Patterson function and δ recycling: derivation of the phasing equations.

IF 1.8 4区材料科学

Acta Crystallographica Section A Pub Date : 2012-05-01 Epub Date: 2012-03-22 DOI:10.1107/S0108767312008768

Jordi Rius

引用次数: 9

Abstract

Two phasing equations based on the Fourier syntheses δ(P) = T(-1)[(E(2) - )exp(iφ)] and δ(M) = T(-1)[(E - )exp(iφ)] were recently described [Rius (2012). Acta Cryst. A 68, 77-81] (E is the quasi-normalized structure factor and is the average over all reflections). These equations were found by comparison with the direct methods origin-free modulus sum function and constitute the core of the `δ recycling' phasing procedure. The derivation of these phasing equations from the minimization of a residual (R(P)) between two differently calculated density functions (one of them including the positivity constraint) is shown.

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帕特森函数和δ循环:相位方程的推导。

最近描述了基于傅里叶合成δ(P) = T(-1)[(E(2) -)exp(iφ)]和δ(M) = T(-1)[(E -)exp(iφ)]的两个相位方程[Rius(2012)]。Acta结晶。[A 68, 77-81] (E是准归一化结构因子，是所有反射的平均值)。这些方程是通过与直接法的无原点模量和函数的比较得到的，它们构成了“δ循环”相位过程的核心。从两个不同计算密度函数(其中一个包括正性约束)之间的残差(R(P))的最小化推导出这些相位方程。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Acta Crystallographica Section A 化学-晶体学

自引率

11.10%

发文量

审稿时长

3 months

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.