New benchmarks in the modelling of X-ray atomic form factors.

IF 1.9 4区材料科学 Q3 CHEMISTRY, MULTIDISCIPLINARY

Acta Crystallographica Section A: Foundations and Advances Pub Date : 2023-07-01 DOI:10.1107/S2053273323003996

Gunnar Thorkildsen

{"title":"New benchmarks in the modelling of X-ray atomic form factors.","authors":"Gunnar Thorkildsen","doi":"10.1107/S2053273323003996","DOIUrl":null,"url":null,"abstract":"Analytical representations of X-ray atomic form factor data have been determined. The original data, f0(s;Z), are reproduced to a high degree of accuracy. The mean absolute errors calculated for all s = sin θ/λ and Z values in question are primarily determined by the precision of the published data. The inverse Mott-Bethe formula is the underlying basis with the electron scattering factor expressed by an expansion in Gaussian basis functions. The number of Gaussians depends upon the element and the data and is in the range 6-20. The refinement procedure, conducted to obtain the parameters of the models, is carried out for seven different form factor tables published in the span Cromer & Mann [(1968), Acta Cryst. A24, 321-324] to Olukayode et al. [(2023), Acta Cryst. A79, 59-79]. The s ranges are finite, the most common span being [0.0, 6.0] Å-1. Only one function for each element is needed to model the full range. This presentation to a large extent makes use of a detailed graphical account of the results.","PeriodicalId":106,"journal":{"name":"Acta Crystallographica Section A: Foundations and Advances","volume":"79 Pt 4","pages":"318-330"},"PeriodicalIF":1.9000,"publicationDate":"2023-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10317139/pdf/","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Acta Crystallographica Section A: Foundations and Advances","FirstCategoryId":"1","ListUrlMain":"https://doi.org/10.1107/S2053273323003996","RegionNum":4,"RegionCategory":"材料科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"CHEMISTRY, MULTIDISCIPLINARY","Score":null,"Total":0}

引用次数: 0

Abstract

Analytical representations of X-ray atomic form factor data have been determined. The original data, f₀(s;Z), are reproduced to a high degree of accuracy. The mean absolute errors calculated for all s = sin θ/λ and Z values in question are primarily determined by the precision of the published data. The inverse Mott-Bethe formula is the underlying basis with the electron scattering factor expressed by an expansion in Gaussian basis functions. The number of Gaussians depends upon the element and the data and is in the range 6-20. The refinement procedure, conducted to obtain the parameters of the models, is carried out for seven different form factor tables published in the span Cromer & Mann [(1968), Acta Cryst. A24, 321-324] to Olukayode et al. [(2023), Acta Cryst. A79, 59-79]. The s ranges are finite, the most common span being [0.0, 6.0] Å^-1. Only one function for each element is needed to model the full range. This presentation to a large extent makes use of a detailed graphical account of the results.

Abstract Image

查看原文本刊更多论文

x射线原子形状因子建模的新基准。

已经确定了x射线原子形状因子数据的分析表示。原始数据f0(s;Z)的再现精度很高。所讨论的所有s = sin θ/λ和Z值计算的平均绝对误差主要取决于已发表数据的精度。反莫特-贝特公式是下基，电子散射系数用高斯基函数展开表示。高斯数的数量取决于元素和数据，范围在6-20之间。为了获得模型的参数，我们对Cromer & Mann [(1968)， Acta crystal]中发表的七种不同的形状因子表进行了改进。[j] ~ Olukayode等[2023]，晶体学报。你姓名,59 - 79]。范围是有限的，最常见的跨度是[0.0,6.0]Å-1。每个元素只需要一个函数就可以对整个范围进行建模。这个演示在很大程度上使用了结果的详细图形说明。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

求助全文

约1分钟内获得全文求助全文

来源期刊

Acta Crystallographica Section A: Foundations and Advances CHEMISTRY, MULTIDISCIPLINARYCRYSTALLOGRAPH-CRYSTALLOGRAPHY

CiteScore

2.60

自引率

11.10%

发文量

419

期刊介绍： Acta Crystallographica Section A: Foundations and Advances publishes articles reporting advances in the theory and practice of all areas of crystallography in the broadest sense. As well as traditional crystallography, this includes nanocrystals, metacrystals, amorphous materials, quasicrystals, synchrotron and XFEL studies, coherent scattering, diffraction imaging, time-resolved studies and the structure of strain and defects in materials. The journal has two parts, a rapid-publication Advances section and the traditional Foundations section. Articles for the Advances section are of particularly high value and impact. They receive expedited treatment and may be highlighted by an accompanying scientific commentary article and a press release. Further details are given in the November 2013 Editorial. The central themes of the journal are, on the one hand, experimental and theoretical studies of the properties and arrangements of atoms, ions and molecules in condensed matter, periodic, quasiperiodic or amorphous, ideal or real, and, on the other, the theoretical and experimental aspects of the various methods to determine these properties and arrangements.