{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,28]],"date-time":"2026-09-28T02:49:50Z","timestamp":1790563790597,"version":"4.1.0"},"reference-count":13,"publisher":"AIP Publishing","issue":"4","funder":[{"DOI":"10.13039\/501100007684","name":"Ministry of Education and Science of Ukraine","doi-asserted-by":"publisher","award":["0118U002048"],"award-info":[{"award-number":["0118U002048"]}],"id":[{"id":"10.13039\/501100007684","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["pubs.aip.org"],"crossmark-restriction":true},"short-container-title":[],"published-print":{"date-parts":[[2026,4,1]]},"abstract":"<jats:p>The article presents a method for experimentally determining the fundamental parameter of interaction between a broadband x-ray spectrum and a material\u2014the ratio of the effective attenuation coefficient \u03bcef of the primary spectrum and the attenuation coefficient \u03bci of the fluorescence line of the i-th element. The determination of the fundamental parameter is necessary to justify the magnitude of the uncertainty of the concentration values found from the intensity of the fluorescence lines. The method is based on the known dependence of the intensity of x-ray fluorescence on the angles of entry \u03c6 and exit \u03c8 of radiation from the surface of the sample. At a constant scattering angle 2\u03b8 = \u03c6 + \u03c8, a series of measurements of the x-ray spectrum are made with different values of the angle \u03c8k and the integrated fluorescence intensity I(\u03c8k) is measured. Varying the angle \u03c8k in the range from 0\u00b0 to 90\u00b0 allows, when measuring a film on a substrate, to move from the \u201csaturated layer\u201d model to the thin film model with all intermediate stages. By fitting the experimental dependence I(\u03c8k), the values \u03bci\u03bcef and \u03bcef\u00b7D are determined, where D is the surface density. The objects of the study were single-component standards as well as zirconium films and nickel foils on single-crystalline silicon substrates. Spectral measurements were performed on an EDXRF spectrometer with SDD X-100 (Amptek). The \u03c8k angle was set in 1\u00b0 increments by rotating the sample on an HGZ (Carl Zeiss) goniometer; the spectrum accumulation time was 600\u00a0s. For single-component standards of zirconium, nickel iron, and titanium, the \u03bci\u03bcef values were determined with a relative error of 3%. The influence of the broadband spectrum shape on the \u03bci\u03bcef ratio and the \u03bbef (effective wavelength of the primary broadband spectrum) value was established: (1) a decrease in the voltage on the tube from 30 to 25\u00a0kV leads to an increase in \u03bbef for zirconium from 0.535 to 0.656\u00a0\u00c5, for nickel from 0.694 to 1.004\u00a0\u00c5, and for iron from 1.135 to 1.408\u00a0\u00c5; (2) the influence of the Cu-K\u03b1 artifact line on the \u03bci\u03bcef ratio was revealed: for iron and nickel, which have absorption jumps on opposite sides of this line, the \u03bci\u03bcef values differ by more than two times due to the effective excitation of iron fluorescence by the Cu\u2013K\u03b1 line. For nickel foils with a thickness of 6\u201312\u00a0\u03bcm, the values of \u03bci\u03bcef and surface density were measured without the use of standards. The \u03bci\u03bcef values of the foils are close to the nickel standard, and the surface density corresponds to the reference values. The relative measurement error does not exceed 5%. For thin zirconium films (0.2\u20136\u00a0\u03bcm), it was not possible to detect the theoretically predicted increase in \u03bbef with decreasing film thickness. The found values of surface density correspond to the reference values within 10% without the use of standards. The values of the parameters \u03bci\u03bcef and \u03bcef\u00b7D can be determined for a multicomponent film, serve as a criterion for selecting film standards of similar composition and thickness, and be used to justify the uncertainty of measurement results by calibrations.<\/jats:p>","DOI":"10.1063\/5.0289940","type":"journal-article","created":{"date-parts":[[2026,4,14]],"date-time":"2026-04-14T12:37:26Z","timestamp":1776170246000},"update-policy":"https:\/\/doi.org\/10.1063\/aip-crossmark-policy-page","source":"Crossref","is-referenced-by-count":1,"title":["Method of x-ray goniometry of fluorescence radiation for analysis of surface layers and films on a substrate"],"prefix":"10.1063","volume":"97","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-1332-5352","authenticated-orcid":false,"given":"Igor F.","family":"Mikhailov","sequence":"first","affiliation":[{"name":"National Technical University \u201cKharkiv Polytechnic Institute,\u201d 1 2, Kyrpychova str., 61002 Kharkiv,","place":["Ukraine"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8058-2183","authenticated-orcid":false,"given":"Anton I.","family":"Mikhailov","sequence":"additional","affiliation":[{"name":"National Technical University \u201cKharkiv Polytechnic Institute,\u201d 1 2, Kyrpychova str., 61002 Kharkiv,","place":["Ukraine"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4007-5205","authenticated-orcid":false,"given":"Svetlana S.","family":"Borisova","sequence":"additional","affiliation":[{"name":"National Technical University \u201cKharkiv Polytechnic Institute,\u201d 1 2, Kyrpychova str., 61002 Kharkiv,","place":["Ukraine"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Alexey O.","family":"Baturin","sequence":"additional","affiliation":[{"name":"National Technical University \u201cKharkiv Polytechnic Institute,\u201d 1 2, Kyrpychova str., 61002 Kharkiv,","place":["Ukraine"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Larisa P.","family":"Fomina","sequence":"additional","affiliation":[{"name":"National Technical University \u201cKharkiv Polytechnic Institute,\u201d 1 2, Kyrpychova str., 61002 Kharkiv,","place":["Ukraine"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0009-0002-0330-8185","authenticated-orcid":false,"given":"Artem D.","family":"Chystiakov","sequence":"additional","affiliation":[{"name":"National Technical University \u201cKharkiv Polytechnic Institute,\u201d 1 2, Kyrpychova str., 61002 Kharkiv,","place":["Ukraine"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4540-5207","authenticated-orcid":false,"given":"Volodymyr V.","family":"Nehoduiko","sequence":"additional","affiliation":[{"name":"Military Medical Clinical Center of the Northern Region 2 , Kharkiv,","place":["Ukraine"]}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"317","published-online":{"date-parts":[[2026,4,14]]},"reference":[{"key":"2026041408372196900_c1","first-page":"456","volume-title":"Physics of X-rays","year":"1953"},{"key":"2026041408372196900_c2","first-page":"985","volume-title":"Handbook of X-ray Spectrometry","author":"Van Grieken","year":"2002","edition":"2"},{"key":"2026041408372196900_c3","doi-asserted-by":"publisher","first-page":"181","DOI":"10.1006\/adnd.1993.1013","article-title":"X-ray interactions: Photoabsorption, scattering transmission and reflection","volume":"54","year":"1993","journal-title":"At. 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