The application of structure envelopes in structure determination from powder diffraction data

Brenner, S.; McCusker, Lynne B.; Baerlocher, Christian

doi:10.1107/s0021889802001759

Cited by 45 publications

(36 citation statements)

References 28 publications

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“…Properly acquired HRTEM images on sufficiently thin samples at special projections allow estimating the phases of corresponding Fourier coefficients (Zou et al, 2011). Combining the estimated phases with the magnitudes of a few low-resolution reflections yields a low-resolution electron density map -a structure envelope (Brenner et al, 2002). Both the phases and the envelope can be used as additional information in the charge-flipping iteration.…”

Section: Powder Diffraction Datamentioning

confidence: 99%

The charge-flipping algorithm in crystallography

Palatinus

2013

Acta Crystallogr B Struct Sci Cryst Eng Mater

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The charge-flipping algorithm (CFA) is a member of the diverse family of dual-space iterative phasing algorithms. These algorithms use alternating modifications in direct and reciprocal space to find a solution to the phase problem. The current state-of-the-art CFA is reviewed and it is put in the context of related dual-space algorithms with relevance for crystallography. The CFA has found applications in many crystallographic problems. The principal applications in various fields are described with sections devoted to routine structure solution, the solution of complex structures from powder diffraction data, the solution of incommensurately modulated crystals and quasicrystals, macromolecular crystallography and single-particle imaging.

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Section: Powder Diffraction Datamentioning

confidence: 99%

The charge-flipping algorithm in crystallography

Palatinus

2013

Acta Crystallogr B Struct Sci Cryst Eng Mater

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“…This feature may be used for generating of a starting model for crystal structure determination routines, which are not based on traditional direct methods [53].…”

Section: Use For Structure Determinationmentioning

confidence: 99%

Periodic Space Partitioners (PSP) and their relations to Crystal Chemistry

Nesper¹,

Grin

2011

Zeitschrift Für Kristallographie

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Abstract. We are looking back on 30 years development of periodic space partitioners (PSP) and their relations to their periodic relatives, i.e. minimal surfaces (PMS), zero potential surfaces (P0PS), nodal surfaces (PNS), and exponential scale surfaces. Hans-Georg von Schnering and Sten Andersson have pioneered this field especially in terms of applications to crystal chemistry. This review relates the early attempts to approximate periodic minimal surfaces which established a systematic classification of all PSP in terms space group symmetry and consecutive applications in a variety of different fields. A consistent nomenclature is outlined and different methods for deriving PSP are described. Characteristic structure factor sets which solely define PNS by can be used to discriminate structure types of a given symmetry or even to determine complicated crystal structures. The concept of PSP relates space group symmetry, topology, and chemical bonding in an intriguing way and tessellations on PSP which can be generated in a straight forward way allow to predict new framework types. Through transformation of such continuous topological forms a new entry has been found for understanding and interpreting reconstructive phase transitions. Finally we indicate the importance of PSP models for soft matter science. History and developmentMinimal surfaces are a middle aged problem in mathematics mostly addressed since the 19 th century, but constitute an eternal fascination for humans probably since the earliest days of conscious thought. The intriguing fascination of soap bubbles is related to a deep feeling of harmony and beauty, the priming of which we simply do not know [1]. It may be due to a comprehensive intuitive understanding of the world without concrete knowing just like the feeling of harmony which is created by the golden ratio and five-fold symmetry. Why does the most irrational number 1 induce such a state of comfort in human minds? We do not know, just as nobody knows why the fine structure constant approaches more and more the value 1/137, the denominator being 33 rd prime number. To solve this question was the last great goal of Wolfgang Pauli who was not only a great physicist and mathematician but also stressed the importance of intuitive solutions to physical problems, amongst others by dreaming [2].A mathematical treatment of minimal surfaces goes back to Lagrange's work in the 18 th century which resulted in the Euler-Lagrange equation [3]. In the 19 th century the experiments of J. Plateau contributed much to mathematical research on such objects and led to the formulations of Plateau's problem which turned out to be unsolvable in general analytical form. The quest for deriving minimal surfaces and periodic minimal surfaces as well as for their analytical formulation increased by the end of the 19 th century especially by H. A. Schwarz [4] and in the beginning of the 20 th century by D. Hilbert [5]. Hilbert was not only one of the greatest mathematicians of modern age but also a mathematical puri...

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“…The main difference between this structure envelope and the molecular envelope that is used in protein crystallography is that the former does not necessarily have a closed form. It is a periodic nodal surface [21] that separates regions of high electron density from those of low electron density, and can be generated from just a few strong, low-index reflections [22].…”

Section: Structure Envelopesmentioning

confidence: 99%

Electron crystallography as a complement to X-ray powder diffraction techniques

McCusker¹,

Baerlocher²

2012

Zeitschrift für Kristallographie - Crystalline Materials

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Abstract. Electron microscopy techniques yield information for crystal structure analysis that is remarkably complementary to that obtained from X-ray powder diffraction data. Structures of polycrystalline materials that resist solution by either method alone can sometimes be solved by combining the two. For example, the intensities extracted from an X-ray powder diffraction pattern are kinematical and can be interpreted easily, while those obtained from a typical selected area electron diffraction (SAED) or precession electron diffraction (PED) pattern are at least partially dynamical and therefore more difficult to use directly. On the other hand, many reflections in a powder diffraction pattern overlap and only the sum of their intensities can be measured, while those in an electron diffraction pattern are from a single crystal and therefore well separated in space. Although the intensities obtained from either SAED or PED data are less reliable than those obtained with Xrays, they can be used to advantage to improve the initial partitioning of the intensities of overlapping reflections. However, it is the partial crystallographic phase information that can be extracted either from high-resolution transmission electron microscopy (HRTEM) images or from PED data that has proven to be particularly useful in combination with high-resolution X-ray powder diffraction data. The dual-space (reciprocal and real space) structure determination programs Focus and Superflip have been shown to be especially useful for combining the two different types of data.

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The application of structure envelopes in structure determination from powder diffraction data

Cited by 45 publications

References 28 publications

The charge-flipping algorithm in crystallography

The charge-flipping algorithm in crystallography

Periodic Space Partitioners (PSP) and their relations to Crystal Chemistry

Electron crystallography as a complement to X-ray powder diffraction techniques

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