{"title":"平均晶粒尺寸和晶粒尺寸分布的测定:包络函数法 EnvACS。","authors":"Thorsten M Gesing, Lars Robben","doi":"10.1107/S1600576724007362","DOIUrl":null,"url":null,"abstract":"<p><p>A procedure is presented to exactly obtain the apparent average crystallite size (ACS) of powder samples using standard in-house powder diffraction experiments without any restriction originating from the Scherrer equation. Additionally, the crystallite size distribution within the sample can be evaluated. To achieve this, powder diffractograms are background corrected and long-range radial distribution functions <i>G</i>(<i>r</i>) up to 300 nm are calculated from the diffraction data. The envelope function <i>f</i> <sup>env</sup> of <i>G</i>(<i>r</i>) is approximated by a procedure determining the absolute maxima of <i>G</i>(<i>r</i>) in a certain interval (<i>r</i> range). Fitting of an ACS distribution envelope function to this approximation gives the ACS and its distribution. The method is tested on diffractograms of LaB<sub>6</sub> standard reference materials measured with different wavelengths to demonstrate the validity of the approach and to clarify the influence of the wavelength used. The latter results in a general description of the maximum observable average crystallite size, which depends on the instrument and wavelength used. The crystallite site distribution is compared with particle size distributions based on transmission electron microscopy investigations, providing an approximation of the average number of crystallites per particle.</p>","PeriodicalId":14950,"journal":{"name":"Journal of Applied Crystallography","volume":null,"pages":null},"PeriodicalIF":6.1000,"publicationDate":"2024-09-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC11460396/pdf/","citationCount":"0","resultStr":"{\"title\":\"Determination of the average crystallite size and the crystallite size distribution: the envelope function approach EnvACS.\",\"authors\":\"Thorsten M Gesing, Lars Robben\",\"doi\":\"10.1107/S1600576724007362\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p><p>A procedure is presented to exactly obtain the apparent average crystallite size (ACS) of powder samples using standard in-house powder diffraction experiments without any restriction originating from the Scherrer equation. Additionally, the crystallite size distribution within the sample can be evaluated. To achieve this, powder diffractograms are background corrected and long-range radial distribution functions <i>G</i>(<i>r</i>) up to 300 nm are calculated from the diffraction data. The envelope function <i>f</i> <sup>env</sup> of <i>G</i>(<i>r</i>) is approximated by a procedure determining the absolute maxima of <i>G</i>(<i>r</i>) in a certain interval (<i>r</i> range). Fitting of an ACS distribution envelope function to this approximation gives the ACS and its distribution. The method is tested on diffractograms of LaB<sub>6</sub> standard reference materials measured with different wavelengths to demonstrate the validity of the approach and to clarify the influence of the wavelength used. The latter results in a general description of the maximum observable average crystallite size, which depends on the instrument and wavelength used. The crystallite site distribution is compared with particle size distributions based on transmission electron microscopy investigations, providing an approximation of the average number of crystallites per particle.</p>\",\"PeriodicalId\":14950,\"journal\":{\"name\":\"Journal of Applied Crystallography\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":6.1000,\"publicationDate\":\"2024-09-17\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC11460396/pdf/\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Applied Crystallography\",\"FirstCategoryId\":\"88\",\"ListUrlMain\":\"https://doi.org/10.1107/S1600576724007362\",\"RegionNum\":3,\"RegionCategory\":\"材料科学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"2024/10/1 0:00:00\",\"PubModel\":\"eCollection\",\"JCR\":\"Q1\",\"JCRName\":\"Biochemistry, Genetics and Molecular Biology\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Applied Crystallography","FirstCategoryId":"88","ListUrlMain":"https://doi.org/10.1107/S1600576724007362","RegionNum":3,"RegionCategory":"材料科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"2024/10/1 0:00:00","PubModel":"eCollection","JCR":"Q1","JCRName":"Biochemistry, Genetics and Molecular Biology","Score":null,"Total":0}
Determination of the average crystallite size and the crystallite size distribution: the envelope function approach EnvACS.
A procedure is presented to exactly obtain the apparent average crystallite size (ACS) of powder samples using standard in-house powder diffraction experiments without any restriction originating from the Scherrer equation. Additionally, the crystallite size distribution within the sample can be evaluated. To achieve this, powder diffractograms are background corrected and long-range radial distribution functions G(r) up to 300 nm are calculated from the diffraction data. The envelope function fenv of G(r) is approximated by a procedure determining the absolute maxima of G(r) in a certain interval (r range). Fitting of an ACS distribution envelope function to this approximation gives the ACS and its distribution. The method is tested on diffractograms of LaB6 standard reference materials measured with different wavelengths to demonstrate the validity of the approach and to clarify the influence of the wavelength used. The latter results in a general description of the maximum observable average crystallite size, which depends on the instrument and wavelength used. The crystallite site distribution is compared with particle size distributions based on transmission electron microscopy investigations, providing an approximation of the average number of crystallites per particle.
期刊介绍:
Many research topics in condensed matter research, materials science and the life sciences make use of crystallographic methods to study crystalline and non-crystalline matter with neutrons, X-rays and electrons. Articles published in the Journal of Applied Crystallography focus on these methods and their use in identifying structural and diffusion-controlled phase transformations, structure-property relationships, structural changes of defects, interfaces and surfaces, etc. Developments of instrumentation and crystallographic apparatus, theory and interpretation, numerical analysis and other related subjects are also covered. The journal is the primary place where crystallographic computer program information is published.