References#
Some references about crystallographic definitions and conventions are shown below. Though spglib may not follow them fully, it doesn’t mean spglib doesn’t respect them, rather it is due to spglib-author’s lack of understanding the crystallography ashamedly.
General materials#
Bilbao Crystallographic Server. The references of many useful papers are found in the Articles page.
M. I. Aroyo, editor. International Tables for Crystallography. Volume A. International Union of Crystallography, December 2016. URL: https://doi.org/10.1107/97809553602060000114, doi:10.1107/97809553602060000114.
Ulrich Müller. Symmetry relationships between crystal structures: applications of crystallographic group theory in crystal chemistry. Volume 18. OUP Oxford, 2013.
Michael Glazer, Gerald Burns, and Alexander N Glazer. Space groups for solid state scientists. Elsevier, 2012.
Specific algorithms#
R. W. Grosse-Kunstleve. Algorithms for deriving crystallographic space-group information. Acta Cryst. A, 55(2-2):383–395, 1999. doi:https://doi.org/10.1107/S0108767398010186.
R. W. Grosse-Kunstleve and P. D. Adams. Algorithms for deriving crystallographic space-group information. II. Treatment of special positions. Acta Cryst. A, 58(1):60–65, Jan 2002. URL: https://doi.org/10.1107/S0108767301016658, doi:10.1107/S0108767301016658.
Setting and standardization#
S. R. Hall. Space-group notation with an explicit origin. Acta Cryst. A, 37(4):517–525, Jul 1981. URL: https://doi.org/10.1107/S0567739481001228, doi:10.1107/S0567739481001228.
E Parthé and LM Gelato. The standardization of inorganic crystal-structure data. Acta Crystallographica Section A: Foundations of Crystallography, 40(3):169–183, 1984.
Erwin Parthé, Karin Cenzual, and Roman E. Gladyshevskii. Standardization of crystal structure data as an aid to the classification of crystal structure types. Journal of Alloys and Compounds, 197(2):291–301, 1993. Proceeding of the Workshop on Regularities, Classifications and Prediction of Advanced Materials. URL: https://www.sciencedirect.com/science/article/pii/092583889390049S, doi:https://doi.org/10.1016/0925-8388(93)90049-S.
E Parthé and LOUISE M Gelato. The'best'unit cell for monoclinic structures consistent with b axis unique and cell choice 1 ofinternational tables for crystallography (1983). Acta Crystallographica Section A: Foundations of Crystallography, 41(2):142–151, 1985.
Magnetic space group#
Javier González-Platas, Nebil A. Katcho, and Juan Rodríguez-Carvajal. Extension of Hall symbols of crystallographic space groups to magnetic space groups. Journal of Applied Crystallography, 54(1):338–342, Feb 2021. URL: https://doi.org/10.1107/S1600576720015897, doi:10.1107/S1600576720015897.
Samuel V. Gallego, J. Manuel Perez-Mato, Luis Elcoro, Emre S. Tasci, Robert M. Hanson, Koichi Momma, Mois I. Aroyo, and Gotzon Madariaga. \it MAGNDATA: towards a database of magnetic structures. I.The commensurate case. Journal of Applied Crystallography, 49(5):1750–1776, Oct 2016. URL: https://doi.org/10.1107/S1600576716012863, doi:10.1107/S1600576716012863.
Branton J. Campbell, Harold T. Stokes, J. Manuel Perez-Mato, and Juan Rodríguez-Carvajal. Introducing a unified magnetic space-group symbol. Acta Crystallographica Section A, 78(2):99–106, Mar 2022. URL: https://doi.org/10.1107/S2053273321012912, doi:10.1107/S2053273321012912.
Daniel B Litvin. Magnetic group tables. IUCr, 2014. URL: https://www.iucr.org/publ/978-0-9553602-2-0.
Mathematical treatment#
Bernd Souvignier. Group theory applied to crystallography. URL: https://www.math.ru.nl/~souvi/krist_09/cryst.pdf.
J. Opgenorth, W. Plesken, and T. Schulz. Crystallographic Algorithms and Tables. Acta Cryst. Section A, 54(5):517–531, Sep 1998. URL: https://doi.org/10.1107/S010876739701547X, doi:10.1107/S010876739701547X.
Bettina Eick and Bernd Souvignier. Algorithms for crystallographic groups. International Journal of Quantum Chemistry, 106(1):316–343, 2005. URL: https://doi.org/10.1002/qua.20747, doi:10.1002/qua.20747.
B. Eick, F. Gähler, and W. Nickel. Computing Maximal Subgroups and Wyckoff Positions of Space Groups. Acta Crystallographica Section A, 53(4):467–474, Jul 1997. URL: https://doi.org/10.1107/S0108767397003462, doi:10.1107/S0108767397003462.
Howard Hiller. Crystallography and cohomology of groups. The American Mathematical Monthly, 93(10):765–779, 1986. URL: https://www.jstor.org/stable/2322930.