where Δλ is the FWHM of the H_α line; α₌ denotes the half-width of the reduced Stark profile.²⁰

2.3. Columnar density Saha–Boltzmann(CD-SB)

Boltzmann and Saha–Boltzmann plot methods are both constrained by the optically thin assumption and may exhibit excessive discrepancies in plasma temperature estimates derived from different particles or elements. The columnar density Saha–Boltzmann (CD-SB) plot method can directly utilize the columnar densities of ground-state or low-energy-state particles to characterize the plasma, thereby circumventing the prerequisite assumption of optically thin spectral lines inherent in conventional approaches. This variant of the CF-LIBS methodology, first proposed by G. Cristoforetti and E. Tognoni,¹⁷ provides a novel perspective for accurate plasma temperature assessment.

The calculation of k(λ)l can be performed using eqn (3). Then the columnar density of the species at a lower level can be rewritten as:

where λ₀ and Δλ₀ are in Angstrom units.

Same as the conventional CF-LIBS method, the plasma was assumed to be spatially homogeneous and under LTE conditions within the observed time window in the CD-SB plot method. The Boltzmann equation and the Saha–Eggert equation were rewritten as:

where I and II represent the neutral and singly ionized states of the same element, respectively; E_i is the energy of the lower level; U^I(T) is the partition function; E_ion is the first ionization energy; and k_B is the Boltzmann constant. Eqn (7) was expressed as y = a × x + b to establish a CD-SB plot, where

The plasma temperature was deduced using the slope of the linear fitting curve in the CD-SB plot. The y-coordinate was calculated from the columnar densities of the atomic and ionic lines, instead of the spectral intensities; the x-coordinate represents the energy of the lower levels. The CD-SB plot method allows for the evaluation of the plasma temperature directly using strong self-absorption lines without searching for optically thin lines and correcting for self-absorption effects in experimental methods and procedures.

In this work, the CD-SB plot was not used to directly correct plasma parameters, but rather integrated as an external validation loop. Specifically, CD-SB plots were constructed using optically thick or resonance lines and compared with the SA-corrected SB plots. Only when the two plots exhibited high parallelism was the SB plot employed for plasma temperature evaluation and subsequent quantification. This procedure, illustrated in Fig. 2, ensured that the spectral line selection and self-absorption correction were reliable before entering the final analytical step.

Fig. 2 Workflow of the proposed method with the CD-SB validation loop.

2.4. Internal reference element method

Following the self-absorption correction and the construction of the CD-SB plot, a more reliable plasma temperature and more accurate characteristic line intensities were obtained, after which elemental determination was carried out. In conventional soil analysis methods like CF-LIBS and OPC-LIBS, the final elemental concentrations are determined through a normalization process, which assumes that the sum of all measured components equals 100%. However, LIBS has difficulty in detecting certain soil elements such as C, P, and S, and is subject to atmospheric interferences, which consequently introduces significant errors for other elements, particularly trace elements, during this normalization.

In conventional CF-LIBS, the mass fraction of an element can be expressed as:

where m denotes the atomic mass, N is the total number density, and F is the experimental factor. The denominator ensures normalization across all detected elements such that . However, this procedure requires reliable measurement of all major constituents, which may not always be feasible in practice.

To overcome this limitation, an internal standard element i with a known concentration C_i can be introduced. Its corresponding expression is:

This method selects an element with abundant content and stable properties in the sample as a reference to serve as the internal standard element (typically the matrix element). Since the denominators in eqn (9) and (10) are identical, the common term can be directly eliminated, and the final expression is obtained as:

where FN, as a whole, was calculated from the intercept q_s of the Saha–Boltzmann plot, defined as q_s = ln (FN_s/U_s(T)), where U_s(T)is the partition function of a specific species s at a given plasma temperature T.

In this work, silicon (Si) was chosen as the internal reference element. The procedure for determining the Si concentration in other samples is illustrated in Fig. 3. The key steps of this analytical procedure are as follows: First, the Si I 288.158 nm spectral line was selected as the primary analytical line because it resides in a spectral region with minimal interference from other common soil elements. More importantly, it possesses a high transition probability and its lower energy level is an excited state rather than the ground state, which results in outstanding resistance to self-absorption and higher sensitivity. Then, the Si I 250.69 nm line was used as the reference for spectral normalization. Specifically, this process involves dividing the intensity of the analytical line (Si I 288.158 nm) by that of the reference line (Si I 250.69 nm). This ratiometric approach is crucial for compensating for experimental fluctuations such as shot-to-shot variations in laser energy and plasma conditions.

Fig. 3 Flowchart for the determination of the internal reference element Si.

After normalization, a self-absorption correction was applied to the 288.158 nm line using the self-absorption coefficient SA calculated from Table 1. A correction was then applied by dividing the measured line intensity by this SA value. This procedure is based on the definition of SA as the ratio of observed-to-ideal intensity, as shown in eqn (3). After the above procedure, the Si concentration in unknown samples can be determined using the following equation:

Table 1 The selected neutral and ionic lines of Si, Al, Mg, and Ca intended for the plasma temperature determination using the CD-SB plot and for self-absorption correction

Elements	Wavelength per nm	ω s A^−1	References	SA	kl	f	n i l cm^−2
Si I	288.158	0.0064	20	0.0838	11.94	0.162	2.297 × 10^14
Si I	390.552	0.0117	20	0.617	1.058	0.091	3.66 × 10^13
Si II	385.602	0.28	23	0.501	1.587	0.0654	1.85 × 10^14
Al I	308.215	0.0281	24	0.707	0.74	0.167	5.3 × 10^13
Al I	394.401	0.0164	25	0.289	3.342	0.116	1.14 × 10^14
Al II	281.619	0.212	26	1	—	0.142	—
Mg I	285.213	0.025	27	0.0233	42.873	1.8	2.96 × 10^13
Mg II	279.553	0.022	27	0.00904	110.618	0.608	2.07 × 10^14
Mg II	280.271	0.0195	27	0.213	4.639	1.8	7.05 × 10^12
Ca I	422.673	0.0063	20	0.0559	17.889	1.75	1.46 × 10^13
Ca II	396.847	0.0846	28	0.037	27.049	0.33	1.77 × 10^14

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The and C_Si are the Si mass fractions in the unknown and the reference sample, respectively. The quantity FN is defined exactly as in eqn (9), where the superscripts I and II denote the neutral and singly ionized states, respectively. The value of is obtained from the intercept q_s of the Saha–Boltzmann plot, and the corresponding singly ionized is then derived through the Saha–Eggert equation. Because the same element (Si) is involved, the relative atomic mass cancels out.

Eqn (12) is not obtained by analogy from eqn (11). Instead, starting from eqn (9) and (10), expressions for the same element (Si) are written separately for the reference sample and the unknown sample. Under matched experimental conditions, similar matrices, and identical spectral treatments (including self-absorption correction), Si I 250.69 nm serves as an internal line to normalize Si I 288.158 nm, thereby reducing energy fluctuation and matrix effects. Under these conditions, the sample-dependent normalization factor becomes common or largely canceled in the cross-sample ratio, which yields the transfer relation of eqn (12).

In this step, Si serves as a same-element anchor for transfer. The primary objective remains improved quantification of other elements; the impact of Si uncertainty on the target elements is quantified via error propagation later.

Once the concentration of Si in each sample has been calculated, the content of the internal reference element is known for all samples. Eqn (9) can therefore be rewritten as:

where C_s is the concentration of the analyte element to be calculated, and C_Si is the concentration of the internal reference element, Si, as determined by the procedure described above. Using this equation, the concentrations of the other elements in each sample can then be calculated.

3. Results and discussion

3.1. LIBS spectra

Plasma emission spectra were acquired for the eleven soil samples under optimized experimental conditions and then analyzed to identify the observed spectral lines using the NIST database.²¹ Almost similar spectral lines with different intensities were found in the spectra of different soil samples. The spectrum of soil sample 1 is presented in Fig. 4, where spectral signatures of Si, Al, Fe, Ca, Mg, Na, K, Ba, Mn, Sr, Ti, O, N, and H were observed. The lines used in this work are listed in Table S2 of the SI, where only the approximately optically thin spectral lines are presented for Fe I, Fe II, Ca I, Ca II, Mg I, and Mg II species, and the determination of the optical thinness relies on the transition probability and energy of lower levels.

Fig. 4 LIBS spectrum of soil sample 1.

3.2. Self-absorption correction

The plasma electron number density of sample 1 was determined to be 1.1422 × 10¹⁷ cm⁻³. The Saha–Boltzmann plot of the plasma species is shown in Fig. 5. The linear curves fitted from the scattered data points yielded varying slopes, indicating different plasma temperatures for different species. An average value for the plasma temperature was ∼0.963 eV. Self-absorption effects caused elevated plasma temperatures and lower intercepts than expected, resulting in suboptimal analytical results in conventional CF-LIBS.²²

Fig. 5 Saha–Boltzmann plot for plasma species of soil sample 1.

The Saha–Boltzmann plot that included only spectral lines for self-absorption correction and optical thinness approximation was reconstructed and is reproduced in Fig. 6, showing almost identical slopes in these lines. The average value of the plasma temperature was ∼0.943 eV, which was fixed for analysis of all other elements. For comparison, the plasma temperature was also estimated from the columnar density Saha–Boltzmann (CD-SB) plot, which allows the direct use of those resonance lines or strong lines (generally with strong self-absorption).

Fig. 6 Saha–Boltzmann plot for plasma of soil sample 1 after self-absorption correction.

The Stark broadening coefficient ω_s, the optical depths kl, and the lower-level columnar densities n_il of Si, Al, Mg, and Ca emission lines are listed in Table 1.

According to Cristoforetti's simulation¹⁷ and the relationship between the optical depth and the self-absorption coefficient in Fig. 7, the calculation of k(λ)l is accurate when the spectral lines suffer from severe self-absorption (SA ≪ 1). The CD-SB plot deduced from Mg and Ca lines, and the Saha–Boltzmann plot after self-absorption correction (data in Fig. 5), are shown in Fig. 8. The plasma temperatures estimated by the two methods are in agreement of ∼0.893 eV.

Fig. 7 Relation between k(λ)l and the SA coefficient, derived from eqn (3).

Fig. 8 Comparison of the CD-SB plot and Saha–Boltzmann plot of soil sample 1 after self-absorption correction.

3.3. Electron density and plasma temperature

Similar to Fig. 8, the comparison of the CD-SB plot and the Saha–Boltzmann plot after self-absorption correction in soil samples 3 and 9 is shown in Fig. 9. As shown in both Fig. 8 and 9, the slopes of the CD-SB plots and the Saha–Boltzmann plots after self-absorption correction are very close, which is also the case for the other soil samples. This strong agreement in slopes indicates that the plasma temperatures calculated using the Saha–Boltzmann plot after self-absorption correction are highly accurate and reliable. Therefore, the plasma temperatures employed in subsequent calculations were all derived from the Saha–Boltzmann plot following self-absorption correction. In addition, the plasma electron number density was calculated using eqn (5) based on the H_α line. The plasma temperatures and electron densities for each soil sample are summarized in Fig. 10.

Fig. 9 Comparison of the CD-SB plot and Saha–Boltzmann plot of soil samples after self-absorption correction: (a) sample 3 and (b) sample 9.

Fig. 10 The plasma temperature and electron number density of the soil samples.

LTE is essential for the Saha–Eggert expression,²⁷ which is estimated using the McWhirter criterion.²⁹ It is usually satisfied at early stages of plasma evolution with electron density in the magnitude of 10¹⁷–10¹⁸ cm⁻³.³⁰

It is crucial to evaluate the accuracy and reliability of the plasma electron density and temperature. Using H_α lines to measure electron density has the distinct advantage of providing a result that is not affected by self-absorption and does not require efforts to find the Stark broadening coefficients. According to the results of numerical simulation by Tognoni et al., the typical uncertainty in electron density, usually about 10–20%, is not one of the major factors contributing to the uncertainty in the final quantitative analysis results.³¹

The plasma temperatures were derived from the Saha–Boltzmann and the columnar density Saha–Boltzmann plots. In the Saha–Boltzmann plot,³² the uncertainty in the calculation of plasma temperature was mainly caused by the statistical uncertainty of spontaneous transition probability, the correction error of the relative efficiency, the measurement error of the emission intensity, and the self-absorption effect of the emission lines. In addition, the plasma was not strictly satisfying the LTE conditions, since the different species in the plasma could not maintain the same temperature, and the temperature determination was hard to evaluate. In the columnar density Saha–Boltzmann plot, the accuracy of the measurement mainly depends on Stark broadening coefficients and oscillator strengths and can be as large as 50% in many cases. However, the accuracy is usually much higher for resonant and/or strong lines, with errors below 10–20%, which is therefore acceptable for analysis.¹⁸ Special attention should also be paid to the line broadening mechanisms other than Stark broadening, which may lead to incorrect estimates of the Δλ values used in eqn (4), resulting in an incorrect assessment of the plasma temperature. In the CD-SB method, resonant and/or strong lines, which usually correspond to optical thickness, were used. Although the ground states were more likely to deviate from the LTE because of their large energy gap with the excited level, the self-absorption tended to repopulate the upper energy levels of the transition at the thick line conditions, rebalancing the level population toward LTE.

3.4. Elemental determination

With the plasma characteristics established, we proceeded to evaluate the elemental determination of the 11 soil samples. In this study, Si in sample 1 was selected as the internal reference element. The concentration of Si was determined following the calculation workflow in Fig. 2, with sample no. 1 serving as the reference sample. The calculated Si content for the other samples, alongside their certified values and relative error (RE), is presented in Table 2.

Table 2 The certified and calculated Si content in other soil samples

Sample	Si (certified value)	Si (evaluated value)	RE (%)
1	26.413	26.413	—
2	30.786	32.942	7.003
3	34.053	40.258	18.221
4	29.554	32.652	10.483
5	28.709	29.676	3.368
6	21.163	27.491	29.901
7	15.741	23.311	41.738
8	28.056	27.409	2.306
9	32.396	32.675	0.861
10	30.277	34.399	13.614
11	31.841	32.11	0.845

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The high relative errors in samples 6 and 7 (29.901% and 41.738%, respectively) can be attributed to: (1) significant differences in the amount of ablation in different soils in the pressed state due to differences in the matrix components; (2) the influence of laser energy fluctuation, sample surface flatness, the position of the laser focus point and the collection point; (3) errors in the calculation of self-absorption coefficients (the Stark broadening in Δλ). However, a 30–40% relative error for the matrix element Si does not result in errors of the same magnitude for other elements in the soil.

According to eqn (13), the order of magnitude of FN_Si is 10¹⁰, while the order of magnitude of FN_S for other elements is 10⁶–10⁹. A relative error of 30–40% for the matrix elements will bring an additional error of less than 4% for the other elements. This is also evident from the full-element quantitative results below.

To evaluate the performance of our proposed method, we conducted an elemental determination comparing the Mean Relative Error (MRE) across different analytical approaches. MRE was chosen as the evaluation metric because it effectively reflects the overall accuracy of multi-element determination by normalizing errors relative to the true concentration values, thereby allowing for fair comparison across elements with widely varying concentration ranges.

For method comparison, our proposed approach was benchmarked against conventional CF-LIBS, CF-LIBS with self-absorption correction (CF-LIBS with SAC), and OPC-LIBS with SAC. The latter two comparative methods employed the same self-absorption correction procedure as described in Section 2.2 to correct the line intensities. Furthermore, the OPC-LIBS with SAC method followed the conventional model, requiring the concentrations of all analytes in the reference sample (sample 1) to be certified.

Fig. 11 illustrates the comparative results obtained from 11 distinct samples. It should be noted that sample 1 served as the reference sample, and its Si element concentration was excluded from the calculations to avoid self-reference bias.

Fig. 11 Comparison of mean relative error across methods for 11 samples.

As depicted in the figure, four methods were assessed: CF-LIBS (lightest blue), CF-LIBS with SAC (light blue), OPC-LIBS with SAC (medium blue), and our proposed method (dark blue). The horizontal axis represents the sample number (1–11), while the vertical axis indicates the MRE values expressed as percentages. The results for CF-LIBS, CF-LIBS with SAC, and OPC-LIBS with SAC were obtained after normalization using the oxide normalization method, where elemental concentrations were converted to their corresponding oxide forms and normalized to 100%. The comprehensive elemental quantitative results for all samples and methods are listed in Table S3 in the SI.

Quantitatively, the CF-LIBS method yielded mean relative error (MRE) values ranging from 25.119% to 59.749%, while the CF-LIBS with self-absorption correction (SAC) method produced MRE values between 19.87% and 60.505%. In contrast, our proposed method exhibited significantly enhanced performance, with MRE values ranging from 16.324% to 42.358% (excluding sample 1, which served as the reference sample), demonstrating a substantial reduction in error margins and underscoring its superior analytical capability. Furthermore, our proposed method consistently achieved lower MRE values compared to both CF-LIBS and CF-LIBS with SAC across the tested samples. However, an anomaly was observed in samples 3 and 5, where CF-LIBS with SAC unexpectedly produced higher MRE values than CF-LIBS alone. This counter-intuitive outcome arises from the interplay between self-absorption correction and oxide normalization: while self-absorption correction enhanced the accuracy of certain elemental concentrations, the subsequent oxide normalization amplified these concentrations, resulting in larger overall errors. This finding highlights the distinct advantage of the non-normalization procedure in our proposed method, particularly for complex samples such as soil.

More importantly, a comparison between the conventional OPC-LIBS method and the proposed method was conducted. Sample 1 was designated as the OPC-LIBS reference, and the detailed quantitative results for OPC-LIBS are provided in Table S3 of the SI. The OPC-LIBS with SAC method produced MRE values between 12.071% and 35.882%, showing that our method delivers performance comparable to that of conventional OPC-LIBS and even outperforms it for several samples. By requiring only the certified concentration of a single internal-standard element, our approach achieves analytical accuracy on par with conventional OPC-LIBS while greatly easing the need to know the precise concentrations of every analyte—a requirement that is particularly challenging when analyzing soil samples.

4. Conclusion

In this work, a modified OPC-LIBS method of combining an internal-element strategy with single-point calibration for multi-element determination in soil samples is presented. Using silicon as the only one certified element in the reference sample, the results demonstrated that mean relative errors in the proposed method were reduced to 16.324–42.358%, significantly outperforming both conventional CF-LIBS and CF-LIBS with self-absorption correction. Notably, the proposed method (only silicon was certified) achieved a performance comparable to the conventional OPC-LIBS (all elements were certified). By combining self-absorption correction with columnar-density Saha–Boltzmann plots, the plasma parameters were corrected for improving accuracy. Through non-normalized processing, it effectively eliminates atmospheric interferences and detection challenges of problematic elements, offering a practical solution for complex matrix samples. This streamlined approach enables convenient and accurate real-time, on-site soil analysis without needing accurate concentration data for all elements in the calibration standards—with only one internal reference element—making it highly valuable for agricultural and environmental monitoring applications where reference samples are limited and matrix effects are significant.

Author contributions

Nan Zhao and Zeren Luo: study conception and design; Shaofeng Zheng and Ruitao Lin: experiments; Bin Wang and Shixiang Ma: data analysis; Kuohu Li and Erlong Jiang: methodology, critical feedback; Jiaming Li and Qingmao Zhang: funding acquisition, supervision, project administration, writing – review and editing; all authors: discussion of results, contribution to the final manuscript.

Conflicts of interest

All authors disclosed no relevant relationships.

Data availability

The main data supporting the findings of this study are available within the article and its supplemenatry information (SI) files. Other datasets are available from the corresponding author upon reasonable request. Supplementary information is available. See DOI: https://doi.org/10.1039/d5ja00206k.

Acknowledgements

This work was supported by the National Natural Science Foundation of China (62475075, 62105105, and 32171627); Guangdong Basic and Applied Basic Research Foundation (2023A1515011641 and 2023A1111120030); The Open Project of Guangdong Provincial Key Laboratory of Intelligent Port Security Inspection (2023B1212010011); Innovation Capacity Building Project of Beijing Academy of Agriculture and Forestry Sciences (KJCX20230408); the Key R&D and Promotion Program (Science and Technology) in Henan Province of China (252102221061).

Notes and references

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