Using NIST crystal data within Siemens software for four-circle and SMART CCD diffractometers

Byram, Susan K.; Campana, Charles F.; Fait, James F.; Sparks, R. A.

doi:10.6028/jres.101.030

Cited by 9 publications

(16 citation statements)

References 6 publications

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“…Two principal uses of Niggli reduction are the determination of Bravais lattice type and the construction of a database using a representation of the unit cell for its key (Andrews et al, 1980;Toby, 1994;Byram et al, 1996).…”

Section: Introductionmentioning

confidence: 99%

The geometry of Niggli reduction:BGAOL–embedding Niggli reduction and analysis of boundaries

Andrews¹,

Bernstein

2014

J Appl Crystallogr

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Niggli reduction can be viewed as a series of operations in a six-dimensional space derived from the metric tensor. An implicit embedding of the space of Niggli-reduced cells in a higher-dimensional space to facilitate calculation of distances between cells is described. This distance metric is used to create a program, , for Bravais lattice determination. Results from are compared with results from other metric based Bravais lattice determination algorithms. This embedding depends on understanding the boundary polytopes of the Niggli-reduced cone in the six-dimensional space. This article describes an investigation of the boundary polytopes of the Niggli-reduced cone in the six-dimensional space by algebraic analysis and organized random probing of regions near one-, two-, three-, four-, five-, six-, seven- and eightfold boundary polytope intersections. The discussion of valid boundary polytopes is limited to those avoiding the mathematically interesting but crystallographically impossible cases of zero-length cell edges. Combinations of boundary polytopes without a valid intersection in the closure of the Niggli cone or with an intersection that would force a cell edge to zero or without neighboring probe points are eliminated. In all, 216 boundary polytopes are found. There are 15 five-dimensional boundary polytopes of the full Niggli cone .

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Section: Introductionmentioning

confidence: 99%

The geometry of Niggli reduction:BGAOL–embedding Niggli reduction and analysis of boundaries

Andrews¹,

Bernstein

2014

J Appl Crystallogr

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“…For example, Byram et al (1996) explicitly describe the problem: First, if the derivatives are approaching zero, least-squares in V 7 is likely to not perform well in some cases.…”

Section: Figurementioning

confidence: 99%

“…Second, in the case of database searches, false-positive reports will be common. For example, Byram et al (1996) explicitly describe the problem:…”

Section: Figurementioning

confidence: 99%

A space for lattice representation and clustering

2019

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Algorithms for quantifying the differences between two lattices are used for Bravais lattice determination, database lookup for unit cells to select candidates for molecular replacement, and recently for clustering to group together images from serial crystallography. It is particularly desirable for the differences between lattices to be computed as a perturbation-stable metric, i.e. as distances that satisfy the triangle inequality, so that standard tree-based nearest-neighbor algorithms can be used, and for which small changes in the lattices involved produce small changes in the distances computed. A perturbation-stable metric space related to the reduction algorithm of Selling and to the Bravais lattice determination methods of Delone is described. Two ways of representing the space, as six-dimensional real vectors or equivalently as three-dimensional complex vectors, are presented and applications of these metrics are discussed. (Note: in his later publications, Boris Delaunay used the Russian version of his surname, Delone.)

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“…Conversely, Buerger (1960) presented an algorithm to calculate the reduced unit cell of any conventional unit cell. This or similar algorithms (Santoro & Mighell, 1970;Křivý & Gruber, 1976;Byram et al, 1996) have been implemented in automated data collection instruments for specific purposes. In addition to their theoretical interest, reduced unit cells are useful in the determination of Bravais lattices and classification of compounds in material science (Santoro & Mighell, 1970;Mighell, 1976).…”

Section: Introductionmentioning

confidence: 99%

Frequency distribution of the reduced unit cells of centred lattices from the Protein Data Bank

Swaminathan

2012

Acta Cryst Sect A

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In crystallography, a centred conventional lattice unit cell has its corresponding reduced primitive unit cell. This study presents the frequency distribution of the reduced unit cells of all centred lattice entries of the Protein Data Bank (as of 23 August 2011) in four unit-cell-dimension-based groups and seven interaxial-angle-based subgroups. This frequency distribution is an added layer of support during space-group assignment in new crystals. In addition, some interesting patterns of distribution are discussed as well as how some reduced unit cells could be wrongly accepted as primitive lattices in a different crystal system.

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Using NIST crystal data within Siemens software for four-circle and SMART CCD diffractometers

Cited by 9 publications

References 6 publications

The geometry of Niggli reduction:BGAOL–embedding Niggli reduction and analysis of boundaries

The geometry of Niggli reduction:BGAOL–embedding Niggli reduction and analysis of boundaries

A space for lattice representation and clustering

Frequency distribution of the reduced unit cells of centred lattices from the Protein Data Bank

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