Определение легких элементов и коррекция матричных эффектов в рентгенофлуоресцентном анализе на основе хемометрических подходов тема диссертации и автореферата по ВАК РФ 00.00.00, кандидат наук Аиден Сораиа

• Аиден Сораиа
• кандидат наук
• 2022

Оглавление диссертации кандидат наук Аиден Сораиа

CONTENTS

INTRODUCTION

CHAPTER 1. LITERATURE REVIEW

1.1. Physics of X-ray fluorescence

1.1.1. The photoelectric effect

1.1.2. Scattering radiation

1.2. X-ray fluorescence measurements

1.2.1. Wavelength dispersive X-Ray fluorescence spectroscopy (WDXRF)

1.2.2. Energy dispersive X-ray fluorescence spectroscopy (EDXRF)

1.3. Quantitative analysis in X-ray spectrometry

1.3.1. Inter-element interactions matrix effects

1.3.2. Physical matrix effects

1.3.3. Background

1.4. Traditional methods to account for matrix effects

1.4.1. Empirical calibration

1.4.2. Theoretical calibration

1.4.2.1. Fundamental parameters calibrations

1.5. The scattering theory

1.6. Application of chemometric methods for XRF data processing

1.6.1. Clustering methods

1.6.2. Mutivariate analysis for quantitative analysis

1.7. Conclusion to the literature review

CHAPTER 2.EXPERIMENTAL PART

2.1. Clustering

2.1.1. Principal component analysis (PCA)

2.2. Multivariate calibration

2.2.1. Partial least squares regression (PLS)

2.2.2. K-nearest neighbor regression (KNNR)

2.2.3. Artificial neural networks (ANN)

2.3. Prediction evaluation

2.3.1. Test set

2.3.2. Cross validation

CHAPTER 3.APPLICATION OF CHEMOMETRICS METHODS FOR MATRIX EFFECTS CORRECTION

3.1. Comparison of data processing methods for quantitative analysis in XRF

3.1.1. Samples

3.1.2. XRF measurements

3.1.3. Data processing

3.1.4. Results and discussion

3.1.4.1. Steel samples

3.1.4.2. Ore samples

3.2. PLS-assisted intensity correction (IC-PLS)

3.2.1. Results and discussion

3.2.1.1. Steel samples

3.2.1.2. Ore samples

3.3. Conclusion to chapter

CHAPTER 4.DETERMINATION OF PHYSICAL PROPERTIES AND LIGHT ELEMENT CONTENT IN PLASTICS

4.1. The use of monochromatic EDXRF radiation at different incident angles for quantitative analysis of plastics

4.1.1. Samples

4.1.2. XRF measurements

4.1.3. Data processing

4.1.4. Results and discussion

4.2. The use of polychromatic EDXRF radiation to obtain quantitative information and physical properties of plastics

4.2.1. Samples

4.2.2. XRF measurements

4.2.3. Data processing

4.2.4. Results and discussion

4.3. Comparison of the results of monochromatic and polychromatic EDXRF radiations

4.4. Conclusion to chapter

CONCLUSION

ACKNOWLEDGMENTS

LIST OF ABBREVIATIONS AND SYMBOLS

REFERENCES

APPENDIX

APPENDIX

APPENDIX

APPENDIX

Введение диссертации (часть автореферата) на тему «Определение легких элементов и коррекция матричных эффектов в рентгенофлуоресцентном анализе на основе хемометрических подходов»

INTRODUCTION

Relevance

X-ray fluorescence analysis (XRF) is a popular spectroscopic method for determining the elemental composition in various samples in materials science, geology, archaeology, biology, ecology, food industry and many other fields. The method is widespread since it provides for a fast non-destructive multielemental analysis of both solids and liquids without the need for a complex sample preparation.

At the same time quantitative analysis with XRF has a number of limitations related to matrix effects, that can significantly reduce the accuracy of the obtained results. The determination of the analyte content in XRF is based on the relationship between the intensity of the X-ray fluorescence line of the element being determined and its concentration. This relationship is linear in the absence of matrix effects. Matrix effects are due to the influence of other elements present in the sample on the analyte line intensity and they can distort the linear dependence, thus leading to systematic errors. Matrix effects can be caused by a number of factors, including the specific chemical composition of the sample, its properties (thickness and surface roughness), the conditions of the experiment, and the spectral distribution of the X-ray source.

There is great interest in reliable data processing methods that would eliminate or at least reduce the influence of matrix effects in XRF. To date, several algorithms, empirical and theoretical, have been developed to correct undesirable matrix effects. Theoretical methods, such as the fundamental parameters method (FP), are based on a theoretical model of the interaction of X-rays with matter and allow calculating the concentrations of analytes based on a set of physical parameters. The application of these methods requires homogeneity of samples and knowledge on their chemical composition that may not be available when analyzing real complex objects. Empirical methods are based on mathematical models that relate the line intensities of both target and matrix elements with the analyte concentration. One of the most popular empirical methods is the intensity correction method (IC). This method employs a regression equation to determine the analyte content, and matrix effects are accounted for by the introduction of additional terms representing the products and ratios of the line intensities of the target and matrix elements. A common disadvantage of such methods is the difficulty in constructing models and their

insufficient accuracy in the case of a small number of standard samples employed for modeling.

Chemometric algorithms can be an alternative to traditional approaches for correcting matrix effects. These algorithms use statistical and mathematical approaches to process high-dimensional spectral data, thus extracting the maximum possible information. Among the chemometric methods for quantitative analysis, the most well-known is the partial least squares regression (PLS), which provides a relation between a set of input data (e.g., spectra) and output data (concentrations or other target parameters). PLS effectively eliminates the problems associated with spectral line overlap, however, it can give unsatisfactory results in the case of nonlinear effects. In this situation, nonlinear methods such as artificial neural networks (ANN) or K-nearest neighbor regression (KNNR) can be applied.

Another limitation of XRF is that simple and broadly available energy dispersive X-ray fluorescence spectrometers (EDXRF) do not allow the determination of elements with atomic numbers less than 11 (sodium). On the other hand, in XRF spectra, in addition to X-ray fluorescence lines of elements, signals from excitation X-rays scattered from the sample are also being registered. The intensity of such signals is related to the concentrations of all the elements included in the sample and to the physical properties of the sample in the non-selective way. The use of chemometric methods taking into account latent correlations in XRF data can probably solve the problem of determining light elements.

The objective of the study

The aim of this study is to develop the methods of quantitative analysis in XRF based on chemometric approaches that would allow determination of the content of light elements and analyzing the samples with strong matrix effects.

To achieve this goal, it was necessary to address the following tasks:

1. To study the advantages and limitations of chemometric methods, both linear (PLS) and nonlinear (ANN and KNNR) for the consideration of matrix effects in XRF using the example of quantitative analysis of complex samples, such as ores and steels. To compare the efficiency of the investigated methods with the traditional methods of XRF

spectra processing - the methods of ordinary least square (OLS), fundamental parameters (FP) and Intensity correction method (IC).

2. To develop a method of XRF data processing for quantitative analysis of complex samples based on chemometric principles. To prove the efficiency of the proposed method in real samples.

3. To develop the methods of light elements determination (hydrogen, oxygen and carbon) based on chemometric processing of X-ray scattering spectra from monochromatic and polychromatic sources. To test the proposed approach for analysis of samples of various commercial plastics.

Scientific novelty

1. The possibilities of linear and nonlinear chemometric methods (PLS, ANN and KNNR) for consideration of matrix effects in XRF have been systematically studied. The advantages and limitations of the investigated methods for XRF data processing were established using steel and ore samples as an example.

2. It is demonstrated that the traditional method of intensity correction allows to consider matrix effects more effectively in comparison with the investigated chemometric algorithms.

3. The new XRF data processing algorithm for quantitative analysis combining the advantages of the traditional intensity correction method and partial least squares regression method has been proposed.

4. It is shown that the use of the PLS method for processing the scattering spectra of mono-and polychromatic X-rays allows to determine the content of light elements in plastics samples, along with their physico-chemical properties.

Practical significance

1. The applicability domain of the most common chemometric algorithms (PLS, ANN, KNNR) for the quantitative analysis of samples of complex composition using XRF was established.

2. The proposed XRF data processing algorithm provides the precision comparable with that of the IC method in quantification the analytes in the samples of complex composition, but at the same time it is much simpler in practical implementation.

3. The method for determining light elements (hydrogen, carbon and oxygen) in plastics, as well as the physical properties of the plastic samples (mass per atom, density, crystalline grain melting temperature range, linear thermal expansion coefficient, water absorption) is proposed. It was shown that the accuracy in quantification of these parameters using available EDXRF spectrometers is comparable to that of more expensive instruments with monochromatic X-ray sources.

The defended statements

1. Chemometric methods like PLS and ANN can be used to correct matrix effects in XRF. In this case, PLS allows taking into account only linear matrix effects such as spectral lines overlap, while ANN takes into account more complex nonlinear effects such as absorption of characteristic X-ray fluorescence by matrix elements.

2. The traditional intensity correction method outperforms chemometric tools such as PLS and ANN in quantitative analysis of complex samples.

3. The proposed new method of XRF data processing based on a combination of IC and PLS allows for more effective consideration of matrix effects compared to the use of these methods separately.

4. Application of chemometric methods for processing X-ray scattering spectra allows to determine the content of light elements (hydrogen, carbon and oxygen) in plastics, as well as their physical properties (mass per atom, density, crystalline grain melting temperature range, coefficient of linear thermal expansion, water absorption).

Structure of the work

The work consists of an introduction, a literature review, an experimental part, two

chapters containing the results and their discussion, a conclusion, acknowledgements, a list

of 183 references and 4 appendices. The material consists of 110 pages of typewritten text

and contain 12 tables and 20 figures.

Publications

The main content of the work has been presented in the following publications:

1. S. Aidene, V. Semenov, D. Kirsanov, D. Kirsanov, V. Panchuk, Assessment of the physical properties, and the hydrogen, carbon, and oxygen content in plastics using

energy-dispersive X-ray fluorescence spectrometry, Spectrochimica Acta Part B: Atomic Spectroscopy, 165 (2020) 105771, DOI: 10.1016/j.sab.2020.105771

2. S. Aidene, V. Semenov, D. Kirsanov, D. Kirsanov, V. Panchuk, Scattering of monochromatic X-rays at different incident radiation angles provides quantitative information on physical and chemical properties of plastics, Measurement: Journal of the International Measurement Confederation, 172 (2021) 108888, DOI: 10.1016/j.measurement.2020.108888

3. S. Aidene, M. Khaydukova, G. Pashkova, V. Chubarov, S. Savinov, V. Semenov, D. Kirsanov, V. Panchuk, Does chemometrics work for matrix effects correction in X-ray fluorescence analysis?, Spectrochimica Acta - Part B Atomic Spectroscopy, 185 (2021) 106310, DOI: 10.1016/j.sab.2021.106310

Work approbation

The results of the work were presented at 4 international conferences: XI

International Conference of Young Scientists in Chemistry "Mendeleev 2019" (St.

Petersburg, 2019). 12th Winter Symposium on Chemometrics "WSC" Saratov, (2020). XII

International Conference of Young Scientists on Chemistry "Mendeleev 2021" (Saint-

Petersburg, 2021). 13th Winter Symposium on Chemometrics "WSC" (Moscow, 2022).

Заключение диссертации по теме «Другие cпециальности», Аиден Сораиа

ЗАКЛЮЧЕНИЕ

В настоящем исследовании продемонстрированы возможности наиболее распространенных хемометрических методов для количественного анализа в РФА.

Проведено сравнение возможностей традиционных методов обработки данных (ФП, КИ) для учета матричных эффектов с хемометрическими методами (ПЛС, ИНС, к-БСР). Показано, что эффективность различных хемометрических методов зависит от особенностей матричных эффектов. Так, например, ПЛС позволяет учитывать перекрытие спектральных линий, но при этом зависимость концентрации от интенсивности должна носить линейный характер. Напротив, ИНС позволяет учитывать более сложные нелинейные матричные эффекты. При этом традиционный метод коррекции по интенсивностям продемонстрировал наивысшую точность анализа по сравнению со всеми исследованными методами.

Предложен новый комбинированный метод, сочетающий в себе преимущества метода коррекции по интенсивностям и ПЛС. Возможности данного метода для опредления содержания аналитов в пробах сложного состава были продемонстрированы на примере анализа руд и сталей. Показано, что предложенный метод позволяет получать сопостовимые с методом КИ результаты анализа, однако является менее трудоемким, так как не требует подбора отдельного регрессионного уравнения для каждого определяемого аналита.

Предложены способы определения легких элементов (водород, кислород, углерод) в пластмассах, а также физических свойств этих материалов (средняя атомная масса, плотность, диапазон температур плавления кристаллического зерна, коэффициент линейного теплового расширения, водопоглощение), основанные на хемометрической обработки РФА спектров, содержащих сигналы рассеянного от образца рентгеновского излучения. Предлагаемые способы основаны на использовании моно- и полихроматического первичного излучения. Показано, что точность определения исследуемых параметров с помощью доступных EDXRF спектрометров сопоставима с точностью более дорогостоящих приборов, основанных на применении монохроматических истоников рентгеновского излучения.

Список литературы диссертационного исследования кандидат наук Аиден Сораиа, 2022 год

СПИСОК ЛИТЕРАТУРЫ

[1] Zvereva, V.V., Trunova, V.A., Sorokoletov, D.S., Polosmak, N.V. Mercury in archeological hair samples from Xiongnu burials (Noin-Ula, Mongolia): SR XRF and CXRM analysis // X-Ray Spectrometry. - 2017. - № 46, C 563-568.

[2] Manso, M., Schiavon, N., Queralt, I., Arruda, A.M., Sampaio, J.M., Brunetti, A. Alloy characterization of a 7th Century BC archeological bronze vase - Overcoming patina constraints using Monte Carlo simulations // Spectrochimica Acta - Part B Atomic Spectroscopy. - 2015. - № 107, C 93-96.

[3] Hampai, D., Liedl, A., Cappuccio, G., Capitolo, E., Iannarelli, M., Massussi, M., Tucci, S., Sardella, R., Sciancalepore, A., Polese, C., Dabagov, S.B. 2D-3D ^XRF elemental mapping of archeological samples // Nuclear Instruments and Methods in Physics Research, Section B: Beam Interactions with Materials and Atoms. - 2017. -№ 402, C 274-277.

[4] Gauthier, G., Burke, A.L. The effects of surface weathering on the geochemical analysis of archaeological lithic samples using non-destructive polarized energy dispersive XRF // Geoarchaeology. - 2011. - № 26, С. 269-291.

[5] Finestone, E.M., Braun, D.R., Plummer, T.W., Bartilol, S., Kiprono, N. Building ED-XRF datasets for sourcing rhyolite and quartzite artifacts: A case study on the Homa Peninsula, Kenya // Journal of Archaeological Science: Reports. - 2020. - № 33, С. 102510.

[6] Geraki, K., Farquharson, M.J., Bradley, D.A. Concentrations of Fe, Cu and Zn in breast tissue: A synchrotron XRF study // Physics in Medicine and Biology. - 2002. - № 47, С. 2327-2339.

[7] Farquharson, M.J., Geraki, K., Falkenberg, G., Leek, R., Harris, A. The localisation and micro-mapping of copper and other trace elements in breast tumours using a synchrotron micro-XRF system // Applied Radiation and Isotopes. - 2007. - № 65, С.183-188.

[8] Dao, E., Zeller, M.P., Wainman, B.C., Farquharson, M.J. Feasibility of the use of a handheld XRF analyzer to measure skin iron to monitor iron levels in critical organs // Journal of Trace Elements in Medicine and Biology. - 2018. - № 50, С. 305-311.

[9] Christoffersson, J.-O., Mattsson, S. Polarised x-rays in XRF-analysis for improved in vivo detectability of cadmium in man // Physics in Medicine and Biology. - 1983. -№ 28, C. 1135-1144.

[10] Borjesson, J., Barregard, L., Sallsten, G., Schutz, A., Jonson, R., Alpsten, M., Mattsson, S. In vivo XRF analysis of mercury: The relation between concentrations in the kidney and the urine // Physics in Medicine and Biology. - 1995. - № 40, C. 413-426.

[11] Zhao, Z., Dong, C., Lin, C., Zhang, X. The method of distinguishing sedimentary environment of sandstone reservoirs by XRF // IOP Conference Series: Earth and Environmental Science. - 2018. - № 208, C. 012022.

[12] Zhao, L., Sun, Y., Hernandez-Viezcas, J.A., Hong, J., Majumdar, S., Niu, G., Duarte-Gardea, M., Peralta-Videa, J.R., Gardea-Torresdey, J.L. Monitoring the environmental effects of CeO2 and ZnO nanoparticles through the life cycle of corn (Zea mays) plants and in situ ^-XRF mapping of nutrients in kernels // Environmental Science and Technology. - 2015. - № 49, C. 2921-2928.

[13] Turner, A. Polystyrene foam as a source and sink of chemicals in the marine environment: An XRF study // Chemosphere. - 2021. - № 263, C. 128087.

[14] Talbi, A., Kerchich, Y., Kerbachi, R., Boughedaoui, M. Assessment of annual air pollution levels with PM1, PM2.5, PM10 and associated heavy metals in Algiers, Algeria // Environmental Pollution. - 2018. - № 232, C. 252-263.

[15] López, M.L., Ceppi, S., Palancar, G.G., Olcese, L.E., Tirao, G., Toselli, B.M. Elemental concentration and source identification of PM10 and PM2.5 by SR-XRF in Córdoba City, Argentina // Atmospheric Environment. - 2011. - № 45, C. 5450-5457.

[16] de Lima Lessa, J.H., Araujo, A.M., Ferreira, L.A., da Silva Júnior, E.C., de Oliveira, C., Corguinha, A.P.B., Martins, F.A.D., de Carvalho, H.W.P., Guilherme, L.R.G., Lopes, G. Agronomic biofortification of rice (Oryza sativa L.) with selenium and its effect on element distributions in biofortified grains // Plant and Soil. - 2019. - № 444, C. 331-342.

[17] Zhou, S., Weindorf, D.C., Cheng, Q., Yang, B., Yuan, Z., Chakraborty, S. Elemental assessment of vegetation via portable X-ray fluorescence: Sample preparation and methodological considerations // Spectrochimica Acta - Part B Atomic Spectroscopy. - 2020. - № 174, C. 105999.

[18] Tóth, T., Kovács, Z.A., Rékási, M. XRF-measured rubidium concentration is the best predictor variable for estimating the soil clay content and salinity of semi-humid soils in two catenas // Geoderma. - 2019. - № 342, C. 106-108.

[19] O'Rourke, S.M., Stockmann, U., Holden, N.M., McBratney, A.B., Minasny, B. An assessment of model averaging to improve predictive power of portable vis-NIR and XRF for the determination of agronomic soil properties // Geoderma. - 2016. - № 279, C. 31-44.

[20] Lozano. R., Bernal. J. P., Lozano. R., Bernal. J. P. Characterization of a new set of eight geochemical reference materials for XRF major and trace element analysis // Revista Mexicana de Ciencias Geológicas. - 2005. - № 22, C. 329-344.

[21] Hannaker, P., Haukka, M., Sen, S.K. Comparative study of ICP-AES and XRF analysis of major and minor constituents on geological materials // Chemical Geology.

- 1984. - № 42, C. 319-324.

[22] Gazylla, M.F., Gómez, M.P., Orduña, M., Rodrigo, M. New methodology for sulfur analysis in geological samples by WD-XRF spectrometry // X-Ray Spectrometry. -2009. - № 38, C. 3-8.

[23] Figueiredo, M.O., Ramos, M.T., Pereira Da Silva, T., Basto, M.J., Chevallier, P. Synchrotron XRF Microprobe Analysis of Geological Samples: Influence of Size and Orientation of Single Mineral Grains // X-Ray Spectrometry. - 1999. - № 28, C. 251254.

[24] Robertson, M.E.A., Feather, C.E. Determination of gold, platinum and uranium in South African ores by high-energy XRF spectrometry // X-Ray Spectrometry. - 2004.

- № 33, C. 164-173.

[25] Aldrian, A., Ledersteger, A., Pomberger, R. Monitoring of WEEE plastics in regards to brominated flame retardants using handheld XRF // Waste Management. - 2015. -№ 36, C. 297-304.

[26] Frahm, E. Ceramic studies using portable XRF: From experimental tempered ceramics to imports and imitations at Tell Mozan, Syria // Journal of Archaeological Science. - 2018. - № 90, C. 12-38.

[27] Moseley, H. G. J. XCIII. The high-frequency spectra of the elements // The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science. - 1913. - № 26, C. 1024-1034.

[28] Moseley, H. G. J. LXXX. The high-frequency spectra of the elements. Part II // The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science. -1913. - № 27, C. 703-713.

[29] Sherman, J. The theoretical derivation of fluorescent X-ray intensities from mixtures // Spectrochimica Acta. - 1955. - № 7, C. 283-306.

[30] Einstein. A. Concerning an Heuristic Point of View Toward the Emission and Transformation of Light [Electronic resource] // American Journal of Physics. - 1905.

- № 33. - http://web.ihep.su/dbserv/compas/src/einstein05/eng.pdf

[31] Whitaker, M.A.B. The Bohr-Moseley synthesis and a simple model for atomic x-ray energies // European Journal of Physics. - 1999. - № 20, C. 213-220.

[32] Jenkins, R. X-Ray Fluorescence Spectrometry, Second Edition / R. Jenkins. - Wiley-Interscience, 1999. - 217 c.

[33] Scofield, J.H. Relativistic hartree-slater values for K and L X-ray emission rates // Atomic Data and Nuclear Data Tables. - 1974. - № 14, C. 121-137.

[34] Krause, M.O. Atomic radiative and radiationless yields for K and L shells // Journal of Physical and Chemical Reference Data. - 1979. - № 8, C. 307-327.

[35] Carron, N. J. An Introduction to the Passage of Energetic Particles through Matter / N. J. Carron. - Taylor & Francis, 2006. - 386 c.

[36] Roy, S.C., Pratt, R.H., Kissel, L. Rayleigh scattering by energetic photons: Development of theory and current status // Radiation Physics and Chemistry. - 1993.

- № 41, C. 725-738.

[37] Blumenthal, G.R., Gould, R.J. Bremsstrahlung, synchrotron radiation, and compton scattering of high-energy electrons traversing dilute gases // Reviews of Modern Physics. - 1970. - № 42, C. 237-270.

[38] Williams, B. G., Sparrow, T. G., Egerton, R. F. Electron Compton scattering from solids // Proceedings of the Royal Society of London. Series A, Mathematical and Physical Science. - 1984. - № 393, C. 409-422.

[39] Van Gysel, M., Lemberge, P., Van Espen, P. Description of Compton peaks in energy-dispersive x-ray fluorescence spectra // X-Ray Spectrometry. - 2003. - № 32, C. 139147.

[40] Wobrauschek, P., Streli, C., Lindgren, E. S., Energy Dispersive, X-ray Fluorescence Analysis / Encyclopedia of Analytical Chemistry Meyers. R.A.- John Wiley & Sons, Ltd., United States, 2010. - 17 c.

[41] Bertin. E. P. Principles and Practice of X-Ray Spectrometric Analysis / E. P. Bertin.

- Springer Science, 1975. - 1078 c.

[42] Jenkins. R. Quantitative X-Ray Spectrometry / R. Jenkins. - New York: Marcel Dekker, 1995. - 475 c.

[43] Grieken. R. V. Markowicz. A. Handbook of X-Ray Spectrometry / R. V. Grieken, A. Markowicz. - CRC Press, New York, 2001. - 985 c.

[44] Beckhoff. B. Kanngiesser. B. Langhoff. N. Wedell. R. Wolff. H. Handbook of Practical X-Ray Fluorescence Analysis / B. Beckhoff, B. Kanngießer, N. Langhoff, R. Wedell, and H. Wolff. - Springer, Berlin Heidelberg, 2007. - 897 c.

[45] Gardner, R.P., Hawthorne, A.R. Monte Carlo simulation of the X-ray fluorescence excited by discrete energy photons in homogeneous samples including tertiary interelement effects // X-Ray Spectrometry. - 1975. - № 4, C. 138-148.

[46] Broll, N. Fluorescence X : de la découverte des rayons de Rontgen aux identités de Tertian // Journal de Physique IV France. - 1996. - № 6, C. 583-597.

[47] Rousseay, R. M., Boivin, J. A. The fundamental algorithm: A natural extension of Sherman equation part I: theory // The Rigaku Journal. - 1998. - № 15, C. 13-28.

[48] Shiraiwa, T., Fujino, N. Theoretical Calculation of Fluorescent X-Ray Intensities in Fluorescent X-Ray Spectrochemical Analysis // Japanese Journal of Applied Physics.

- 1966. - № 5, C. 886-899.

[49] Friedman, H., Birks, L. S. A Geiger Counter Spectrometer for X-Ray Fluorescence Analysis // Review of Scientific Instruments. - 1948. - № 19, C. 323-330.

[50] McIntosh, K.G., Cordes, N.L., Patterson, B.M., Havrilla, G.J. Laboratory-based characterization of plutonium in soil particles using micro-XRF and 3D confocal XRF // Journal of Analytical Atomic Spectrometry. - 2015. - № 30, C. 1511-1517.

[51] Zakharova, E.V., Dzidziguri, E.L., Sidorova, E.N., Vasiliev, A.A., Pelevin, I.A., Ozherelkov, D.Yu., Nalivaiko, A.Yu., Gromov, A.A. Characterization of multiphase oxide layer formation on micro and nanoscale iron particles // Metals. - 2021. - № 11,C. 1-13.

[52] Kempenaers, L., Vincze, L., Janssens, K. Use of synchrotron micro-XRF for characterization of the micro-heterogeneity of heavy metals in low-Z reference materials // Spectrochimica acta, Part B: Atomic spectroscopy. - 2000. - № 55, C. 651-669.

[53] Chebakova, K.A., Dzidziguri, E.L., Sidorova, E.N., Vasiliev, A.A., Ozherelkov, D.Yu., Pelevin, I.A., Gromov, A.A., Nalivaiko, A.Yu. X-ray fluorescence spectroscopy features of micro-and nanoscale copper and nickel particle compositions // Nanomaterials. - 2021. - № 11, C. 2388.

[54] Finkel'shtein, A.L., Gunicheva, T.N. Description of the dependence of intensity of x-ray fluorescence on the particle size of powder samples and pulp during x-ray fluorescent analysis // Inorganic Materials. - 2008. - № 44, C. 1567-1571.

[55] Finkelshtein, A.L., Brjansky, N. Estimating particle size effects in X-ray fluorescence spectrometry // Nuclear Instruments and Methods in Physics Research, Section B: Beam Interactions with Materials and Atoms. - 2009. - № 267, C. 2437-2439.

[56] Potts, P.J., Webb, P.C., Williams-Thorpe, O. Investigation of a correction procedure for surface irregularity effects based on scatter peak intensities in the field analysis of geological and archaeological rock samples by portable X-ray fluorescence spectrometry // Journal of Analytical Atomic Spectrometry. - 1997. - № 12, C. 769776.

[57] Liangquan, G., Ye, Z., Yeshun, C., Wangchang, L. The surface geometrical structure effect in in situ X-ray fluorescence analysis of rocks // Applied Radiation and Isotopes. - 1998. - № 49, C. 1713-1720.

[58] Margui, E., Van Grieken, R., Fonta'S, C., Hidalgo, M., Queralt, I. Preconcentration methods for the analysis of liquid samples by X-ray fluorescence techniques // Applied Spectroscopy Reviews. - 2010. - № 45, C. 179-205.

[59] Ulrey., C.T. An experimental investigation of the energy in the continuous X-Ray spectra of certain elements // Physical Review. - 1918. - № 11, C. 401-410.

[60] Lucas-Tooth, J., Pyne, C. The Accurate Determination of Major Constituents by X-Ray Fluorescent Analysis in the Presence of Large Interelement Effects // Advances in X-Ray Analysis. - 1963. - № 7, C. 523-541.

[61] Lucas-Tooth, J., Price, BJ. A mathematical method for the investigation of interelement effects in X-ray fluorescent analyses // Metallurgia. - 1961. - № 64, C. 149-152.

[62] Rousseau, R. M., Willis, J. P., Duncan, A. R. Practical XRF calibration procedures for major and trace elements // X-Ray Spectrometry. - 1996. - № 25, C. 179-189.

[63] Markowicz, A. An overview of quantificationmethods in energy-dispersive X-ray fluorescence analysis // Pramana - Journal of Physics. - 2011. - № 76, C. 321-329.

[64] Rousseau, R.M. Fundamental algorithm between concentration and intensity in XRF analysis 1—theory // X-Ray Spectrometry. - 1984. - № 13, C. 115-120.

[65] de Boer, D.K.G. Fundamental parameters for X-ray fluorescence analysis // Spectrochimica Acta Part B: Atomic Spectroscopy. - 1989. - № 44, C. 1171-1190.

[66] Criss, J.W., Birks, L.S.Calculation Methods for Fluorescent X-Ray Spectrometry: Empirical Coefficients vs. Fundamental Parameters // Analytical Chemistry. - 1968.

- № 40, C. 1080-1086.

[67] Koncz-Horvath, D., Gacsi, Z. Analysis of lead in SnAg based solders using X-Ray fluorescence // Materials Science Forum. - 2013. - № 752, C. 37-41.

[68] Criss, J.W., Birks, L.S., Gilfrich, J.V. Versatile X-ray Analysis Program Combining Fundamental Parameters and Empirical Coefficients // Analytical Chemistry. - 1978.

- № 50, C. 33-37.

[69] Cernohorsky, T., Pouzar, M., Jakubec, K. ED XRF analysis of precious metallic alloys with the use of combined FP method // Talanta. - 2006. - № 69, C. 538-541.

[70] Rachetti, A., Wegscheider, W. A fundamental parameters approach including scattered radiation for mono-energetically excited samples in energy-dispersive x-ray fluorescence spectrometry // Analytica Chimica Acta. - 1986. - № 188, C. 37-50.

[71] Espen, P.V., dack, L.V., Adams, F., Grieken, R.V. Effective Sample Weight from Scatter Peaks in Energy-Dispersive X-Ray Fluorescence // Analytical Chemistry. -1979. - № 51, C. 961-967.

[72] Dwiggins, C. W. Quantitative Determination of Low Atomic Number Elements Using Intensity Ratio of Coherent to Incoherent Scattering of X-Rays // Analytical chemistry. - 1961. - № 33, C. 67-70.

[73] Pessanha, S., Silva, S., Martins, L., Santos, J.P., Silveira, J.M. Suitability of the Compton-to-Rayleigh ratio in X-ray fluorescence spectroscopy: Hydroxyapatite-

based materials characterization // Journal of Analytical Atomic Spectrometry. -2019. - № 34, C. 854-859.

[74] Candido, M., Silveira, J.M., Mata, A., Carvalho, M.L., Pessanha, S. In vitro study of the demineralization induced in human enamel by an acidic beverage using X-ray fluorescence spectroscopy and Raman microscopy // X-Ray Spectrometry. - 2019. -№ 48, C. 61-69.

[75] Hodoroaba, V.-D., Rackwitz, V. Gaining improved chemical composition by exploitation of compton-to-rayleigh intensity ratio in XRF analysis // Analytical Chemistry. - 2014. - № 86, C. 6858-6864.

[76] Mikhailov, I.F., Baturin, A.A., Mikhailov, A.I., Borisova, S.S., Fomina, L.P. Determination of coal ash content by the combined x-ray fluorescence and scattering spectrum // Review of Scientific Instruments. - 2018. - № 89, C. 023103.

[77] Toussaint, C. J., Vos, G. Quantitative Determination of Carbon in Solid Hydrocarbons Using the Intensity Ratio of Incoherent to Coherent Scattering of X-Rays // Applied Spectroscopy. - 1964. - № 18, C. 171-174.

[78] O'Neil, L.P., Catling, D.C., Elam, W.T. Optimized Compton fitting and modeling for light element determination in micro-X-ray fluorescence map datasets // Nuclear Instruments and Methods in Physics Research, Section B: Beam Interactions with Materials and Atoms. - 2018. - № 436, C. 173-178.

[79] Garmay, A.V., Oskolok, K.V., Monogarova, O.V., Alov, N.V. Total reflection X-ray fluorescence analysis of highly mineralized water samples using relative intensities and scattered radiation // Spectrochimica Acta - Part B Atomic Spectroscopy. - 2019. - № 152, C. 74-83.

[80] Li, F., Liu, Z., Sun, T. Authentication of vegetable oils by confocal X-ray scattering analysis with coherent/incoherent scattered X-rays // Food Chemistry. - 2016. - № 210, C. 435-441.

[81] Li, F., Liu, Z., Sun, T., Yang, C., Sun, X., Sun, W., He, J., Ding, X. A confocal three-dimensional micro X-ray scattering technology based on Rayleigh to Compton ratio for identifying materials with similar density and different weight percentages of low-Z elements // Radiation Physics and Chemistry. - 2015. - № 112, C. 163-168.

[82] Uzunoglu, Z., Yilmaz, D., §ahin, Y. Quantitative x-ray spectrometric analysis with peak to Compton ratios // Radiation Physics and Chemistry. - 2015. - № 112, C. 189194.

[83] Esbensen. K. H., Guyot. D., Westad. F., Houmoller. L. P., Multivariate Data Analysis: In Practice: an Introduction to Multivariate Data Analysis and Experimental Design / K. H. Esbensen, D. Guyot, F. Westad, and L. P. Houmoller. - Corvallis: CAMO, 2000. - 598 c.

[84] Selinus, O. Factor and discriminant analysis to lithogeochemical prospecting in an area of central Sweden // Journal of Geochemical Exploration. - 1983. - № 19, C. 619-628.

[85] Duchesne, J.C., Rouhart, A., Schoumacher, C., Dillen, H. Thallium, nickel, cobalt and other trace elements in iron sulfides from belgian lead-zinc vein deposits // Mineralium Deposita. - 1983. - № 18, C. 303-313.

[86] Wang, Yongdong, Zhao, Xinna, Kowalski, Bruce R. X-ray fluorescence calibration with partial least-squares // Applied Spectroscopy. - 1990. - № 44, C. 998-1002.

[87] Papachristodoulou, C., Oikonomou, A., Ioannides, K., Gravani, K. A study of ancient pottery by means of X-ray fluorescence spectroscopy, multivariate statistics and mineralogical analysis // Analytica Chimica Acta. - 2006. - № 573, C. 347-353.

[88] Renson, V., Martinez-Cortizas, A., Mattielli, N., Coenaerts, J., Sauvage, C., De Vleeschouwer, F., Lorre, C., Vanhaecke, F., Bindler, R., Rautman, M., Nys, K., Claeys, P. Lead isotopic analysis within a multiproxy approach to trace pottery sources. The example of White Slip II sherds from Late Bronze Age sites in Cyprus and Syria // Applied Geochemistry. - 2013. - № 28, C. 220-234.

[89] Papageorgiou, I., Liritzis, I. Mumtivariate mixture of normals with unknown number of components: An application to cluster Neolithic ceramics from Aegean and Asia Minor using portable XRF // Archaeometry. - 2007. - № 49, C. 795-813.

[90] Modica, A., Alberghina, M.F., Brai, M., Bruno, M., Di Bella, M., Fontana, D., Tranchina, L. XRF analysis to identify historical photographic processes: The case of some Interguglielmi Jr.'s images from the Palermo Municipal Archive // Radiation Physics and Chemistry. - 2017. - № 135, C. 76-80.

[91] Marini, F., Tomassetti, M., Piacentini, M., Campanella, L., Flamini, P. Application of near infrared spectroscopy (NIR), X-ray fluorescence (XRF) and chemometrics to the

differentiation of marmora samples from the Mediterranean basin // Natural Product Research. - 2019. - № 33, C. 1006-1014.

[92] Machado, A.S., Oliveira, D.F., Gama Filho, H.S., Latini, R., Bellido, A.V.B., Assis, J.T., Anjos, M.J., Lopes, R.T. Archeological ceramic artifacts characterization through computed microtomography and X-ray fluorescence // X-Ray Spectrometry. - 2017. - № 46, C. 427-434.

[93] Cui, Y., Dong, G., Li, H., An, T., Liu, X., Wang, J., Wang, H., Ren, X., Li, X., Chen, F. Early ceramic trade in Gansu and Qinghai regions, northwest China: A comparative elemental analysis on sherds of Majiayao culture, Yangshao culture and Qijia culture // Journal of Archaeological Science: Reports. - 2015. - № 3, C. 65-72.

[94] Colao, F., Fantoni, R., Ortiz, P., Vazquez, M.A., Martin, J.M., Ortiz, R., Idris, N. Quarry identification of historical building materials by means of laser induced breakdown spectroscopy, X-ray fluorescence and chemometric analysis // Spectrochimica Acta - Part B Atomic Spectroscopy. - 2010. - № 65, C. 688-694.

[95] Calparsoro, E., Maguregui, M., Morillas, H., Arana, G., Inanez, J. G. Non-destructive screening methodology based on ED-XRF for the classification of medieval and post-medieval archaeological ceramics // Ceramics International. - 2019. - № 45, C. 10672-10683.

[96] Bonizzoni, L., Galli, A., Milazzo, M. XRF analysis without sampling of Etruscan depurata pottery for provenance classification // X-Ray Spectrometry. - 2010. - № 39, C. 346-352.

[97] Barone, G., Mazzoleni, P., Ingoglia, C., Vanaria, M.G. Archaeometric evidences of the 4th-2nd century BC amphorae productions in north eastern Sicily // Journal of Archaeological Science. - 2011. - № 38, C. 3060-3071.

[98] Asfora, V.K., Bueno, C.C., de Barros, V.M., Khoury, H., Van Grieken, R. X-ray spectrometry applied for characterization of bricks of Brazilian historical sites // X-Ray Spectrometry. - 2021. - № 50, C. 45-52.

[99] Aoyama, H., Yamagiwa, K., Fujimoto, S., Izumi, J., Ishikawa, R., Kameshima, S., Arakaki, T. A new nondestructive approach to chemical analysis of potsherds using an X-ray fluorescence microscope: Case study about the past pottery manufacture in the Yaeyama Islands // X-Ray Spectrometry. - 2018. - № 47, C. 265-272.

[100] Amadori, M.L., Del Vais, C., Fermo, P., Pallante, P. Archaeometric researches on the provenance of Mediterranean Archaic Phoenician and Punic pottery // Environmental Science and Pollution Research. - 2017. - № 24, C. 13921-13949.

[101] Rebiere, H., Kermai'dic, A., Ghyselinck, C., Brenier, C. Inorganic analysis of falsified medical products using X-ray fluorescence spectroscopy and chemometrics // Talanta. - 2019. - № 195, C. 490-496.

[102] Soares, F., Anzanello, M.J., Fogliatto, F.S., Ortiz, R.S., Mariotti, K.C., Ferrao, M.F. Enhancing counterfeit and illicit medicines grouping via feature selection and X-ray fluorescence spectrometry // Journal of Pharmaceutical and Biomedical Analysis. -2019. - № 174, C. 198-205.

[103] Ortiz, R.S., Mariotti, K.C., Schwab, N.V., Sabin, G.P., Rocha, W.F.C., de Castro, E.V.R., Limberger, R.P., Mayorga, P., Bueno, M.I.M.S., Romao, W. Fingerprinting of sildenafil citrate and tadalafil tablets in pharmaceutical formulations via X-ray fluorescence (XRF) spectrometry // Journal of Pharmaceutical and Biomedical Analysis. - 2012. - № 58, C. 7-11.

[104] Anzanello, M.J., Ortiz, R.S., Limberger, R., Mariotti, K. A framework for selecting analytical techniques in profiling authentic and counterfeit Viagra and Cialis // Forensic Science International. - 2014. - № 235, C. 1-7.

[105] Bortoleto, G.G., Pataca, L.C.M., Bueno, M.I.M.S. A new application of X-ray scattering using principal component analysis - Classification of vegetable oils // Analytica Chimica Acta. - 2005. - № 539, C. 283-287.

[106] Bortoleto, G.G., Borges, S.S.d.O., Bueno, M.I.M.S. X-ray scattering and multivariate analysis for classification of organic samples: A comparative study using Rh tube and synchrotron radiation // Analytica Chimica Acta. - 2007. - № 595, C. 38-42.

[107] Singh, S.P., Vogel-Mikus, K., Vavpetic, P., Jeromel, L., Pelicon, P., Kumar, J., Tuli, R. Spatial X-ray fluorescence micro-imaging of minerals in grain tissues of wheat and related genotypes // Planta. - 2014. - № 240, C. 277-289.

[108] Nedjimi, B. Determination of Some Major and Trace Elements in Cladodes of Barbary fig (Opuntia ficus-indica Mill.) by X-ray Fluorescence Spectrometry // Biological Trace Element Research. - 2021. - № 199, C. 4353-4359.

[109] Sharma, S., Sarika Bharti, A., Tiwari, M.K., Uttam, K.N. Effect of manganese stress on the mineral content of the leaves of wheat seedlings by use of X-ray fluorescence excited by synchrotron radiation // Spectroscopy Letters. - 2018. - № 51, C. 302-310.

[110] Scatigno, C., Festa, G. A first elemental pattern and geo-discrimination of Italian EVOO by energy dispersive X-ray fluorescence and chemometrics // Microchemical Journal. - 2021. - № 171, C. 106863.

[111] Alexandre, T.L., Bueno, M.I.M.S. Classification of some species, genera and families of plants by x-ray spectrometry // X-Ray Spectrometry. - 2006. - № 35, C. 257-260.

[112] Schreiber, N., Garcia, E., Kroon, A., Ils0e, P.C., Kjsr, K.H., Andersen, T.J. Pattern recognition on X-ray fluorescence records from copenhagen lake sediments using principal component analysis // Water, Air, and Soil Pollution. - 2014. - № 225, C. 2221.

[113] Giralt, S., Rico-Herrero, M.T., Vega, J.C., Valero-Garces, B.L. Quantitative climate reconstruction linking meteorological, limnological and XRF core scanner datasets: The Lake Sanabria case study, NW Spain // Journal of Paleolimnology. - 2011. - № 46, C. 487-502.

[114] Evans, G., Augustinus, P., Gadd, P., Zawadzki, A., Ditchfield, A., Hopkins, J. A multi-proxy paleoenvironmental interpretation spanning the last glacial cycle (ca. 117 ± 8.5 ka BP) from a lake sediment stratigraphy from Lake Kai Iwi, Northland, New Zealand // Journal of Paleolimnology. - 2021. - № 65, C. 101-122.

[115] Morlock, M.A., Vogel, H., Russell, J.M., Anselmetti, F.S., Bijaksana, S. Quaternary environmental changes in tropical Lake Towuti, Indonesia, inferred from end-member modelling of X-ray fluorescence core-scanning data // Journal of Quaternary Science. - 2021. - № 36, C. 1040-1051.

[116] Miranda, J., Andrade, E., Lopez-Suarez, A., Ledesma, R., Cahill, T.A., Wakabayashi, P.H. A receptor model for atmospheric aerosols from a southwestern site in Mexico City // Atmospheric Environment. - 1996. - № 30, C. 3471-3479.

[117] Guerra, M.B.B., Neto, E.L., Prianti, M.T.A., Pereira-Filho, E.R., Schaefer, C.E.G.R. Post-fire study of the Brazilian Scientific Antarctic Station: Toxic element contamination and potential mobility on the surrounding environment // Microchemical Journal. - 2013. - № 110, C. 21-27.

[118] Boyer-Villemaire, U., St-Onge, G., Bernatchez, P., Lajeunesse, P., Labrie, J. Highresolution multiproxy records of sedimentological changes induced by dams in the Sept-iles area (Gulf of St. Lawrence, Canada)// Marine Geology. - 2013. - № 338, C. 17-29.

[119] Flood, R.P., Bloemsma, M.R., Weltje, G.J., Barr, I.D., O'Rourke, S.M., Turner, J.N., Orford, J.D. Compositional data analysis of Holocene sediments from the West Bengal Sundarbans, India: Geochemical proxies for grain-size variability in a delta environment // Applied Geochemistry. - 2016. - № 75, C. 222-235.

[120] Evans, G., Augustinus, P., Gadd, P., Zawadzki, A., Ditchfield, A. A multi-proxy XRF inferred lake sediment record of environmental change spanning the last ca. 2230 years from Lake Kanono, Northland, New Zealand // Quaternary Science Reviews. -2019. - № 225, C. 106000.

[121] Donais, M.K., Wojtas, S., Desmond, A., Duncan, B., George, D.B. Differentiation of hypocaust and floor tiles at Coriglia, Castel Viscardo (Umbria, Italy) using principal component analysis (PCA) and portable x-ray fluorescence (XRF) spectrometry // Applied Spectroscopy. - 2012. - № 66, C. 1005-1012.

[122] Rosi, F., Burnstock, A., Van den Berg, K.J., Miliani, C., Brunetti, B.G., Sgamellotti, A. A non-invasive XRF study supported by multivariate statistical analysis and reflectance FTIR to assess the composition of modern painting materials // Spectrochimica Acta - Part A: Molecular and Biomolecular Spectroscopy. - 2009. -№ 71, C. 1655-1662.

[123] Pires, C.T.G.V.M.T., Oliveira Jr., N.G., Airoldi, C. Structural incorporation of titanium and/or aluminum in layered silicate magadiite through direct syntheses // Materials Chemistry and Physics. - 2012. - № 135, C. 870-879.

[124] Molloy, J., Sieber, J. Assessing microscale heterogeneity in batches of reference materials using microbeam XRF // X-Ray Spectrometry. - 2011. - № 40, C. 306-314.

[125] Angeyo, K.H., Gari, S., Mangala, J.M., Mustapha, A.O. Principal component analysis-assisted energy dispersive X-ray fluorescence spectroscopy for non-invasive quality assurance characterization of complex matrix materials // X-Ray Spectrometry. - 2012. - № 41, C. 321-327.

[126] Rosi, F., Miliani, C., Clementi, C., Kahrim, K., Presciutti, F., Vagnini, M., Manuali, V., Daveri, A., Cartechini, L., Brunetti, B.G., Sgamellotti, A. An integrated

spectroscopic approach for the non-invasive study of modern art materials and techniques // Applied Physics A: Materials Science and Processing. - 2010. - № 100, C. 613-624.

[127] Renda, V., Mollica Nardo, V., Anastasio, G., Caponetti, E., Vasi, C.S., Saladino, M.L., Armetta, F., Trusso, S., Ponterio, R.C. A multivariate statistical approach of X-ray fluorescence characterization of a large collection of reverse glass paintings // Spectrochimica Acta - Part B Atomic Spectroscopy. - 2019. - № 159, C. 105655.

[128] Mirea, D.A., Ciulavu, F., Ilie, M.V., Iancu, D.A. PIXE, ED-XRF and optical analysis to authenticate the Garvän gold monetary treasury // Archaeometry. - 2021. - № 63, C. 641-650.

[129] Gebremariam, K.F., Kvittingen, L., Banica, F.-G. Application of a portable XRF analyzer to investigate the medieval wall paintings of yemrehanna krestos church, Ethiopia // X-Ray Spectrometry. - 2013. - № 42, C. 462-469.

[130] Fichera, G.V., Rovetta, T., Fiocco, G., Alberti, G., Invernizzi, C., Licchelli, M., Malagodi, M. Elemental analysis as statistical preliminary study of historical musical instruments // Microchemical Journal. - 2018. - № 137, C. 309-317.

[131] Albertin, F., Balliana, E., Pizzol, G., Colavizza, G., Zendri, E., Raines, D. Printing materials and technologies in the 15 th-17 th century book production: An undervalued research field // Microchemical Journal. - 2018. - № 138, C. 147-153.

[132] Alberghina, M.F., Barraco, R., Brai, M., Pellegrino, L., Prestileo, F., Schiavone, S., Tranchina, L. Gilding and pigments of Renaissance marble of Abatellis Palace: Non-invasive investigation by XRF spectrometry // X-Ray Spectrometry. - 2013. - № 42, C. 68-78.

[133] Zdiniakova, T., de la Calle, M.B. Feasibility study about the use of element profiles determined by ED-XRF as screening method to authenticate coconut sugar commercially available // European Food Research and Technology. - 2020. - № 246, C. 2101-2109.

[134] Sussulini, A., Lima, A.G., Figueiredo, E.C., Fernandes, H.L., Pinheiro, S.C.L.P., Buenoa, M.I.M.S., Pereira, F.M.V. X-ray scattering information of ED-XRF technique for powdered fruit juice mixes // X-Ray Spectrometry. - 2009. - № 38, C. 254-257.

[135] Rajapaksha, D., Waduge, V., Padilla-Alvarez, R., Kalpage, M., Rathnayake, R.M.N.P., Migliori, A., Frew, R., Abeysinghe, S., Abrahim, A., Amarakoon, T. XRF to support food traceability studies: Classification of Sri Lankan tea based on their region of origin // X-Ray Spectrometry. - 2017. - № 46, C. 220-224.

[136] Mir-Marques, A., Elvira-Saez, C., Cervera, M.L., Garrigues, S., de la Guardia, M. Authentication of protected designation of origin artichokes by spectroscopy methods // Food Control. - 2016. - № 59, C. 74-81.

[137] Ghidotti, M., Papoci, S., Dumitrascu, C., Zdiniakova, T., Fiamegos, Y., Gutinas, M.B.D.L.C. ED-XRF as screening tool to help customs laboratories in their fight against fraud. State-of-the-art // Talanta Open. - 2021. - № 3, C. 100040.

[138] Ghidotti, M., Fiamegos, Y., Dumitrascu, C., de la Calle, M.B. Use of elemental profiles to verify geographical origin and botanical variety of Spanish honeys with a protected denomination of origin // Food Chemistry. - 2021. - № 342, C. 128350.

[139] Fiamegos, Y., Papoci, S., Dumitrascu, C., Ghidotti, M., Zdiniakova, T., Ulberth, F., de la Calle Guntinas, M.B. Are the elemental fingerprints of organic and conventional food different? ED-XRF as screening technique // Journal of Food Composition and Analysis. - 2021. - № 99, C. 103854.

[140] Adams, M.J., Allen, J.R. Quantitative X-ray fluorescence analysis of geological materials using partial least-squares regression // Analyst. - 1998. - № 123, C. 537541.

[141] Ghasemi, J.B., Rofouei, M.K., Amiri, N. Using chemometric methods for overlap correction of sodium-zinc spectral lines generated by wavelength dispersive X-ray fluorescence in mineral samples // X-Ray Spectrometry. - 2014. - № 43, C. 131-137.

[142] Malherbe, J., Claverie, F. Toward chromium speciation in solids using wavelength dispersive X-ray fluorescence spectrometry Cr Kp lines // Analytica Chimica Acta. -2013. - № 773, C. 37-44.

[143] Lopes, F., Melquiades, F.L., Appoloni, C.R., Cesareo, R., Rizzutto, M., Silva, T.F. Thickness determination of gold layer on pre-Columbian objects and a gilding frame, combining pXRF and PLS regression // X-Ray Spectrometry. - 2016. - № 45, C. 344351.

[144] Lemberge, P., De Raedt, I., Janssens, K.H., Wei, F., Van Espen, P.J. Quantitative analysis of 16-17th century archaeological glass vessels using PLS regression of EPXMA and ^-XRF data // Journal of Chemometrics. - 2000. - № 14, C. 751-763.

[145] Tavares, T.R., Mouazen, A.M., Alves, E.E.N., Dos Santos, F.R., Melquiades, F.L., De Carvalho, H.W.P., Molin, J.P. Assessing soil key fertility attributes using a portable X-ray fluorescence: A simple method to overcome matrix effect // Agronomy. - 2020. - № 10, C. 787.

[146] Melquiades, F.L., Thomaz, E.L. X-ray fluorescence to estimate the maximum temperature reached at soil surface during experimental slash-and-burn fires // Journal of Environmental Quality. - 2016. - № 45, C. 1104-1109.

[147] Janik, L.J., Skjemstand, J.O., Raven, M.D. Characterization and analysis of soils using mid-infrared partial least squares. I. correlations with xrf-determined major element composition // Australian Journal of Soil Research. - 1995. - № 33, C. 621636.

[148] dos Santos, F.R., de Oliveira, J.F., Bona, E., dos Santos, J.V.F., Barboza, G.M.C., Melquiades, F.L. EDXRF spectral data combined with PLSR to determine some soil fertility indicators // Microchemical Journal. - 1920. - № 152, C. 104275.

[149] Da-Col, J.A., Bueno, M.I.M.S., Melquiades, F.L. Fast and direct Na and K determination in table, marine, and low-sodium salts by X-ray fluorescence and chemometrics // Journal of Agricultural and Food Chemistry. - 2015. - № 63, C. 2406-2412.

[150] Terra, J., Antunes, A.M., Pradob, M.A., Bueno, M.I.M.S. Energy value determinations of industrialized foods: The potential of using X-ray spectroscopy and partial least squares // X-Ray Spectrometry. - 2010. - № 39, C. 167-175.

[151] Speran^a, M.A., Nascimento, P.A.M., Pereira, F.M.V. Impurity in sugarcane juice as mineral content: A prospect for analysis using energy-dispersive X-ray fluorescence (EDXRF) and chemometrics // Microchemical Journal. - 2021. - № 164, C.105951.

[152] Speran^a, M.A., Mayorquin-Guevara, J.E., da Cruz, M.C.P., de Almeida Teixeira, G.H., Pereira, F.M.V. Biofortification quality in bananas monitored by energy-dispersive X-ray fluorescence and chemometrics // Food Chemistry. - 2021. - № 362, C.130172.

[153] Herreros-Chavez, L., Oueghlani, F., Morales-Rubio, A., Cervera, M.L., de la Guardia, M. Mineral profiles of legumes and fruits through partial least squares energy dispersive X-ray fluorescence // Journal of Food Composition and Analysis. - 2019.

- № 82, C. 103240.

[154] Herreros-Chavez, L., Morales-Rubio, A., Cervera, M.L., de la Guardia, M. Partial least squares modelization of energy dispersive X-ray fluorescence // Talanta. - 2019.

- № 194, C. 158-163.

[155] Liu, S., Su, B.-M., Li, Q.-H., Gan, F.-X. Application of calibration curve method and partial least squares regression analysis to quantitative analysis of nephrite samples using XRF // Guang Pu Xue Yu Guang Pu Fen Xi/Spectroscopy and Spectral Analysis. - 2015. - № 35, C. 245-251.

[156] Pereira, F.M.V., Bueno, M.I.M.S. Calibration of paint and varnish properties: Potentialities using X-ray Spectroscopy and Partial Least Squares // Chemometrics and Intelligent Laboratory Systems. - 2008. - № 92, C. 131-137.

[157] Moros, J., Gredilla, A., Fdez-Ortiz De Vallejuelo, S., De Diego, A., Madariaga, J.M., Garrigues, S., De La Guardia, M. Partial least squares X-ray fluorescence determination of trace elements in sediments from the estuary of Nerbioi-Ibaizabal River // Talanta. - 2010. - № 82, C. 1254-1260.

[158] Brocchieri, J., Scialla, E., Sabbarese, C. Estimation of Ag coating thickness by different methods using a handheld XRF instrument // Nuclear Instruments and Methods in Physics Research, Section B: Beam Interactions with Materials and Atoms. - 2021. - № 486, C. 73-84.

[159] Ghasemi, J.B., Rofouei, M.K., Amiri, N. Using chemometric methods for overlap correction of sodium-zinc spectral lines generated by wavelength dispersive X-ray fluorescence in mineral samples // X-Ray Spectrometry. - 2014. - № 486, C. 131137.

[160] Kirsanov, D., Panchuk, V., Goydenko, A., Khaydukova, M., Semenov, V., Legin, A. Improving precision of X-ray fluorescence analysis of lanthanide mixtures using partial least squares regression // Spectrochimica Acta - Part B Atomic Spectroscopy.

- 2015. - № 113, C. 126-131.

[161] Melquiades, F.L., Bortoleto, G.G., Marchiori, L.F.S., Bueno, M.I.M.S. Direct determination of sugar cane quality parameters by X-ray spectrometry and

multivariate analysis // Journal of Agricultural and Food Chemistry. - 2012. - № 60, C. 10755-10761.

[162] Angeyo, K.H., Gari, S., Mustapha, A.O., Mangala, J.M. Feasibility for direct rapid energy dispersive X-ray fluorescence (EDXRF) and scattering analysis of complex matrix liquids by partial least squares // Applied Radiation and Isotopes. - 2012. - № 70, C. 2596-2601.

[163] Kaniu, M.I., Angeyo, K.H., Mwala, A.K., Mangala, M.J. Direct rapid analysis of trace bioavailable soil macronutrients by chemometrics-assisted energy dispersive X-ray fluorescence and scattering spectrometry // Analytica Chimica Acta. - 2012. - № 729, C. 21-25.

[164] Goraieb, K., Alexandre, T.L., Bueno, M.I.M.S. X-ray spectrometry and chemometrics in sugar classification, correlation with degree of sweetness and specific rotation of polarized light // Analytica Chimica Acta. - 2007. - № 595, C. 170-175.

[165] Kaniu, M.I., Angeyo, K.H., Mangala, M.J., Mwala, A.K., Bartilol, S.K. Feasibility for chemometric energy dispersive X-ray fluorescence and scattering (EDXRFS) spectroscopy method for rapid soil quality assessment // X-Ray Spectrometry. - 2011. - № 40, C. 432-440.

[166] Kaniu, M.I., Angeyo, K.H., Mwala, A.K., Mwangi, F.K. Energy dispersive X-ray fluorescence and scattering assessment of soil quality via partial least squares and artificial neural networks analytical modeling approaches // Talanta. - 2012. - № 98, C. 236-240.

[167] Facchin, I., Mello, C., Bueno, M.I.M.S., Poppi, R.J. Simultaneous Determination of Lead and Sulfur by Energy-Dispersive X-Ray Spectrometry. Comparison between Artificial Neural Networks and Other Multivariate Calibration Methods // X-Ray Spectrometry. - 1999. - № 28, C. 173-177.

[168] Li, F., Gu, Z., Ge, L., Sun, D., Deng, X., Wang, S., Hu, B., Xu, J. Application of artificial neural networks to X-ray fluorescence spectrum analysis // X-Ray Spectrometry. - 2019. - № 48, C. 138-150.

[169] Karamizadeh, S., Abdullah, S. M., Manaf, A. A., Zamani, M., Hooman, A. An Overview of Principal Component Analysis // Journal of Signal and Information Processing. - 2013. - № 4, C. 173-175.

[170] Bro, R., Smilde, A.K. Principal component analysis // Analytical Methods. - 2014.

- № 6, C. 2812-2831.

[171] Wold, S., Sjöström, M., Eriksson, L. PLS-regression: A basic tool of chemometrics // Chemometrics and Intelligent Laboratory Systems. - 2001. - № 58, C. 109-130.

[172] Hsing, T. Nearest neighbor inverse regression // Annals of Statistics. - 1999. - № 27, C. 697-731.

[173] Leardi. R. Nature-inspired Methods in Chemometrics: Genetic Algorithms and Artificial Neural Networks / R. Leardi. - Elsevier Science, 2003. - 402 c.

[174] Westad, F., Marini, F. Validation of chemometric models - A tutorial // Analytica Chimica Acta. - 2015. - № 893, C. 14-24.

[175] Kennard, R.W., Stone, L.A. Computer Aided Design of Experiments // Technometrics. - 1969. - № 11, C. 137-148.

[176] Tropsha, A., Gramatica, P., Gombar, V. The Importance of Being Earnest: Validation is the Absolute Essential for Successful Application and Interpretation of QSPR Models // QSAR and Combinatorial Science. - 2003. - № 22, C. 69-77.

[177] R: The R Project for Statistical Computing [Electronic resource]. - 2021. https://www.r-project.org/.

[178] Kucheryavskiy, S. mdatools - R package for chemometrics // Chemometrics and Intelligent Laboratory Systems. - 2020. - № 198, C. 103937.

[179] Kuhn, M. Building predictive models in R using the caret package // Journal of Statistical Software. - 2008. - № 28, C. 1-26.

[180] Günther, F., Fritsch, S. Neuralnet: Training of neural networks // R Journal. - 2010.

- № 2, C. 30-38.

[181] Aidene, S., Khaydukova, M., Pashkova, G., Chubarov, V., Savinov, S., Semenov, V., Kirsanov, D., Panchuk, V. Does chemometrics work for matrix effects correction in X-ray fluorescence analysis? // Spectrochimica Acta - Part B Atomic Spectroscopy.

- 2021. - № 185, C. 106310.

[182] Aidene, S., Semenov, V., Kirsanov, D., Kirsanov, D., Panchuk, V. Scattering of monochromatic X-rays at different incident radiation angles provides quantitative information on physical and chemical properties of plastics // Measurement: Journal of the International Measurement Confederation. - 2021. - № 172, C. 108888.

[183] Aidene, S., Semenov, V., Kirsanov, D., Kirsanov, D., Panchuk, V. Assessment of the physical properties, and the hydrogen, carbon, and oxygen content in plastics using energy-dispersive X-ray fluorescence spectrometry // Spectrochimica Acta - Part B Atomic Spectroscopy. - 2020. - № 165, C. 105771.