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B. Gruber (1989)
Reduced cells based on extremal principlesActa Crystallographica Section A, 45
R. Oishi-Tomiyasu (2012)
Rapid Bravais-lattice determination algorithm for lattice parameters containing large observation errors.Acta crystallographica. Section A, Foundations of crystallography, 68 Pt 5
Yanchao Wang, Jian Lv, Li Zhu, Yanming Ma (2012)
CALYPSO: A method for crystal structure predictionComput. Phys. Commun., 183
B. Delaunay (1933)
Neue Darstellung der geometrischen KristallographieZeitschrift für Kristallographie - Crystalline Materials, 84
Andrews (2014)
10.1107/S1600576713031002J. Appl. Cryst., 47
C. Pickard, R. Needs (2011)
Ab initio random structure searchingJournal of Physics: Condensed Matter, 23
Selling (1874)
10.1515/crll.1874.77.143J. Reine Angew. Math., 1874
A. Oganov, C. Glass (2006)
Crystal structure prediction using ab initio evolutionary techniques: principles and applications.The Journal of chemical physics, 124 24
A. Mujica, Á. Rubio, A. Muñoz, R. Needs (2003)
High-pressure phases of group-IV, III–V, and II–VI compoundsReviews of Modern Physics, 75
Yanchao Wang, Jian Lv, Li Zhu, Yanming Ma (2010)
Crystal structure prediction via particle-swarm optimizationPhysical Review B, 82
(2012)
Lattice reduction using a Euclidean algorithm Acta Cryst
C. Glass, A. Oganov, N. Hansen (2006)
USPEX - Evolutionary crystal structure predictionComput. Phys. Commun., 175
V. Schomaker, R. Marsh (1979)
Some comments on refinement in a space group of unnecessarily low symmetryActa Crystallographica Section B Structural Crystallography and Crystal Chemistry, 35
A. Oganov, A. Lyakhov, Mario Valle (2011)
How evolutionary crystal structure prediction works--and why.Accounts of chemical research, 44 3
L. Andrews, H. Bernstein (1988)
Lattices and Reduced Cells as Points in 6-Space and Selection of Bravais Lattice Type by ProjectionsActa Crystallographica Section A, 44
Théorie générale des équations algébriques (sic)
A. Mujica, C. Pickard, R. Needs (2015)
Low-energy tetrahedral polymorphs of carbon, silicon, and germaniumPhysical Review B, 91
P. Niggli
Krystallographische und strukturtheoretische Grundbegriffe
José Soler, Emilio Artacho, Julian Gale, Alberto García, Javier Junquera, Pablo Ordejón, Daniel Sánchez-Portal (2001)
The SIESTA method for ab initio order-N materials simulationJournal of Physics: Condensed Matter, 14
The need to reduce a periodic structure given in terms of a large supercell and associated lattice generators arises frequently in different fields of application of crystallography, in particular in the ab initio theoretical modelling of materials at the atomic scale. This paper considers the reduction of crystals and addresses the reduction associated with the existence of a commensurate translation that leaves the crystal invariant, providing a practical scheme for it. The reduction procedure hinges on a convenient integer factorization of the full period of the cycle (or grid) generated by the repeated applications of the invariant translation, and its iterative reduction into sub‐cycles, each of which corresponds to a factor in the decomposition of the period. This is done in successive steps, each time solving a Diophantine linear equation by means of a Euclidean reduction algorithm in order to provide the generators of the reduced lattice.
Acta Crystallographica Section A Foundations of Crystallography – Wiley
Published: Jan 1, 2017
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