Development and validation of a portable X-ray fluorescence approach for quantifying silicon in plants

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This study developed and validated an empirical calibration of pXRF for quantifying silicon (Si) in plants, using autoclave-induced digestion (AID) as the reference method. Methods A total of 374 samples from seven plant species (rice, maize, soybean, cowpea, sorghum, lettuce, and beet) were analyzed. Silicon concentrations obtained via AID ranged from 1.07 to 19.23 g kg − ¹ (mean = 4.48 g kg − ¹; coefficient of variation = 67%), reflecting substantial interspecific variability. Each sample was also analyzed by pXRF under optimized instrumental conditions, and a calibration model was constructed using 75% of the dataset to predict Si concentrations relative to AID values. Results The pXRF calibration exhibited a strong linear relationship with AID results (R² = 0.94; R = 0.97; p < 0.001). Validation using the remaining 25% of samples confirmed high predictive accuracy, with consistent performance across all species, particularly rice (R = 0.96) and soybean (R = 0.93). Conclusions The pXRF exhibited excellent agreement with the reference method and high predictive accuracy, while markedly reducing analytical time and eliminating the use of hazardous reagents. These results establish pXRF as a reliable, rapid, and sustainable alternative for large-scale Si monitoring in both agronomic and environmental applications. Autoclave-induced digestion Elemental analysis Non-destructive technique Spectrometric methods Figures Figure 1 Figure 2 Figure 3 Introduction Silicon (Si) is widely recognized for its beneficial effects on plants, particularly in enhancing resistance to abiotic and biotic stresses, strengthening cell walls, and improving yield in a wide range of crops (Barão, 2023 ; Camargo et al., 2021 ; Ma, 2004 ; Nascimento et al., 2019). Its uptake and accumulation vary markedly among plant species, and Si can account for up to 10% of the plant’s dry mass in strong accumulators (Coskun et al., 2018; Hodson et al., 2009). Despite the growing recognition of Si’s importance in plant science, methodological limitations, particularly the scarcity of fast, affordable, and reliable techniques, continue to constrain advances in Si analysis. The quantification of Si in plant tissues is traditionally performed through laborious wet-chemical procedures, most commonly autoclave-induced digestion (AID) followed by colorimetric determination (Elliot et al., 1988; Korndörfer et al., 2004 ). Although these methods provide good precision and accuracy, they require hazardous reagents, involve long processing times, and often yield poor reproducibility (Guntzer et al., 2010; Kraska & Breitenbeck, 2010 ; Taber et al., 2014). Alternative approaches, including alkaline fusion with sodium hydroxide or lithium carbonate, demand high temperatures, produce insoluble residues, and frequently lead to incomplete Si-solubilization, particularly in Si-accumulating species, resulting in concentration underestimation (Haysom & Ostatek-Boczynski, 2006 ; Kraska & Breitenbeck, 2010 ). Furthermore, these destructive procedures preclude subsequent analyses on the same sample material. In addition to colorimetric methods, instrumental techniques such as inductively coupled plasma optical emission spectrometry (ICP-OES) have been employed for Si determination in plant digests (Barros et al. 2016 ; Haysom & Ostatek-Boczynski, 2006 ). While these approaches offer excellent sensitivity and multi-elemental capability, they still rely on wet digestion or fusion steps for complete Si extraction, which increases the analytical cost, reagent consumption, and waste generation. Moreover, silica polymerization and precipitation during acid digestion can lead to Si losses, compromising accuracy and long-term instrument performance due to nebulizer clogging and residue deposition in the plasma torch (Langenfeld & Bugbee, 2023 ). Consequently, despite its analytical robustness, ICP-based techniques remain resource-intensive and environmentally demanding. In this context, energy-dispersive X-ray fluorescence spectrometry (ED-XRF), which has recently been adapted into portable XRF analyzers (pXRF), offers a promising alternative for Si determination in plants. The technique enables rapid, non-destructive, and multi-elemental analysis of plant tissues with minimal sample preparation (Costa et al., 2023 ; Lima et al., 2024 ). It operates by detecting element-specific fluorescent photons emitted after excitation by primary X-rays, using high-resolution silicon drift detectors (SDD) (Towett et al., 2015). Previous studies have focused on quantifying nutrients and trace elements, demonstrating strong correlations between pXRF and conventional laboratory methods (Queralt et al., 2005; Singh et al., 2020). For instance, in rice and millet grains, pXRF achieved deviations below 2 mg kg − ¹ for iron (Fe) and zinc (Zn), with coefficients of determination (R²) ranging from 0.79 to 0.98 compared with ICP-OES (Paltridge et al., 2012). The portability of the instrument additionally allows in-field measurements, enabling real-time monitoring of plant nutrient status (Soares et al., 2021 ; Silva et al., 2024 ). Despite these advantages, studies specifically addressing pXRF calibration for Si quantification in plants remain scarce. Reidinger et al. ( 2012 ) evaluated the accuracy and reliability of the technique using synthetic matrices enriched with SiO₂ (0–10%), obtaining an excellent linear calibration (R² = 0.998). The increasing use of pXRF in agronomic and environmental studies highlights the need to adapt and validate the technique under different analytical conditions and plant matrices, since instrumental responses may vary depending on the analyzer model, X-ray tube configuration, detector type, and measurement atmosphere (Lemière, 2018; Towett et al., 2015). Additionally, sample characteristics such as moisture content, particle size, compaction, and organic matter composition can significantly impact fluorescence intensity and analytical precision (Lenormand et al., 2022; Ran et al., 2014). Therefore, developing matrix-specific calibrations is essential to ensure data reliability, reproducibility, and comparability across studies. Standardization and validation are critical steps toward establishing pXRF as a routine tool for plant nutritional analysis (Horta et al., 2021; Touzé et al., 2022). Accordingly, this study aims to evaluate the performance and analytical reliability of portable X-ray fluorescence spectrometry for Si quantification in plant tissues, using autoclave-induced digestion as the reference method. The results are expected to advance the application of pXRF as a rapid, reliable, and environmentally sustainable technique for routine Si analysis, contributing to improved agronomic management and crop productivity. Material and methods Plant samples A total of 374 plant samples, representing a wide range of Si accumulation capacities, were analyzed. Samples were obtained from the Soil Environmental Chemistry Group (GQAS) experimental collection, including rice ( Oryza sativa , n = 26), soybean ( Glycine max , n = 42), maize ( Zea mays , n = 250), cowpea ( Vigna unguiculata , n = 20), sorghum ( Sorghum bicolor , n = 12), beet ( Beta vulgaris , n = 6), and lettuce ( Lactuca sativa , n = 6). All plant materials were carefully washed to remove impurities, oven-dried at 65°C for 48 h under forced-air circulation, and ground using a Willey-type mill to pass a 2 mm sieve. Subsequently, the samples were homogenized in a ball mill to obtain fine powders with uniform granulometry. Silicon determination by the standard method Total Si concentrations in plant tissues were determined following the autoclave-induced digestion (AID) method adapted from Korndörfer et al. ( 2004 ). For each sample, 0.1 g of dried plant material was weighed into 50 mL centrifuge tubes, to which 2 mL of H₂O₂ (500 g L − ¹) and 3 mL of NaOH (500 g L − ¹) were added. Tubes were heated in a water bath at 75°C for 1 h, followed by autoclaving at 123°C and 1.5 atm for 1 h. After digestion, 45 mL of deionized water was added, and the solutions were allowed to stand for 12 h to complete solubilization. Aliquots of 5 mL from the supernatant were diluted in 20 mL of deionized water, followed by the addition of 1 mL of HCl (500 g L − ¹) and 2 mL of ammonium molybdate (100 g L⁻¹). After 4 min, 2 mL of oxalic acid (75 g L − ¹) was added to eliminate Fe and P interferences. The colorimetric determination of Si was performed by UV-Vis spectrophotometry at 410 nm. Silicon determination by portable X-ray fluorescence (pXRF) Silicon quantification was performed using a portable energy-dispersive X-ray fluorescence (ED-XRF) spectrometer (S1 TITAN 800, Bruker, USA) equipped with a 4 W rhodium X-ray tube (6–50 kV, 5–200 µA). For pXRF analysis, plant tissues were oven-dried at 65°C, pulverized in a ball mill, and sieved to < 300 µm to obtain a homogeneous fine powder. Subsequently, 100 mg of each sample was loaded into XRF sample cups and sealed with MYLAR® film (3.6 µm thickness), which ensures high X-ray transmittance and minimal background interference (Fig. 1 ). Fluorescent X-rays were detected using a silicon drift detector (SDD) featuring a graphene window, an energy resolution < 145 eV, and a count rate of 450,000 cps. Each sample was analyzed in triplicate, in the “Plant Mode”, with a 60 s acquisition time (Lima et al., 2024 ). The complete dataset was randomly divided into two subsets: 75% of the samples were used for model calibration, and the remaining 25% were reserved for cross-validation of the predictive model. Model performance evaluation The performance of the pXRF predictive model was assessed using standard statistical metrics as described by Sevastas et al. ( 2018 ), including: (a) the Coefficient of Determination (R²), (b) the Mean Absolute Error (MAE), (c) the Mean Absolute Percentage Error (MAPE), (d) the Mean Squared Error (MSE), and (e) the Root Mean Squared Error (RMSE). The CV quantifies the proportion of variance in the observed data that is explained by the regression model, providing a measure of the model’s predictive capability. According to Li et al. ( 2016 ), R² values below 0.50 indicate an unacceptable prediction, values ranging from 0.50 to 0.75 denote an acceptable prediction, and R² values equal to or greater than 0.75 reflect a good prediction, indicating that the model successfully captures most of the variability in the measured data. The MAE represents the average absolute difference between the measured and predicted values (Eq. 1), providing a direct measure of the magnitude of prediction errors in the same units as the observed data. Lower MAE values indicate smaller average deviations and, consequently, higher predictive accuracy. According to Li et al. ( 2016 ), an MAE equal to zero denotes perfect prediction, values below 10% of the mean measured value correspond to low error and indicate high model precision, MAE values between 10% and 20% are classified as moderate error and suggest reasonable predictive performance, whereas MAE values exceeding 20% of the mean measured value are interpreted as high error, reflecting reduced model reliability. The MAPE expresses the average percentage deviation between the measured and predicted values (Eq. 2), providing a normalized and scale-independent measure of predictive performance. Lower MAPE values indicate greater predictive accuracy, as they reflect smaller relative discrepancies between observed and estimated results. MAPE values below 10% are generally interpreted as excellent predictions, values ranging from 10% to 20% are considered acceptable, while values exceeding 20% may suggest the need for further adjustments in the regression model or calibration procedure (Sevastas et al. 2018 ). The MSE and the RMSE were also employed to evaluate the predictive performance of the model. The MSE quantifies the average of the squared differences between predicted and measured values (Eq. 3), thereby assigning greater weight to large deviations and effectively penalizing substantial prediction errors. The RMSE, obtained as the square root of the MSE, provides a more intuitive assessment of model accuracy because it expresses error in the same units as the observed data. Lower RMSE values indicate stronger agreement between predicted and measured results, with smaller dispersion around the 1:1 relationship line. In this study, MSE and RMSE values were interpreted relative to the mean of the measured data. An MSE or RMSE value of zero indicates excellent prediction and a perfect fit between predicted and observed data. MSE values below 1% and RMSE values below 10% of the mean measured value were classified as low error, reflecting high predictive accuracy. MSE values between 1–4% and RMSE values between 10–20% were considered moderate error and acceptable performance, whereas values above these thresholds were regarded as high error, indicating reduced model reliability and potential calibration limitations. Statistical analysis The collected data were subjected to univariate statistical analyses, including the calculation of frequency distributions, minimum and maximum values, mean, median, standard deviation, and coefficient of variation. Empirical calibration was performed using linear regression, while model validation was based on Pearson’s correlation coefficient (r) to assess the strength and significance of the relationship between predicted and measured Si concentrations. All statistical procedures were conducted using OriginPro 2019, SISVAR, and R software (version 4.0.2). Results Distribution of Si concentrations in samples analyzed by the AID method Descriptive analysis of Si concentrations in leaf tissues revealed a wide variation among the evaluated species, with values ranging from 1.07 to 19.23 g kg − ¹ (Table 1 ). The overall mean Si concentration across all samples was 4.48 g kg⁻¹, with a standard deviation (SD) of 3.03 g kg − ¹ and a coefficient of variation (CV) of 67.6%, indicating high heterogeneity in Si accumulation capacity among the studied crops. Additionally, the plants included in this study were subjected to different Si sources (or none) and application rates, as well as distinct cultivars within the same species, which likely contributed to the observed variability in Si accumulation, even within a single crop type. Table 1 Descriptive statistics, including mean, standard deviation, coefficient of variation, and concentration range of silicon (Si) in leaf tissues, determined by the autoclave-induced digestion (AID) method Species (n) Scientific name Silicon (g kg − ¹) SD (±) Rice (n = 27) Oryza sativa 9.25–19.23 2.79 Soybean (n = 42) Glycine max 2.18–6.47 1.24 Maize (n = 249) Zea mays 1.07–8.17 1.88 Cowpea (n = 20) Vigna unguiculata 2.48–4.40 0.62 Sorghum (n = 12) Sorghum bicolor (L.) Moench 3.79–6.28 0.93 Lettuce (n = 6) Lactuca sativa 2.09–3.10 0.42 Beet (n = 6) Beta vulgaris 1.97–2.76 0.30 Overall mean — 4.48 — Standard deviation — 3.03 — Minimum — 1.07 — Maximum — 19.23 — Coefficient of variation (%) — 67.58 — The distribution of Si concentrations among species reflects clear phylogenetic and physiological differences in Si transport mechanisms. Members of the Poaceae family, such as rice and sorghum, are active Si accumulators (> 8 g kg − ¹), whereas legumes and other broadleaf crops, including maize, cowpea, and soybean, exhibit intermediate accumulation levels (3–8 g kg − ¹). Leafy vegetables such as beet and lettuce typically behave as passive accumulators, relying mainly on diffusion-driven uptake (Bokor et al., 2015 ; Hodson et al., 2009). In this study, rice presented the highest Si concentrations (9.25–19.23 g kg − ¹), consistent with its classification as a strong accumulator due to the presence of active Si transporters (Lsi1 and Lsi2) that mediate efficient uptake and translocation to aerial tissues (Ma & Yamaji, 2006 ; Coskun et al., 2016). Conversely, beet and lettuce exhibited the lowest concentrations (1.97–2.76 g kg − ¹ and 2.09–3.10 g kg − ¹, respectively), in agreement with their status as non-accumulator species. Model validation and predictive performance The results obtained in this study demonstrate the feasibility of pXRF as an alternative and efficient tool for the determination of Si in plant tissues. The strong correlation between the values obtained by pXRF and the conventional autoclave-induced alkaline digestion (AID) method (R² = 0.94, R = 0.97, p < 0.001) reinforces the accuracy and reliability of the technique, indicating its potential to replace traditional analytical methods (Fig. 2 ). These findings are consistent with previous studies validating the use of pXRF for the quantification of elements in biological materials and soils (Soares et al., 2021 ; Singh et al., 2020; Teixeira et al., 2022 ; Paes et al., 2022 ). Importantly, this work helps to fill a critical gap in the literature regarding the validation of pXRF for Si determination in plants (Reidinger et al., 2012 ), representing one of the few studies to date that specifically addresses this application. The accuracy of the pXRF model was confirmed by the MAE and MAPE, which were 0.45 g kg⁻¹ and 8.2%, respectively, values considered excellent according to the criteria proposed by Piekutowska et al. ( 2021 ). Furthermore, cross-validation using 25% of the samples (n = 94) not included in the calibration confirmed the robustness of the model (Fig. 3 ). The resulting MAE (0.44 g kg⁻¹) and MAPE (8.0%) corresponded to a mean accuracy of 97%, with values ranging between 81% and 109%. A slight underestimation was observed for concentrations below 2 g kg⁻¹, and a modest overestimation for higher Si contents (5–6 g kg⁻¹). Despite these trends, no statistically significant differences were detected between the measured (AID) and predicted (pXRF) data, confirming the good predictive performance of the model even for external validation samples. Discussion The pronounced variability in Si concentrations observed across plant tissues (Fig. 2 ) reflects the inherent physiological diversity in Si uptake, transport, and deposition among species. This variability also points to considerable intraspecific differences, likely associated with genotypic variation in Si transporter expression, root architecture, and uptake efficiency. Such findings align with previous reports indicating that Si accumulation is governed not only by taxonomic distinctions between monocots and dicots but also by species-specific and genotypic traits, including root activity, transporter regulation, and external Si availability (Liang et al., 2015; Ma & Yamaji, 2015). This degree of variability is advantageous for the calibration of alternative analytical techniques, as it encompasses a wide concentration range representative of both low and high Si accumulators. From a physiological perspective, such diversity underscores the adaptive significance of Si in enhancing plant resilience to abiotic and biotic stresses through mechanisms that strengthen structural integrity, mitigate oxidative damage, and improve defense responses (Debona et al., 2017 ; Epstein, 2009 ). Therefore, precise quantification of this variability using pXRF can contribute to more accurate screening and breeding programs aimed at improving Si use efficiency and stress tolerance in agricultural species. Reliable empirical calibration requires a dataset encompassing a broad concentration range (Lima et al. 2024 ). In this study, the coefficient of variation (~ 68%) highlights the presence of significant intraspecific heterogeneity, which must be accounted for during calibration to maintain analytical robustness. High variability within species may influence fluorescence intensity, especially due to differences in tissue density, surface roughness, and organic matrix composition. Hence, the AID results serve as a critical benchmark for refining predictive models and constructing species-specific calibration curves, enhancing the reliability of pXRF in both agronomic and environmental contexts. The regression slope (1.15) and intercept (-0.36) indicate a minor systematic overestimation of Si by pXRF compared with AID, likely reflecting matrix-related effects and differences in sample preparation. Indeed, the NaOH + H₂O₂ extraction stimulated by autoclaving may be underestimating the Si contents, since plants vary in both the total amount of silica and the quantity of their phytoliths. Previous studies have also highlighted the importance of matrix calibration and adjustment to ensure the accuracy of the technique (Paes et al., 2022 ; Piekutowska et al., 2021 ). The model validation confirmed the high analytical performance of portable X-ray fluorescence. Across the seven tested crops (rice, soybean, maize, cowpea, sorghum, lettuce, and beet), results showed strong agreement with AID (R = 0.93–0.96). For rice, Si concentrations ranged from 9.97 to 19.29 g kg⁻¹ using the autoclave method and from 10.23 to 23.02 g kg⁻¹ by pXRF, with a mean correlation of R = 0.96. For soybean, values ranged from 2.19 to 6.47 g kg⁻¹ (AID) and 2.09 to 6.06 g kg⁻¹ (pXRF), with R = 0.93. The MAE (0.45 g kg⁻¹) and MAPE (8.2%) values denote excellent prediction accuracy, consistent with the criteria proposed by Piekutowska et al. ( 2021 ). Cross-validation using 25% of independent samples (n = 94) yielded similar outcomes (MAE = 0.44 g kg⁻¹, MAPE = 8.0%), confirming the robustness and generalization ability of the predictive model. Slight underestimation at low Si concentrations (< 2 g kg⁻¹) and overestimation at higher levels (5–6 g kg⁻¹) suggest minor non-linearities possibly linked to detector sensitivity or matrix effects. Nevertheless, no statistically significant differences were found between AID and pXRF results, validating the method’s transferability beyond the calibration dataset. The time efficiency of pXRF represents a major operational advantage. Traditional chemical digestion methods are labor-intensive and reagent-dependent, whereas pXRF enables non-destructive, real-time quantification, processing hundreds of samples per day (Teixeira et al., 2022 ). Despite these advantages, matrix-specific calibrations remain indispensable, as the spectrometric response can be influenced by plant composition, especially by lignin, cellulose, and residual moisture. Integrating pXRF with other sensing techniques, such as hyperspectral or LIBS, may further enhance predictive accuracy and broaden its application in nutrient diagnostics (Soares et al., 2021 ; Teixeira et al., 2022 ). In summary, pXRF constitutes a rapid, reliable, and environmentally sustainable alternative for quantifying Si in plant tissues, supporting both routine nutrient monitoring and advanced research applications. With further refinement of calibration protocols and matrix corrections, the technique has the potential to markedly reduce analytical costs and processing time while maintaining, or even surpassing, the accuracy of conventional wet-chemistry methods. Conclusions This study demonstrated that pXRF is a reliable, rapid, and non-destructive analytical tool for quantifying Si in plant tissues. The method showed a strong correlation with the conventional AID technique and achieved excellent predictive performance, confirming accuracy comparable to traditional laboratory methods while substantially reducing analytical time and eliminating the use of hazardous reagents. In addition to its precision, pXRF offers exceptional analytical throughput, allowing the processing of up to 300 plant samples per day, a major advantage for large-scale monitoring programs. Given its portability, scalability, and environmental sustainability, pXRF stands out as a robust and practical alternative for Si determination in both agronomic and ecological applications. Declarations Competing interests We confirm that there are no conflicts of interest associated with this publication. All authors have approved the submission and are aware of its content. Neither the manuscript nor any part of it is currently under consideration or published in another journal. Funding This study was financed in part by the Brazilian Federal Agency for Support and Evaluation of Graduate Education (CAPES) and the National Council for Scientific and Technological Development (CNPq) for granting scholarships. Author contributions All authors contributed to the conception and design of the study. Material preparation, data collection, and analysis were performed by Franklone Lima da Silva, Jonathan José de Melo, Everton Estevão Alves do Nascimento, Luiz Henrique Vieira Lima, and Simone Aparecida da Silva Lins. The first draft of the manuscript was written by Franklone Lima da Silva and Clístenes Williams Araújo do Nascimento, and all authors provided comments on previous versions of the manuscript. All authors read and approved the final version of the manuscript. Data Availability The datasets generated and/or analyzed during the current study are available from the corresponding author upon reasonable request. 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Soil Sci 181(9):1–14. https://doi.org/10.1097/SS.0000000000000179 Cite Share Download PDF Status: Posted Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-7940601","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":537024880,"identity":"360c4159-255f-472d-81a1-d34fbdfb2d39","order_by":0,"name":"Franklone Lima da Silva","email":"","orcid":"","institution":"","correspondingAuthor":false,"prefix":"","firstName":"Franklone","middleName":"Lima da","lastName":"Silva","suffix":""},{"id":537024881,"identity":"735a753e-ddfe-4e43-9b5f-4ffb80e81e06","order_by":1,"name":"Jonathan José de 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09:18:00","extension":"html","order_by":23,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":112899,"visible":true,"origin":"","legend":"","description":"","filename":"earlyproof.html","url":"https://assets-eu.researchsquare.com/files/rs-7940601/v1/b153e29c70eacff0d39dea27.html"},{"id":95618644,"identity":"4cd0927d-885f-4b8f-bdbd-7cc2d1684c47","added_by":"auto","created_at":"2025-11-11 09:18:00","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":298335,"visible":true,"origin":"","legend":"\u003cp\u003ePreparation and measurement setup for portable X-ray fluorescence (pXRF) analysis of plant samples. (a) sample loading (100 mg) into XRF cups sealed with MYLAR® film (3.6 µm thickness) and (b) measurement of silicon concentrations using the spectrometer.\u003c/p\u003e","description":"","filename":"1.png","url":"https://assets-eu.researchsquare.com/files/rs-7940601/v1/bb8ec4637a3aa680729f585a.png"},{"id":95657177,"identity":"374cca73-c19a-41a1-8bb2-13d8dde09d29","added_by":"auto","created_at":"2025-11-11 16:20:15","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":141366,"visible":true,"origin":"","legend":"\u003cp\u003eCorrelation between silicon (Si) concentrations determined by portable X-ray fluorescence (pXRF) and by autoclave-induced digestion (AID) in plant samples.\u003c/p\u003e","description":"","filename":"2.png","url":"https://assets-eu.researchsquare.com/files/rs-7940601/v1/d9a64afe23d8a64c6453e22d.png"},{"id":95618648,"identity":"d913b61e-1f89-4f46-b54b-cc89eab34806","added_by":"auto","created_at":"2025-11-11 09:18:00","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":80318,"visible":true,"origin":"","legend":"\u003cp\u003eCross-validation of the predictive model using 25% of the samples (n = 94). Comparison between silicon (Si) concentrations obtained by the reference method (autoclave-induced digestion - AID) and those estimated by portable X-ray fluorescence (pXRF).\u003c/p\u003e","description":"","filename":"3.png","url":"https://assets-eu.researchsquare.com/files/rs-7940601/v1/57a0b6c6d4c8bb978aacc0b7.png"},{"id":96913277,"identity":"da74ba35-e2c9-43b7-822d-f42383a0ddd2","added_by":"auto","created_at":"2025-11-27 13:56:54","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1247725,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-7940601/v1/e2eb80cb-d27f-44f1-adf8-58f8f5a6d57f.pdf"}],"financialInterests":"","formattedTitle":"Development and validation of a portable X-ray fluorescence approach for quantifying silicon in plants","fulltext":[{"header":"Introduction","content":"\u003cp\u003eSilicon (Si) is widely recognized for its beneficial effects on plants, particularly in enhancing resistance to abiotic and biotic stresses, strengthening cell walls, and improving yield in a wide range of crops (Bar\u0026atilde;o, \u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e2023\u003c/span\u003e; Camargo et al., \u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e2021\u003c/span\u003e; Ma, \u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e2004\u003c/span\u003e; Nascimento et al., 2019). Its uptake and accumulation vary markedly among plant species, and Si can account for up to 10% of the plant\u0026rsquo;s dry mass in strong accumulators (Coskun et al., 2018; Hodson et al., 2009). Despite the growing recognition of Si\u0026rsquo;s importance in plant science, methodological limitations, particularly the scarcity of fast, affordable, and reliable techniques, continue to constrain advances in Si analysis.\u003c/p\u003e\u003cp\u003eThe quantification of Si in plant tissues is traditionally performed through laborious wet-chemical procedures, most commonly autoclave-induced digestion (AID) followed by colorimetric determination (Elliot et al., 1988; Kornd\u0026ouml;rfer et al., \u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e2004\u003c/span\u003e). Although these methods provide good precision and accuracy, they require hazardous reagents, involve long processing times, and often yield poor reproducibility (Guntzer et al., 2010; Kraska \u0026amp; Breitenbeck, \u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e2010\u003c/span\u003e; Taber et al., 2014). Alternative approaches, including alkaline fusion with sodium hydroxide or lithium carbonate, demand high temperatures, produce insoluble residues, and frequently lead to incomplete Si-solubilization, particularly in Si-accumulating species, resulting in concentration underestimation (Haysom \u0026amp; Ostatek-Boczynski, \u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e2006\u003c/span\u003e; Kraska \u0026amp; Breitenbeck, \u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e2010\u003c/span\u003e). Furthermore, these destructive procedures preclude subsequent analyses on the same sample material.\u003c/p\u003e\u003cp\u003eIn addition to colorimetric methods, instrumental techniques such as inductively coupled plasma optical emission spectrometry (ICP-OES) have been employed for Si determination in plant digests (Barros et al. \u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e2016\u003c/span\u003e; Haysom \u0026amp; Ostatek-Boczynski, \u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e2006\u003c/span\u003e). While these approaches offer excellent sensitivity and multi-elemental capability, they still rely on wet digestion or fusion steps for complete Si extraction, which increases the analytical cost, reagent consumption, and waste generation. Moreover, silica polymerization and precipitation during acid digestion can lead to Si losses, compromising accuracy and long-term instrument performance due to nebulizer clogging and residue deposition in the plasma torch (Langenfeld \u0026amp; Bugbee, \u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e2023\u003c/span\u003e). Consequently, despite its analytical robustness, ICP-based techniques remain resource-intensive and environmentally demanding.\u003c/p\u003e\u003cp\u003eIn this context, energy-dispersive X-ray fluorescence spectrometry (ED-XRF), which has recently been adapted into portable XRF analyzers (pXRF), offers a promising alternative for Si determination in plants. The technique enables rapid, non-destructive, and multi-elemental analysis of plant tissues with minimal sample preparation (Costa et al., \u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e2023\u003c/span\u003e; Lima et al., \u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e2024\u003c/span\u003e). It operates by detecting element-specific fluorescent photons emitted after excitation by primary X-rays, using high-resolution silicon drift detectors (SDD) (Towett et al., 2015).\u003c/p\u003e\u003cp\u003ePrevious studies have focused on quantifying nutrients and trace elements, demonstrating strong correlations between pXRF and conventional laboratory methods (Queralt et al., 2005; Singh et al., 2020). For instance, in rice and millet grains, pXRF achieved deviations below 2 mg kg\u003csup\u003e\u0026minus;\u003c/sup\u003e\u0026sup1; for iron (Fe) and zinc (Zn), with coefficients of determination (R\u0026sup2;) ranging from 0.79 to 0.98 compared with ICP-OES (Paltridge et al., 2012). The portability of the instrument additionally allows in-field measurements, enabling real-time monitoring of plant nutrient status (Soares et al., \u003cspan citationid=\"CR37\" class=\"CitationRef\"\u003e2021\u003c/span\u003e; Silva et al., \u003cspan citationid=\"CR35\" class=\"CitationRef\"\u003e2024\u003c/span\u003e).\u003c/p\u003e\u003cp\u003eDespite these advantages, studies specifically addressing pXRF calibration for Si quantification in plants remain scarce. Reidinger et al. (\u003cspan citationid=\"CR33\" class=\"CitationRef\"\u003e2012\u003c/span\u003e) evaluated the accuracy and reliability of the technique using synthetic matrices enriched with SiO₂ (0\u0026ndash;10%), obtaining an excellent linear calibration (R\u0026sup2; = 0.998). The increasing use of pXRF in agronomic and environmental studies highlights the need to adapt and validate the technique under different analytical conditions and plant matrices, since instrumental responses may vary depending on the analyzer model, X-ray tube configuration, detector type, and measurement atmosphere (Lemi\u0026egrave;re, 2018; Towett et al., 2015). Additionally, sample characteristics such as moisture content, particle size, compaction, and organic matter composition can significantly impact fluorescence intensity and analytical precision (Lenormand et al., 2022; Ran et al., 2014). Therefore, developing matrix-specific calibrations is essential to ensure data reliability, reproducibility, and comparability across studies. Standardization and validation are critical steps toward establishing pXRF as a routine tool for plant nutritional analysis (Horta et al., 2021; Touz\u0026eacute; et al., 2022).\u003c/p\u003e\u003cp\u003eAccordingly, this study aims to evaluate the performance and analytical reliability of portable X-ray fluorescence spectrometry for Si quantification in plant tissues, using autoclave-induced digestion as the reference method. The results are expected to advance the application of pXRF as a rapid, reliable, and environmentally sustainable technique for routine Si analysis, contributing to improved agronomic management and crop productivity.\u003c/p\u003e"},{"header":"Material and methods","content":"\u003cdiv id=\"Sec3\" class=\"Section2\"\u003e\n \u003ch2\u003ePlant samples\u003c/h2\u003e\n \u003cp\u003eA total of 374 plant samples, representing a wide range of Si accumulation capacities, were analyzed. Samples were obtained from the Soil Environmental Chemistry Group (GQAS) experimental collection, including rice (\u003cem\u003eOryza sativa\u003c/em\u003e, n\u0026thinsp;=\u0026thinsp;26), soybean (\u003cem\u003eGlycine max\u003c/em\u003e, n\u0026thinsp;=\u0026thinsp;42), maize (\u003cem\u003eZea mays\u003c/em\u003e, n\u0026thinsp;=\u0026thinsp;250), cowpea (\u003cem\u003eVigna unguiculata\u003c/em\u003e, n\u0026thinsp;=\u0026thinsp;20), sorghum (\u003cem\u003eSorghum bicolor\u003c/em\u003e, n\u0026thinsp;=\u0026thinsp;12), beet (\u003cem\u003eBeta vulgaris\u003c/em\u003e, n\u0026thinsp;=\u0026thinsp;6), and lettuce (\u003cem\u003eLactuca sativa\u003c/em\u003e, n\u0026thinsp;=\u0026thinsp;6). All plant materials were carefully washed to remove impurities, oven-dried at 65\u0026deg;C for 48 h under forced-air circulation, and ground using a Willey-type mill to pass a 2 mm sieve. Subsequently, the samples were homogenized in a ball mill to obtain fine powders with uniform granulometry.\u003c/p\u003e\n\u003c/div\u003e\n\u003ch3\u003eSilicon determination by the standard method\u003c/h3\u003e\n\u003cp\u003eTotal Si concentrations in plant tissues were determined following the autoclave-induced digestion (AID) method adapted from Kornd\u0026ouml;rfer et al. (\u003cspan class=\"CitationRef\"\u003e2004\u003c/span\u003e). For each sample, 0.1 g of dried plant material was weighed into 50 mL centrifuge tubes, to which 2 mL of H₂O₂ (500 g L\u003csup\u003e\u003cem\u003e\u0026minus;\u003c/em\u003e\u003c/sup\u003e\u0026sup1;) and 3 mL of NaOH (500 g L\u003csup\u003e\u003cem\u003e\u0026minus;\u003c/em\u003e\u003c/sup\u003e\u0026sup1;) were added. Tubes were heated in a water bath at 75\u0026deg;C for 1 h, followed by autoclaving at 123\u0026deg;C and 1.5 atm for 1 h. After digestion, 45 mL of deionized water was added, and the solutions were allowed to stand for 12 h to complete solubilization.\u003c/p\u003e\n\u003cp\u003eAliquots of 5 mL from the supernatant were diluted in 20 mL of deionized water, followed by the addition of 1 mL of HCl (500 g L\u003csup\u003e\u003cem\u003e\u0026minus;\u003c/em\u003e\u003c/sup\u003e\u0026sup1;) and 2 mL of ammonium molybdate (100 g L⁻\u0026sup1;). After 4 min, 2 mL of oxalic acid (75 g L\u003csup\u003e\u003cem\u003e\u0026minus;\u003c/em\u003e\u003c/sup\u003e\u0026sup1;) was added to eliminate Fe and P interferences. The colorimetric determination of Si was performed by UV-Vis spectrophotometry at 410 nm.\u003c/p\u003e\n\u003ch3\u003eSilicon determination by portable X-ray fluorescence (pXRF)\u003c/h3\u003e\n\u003cp\u003eSilicon quantification was performed using a portable energy-dispersive X-ray fluorescence (ED-XRF) spectrometer (S1 TITAN 800, Bruker, USA) equipped with a 4 W rhodium X-ray tube (6\u0026ndash;50 kV, 5\u0026ndash;200 \u0026micro;A). For pXRF analysis, plant tissues were oven-dried at 65\u0026deg;C, pulverized in a ball mill, and sieved to \u0026lt;\u0026thinsp;300 \u0026micro;m to obtain a homogeneous fine powder. Subsequently, 100 mg of each sample was loaded into XRF sample cups and sealed with MYLAR\u0026reg; film (3.6 \u0026micro;m thickness), which ensures high X-ray transmittance and minimal background interference (Fig.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e1\u003c/span\u003e). Fluorescent X-rays were detected using a silicon drift detector (SDD) featuring a graphene window, an energy resolution\u0026thinsp;\u0026lt;\u0026thinsp;145 eV, and a count rate of 450,000 cps. Each sample was analyzed in triplicate, in the \u0026ldquo;Plant Mode\u0026rdquo;, with a 60 s acquisition time (Lima et al., \u003cspan class=\"CitationRef\"\u003e2024\u003c/span\u003e). The complete dataset was randomly divided into two subsets: 75% of the samples were used for model calibration, and the remaining 25% were reserved for cross-validation of the predictive model.\u003c/p\u003e\n\u003cp\u003e\u003cbr\u003e\u003c/p\u003e\n\u003ch3\u003eModel performance evaluation\u003c/h3\u003e\n\u003cp\u003eThe performance of the pXRF predictive model was assessed using standard statistical metrics as described by Sevastas et al. (\u003cspan class=\"CitationRef\"\u003e2018\u003c/span\u003e), including: (a) the Coefficient of Determination (R\u0026sup2;), (b) the Mean Absolute Error (MAE), (c) the Mean Absolute Percentage Error (MAPE), (d) the Mean Squared Error (MSE), and (e) the Root Mean Squared Error (RMSE). The CV quantifies the proportion of variance in the observed data that is explained by the regression model, providing a measure of the model\u0026rsquo;s predictive capability. According to Li et al. (\u003cspan class=\"CitationRef\"\u003e2016\u003c/span\u003e), R\u0026sup2; values below 0.50 indicate an unacceptable prediction, values ranging from 0.50 to 0.75 denote an acceptable prediction, and R\u0026sup2; values equal to or greater than 0.75 reflect a good prediction, indicating that the model successfully captures most of the variability in the measured data.\u003c/p\u003e\n\u003cp\u003eThe MAE represents the average absolute difference between the measured and predicted values (Eq.\u0026nbsp;1), providing a direct measure of the magnitude of prediction errors in the same units as the observed data. Lower MAE values indicate smaller average deviations and, consequently, higher predictive accuracy. According to Li et al. (\u003cspan class=\"CitationRef\"\u003e2016\u003c/span\u003e), an MAE equal to zero denotes perfect prediction, values below 10% of the mean measured value correspond to low error and indicate high model precision, MAE values between 10% and 20% are classified as moderate error and suggest reasonable predictive performance, whereas MAE values exceeding 20% of the mean measured value are interpreted as high error, reflecting reduced model reliability.\u003c/p\u003e\n\u003cp\u003e\u003cimg 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qJk8nRa4nHPOOeWeBO+oN8H9iTPeMuJipr1gXYtRexbCW8yInQZmOngIPf+0EPMqK4+yGJmVOVxjrq83lSZvTyEGjdjE77zzne8sf6tg/l8XyS0UOmGNi7xU5uzEOWUqdufcc88t5xaS2vi676R4IHYsL9k8j7zGd7HjncLqiQ7qyU9+crFHnfekLQKvuOKKsvCUbdobeim9eS/0F4JL3+VlK3UWDM5p//TT47yU4zCgEgpGNNIFhBhRSfhxUNR1Lmzd1LZ4zdF2VT/tOjy++oqK123bitKi2V/8xV8sz+UFQmJsu+KT88rONPoYTjP1xkwjh5b0WaBNoHdnhH1Xn6mv8lvPTlfoQ/WrZnArBpTSQgALn9CH8Uo7r48lWufapxGh8ma29TycT0R893n6zqIJVp5OmWVkwGAqprQYltFGFY1GAKZ9CVQi6SUveUk5b8RTN/r3utNJLnkGZOpLA85wdttttzK66MJjyOXvu4x8Jg+rcIC6Qt3vPP9sh+nfGnw+DQS0xVxCH8SbrMzhDVWrS2yaQQIvq0pdBzTKVAX/27/929IwLiTKVSiLxostjpte+exnP1sGDZ6TMBCvFZYOPJU6zWkbdu2S3+gMV+ZwDZ6duaDDZpPqhjZs1OOE6tXxuXqkY+125ksVeaacunmmPSc6iIxp9vfuGzVNMzlQ+gKPJ7Fnp57Rvk77TESxS2XxL//yL8sO7aPwstqeg6PlL/7iL8oOPkKpeDkJOIsDzRaaDdDnw3X93gLsbggCzGrKO+1ud0ZQn0jkvutd7yoimHf2/PPPL7OJvJ1EHzgX6A39sbhcOoKoNNsHYQ6EX7dN59F9xzveUZxiFojzyJ544olFILNFzouK/opdstnnP//55d5ekCOt+m5Ce64Lo8z06Yee8pSnLDdoGIUQdnQ9yr2nfeAFp82gwWte85rBxhtvPGhF2eDyyy8ffjIYfOITnxi0GT3YdtttB1deeWU51xbwoBWqg80226x8XmkNfbDlllsO2soxeP3rXz9oC3/4yfJcddVVg6233nqw6aabDnbdddfB7bffPvxkedoRUHmmVjQPWqMbnl2etlIN3vjGN5bvuXc7khq0FXVw7bXXznq0I7ThVcK9pa3cgyOPPHKwxRZblEMZsJcdd9xxcN111w2/tfK4z/bbbz948pOfPDj22GOHZ1ekbYgH+++/f7HBtsEZtAOt4Sd34++2cSufP/e5zx20Ddzwk7BUOPzwwwcbbrjh4DOf+czwzMycfvrpxRa22267lTraTnbw1re+tbSXc0HbpQ3T3p188snDs/dwwQUXlLZUvTnhhBMGragbfrJ0kYZDDjmktMuf/vSnh2cHg1tvvXXw7Gc/e/Cc5zxn8O1vf3t49t7xzW9+s9TfVgwMz8wv+rODDz64lNMll1wyPHsP0rvRRhsN9tprrwV7ppn40Ic+VNpL9jXKxz/+8WJzW2211QrH5ptvXtrI2n+3YnHQisTBnnvuWf7fpRV8pS8/4IADln2mTPQF6sooH/vYx0pduPjii4dn7uHOO+8c3HDDDUUfXHHFFYMvfOELg1YQD1oxO2gHncNvDQatoB204nHQit/hmbuR54cddthghx12WJb/rfAcPO95zxvst99+g3ZgWM5VbrnllnId7QkdgVawF5s97rjjyt9djj/++GK3c+0z3vSmNxWb+fKXvzw8syLuf8wxxwye+cxnDm666abh2f6zKMNqngojCurf9ICRUaWuuDfqEK/KC8BlbsTQFt5ycTGm7o2gXcfIqDuCqhjBmMbmpeV9EBM6yRPLM2Ek1eZLGQmNw3WEAfBI+G4rQkoco2m42Q7e5HDvUdbeFmY6B8pd+fKWixUSC73QCCPhYeUdYK+jr/Y17Woayee77757iTEMSwftDo+FmRShRNOgzfIbtrAyh2uIkWM7c0EsG5tUX1xHe1bhbbIWQL3R7gqvWR28qzx4vGw8b2bKKtpqU9H6lZVZxa0M2oFyiUWsU9HzjUXCV155ZXl2/Uff8fpsfdy4mUReVXWpHSA1n/jEJ5Y7hMrxSNb+m+dTmdlFZTR8QJ/re9rR+pnZTrMG3XKvmKXwffW3YvZWmMBOO+3U7LrrrmXGTgw3r6k4W/1IvbYwALMUZklHvbfu6/r0RH12U/v0jbZ+dG9233GuWx95kqXJs3RRP3nX2exjHvOY4dnp8EzqQdVS49A2+J7n4SFeKixKS6XRVOkJDoYgfqQiNpVhcMlrbDSu3PrOiwVVuBUFyp0tLnCSWGlHVqWymI4lSBkNATF6mOYX4FxjYDT041zlnruK7bXXXrvEp6wuqEgM+d4c841nM41pukUZVrGqYnq5gB0jFgudCbvxPGypQmyY/mFHQlk0jmFpoe0xxa+eT7sbiEGsPSitHF6Zw9Qgm9F2zQXtnDaVyCKeux2kwb+2Tf0xvVqnVZc62mTOBOnpCgudvelVbYQ031tcX3+kvdHfLATKjhAnWvR/fccASx2RR6NIi8/UIwJv9OgKU2s3iKhxwpeIJ067Iqsu0B4n6glfNlH7aQL0uOOOK+EGpvEt3hIOIFaUaGUj3RcBmfIX6kAMjwpQz2E9C+1RbUssq/RblzMK+1Se3ThbC8g420bLl0ZyX/qo+/3Z0Ae5hwXsM/1Oebi+QfjooKDPLIpglVm8URCz2kXBWe2vkeWdskE8Y9hhhx2WW11YRyAaZRk+zkB0NASvkZ1G38Kjww8/vMRsjR5WCfLeERc8DirGuBV6BKuGyzPxUMzFmOaCyiDtYmzE767MocGe5DHuQmzxQFuNOe0hP9/4xjcWcTafiB2yKTq7UD7K3ahZx1730l0sLFoxeGE7dScIIl7gvXxhIxrDcQ35bMw0GJjrQIFNs1+N9jSwQXXIb2pM12z4jbrtNwsRMzhuUFnhSZlLen332muvLYJOmwHxYzoA8eTTNuzaL96a0YWXcz3YjBmluXpADeiIA7/TgdY39/lXPKC6Y9cPbeok1DMepG4Z6kTlj5mtmj/TMqmc3Geu5cSDVZ+jXpcXzDPJ+67Alw/2lx3tZ0aRTv0Se5c/XTyjtlF/UGfy9D+O0e+imyb1YRrGpalu2fiUWWIR+4C8l2azXaMziTVviajZvHnyjh34HiE7irUv8rzb34tpJUhHPejyj9eX2KzbZRG3ZujUT4PK7bbbrnnhC19Y3qpokZL7E4kV7bnnVwajELNEaJ319Vs2If3jBjXKVj6YkVWe2lRpdb/RtGpz2I/P5lL2BDB90vVAj4Nnl62Ls53rgHgxWbh9iToYiamICoI3oItRDNWvsTUCYAQqgVWHXYycGKTv+c04TwH3PAPVwDCgOt0/Cc/DOAkB/7p+13ihM2Nkvmsh01w7k2lxD945QtPzrwwaTd6a2Vb1qyC235qLB0F+yte6CG0+sJiKWIX81mD51/SczmixYXsaB3mhU/OvDs6qVf/3Frdf//VfH357PBYeeKlFXSBnk2oLEtjZxhtvXMRL9RyxCatxiWFlZVGAbdrGIa+sVOWZVr5sm4DWyBJF48rafS0s0FizHWmQPvscmz4bN9Wkrlgw4NnqbzTcBIMtvITzQINqYGja2v1HMT0o7fKhK6jYpelD+ajzILzkl3aEp7AuxPS3WRV1X+cg/dLI6+l+o14SEPIGtq7Hk8aeDUYt9JDHbFsHOZeOY7F55jOfWbb6kR7TnLxGBq86KZ0je5qpQ2Mr0q/89tprr1K2ZqrklfxkowasOt8utvJh90SAzyw6sWhIudjXWTnA3xboKCcDHOUkvMbCE2EK3Zm0SnVAKCdlqyyVi22PiAd2N7q41NvwzJ7Z43P0WdkoQaMuVcGr8zb4JGDYlWlT3jdiQ/lbBGPLIb/1t1XsXjoDYqWmqQpfadJG6b/GpUnazRyxe2nyHWJDmghY1xznjOkbtW7U2a8uyoazyCCJPc2E3yoD+cfWujOYykLbYPag7rmuHHg5OQPkdRftAJ1g8VLtp13Db0YFKOeXNpJQ7nrolY8yGbdomSdYHaoLuOuzE5uObjtJ2ApNlJ4dd9yxnNO+qp/2gB8V+X5PA8w1FISte2a/myREaRt1iPaabSDXNxZcsGqoxOUwbJ3nuM6P4fmMkTEClb1ruDCKMCr1OYE7OkLRAGksXUfB2CvN9JC/J6GAvWLTZroKVUUYhUH4nnTMNbZkLqgkGkIe50mGNy0avWni73QmRqujDc40dGOEViU6ACNh5SYfNDYgVm1v1gdqo6Vx1Dizb50Qj4PyM5qfadChYyPK2av0EbtEkoZTR0lAuq44XW9cOeOMM0p5+q4OV8OpjEffnOX+Olvik62aulKnDBi9GELjbeVrV7SyeZ27NPEmEbfyntCUJuLHtjJdsUOk2ghc40sYqdOeTSP9mc98pty3ClaDUDMHkzou1zf6Jxi66HwM4DTspvCq94GXonZGOnyf8aCo8zp+n7mnfRi1CVYEd0Wr39hqRh6awSGIPbsydF75qQ/jvD19hkdYXskfdkBEGrjAYMCAYSZ04OxORy0f1D35419OAB2eNtLUanc6U/tB3Or4rYomPJQTW2Cj0G4rJ2/Zcv06GHBdNu7eZk665cS7yy49kw7e4Fs5EZBHHHFE+b2/u2LDPdkNJ0O1kYp8MXAiVrW1Om5tGJHAi6fT532Td+oiMex7hJF/1Qn5W2fY2P6f/umflr5jNE2moNme5++mSR/m2aVJedQ0GZxJv3u6xmjf10fkiYG7NCnnrgCT/+qZc9oR7V0Xae7OVhKjdlVhRwYHykW7oM1yfeXfDSNka+6hDvuMfbF1s3KuWQUlqq2yU55XbZ9nMpPJxuT1qBNNOSijqh20i55J++l63fbT/c0Ma6O1+57NLA2Hi/uoE3W7KbbBRseFPthiy7NzVswG4ctO2YpZFL+Tx65f87ZbHvLW4FOYzFKwreVoE7SgtJW/rIC1grUdhQ/awhx+cg9thR20HWBZgdc2YCusvEZrcGX1n9Vwp5122vDs3bSGNTjqqKPKPXxn9POZaDvlsiOBlXttYzw8ew9WZLqmFY9tpRieXfW0Blfyqu0UVsnRNiLDKy8d7B7xghe8oJRH2xCUlaD+3zZcc145PVfk2TS7BFTOO++8Youece+99162K0XbMS9bETqJtlMfvOIVryhps6K5FYRlRXLbmJVVpO1AoqymbRvAwUtf+tJBKxYGbQdQjrbTLc+4++67L1fGbSNbVotaRfzmN7+5XE+98CzqnGu5X9t4DX9xNz5rxU1ZEfvj4cpXv3Neuqzo/URnpw7PuO+++5bdPlzL33CfO+64o9TltuEs56A+q1tnn3328MzytA16qVvdld6wM4T8lQ+tyC47c9x+++1lFbj7qCutICi7MbQDnBXSq976fStghle8e7cS3/WbdqA6aEXw8JPBoBVNZUWvum6l7pe+9KXhJ0uDm2++uTy/NNvFYueddy7/f/GLXzy2zR2lHTwV+5B+9tOKgOEng0HbURc7ZHfd/MShhx5a7J79a4PbgdaycmIbrVActAK45LlVyjfddNOycvLdPfbYo9hYd1V8tWXPbzV1tz/wLFZ1e071pGtrrcgp9elVr3rVMruEe2nb1Y199tln0IreYj9g89dee+2gFZ7lvmxEPbPq28417EAatA/+9ezsz8pvds2OapocrUgpdVO70LXpVhgPWlFa0tQK3eV2rrnxxhtLOUlTO4AatGJs+Mny9G2XAKvapXN0NwZtlLzZZpttyu4ZVtHXQ/rYafc38vaggw4q6bdTBtvVFp944omDpz/96cUWlGHloosuKufZnF2AfJcd6ifYktX/Ffls5wW27b7tIL98X7vkXnYv6l5b+b3sZS8bPO1pTyvtAFtzTtnaUYBdeN6KNpiNtgOQZdd/1rOeVf5vx4LutT2fZ77hhhuGZ+7Gd6TZzjddux2H70qPe8hP11MGbFXe2sGgHUwNvz0o9dgODC9/+csn7pbUZxZcsOqcZSYDltEahXtDO2IplV3jqAPvopNnYAxewzpboXfRGdeGurt1BjyrhsR9GbmGaXVFJZKvtSFpR25FzL/zne8cfPjDHy6N9HyiY5DXyoJYdejkNAYLIb7nKlivvvrqZaKa4PLcGrdxg61RiCODNzb33ve+d3j2HoheHZNGz3e7ECbq02677bZcw0lA1zo2Lr+IUvn59re/fXhmdt7//vcP2tH64KSTThqeGQy+8Y1vlE6BmJ0NosBWNTouQmMUglF91fASLxVthk75SU960uDoo49ertGvEFg+P+KII8Z+fuGFFw6e+MQnFuFbMeDUfhBJ49oh9r7hhhuWwQSBsZSQ1zp96WOTyoh9nXnmmcNvTEb+EVHSLt/HtZ/aX/nZtVflp3Nnq+O2GMIHPvCB8rmtgsbBbjfYYINy/wrnBFs2yOq2xxXbEfrNaHtNTEv/2972tuGZuyGG1VHPqv7Mhk6eTXK0jMsLeSpNBlLjsM2Y5yO4Kuqf3xhMjEuTOuY3Bx544NjP0TfBWtuUz33uc8Mzd2PQetZZZ5VBqn+7h7xT5nXAUJHP5557btmW7V3velcZZGn7tKtnnHHG8Fv3YNDBDnzfcxhofPGLXyz2Nuna8vjd7353GRAQb57Fs46iDdd+uO9HP/rR0vdpL/yf1hhF/bn00ktLHfE855xzznKDYfiObTk9x2jb49md1/8SxjOh3AlhW3/KT220NMtrz2s7sa7jQb3UX+ivliLzE4A5A6ba2o61uK9NC46LKZuNtgCKy9z0lKnW7nR02zmXqcO2kpdri4eay3R1jYV1bVNTrXGWv2GqqLreTYEIDzBlXbfnmHSYfjBNsZSw7YcFVcrLNIa3cJjWsP2IqQTHfKXJVIvQDFMddSpdmbcCsjzTTNPriwUbMz3UNkRl+tFhIZ8podlgY2Jf28Z44vvc2ZzPRkM72kao/Ot+bBbOtY1keSbTUm2DuCyuqh7qhml9Zdi2A+V3FXXH85g2MsVpQ+26PZfpJjF+lfpbU56m4Vx7Ep7LlJ56Py5ERbyoaSzTut1pPNN9pgRN1e07XMnbpe2ASqiE9FpV7/lH0yvMyLP7Ljy3Kem2cyjTjuPaoVbgle9ZsNGdUlsKSGsr1srzyy922Q60m5133nn4jcmYFhdz6BrCTMa1n+xaGyg0oyL0QpupbMU6j6Ldt0uBKVFxzf4eLSc26b6m5D27g/35VwxyNxSlYmpX+oSidD83xcv2u3XQPcQqKvd99tlnqq2uxGezW3bfnf4FW3M9oQLq56Q0sZ+aV9IiLEadFdY0Lk3CCqRJXRj3eR8R1iB2Utrkb0Vom35YaJ9/u4f0s0ll3oXNsT2LgG3eLz+EF7muEKNRTMVbPO37Yoa1heqv7aUmXVv8sbhqU+ZCfjxLjUfuwn7EZLcDgxJ/qi3RXvj/VlttNfzWPahvYsiFrXkeLz/ohjDAd+xS4DlG2x7P7rwwqtFQllHUQaEr6ob8FHctzfLa84rt9x02R4tox/Wh2oKlyIILVp2aTkNlnO3VYZNoR0MlLoSIEYNRVwBCJ2Sxgc6RwXrDxVyoMSmEr7gkDV5FjIyGlLHpRMUkEXJe5zbpUCnEa3Ur8FJA2hm5HQbEPLYj/RLDKE5LoyTmsu6HuipxX28GseCgVmQdqAZAvNc4YdEH2KFFHcqZ7Wy99dalkZsGIo2dydfRxtV5cXrqyrjGUScoz+RLzRv7URL96hjbI5y7h3dbi+lUDzXeVQAqbzF/ytrggNgVvyieTt4bnHmObmOnvqhjxAF712kY1Fh8M2rzBnsOnXC9ZxdxbvKOMO0KROLZ73QmXSFbIWbF3hrISNdoeglSdisv62CHsDIAFdsr1nUc8lXnMW5B51KAPeqIlQO7UjajC1PGceedd5b8EatnEdQ4lJM2thszyga0j2Lhu21yRaxzHSB5J/u4cjr55JNLOSl/NsKOla8ykJ5xuKdy6gpTz6Z8pbu71oCdGIiJk9y2s6f3TGj/XE/9GxUQYsilSR4bZI9Lk5hvfVUVntKkfZN36vw42Lt7TTPg7QtEGcGk/yTUVzUW72lvxtlWmBl1it3TIzPtDtJ3FlywUvtGSyrqbIH/kyBgNKYOK7CrAROyAtY32WST0iDpeEcFwGwYRRuh8U7oyDQ0FQ2oewqod/jc6H6mw3eM/lZm0+qFRj5aLMHIjT4JEKNgeeJVsbwnGt9V7WHlndDo8+RVwSL/5Z/FMl3PXt/QockvnTFRQOyNemMmwWYJqe7r/So6Yx2cjovtjaIzJ0x5HaoItOOADqMrtHxWD7ieOrJxJ6ifl9LiKfez+MhikTPPPLOserY6V8evXNTfijTaUF35GCASLezlkEMOaQ466KDiqatYuMAjNUkg8qjrpEc7ccLRfdnfOAgK+cQ+qpe5m15lQrhtscUWy1YXW8RmkZz0T9pujHhXLpOEUt/RTrINYkp5GkRNA9vhUZRnkwSuz+VrVzwQWfJLmzEOszW+w8Nehd9oORkQqe+1rDkGtDPOjSsn6VN/2GF3IKUNI5B5XWuZw/3ZoGecRrzDwkeM876pawZ+nk0aMJomQs7z17omTdpX5THOaaMt8ezyf5LN9xX9hMHtqhbaBkj6HK99nW2ngbAinBkcbDyvS5q2Qi0obQMz/N+9xzXq0cXfbWUf/rXqqffr3n+aY6khBsniFguexsXpig1rO4HyWsdVhRhBMWBioNrGvRxtYz3YaaedJi46mE9a8TynGFbxRmIFxdpN8/0ue+6556DtDAet2BueuYerrrqq5LV4tXHIM/fsxo2J820HVGXhyLS0IrUsUBGoPy6+ySIsNiEutxXmw7MrYnHN6aefXuL9WmFaFk5WLDJpB3ErLPSqvPa1ry1p6S64gUU68lac2jgsXmhFdHlN8rSI+/IsFhSNoxUhJa7Y4glxuksN9ivmU7y9xSKtqB9+MjvKh92L3R3Xft1yyy1lMYfXOoptRysoykIXdnzZZZeVc6OoF8pJvPG0XHDBBcUmxHGPQzq1UxadtMJ2ePZuO7QAxcKYbhrES4r7HI1rnQmxsdqi7oKuilhcaRIrOC1iH7Vz7HYc7YChLE5SF9uB2PDsivQthnW+WYp9aVi1LLiHtY5CV4buCLaLv2eL+VgZ6v2695/mWGrwivFqPeMZzxjrGTZdyEuxqkbRPEBt49185CMfWeYRd04snP0IJ3ls+gIPi2k/Hlae97lst8WDzOvDE9SdBq8oC96FSTFH4j7lWXcrlmp3rjstPLW8lMIYxt2Lh5XXind0prAM6eCB52WRHtPLFfnkWcdtpcLj6RlcuzuF6/emdkfPd6nT/GxmWrQTvLHsvPuMlVbYFG+xEITR+LOlgK3BzFRIp9hKsz3T4nfg6RuHsC7xqry2rWAq59ia32kTJtXX2jbz/E6LMnKIkR73O3YpZMT0erc9YsvaqFGbYX9tvzf1M/CEqmO8euNieWua3Gta2Ks01bo9ijhfaeK17fOs0kKzFPvSsGpZcMEa+o9YQg074TI6AGhHuSV+WKPfjV9bGYg9i4SEi4Dw0DnYf7XvU2LywWbm4lDlFbE2bup+EvbNM+VJcFax3oWII4THxW0RWkSVjrqKNhAnps/EGXdDWrroKLuddg1nGCfeLBq08AXduD8CdtL1dbjKsSv2/M1+Rn9DyJ544olFPBI74tQqFrwQQ4TjpKlAeSe9BNMk4eCe0lixNyj7NU1dp3wrYr0sOpRHBiDjyqXPiI+0QFKa1Z9JC/kmwaYgZIJdd7HQ1P6l7NHArIZgaDOEEhiMTConeamcxCJ2y6KL893PCE7T5sJJRsvJIhwhK2yKfdRngal65WeA1RU6nk9dUe888zi6Qp3wFapk8DVuoOb67EP4yDjxidE0sT111jMaqHWx/oJgVReXUhhZCAvB/Y+ywiWEIUSFDezFqFl5ONpoEik229YJ7HsvXzda0dEQe15hCoLPOde0KGPamLv5QOcjdtOiJp2+t7RAZ0aM6ewITRtOWyXs+7yTVoZ2xeNsWLVpMZPVnDzaXQgOeW2hCHEw6pm04ENZiY2zYrUKfgLOoidijCdMfrqWtHh2q3jlrxjyKg51kISp7xMV4vuk0Y4bVRRIu5XVVTz7zEbvOmOdNtuQJwYfRA3b8bakGqcn1tCCMIJIzK3v856KWyaOiGUrY+VjFRnSQHjLH/Hq45AGeeH6BAAvr2eSXt4xL04QVys2tsb1+o1YXSLXMykzeUSoOsREEiueZ7Rc+gZBxUY8r/Qce+yx5W+iSP7PZYZC/a+r6Ak0K4vZA/smpMyEGOiIh+vmizxUThbgTXpVMvtVRhYRiuNUTq6lnDwvWz7hhBNKLLTPYFBBNLMTh3JStt7axS49Gy+o2HrxjRVtCg+mFebdHSnUEWKVvdjInSD2DOyWgLQ4j7Cu7Z56QIyqFwbqntPza6vUA4NTi3HlO0HtebtpUhdcUwxrHeD7V1oMLOSbZ5Imb0I666yzlqXJwseZ1nnworunNKj/XcEewurIGm1HNfldpeE+BxGx2267Leu4asdRISxsl6ETIDZXppHktSOcdIbVk0sU8RDaFcD/V4V5Sosto+ayYwRPne1BdKwC1S0qgo6NKCW6dDK8g8ScTtZbpSZNW09CyINOihAgyrqYBrXSmHjSAdcOr0Iw+r0FTgcffPDw7N3oYO0QwFtI/NUFYEShMrPAy3Zl1Rsmn+0IodOUdh5u+a/8rf4ncnXyxJxFSL5vRTfhoPx0ukSr/8sXC5z8zr8VAtHrPAkQ3+e18my2oiIgrfC3ilX+VjwTEeNZbQ8zCZ0/YUDgerbR9BpweKvXqPeWWCY4iFXPwq6JHM9KQCl328b0GaKIh1qeEjrKgOixg4m6Ohd49C1WVQfZHrsk8NiC6wsB8Dkh38Ubr3h11WflOQnXUk5sqdql8qrlxINvZqXrpVUPlD8vq7T5nUEZO1He3tzD1uugkv0ZTCtDIru7SBAGNa5HeNZn0Eawewt2pbm7G4U6xNYt7vOcru9V1zVviU73lybtmLyH7xLY0sQv1F1gJazKM7h2bf+IX2mSToNHzzFuZ5CK8r3wwgvLYjD1UPmEsDoTwRqWQ6NsClEjz8NYhWSF2LCHoq1rvKf73kL42gOPJ3e0odU5EhCryjR5PGy3ooOYlkmCVedJWOpkalwlsUpomeqbC9Knk+OJ4U3uiikQH7w+zuuUdK5deIgIDKJwXBiCNBByvFq8pTpSU5hWTROiVdRVCG+dL4+SPNt8882LsNXRygfl4j411pZnz3X9ht2YEiaqpYUHddwqbEKf1656hggfHi3XYRPOdQdJwgFcl4CpQmASnkd+8C7zcEkf4VU9dqPphXR6FjsU8L5Kn/S6p894KcdNBfcFQssgwBZzBgyeXX7yuBGOo/V3NohfeywTfHZ/MCAj8JQbMe8YF8tZY0Z582cLoVBObIZXUjmxE/ZSy2lcORN/bFBd4f1UTuI7PR8B6f+1HWHH7En98jzjBtWegZeTYGRj7Es9IliV+WhdYw9+49quK9Sl+5w+lyYCWprkUTdN4/KkmybeWiK8myZlOdNsTQRruK8RwRqWQwNo700CT4c1ioVR9uUULjDu82khcOwHyqM71051rhAevHM8N9Oi8yXMdSg2ZOZRgec1FeeZdUKm4wmEEBYDgvWTn/xkEYyEGeFj+nncAr5p4NHm2VNXtAGhv5hVqYLVbFcEa1jdmV+lEJYcvHbEmin0cXjDGC9DN17s3mCcREi610IcPLZzgVfNG0FMX/JWVXhfCFlhE6aKI1bDYsIDZ99oNsmjKq703opVddKMBxsf57EP/UJcu/bJCyHGeZFDWN2IhzUshylBU6ri10xpjXLKKaeU6VPTkJNWA08DT6VVvjV2cD6pU9mmuEMI41Enhb8IRbFd1Li3ioUQwmIRwRqWg/cUk6bpfU5gzrfIDCEsLOI+LeIT9ynsJ1PMIYQ+EcEaQgghhBB6TWJYQwghhBBCr4lgDSGEEEIIvSaCNcwrIk5stu+NQ7bgCSGEEEKYK4lhDfOKV4Haw9QiruOOO26ldha4t9jw2wpoG3ITzTb8Hn37TQghhBD6SwRrmFe8ZtAWWc9//vPL6wsXcuWxN8l4lag3K3lDFVO3y4G3z3itaQghhBCWBgkJCPMKj+o+++zT7LLLLgu+TY63/7znPe8p4QiPfvSjyyb/9mStW3eFEEIIYWkQD2tYbfF+74suuqhM/3tH+Kc+9anmkEMOKa+uPOOMM4bfCiGEEELfiYc1zBu8mV71es0115Tp+YVmrbXWanbaaafymlmvsMzYLIQQQliaRLCGecMrHg844IDmDW94Q3YICCGEEMK9JiEBYd6wQ8D2229fFjmddtppw7MrYvX+DTfcMKfXvdp1wFQ/L+q0WHx16KGHJiQghBBCWGJEsIZ548orr1y24Oroo48enl0ROwnsvffeZdp+GtFq0RSh+o53vKPZaquthmdnJ4I1hBBCWJpEsIZ54/jjjy+r9O3DusceewzPrghPrMVRvKbTwGTtOLDttts266233vDs7ESwhhBCCEuTCNYwLzCrV77ylc1ll13WnH322c3mm28+/GTxiGANIYQQliZZdBXmBbsC/PCHPyz7nz7ykY8cnh2PKX7fn8tx1113ZT/VEEII4T5CPKxhXvj617/e7L///s3666/fnHTSSc2aa645/GRFvvKVr5Twgfvf//7DMzPDZL1e9aCDDmo22mij4dnZiYc1hBBCWJrEwxrmheuvv768YUqM6UMe8pDh2fHwlP7oRz8qx49//ONZj/rdeFhDCCGE+wbxsIZ54dRTTy1e08MPP7zsxdoHLr744uZ1r3td89SnPrV53/veNzwbQgghhL4TD2tY5XjD1Y033tiss846i7rYyljsW9/6VvO1r32t7PN60003lW2zxMDyANfD3yGEEELoL/GwhlWOxVa2sbrtttua888/v1l33XWHnywsFmYdfPDBzdVXX122wRJGcMcdd5T9Xh/2sIeV7zD/U045pdl0003L3yGEEELoHxGsYZXzgx/8oDnmmGPKwqgjjzyyeeADHzj8ZGER73ryyScXb689XnlX616vvMCVww47rLw1K4QQQgj9JII1hBBCCCH0msSwhhBCCCGEXhPBGkIIIYQQek0EawghhBBC6DURrCGEEEIIoddEsIYQQgghhF4TwRpCCCGEEHpNBGsIIYQQQug1EawhhBBCCKHXRLCGEEIIIYReE8EaQgghhBB6TQRrCCGEEELoNRGsIYQQQgih10SwhhBCCCGEXhPBGkIIIYQQek0EawghhBBC6DURrCGEEEIIoddEsIYQQgghhF4TwRpCCCGEEHpNBGsIIYQQQugxTfP/Ia6vRtT86HUAAAAASUVORK5CYII=\" style=\"width: 546px;\"\u003e\u003c/p\u003e\n\u003cp\u003eThe MAPE expresses the average percentage deviation between the measured and predicted values (Eq.\u0026nbsp;2), providing a normalized and scale-independent measure of predictive performance. Lower MAPE values indicate greater predictive accuracy, as they reflect smaller relative discrepancies between observed and estimated results. MAPE values below 10% are generally interpreted as excellent predictions, values ranging from 10% to 20% are considered acceptable, while values exceeding 20% may suggest the need for further adjustments in the regression model or calibration procedure (Sevastas et al. \u003cspan class=\"CitationRef\"\u003e2018\u003c/span\u003e).\u003c/p\u003e\n\u003cp\u003e\u003cimg 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\" style=\"width: 480px;\"\u003e\u003c/p\u003e\n\u003cp\u003eThe MSE and the RMSE were also employed to evaluate the predictive performance of the model. The MSE quantifies the average of the squared differences between predicted and measured values (Eq.\u0026nbsp;3), thereby assigning greater weight to large deviations and effectively penalizing substantial prediction errors. The RMSE, obtained as the square root of the MSE, provides a more intuitive assessment of model accuracy because it expresses error in the same units as the observed data. Lower RMSE values indicate stronger agreement between predicted and measured results, with smaller dispersion around the 1:1 relationship line.\u003c/p\u003e\n\u003cp\u003e\u003cimg 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\" style=\"width: 494px;\"\u003e\u003c/p\u003e\n\u003cp\u003eIn this study, MSE and RMSE values were interpreted relative to the mean of the measured data. An MSE or RMSE value of zero indicates excellent prediction and a perfect fit between predicted and observed data. MSE values below 1% and RMSE values below 10% of the mean measured value were classified as low error, reflecting high predictive accuracy. MSE values between 1\u0026ndash;4% and RMSE values between 10\u0026ndash;20% were considered moderate error and acceptable performance, whereas values above these thresholds were regarded as high error, indicating reduced model reliability and potential calibration limitations.\u003c/p\u003e\n\u003cdiv id=\"Sec7\" class=\"Section2\"\u003e\n \u003ch2\u003eStatistical analysis\u003c/h2\u003e\n \u003cp\u003eThe collected data were subjected to univariate statistical analyses, including the calculation of frequency distributions, minimum and maximum values, mean, median, standard deviation, and coefficient of variation. Empirical calibration was performed using linear regression, while model validation was based on Pearson\u0026rsquo;s correlation coefficient (r) to assess the strength and significance of the relationship between predicted and measured Si concentrations. All statistical procedures were conducted using OriginPro 2019, SISVAR, and R software (version 4.0.2).\u003c/p\u003e\n\u003c/div\u003e"},{"header":"Results","content":"\u003cdiv id=\"Sec9\" class=\"Section2\"\u003e\u003ch2\u003eDistribution of Si concentrations in samples analyzed by the AID method\u003c/h2\u003e\u003cp\u003eDescriptive analysis of Si concentrations in leaf tissues revealed a wide variation among the evaluated species, with values ranging from 1.07 to 19.23 g kg\u003csup\u003e\u0026minus;\u003c/sup\u003e\u0026sup1; (Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e). The overall mean Si concentration across all samples was 4.48 g kg⁻\u0026sup1;, with a standard deviation (SD) of 3.03 g kg\u003csup\u003e\u0026minus;\u003c/sup\u003e\u0026sup1; and a coefficient of variation (CV) of 67.6%, indicating high heterogeneity in Si accumulation capacity among the studied crops. Additionally, the plants included in this study were subjected to different Si sources (or none) and application rates, as well as distinct cultivars within the same species, which likely contributed to the observed variability in Si accumulation, even within a single crop type.\u003c/p\u003e\u003cp\u003e\u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab1\" border=\"1\"\u003e\u003ccaption language=\"En\"\u003e\u003cdiv class=\"CaptionNumber\"\u003eTable 1\u003c/div\u003e\u003cdiv class=\"CaptionContent\"\u003e\u003cp\u003eDescriptive statistics, including mean, standard deviation, coefficient of variation, and concentration range of silicon (Si) in leaf tissues, determined by the autoclave-induced digestion (AID) method\u003c/p\u003e\u003c/div\u003e\u003c/caption\u003e\u003ccolgroup cols=\"4\"\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e\u003cthead\u003e\u003ctr\u003e\u003cth align=\"left\" colname=\"c1\"\u003e\u003cp\u003eSpecies (n)\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c2\"\u003e\u003cp\u003eScientific name\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c3\"\u003e\u003cp\u003eSilicon (g kg\u003csup\u003e\u0026minus;\u003c/sup\u003e\u0026sup1;)\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c4\"\u003e\u003cp\u003eSD (\u0026plusmn;)\u003c/p\u003e\u003c/th\u003e\u003c/tr\u003e\u003c/thead\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eRice (n\u0026thinsp;=\u0026thinsp;27)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e\u003cem\u003eOryza sativa\u003c/em\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e9.25\u0026ndash;19.23\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e2.79\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eSoybean (n\u0026thinsp;=\u0026thinsp;42)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e\u003cem\u003eGlycine max\u003c/em\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e2.18\u0026ndash;6.47\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e1.24\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eMaize (n\u0026thinsp;=\u0026thinsp;249)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e\u003cem\u003eZea mays\u003c/em\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e1.07\u0026ndash;8.17\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e1.88\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eCowpea (n\u0026thinsp;=\u0026thinsp;20)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e\u003cem\u003eVigna unguiculata\u003c/em\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e2.48\u0026ndash;4.40\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e0.62\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eSorghum (n\u0026thinsp;=\u0026thinsp;12)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e\u003cem\u003eSorghum bicolor\u003c/em\u003e (L.) Moench\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e3.79\u0026ndash;6.28\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e0.93\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eLettuce (n\u0026thinsp;=\u0026thinsp;6)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e\u003cem\u003eLactuca sativa\u003c/em\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e2.09\u0026ndash;3.10\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e0.42\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eBeet (n\u0026thinsp;=\u0026thinsp;6)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e\u003cem\u003eBeta vulgaris\u003c/em\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e1.97\u0026ndash;2.76\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e0.30\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eOverall mean\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e\u0026mdash;\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e4.48\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e\u0026mdash;\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eStandard deviation\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e\u0026mdash;\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e3.03\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e\u0026mdash;\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eMinimum\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e\u0026mdash;\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e1.07\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e\u0026mdash;\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eMaximum\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e\u0026mdash;\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e19.23\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e\u0026mdash;\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eCoefficient of variation (%)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e\u0026mdash;\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e67.58\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e\u0026mdash;\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003c/tbody\u003e\u003c/colgroup\u003e\u003c/table\u003e\u003c/div\u003e\u003c/p\u003e\u003cp\u003eThe distribution of Si concentrations among species reflects clear phylogenetic and physiological differences in Si transport mechanisms. Members of the Poaceae family, such as rice and sorghum, are active Si accumulators (\u0026gt;\u0026thinsp;8 g kg\u003csup\u003e\u0026minus;\u003c/sup\u003e\u0026sup1;), whereas legumes and other broadleaf crops, including maize, cowpea, and soybean, exhibit intermediate accumulation levels (3\u0026ndash;8 g kg\u003csup\u003e\u0026minus;\u003c/sup\u003e\u0026sup1;). Leafy vegetables such as beet and lettuce typically behave as passive accumulators, relying mainly on diffusion-driven uptake (Bokor et al., \u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e2015\u003c/span\u003e; Hodson et al., 2009). In this study, rice presented the highest Si concentrations (9.25\u0026ndash;19.23 g kg\u003csup\u003e\u0026minus;\u003c/sup\u003e\u0026sup1;), consistent with its classification as a strong accumulator due to the presence of active Si transporters (Lsi1 and Lsi2) that mediate efficient uptake and translocation to aerial tissues (Ma \u0026amp; Yamaji, \u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e2006\u003c/span\u003e; Coskun et al., 2016). Conversely, beet and lettuce exhibited the lowest concentrations (1.97\u0026ndash;2.76 g kg\u003csup\u003e\u0026minus;\u003c/sup\u003e\u0026sup1; and 2.09\u0026ndash;3.10 g kg\u003csup\u003e\u0026minus;\u003c/sup\u003e\u0026sup1;, respectively), in agreement with their status as non-accumulator species.\u003c/p\u003e\u003c/div\u003e\n\u003ch3\u003eModel validation and predictive performance\u003c/h3\u003e\n\u003cp\u003eThe results obtained in this study demonstrate the feasibility of pXRF as an alternative and efficient tool for the determination of Si in plant tissues. The strong correlation between the values obtained by pXRF and the conventional autoclave-induced alkaline digestion (AID) method (R\u0026sup2; = 0.94, R\u0026thinsp;=\u0026thinsp;0.97, p\u0026thinsp;\u0026lt;\u0026thinsp;0.001) reinforces the accuracy and reliability of the technique, indicating its potential to replace traditional analytical methods (Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e). These findings are consistent with previous studies validating the use of pXRF for the quantification of elements in biological materials and soils (Soares et al., \u003cspan citationid=\"CR37\" class=\"CitationRef\"\u003e2021\u003c/span\u003e; Singh et al., 2020; Teixeira et al., \u003cspan citationid=\"CR39\" class=\"CitationRef\"\u003e2022\u003c/span\u003e; Paes et al., \u003cspan citationid=\"CR31\" class=\"CitationRef\"\u003e2022\u003c/span\u003e). Importantly, this work helps to fill a critical gap in the literature regarding the validation of pXRF for Si determination in plants (Reidinger et al., \u003cspan citationid=\"CR33\" class=\"CitationRef\"\u003e2012\u003c/span\u003e), representing one of the few studies to date that specifically addresses this application.\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003eThe accuracy of the pXRF model was confirmed by the MAE and MAPE, which were 0.45 g kg⁻\u0026sup1; and 8.2%, respectively, values considered excellent according to the criteria proposed by Piekutowska et al. (\u003cspan citationid=\"CR32\" class=\"CitationRef\"\u003e2021\u003c/span\u003e). Furthermore, cross-validation using 25% of the samples (n\u0026thinsp;=\u0026thinsp;94) not included in the calibration confirmed the robustness of the model (Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e). The resulting MAE (0.44 g kg⁻\u0026sup1;) and MAPE (8.0%) corresponded to a mean accuracy of 97%, with values ranging between 81% and 109%. A slight underestimation was observed for concentrations below 2 g kg⁻\u0026sup1;, and a modest overestimation for higher Si contents (5\u0026ndash;6 g kg⁻\u0026sup1;). Despite these trends, no statistically significant differences were detected between the measured (AID) and predicted (pXRF) data, confirming the good predictive performance of the model even for external validation samples.\u003c/p\u003e\u003cp\u003e\u003c/p\u003e"},{"header":"Discussion","content":"\u003cp\u003eThe pronounced variability in Si concentrations observed across plant tissues (Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e) reflects the inherent physiological diversity in Si uptake, transport, and deposition among species. This variability also points to considerable intraspecific differences, likely associated with genotypic variation in Si transporter expression, root architecture, and uptake efficiency. Such findings align with previous reports indicating that Si accumulation is governed not only by taxonomic distinctions between monocots and dicots but also by species-specific and genotypic traits, including root activity, transporter regulation, and external Si availability (Liang et al., 2015; Ma \u0026amp; Yamaji, 2015).\u003c/p\u003e\u003cp\u003eThis degree of variability is advantageous for the calibration of alternative analytical techniques, as it encompasses a wide concentration range representative of both low and high Si accumulators. From a physiological perspective, such diversity underscores the adaptive significance of Si in enhancing plant resilience to abiotic and biotic stresses through mechanisms that strengthen structural integrity, mitigate oxidative damage, and improve defense responses (Debona et al., \u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e2017\u003c/span\u003e; Epstein, \u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e2009\u003c/span\u003e). Therefore, precise quantification of this variability using pXRF can contribute to more accurate screening and breeding programs aimed at improving Si use efficiency and stress tolerance in agricultural species.\u003c/p\u003e\u003cp\u003eReliable empirical calibration requires a dataset encompassing a broad concentration range (Lima et al. \u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e2024\u003c/span\u003e). In this study, the coefficient of variation (~\u0026thinsp;68%) highlights the presence of significant intraspecific heterogeneity, which must be accounted for during calibration to maintain analytical robustness. High variability within species may influence fluorescence intensity, especially due to differences in tissue density, surface roughness, and organic matrix composition. Hence, the AID results serve as a critical benchmark for refining predictive models and constructing species-specific calibration curves, enhancing the reliability of pXRF in both agronomic and environmental contexts.\u003c/p\u003e\u003cp\u003eThe regression slope (1.15) and intercept (-0.36) indicate a minor systematic overestimation of Si by pXRF compared with AID, likely reflecting matrix-related effects and differences in sample preparation. Indeed, the NaOH\u0026thinsp;+\u0026thinsp;H₂O₂ extraction stimulated by autoclaving may be underestimating the Si contents, since plants vary in both the total amount of silica and the quantity of their phytoliths. Previous studies have also highlighted the importance of matrix calibration and adjustment to ensure the accuracy of the technique (Paes et al., \u003cspan citationid=\"CR31\" class=\"CitationRef\"\u003e2022\u003c/span\u003e; Piekutowska et al., \u003cspan citationid=\"CR32\" class=\"CitationRef\"\u003e2021\u003c/span\u003e).\u003c/p\u003e\u003cp\u003eThe model validation confirmed the high analytical performance of portable X-ray fluorescence. Across the seven tested crops (rice, soybean, maize, cowpea, sorghum, lettuce, and beet), results showed strong agreement with AID (R\u0026thinsp;=\u0026thinsp;0.93\u0026ndash;0.96). For rice, Si concentrations ranged from 9.97 to 19.29 g kg⁻\u0026sup1; using the autoclave method and from 10.23 to 23.02 g kg⁻\u0026sup1; by pXRF, with a mean correlation of R\u0026thinsp;=\u0026thinsp;0.96. For soybean, values ranged from 2.19 to 6.47 g kg⁻\u0026sup1; (AID) and 2.09 to 6.06 g kg⁻\u0026sup1; (pXRF), with R\u0026thinsp;=\u0026thinsp;0.93.\u003c/p\u003e\u003cp\u003eThe MAE (0.45 g kg⁻\u0026sup1;) and MAPE (8.2%) values denote excellent prediction accuracy, consistent with the criteria proposed by Piekutowska et al. (\u003cspan citationid=\"CR32\" class=\"CitationRef\"\u003e2021\u003c/span\u003e). Cross-validation using 25% of independent samples (n\u0026thinsp;=\u0026thinsp;94) yielded similar outcomes (MAE\u0026thinsp;=\u0026thinsp;0.44 g kg⁻\u0026sup1;, MAPE\u0026thinsp;=\u0026thinsp;8.0%), confirming the robustness and generalization ability of the predictive model. Slight underestimation at low Si concentrations (\u0026lt;\u0026thinsp;2 g kg⁻\u0026sup1;) and overestimation at higher levels (5\u0026ndash;6 g kg⁻\u0026sup1;) suggest minor non-linearities possibly linked to detector sensitivity or matrix effects. Nevertheless, no statistically significant differences were found between AID and pXRF results, validating the method\u0026rsquo;s transferability beyond the calibration dataset.\u003c/p\u003e\u003cp\u003eThe time efficiency of pXRF represents a major operational advantage. Traditional chemical digestion methods are labor-intensive and reagent-dependent, whereas pXRF enables non-destructive, real-time quantification, processing hundreds of samples per day (Teixeira et al., \u003cspan citationid=\"CR39\" class=\"CitationRef\"\u003e2022\u003c/span\u003e). Despite these advantages, matrix-specific calibrations remain indispensable, as the spectrometric response can be influenced by plant composition, especially by lignin, cellulose, and residual moisture. Integrating pXRF with other sensing techniques, such as hyperspectral or LIBS, may further enhance predictive accuracy and broaden its application in nutrient diagnostics (Soares et al., \u003cspan citationid=\"CR37\" class=\"CitationRef\"\u003e2021\u003c/span\u003e; Teixeira et al., \u003cspan citationid=\"CR39\" class=\"CitationRef\"\u003e2022\u003c/span\u003e).\u003c/p\u003e\u003cp\u003eIn summary, pXRF constitutes a rapid, reliable, and environmentally sustainable alternative for quantifying Si in plant tissues, supporting both routine nutrient monitoring and advanced research applications. With further refinement of calibration protocols and matrix corrections, the technique has the potential to markedly reduce analytical costs and processing time while maintaining, or even surpassing, the accuracy of conventional wet-chemistry methods.\u003c/p\u003e"},{"header":"Conclusions","content":"\u003cp\u003eThis study demonstrated that pXRF is a reliable, rapid, and non-destructive analytical tool for quantifying Si in plant tissues. The method showed a strong correlation with the conventional AID technique and achieved excellent predictive performance, confirming accuracy comparable to traditional laboratory methods while substantially reducing analytical time and eliminating the use of hazardous reagents. In addition to its precision, pXRF offers exceptional analytical throughput, allowing the processing of up to 300 plant samples per day, a major advantage for large-scale monitoring programs. Given its portability, scalability, and environmental sustainability, pXRF stands out as a robust and practical alternative for Si determination in both agronomic and ecological applications.\u003c/p\u003e"},{"header":"Declarations","content":"\u003cp\u003e\u003ch2\u003eCompeting interests\u003c/h2\u003e\u003cp\u003eWe confirm that there are no conflicts of interest associated with this publication. All authors have approved the submission and are aware of its content. Neither the manuscript nor any part of it is currently under consideration or published in another journal.\u003c/p\u003e\u003c/p\u003e\u003ch2\u003eFunding\u003c/h2\u003e\u003cp\u003eThis study was financed in part by the Brazilian Federal Agency for Support and Evaluation of Graduate Education (CAPES) and the National Council for Scientific and Technological Development (CNPq) for granting scholarships.\u003c/p\u003e\u003ch2\u003eAuthor contributions\u003c/h2\u003e\u003cp\u003eAll authors contributed to the conception and design of the study. Material preparation, data collection, and analysis were performed by Franklone Lima da Silva, Jonathan Jos\u0026eacute; de Melo, Everton Estev\u0026atilde;o Alves do Nascimento, Luiz Henrique Vieira Lima, and Simone Aparecida da Silva Lins. The first draft of the manuscript was written by Franklone Lima da Silva and Cl\u0026iacute;stenes Williams Ara\u0026uacute;jo do Nascimento, and all authors provided comments on previous versions of the manuscript. All authors read and approved the final version of the manuscript.\u003c/p\u003e\u003ch2\u003eData Availability\u003c/h2\u003e\u003cp\u003eThe datasets generated and/or analyzed during the current study are available from the corresponding author upon reasonable request.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\u003cli\u003e\u003cspan\u003eAzeen A, Javed Q, Sun J, Du D (2020) Artificial neural networking to estimate the leaf area for invasive plant Wedelia trilobata. 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Soil Sci 181(9):1\u0026ndash;14. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1097/SS.0000000000000179\u003c/span\u003e\u003cspan address=\"10.1097/SS.0000000000000179\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"Autoclave-induced digestion, Elemental analysis, Non-destructive technique, Spectrometric methods","lastPublishedDoi":"10.21203/rs.3.rs-7940601/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-7940601/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003ch2\u003eBackground and Aims:\u003c/h2\u003e\u003cp\u003ePortable X-ray fluorescence spectrometry (pXRF) has emerged as a robust analytical approach for elemental determination in plant tissues, enabling rapid, non-destructive, and reagent-free measurements. This study developed and validated an empirical calibration of pXRF for quantifying silicon (Si) in plants, using autoclave-induced digestion (AID) as the reference method.\u003c/p\u003e\u003ch2\u003eMethods\u003c/h2\u003e\u003cp\u003eA total of 374 samples from seven plant species (rice, maize, soybean, cowpea, sorghum, lettuce, and beet) were analyzed. Silicon concentrations obtained via AID ranged from 1.07 to 19.23 g kg\u003csup\u003e\u0026minus;\u003c/sup\u003e\u0026sup1; (mean\u0026thinsp;=\u0026thinsp;4.48 g kg\u003csup\u003e\u0026minus;\u003c/sup\u003e\u0026sup1;; coefficient of variation\u0026thinsp;=\u0026thinsp;67%), reflecting substantial interspecific variability. Each sample was also analyzed by pXRF under optimized instrumental conditions, and a calibration model was constructed using 75% of the dataset to predict Si concentrations relative to AID values.\u003c/p\u003e\u003ch2\u003eResults\u003c/h2\u003e\u003cp\u003eThe pXRF calibration exhibited a strong linear relationship with AID results (R\u0026sup2; = 0.94; R\u0026thinsp;=\u0026thinsp;0.97; p\u0026thinsp;\u0026lt;\u0026thinsp;0.001). Validation using the remaining 25% of samples confirmed high predictive accuracy, with consistent performance across all species, particularly rice (R\u0026thinsp;=\u0026thinsp;0.96) and soybean (R\u0026thinsp;=\u0026thinsp;0.93).\u003c/p\u003e\u003ch2\u003eConclusions\u003c/h2\u003e\u003cp\u003eThe pXRF exhibited excellent agreement with the reference method and high predictive accuracy, while markedly reducing analytical time and eliminating the use of hazardous reagents. These results establish pXRF as a reliable, rapid, and sustainable alternative for large-scale Si monitoring in both agronomic and environmental applications.\u003c/p\u003e","manuscriptTitle":"Development and validation of a portable X-ray fluorescence approach for quantifying silicon in plants","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-11-11 09:17:55","doi":"10.21203/rs.3.rs-7940601/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"fae9ecfb-32d1-410e-8b80-8e913c4b8f82","owner":[],"postedDate":"November 11th, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[],"tags":[],"updatedAt":"2025-11-23T19:38:26+00:00","versionOfRecord":[],"versionCreatedAt":"2025-11-11 09:17:55","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-7940601","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-7940601","identity":"rs-7940601","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}