Selling reduction versus Niggli reduction for crystallographic lattices

Andrews, Lawrence C.; Bernstein, Herbert J.; Sauter, Nicholas K.

doi:10.1107/S2053273318015413

Title: Selling reduction versus Niggli reduction for crystallographic lattices

Abstract

The unit-cell reduction described by Selling and used by Delone (whose early publications were under the spelling Delaunay) is explained in a simple form. The transformations needed to implement the reduction are listed. The simplicity of this reduction contrasts with the complexity of Niggli reduction.

Authors:: Andrews, Lawrence C.; Bernstein, Herbert J.; Sauter, Nicholas K.

Publication Date:: 2019-01-01

Research Org.:: Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)

Sponsoring Org.:: USDOE Office of Science (SC), Basic Energy Sciences (BES)

OSTI Identifier:: 1579421

Alternate Identifier(s):: OSTI ID: 1580352

Grant/Contract Number:: AC02-98CH10886; SC0012704; AC02-05CH11231; P41RR012408; P41GM103473; P41GM111244; R01GM117126

Resource Type:: Published Article

Journal Name:: Acta Crystallographica. Section A, Foundations and Advances (Online)

Additional Journal Information:: Journal Name: Acta Crystallographica. Section A, Foundations and Advances (Online) Journal Volume: 75 Journal Issue: 1; Journal ID: ISSN 2053-2733

Publisher:: International Union of Crystallography

Country of Publication:: Denmark

Language:: English

Subject:: 36 MATERIALS SCIENCE; unit-cell reduction; Delaunay; Delone; Niggli; Selling

Citation Formats


                    Andrews, Lawrence C., Bernstein, Herbert J., and Sauter, Nicholas K. Selling reduction versus Niggli reduction for crystallographic lattices.  Denmark: N. p., 2019. 
        Web.  doi:10.1107/S2053273318015413.

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                    Andrews, Lawrence C., Bernstein, Herbert J., & Sauter, Nicholas K. Selling reduction versus Niggli reduction for crystallographic lattices.  Denmark.  doi:https://doi.org/10.1107/S2053273318015413

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                    Andrews, Lawrence C., Bernstein, Herbert J., and Sauter, Nicholas K. Tue .  
        "Selling reduction versus Niggli reduction for crystallographic lattices".  Denmark.  doi:https://doi.org/10.1107/S2053273318015413.

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@article{osti_1579421,

  title        = {Selling reduction versus Niggli reduction for crystallographic lattices},

  author       = {Andrews, Lawrence C. and Bernstein, Herbert J. and Sauter, Nicholas K.},

  abstractNote = {The unit-cell reduction described by Selling and used by Delone (whose early publications were under the spelling Delaunay) is explained in a simple form. The transformations needed to implement the reduction are listed. The simplicity of this reduction contrasts with the complexity of Niggli reduction.},

  doi          = {10.1107/S2053273318015413},

  journal      = {Acta Crystallographica. Section A, Foundations and Advances (Online)},

  number       = 1,

  volume       = 75,

  place        = {Denmark},

  year         = {2019},

  month        = {1}

}

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DOI: https://doi.org/10.1107/S2053273318015413

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Works referenced in this record:

The geometry of Niggli reduction: BGAOL –embedding Niggli reduction and analysis of boundaries
journal, January 2014

Andrews, Lawrence C.; Bernstein, Herbert J.
Journal of Applied Crystallography, Vol. 47, Issue 1
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Note on reduced cells
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Buerger, M. J.
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The relationship between reduced cells in a general Bravais lattice
journal, July 1973

Gruber, B.
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DOI: 10.1107/S0567739473001063

Remarks on the Delaunay reduction
journal, February 1957

Patterson, A. L.; Love, W. E.
Acta Crystallographica, Vol. 10, Issue 2
DOI: 10.1107/S0365110X57000328

Some remarks on reduced cells ¹
journal, July 1968

Allmann, Rudolf
Zeitschrift für Kristallographie, Vol. 126, Issue 4
DOI: 10.1524/zkri.1968.126.4.272

The geometry of Niggli reduction: SAUC – search of alternative unit cells
journal, January 2014

McGill, Keith J.; Asadi, Mojgan; Karakasheva, Maria T.
Journal of Applied Crystallography, Vol. 47, Issue 1
DOI: 10.1107/S1600576713031014

Lattices and reduced cells as points in 6-space and selection of Bravais lattice type by projections
journal, November 1988

Andrews, L. C.; Bernstein, H. J.
Acta Crystallographica Section A Foundations of Crystallography, Vol. 44, Issue 6
DOI: 10.1107/S0108767388006427

On the Bravais types of lattices
journal, July 1975

Delone, B. N.; Galiulin, R. V.; Shtogrin, M. I.
Journal of Soviet Mathematics, Vol. 4, Issue 1
DOI: 10.1007/BF01084661

Diskontinuitätsbereich für arithmetische Äquivalenz.
journal, July 1905

Minkowski, Hermann
Journal für die reine und angewandte Mathematik (Crelles Journal), Vol. 1905, Issue 129
DOI: 10.1515/crll.1905.129.220

Rapid Bravais-lattice determination algorithm for lattice parameters containing large observation errors
journal, July 2012

Oishi-Tomiyasu, R.
Acta Crystallographica Section A Foundations of Crystallography, Vol. 68, Issue 5
DOI: 10.1107/S0108767312024579

Works referencing / citing this record:

Best practices for high data-rate macromolecular crystallography (HDRMX)
journal, January 2020

Bernstein, Herbert J.; Andrews, Lawrence C.; Diaz, Jorge A.
Structural Dynamics, Vol. 7, Issue 1
DOI: 10.1063/1.5128498

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Title: Selling reduction versus Niggli reduction for crystallographic lattices

Abstract

Citation Formats

The geometry of Niggli reduction: BGAOL –embedding Niggli reduction and analysis of boundaries journal, January 2014

Note on reduced cells journal, April 1960

The relationship between reduced cells in a general Bravais lattice journal, July 1973

Remarks on the Delaunay reduction journal, February 1957

Some remarks on reduced cells 1 journal, July 1968

The geometry of Niggli reduction: SAUC – search of alternative unit cells journal, January 2014

Lattices and reduced cells as points in 6-space and selection of Bravais lattice type by projections journal, November 1988

On the Bravais types of lattices journal, July 1975

Diskontinuitätsbereich für arithmetische Äquivalenz. journal, July 1905

Rapid Bravais-lattice determination algorithm for lattice parameters containing large observation errors journal, July 2012

Best practices for high data-rate macromolecular crystallography (HDRMX) journal, January 2020

The geometry of Niggli reduction: BGAOL –embedding Niggli reduction and analysis of boundaries
journal, January 2014

Note on reduced cells
journal, April 1960

The relationship between reduced cells in a general Bravais lattice
journal, July 1973

Remarks on the Delaunay reduction
journal, February 1957

Some remarks on reduced cells ¹
journal, July 1968

The geometry of Niggli reduction: SAUC – search of alternative unit cells
journal, January 2014

Lattices and reduced cells as points in 6-space and selection of Bravais lattice type by projections
journal, November 1988

On the Bravais types of lattices
journal, July 1975

Diskontinuitätsbereich für arithmetische Äquivalenz.
journal, July 1905

Rapid Bravais-lattice determination algorithm for lattice parameters containing large observation errors
journal, July 2012

Best practices for high data-rate macromolecular crystallography (HDRMX)
journal, January 2020