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<article article-type="research-article" dtd-version="1.3" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xml:lang="en"><front><journal-meta><journal-id journal-id-type="publisher-id">najo</journal-id><journal-title-group><journal-title xml:lang="en">Nanosystems: Physics, Chemistry, Mathematics</journal-title><trans-title-group xml:lang="ru"><trans-title>Наносистемы: физика, химия, математика</trans-title></trans-title-group></journal-title-group><issn pub-type="ppub">2220-8054</issn><issn pub-type="epub">2305-7971</issn><publisher><publisher-name>Университет ИТМО</publisher-name></publisher></journal-meta><article-meta><article-id pub-id-type="doi">10.17586/2220-8054-2022-13-1-62-70</article-id><article-id custom-type="elpub" pub-id-type="custom">najo-217</article-id><article-categories><subj-group subj-group-type="heading"><subject>Research Article</subject></subj-group><subj-group subj-group-type="section-heading" xml:lang="ru"><subject>Статьи</subject></subj-group></article-categories><title-group><article-title>Iterative method of reconstructing the size distribution function of spherical nanoparticles based on the intensity of the small-angle X-ray scattering including the interference contribution to the intensity</article-title><trans-title-group xml:lang="ru"><trans-title></trans-title></trans-title-group></title-group><contrib-group><contrib contrib-type="author" corresp="yes"><name-alternatives><name name-style="western" xml:lang="en"><surname>Kuchko</surname><given-names>A. V.</given-names></name></name-alternatives><email xlink:type="simple">artemkav@gmail.com</email><xref ref-type="aff" rid="aff-1"/></contrib><contrib contrib-type="author" corresp="yes"><name-alternatives><name name-style="western" xml:lang="en"><surname>Smirnov</surname><given-names>A. V.</given-names></name></name-alternatives><email xlink:type="simple">smirnav_2@mail.ru</email><xref ref-type="aff" rid="aff-1"/></contrib></contrib-group><aff xml:lang="en" id="aff-1"><institution>ITMO University</institution><country>Russian Federation</country></aff><pub-date pub-type="collection"><year>2022</year></pub-date><pub-date pub-type="epub"><day>06</day><month>06</month><year>2025</year></pub-date><volume>13</volume><issue>1</issue><fpage>62</fpage><lpage>70</lpage><permissions><copyright-statement>Copyright &amp;#x00A9; Kuchko A.V., Smirnov A.V., 2025</copyright-statement><copyright-year>2025</copyright-year><copyright-holder xml:lang="ru">Kuchko A.V., Smirnov A.V.</copyright-holder><copyright-holder xml:lang="en">Kuchko A.V., Smirnov A.V.</copyright-holder><license xml:lang="ru" license-type="creative-commons-attribution" xlink:href="https://creativecommons.org/licenses/by/4.0/" xlink:type="simple"><license-p>Данная работа распространяется под лицензией Creative Commons Attribution 4.0.</license-p></license><license xml:lang="en" license-type="creative-commons-attribution" xlink:href="https://creativecommons.org/licenses/by/4.0/" xlink:type="simple"><license-p>This work is licensed under a Creative Commons Attribution 4.0 License.</license-p></license></permissions><self-uri xlink:href="https://nanojournal.ifmo.ru/jour/article/view/217">https://nanojournal.ifmo.ru/jour/article/view/217</self-uri><abstract><p>It has been shown that for systems of polydisperse spherical particles the interference distortions of the scattering intensity significantly affect the result of reconstructing the particle size distribution when the volume fraction of the scattering substance is higher than 10 %. We have developed an iterative method that reconstructs the size distribution function from the small-angle X-ray scattering intensity with interference distortions. The efficiency of this method is confirmed based on simulated scattering intensities and experimentally measured intensities of samples with a volume fraction of a scattering substance up to 40 %.</p></abstract><kwd-group xml:lang="en"><kwd>small-angle X-ray scattering</kwd><kwd>polydisperse nanoparticle system</kwd><kwd>interference contribution</kwd><kwd>volume fractions distribution</kwd><kwd>statistical regularization method</kwd><kwd>iterative methods</kwd></kwd-group></article-meta></front><back><ref-list><title>References</title><ref id="cit1"><label>1</label><citation-alternatives><mixed-citation xml:lang="ru">Precious-Ayanwale A., Donohu’e-Cornejo A., et al. Review of the synthesis, characterization and application of zirconia mixed metal oxide nanoparticles.Int. 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