Symmetry in the solid state; working beyond the space group

Journal of Materials Chemistry

Volumn 15, Issue 2, 2005, Pages 245-252

  Wills, Andrew S ^a,b,c,d,e  

^a UNIVERSITY OF OXFORD   (United Kingdom)

^b UNIVERSITY OF EDINBURGH   (United Kingdom)

^c MCMASTER UNIVERSITY   (Canada)

^d UNIVERSITY COLLEGE LONDON   (United Kingdom)

^e DAVY FARADAY RESEARCH LABORATORY   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

SPACE GROUP THEORY; SUPERSPACE GROUPS; THREE-DIMENSIONAL (3D) SPACE;

CELLS; CRYSTALS;

CRYSTALLOGRAPHY;

FUNCTIONAL GROUP; SPACE GROUP; SUPERSPACE GROUP; UNCLASSIFIED DRUG;

APERIODIC STRUCTURE; CRYSTAL STRUCTURE; CRYSTALLOGRAPHY; GEOMETRY; MOLECULAR MECHANICS; REVIEW; SOLID STATE; SPACE GROUP THEORY; THEORY;

EID: 12344297356     PISSN: 09599428     EISSN: None     Source Type: Journal    
DOI: 10.1039/b404156a     Document Type: Review

References (40)

1. W. Friedrich, P. Knipping and M. von Laue, Sitzungsber. Bayer. Akad. Wiss., Math.-Naturwiss. Kl., 1912, 303.
2. W. H. Bragg and W. L. Bragg, Nature, 1913, 91, 557.
3. W. H. Bragg and W. L. Bragg, X-Rays and Crystal Structure, G. Bell and Sons Ltd., London, 1915.
4. P. M. de Wolff, Acta Crystallogr., Sect. A, 1974, 30, 777.
5. A. Janner, T. Janssen and P. M. de Wolff, Acta Crystallogr., Sect. A, 1983, 39, 658.
6. L. Néel, Selected Works ed. N. Kurti, Gordon and Breach Science Publishers, New York, 1989.
7. C. J. Bradley and A. P. Cracknell, The Mathematical Theory of Symmetry in Solids, Clarendon Press, Oxford, 1972.
8. A. P. Cracknell, Magnetism in Crystalline Materials, Pergamon Press, Oxford, 1975.
9. J. Sivardière, Acta Crystallogr., Sect. A, 1969, 25, 658.
10. J. Sivardière, Acta Crystallogr., Sect. A, 1973, 29, 639.
11. Inclusion of colour simply requires an augmentation in the order of the symmetry operation and position matrices.
12. O. V. Kovalev, Irreducible Representations of the Space Groups, Gordon and Breach, New York, 1965; O. V. Kovalev, Representations of the Crystallographic Space Groups: Edition 2, Gordon and Breach Science Publishers, Switzerland, 1993.
13. O. V. Kovalev, Irreducible Representations of the Space Groups, Gordon and Breach, New York, 1965; O. V. Kovalev, Representations of the Crystallographic Space Groups: Edition 2, Gordon and Breach Science Publishers, Switzerland, 1993.
14. J. R. Stewart, G. Ehlers, A. S. Wills, S. T. Bramwell and J. S. Gardner, J. Phys.: Condens. Matter, 2004, 16, L321.
15. The principle of Ockham's Razor was proposed by William of Ockham in the 14th century: "Pluralitas non est ponenda sine necessitate", which translates as "entities should not be multiplied unnecessarily".
16. F. Bloch, Z. Phys., 1928, 52, 555.
17. Yu. A. Izyumov, V. E. Naish and R. P. Ozerov, Neutron Diffraction of Magnetic Materials, Consultants Bureau, New York, 1991.
18. J. Rossat-Mignod, in Neutron Scattering in Condensed Matter Research, ed. K. Sköld and D. L. Price, Academic Press, Amsterdam, 1986.
19. E. F. Bertaut, J. Appl. Phys., 1962, 33, 1138.
20. E. F. Bertaut, Acta. Crystallogr., Sect. A, 1968, 24, 217.
21. E. F. Bertaut, J. Phys. Colloq., 1971, C1, 462.
22. E. F. Bertaut, J. Magn. Magn. Mater., 1981, 24, 267.
23. A. M. Schönflies, Theorie der Kristallstruktur, [Theory of Crystal Symmetry], Borntraeger, Berlin, 1923.
24. E. S. Federov, Simmetriya i struklura kristallov [The Symmetry and Structure of Crystals], Izd-vo AN SSSR, Moscow, 1949.
25. International Tables for X-ray crystallography, ed. N.F.M. Henry and K. Lonsdale, Kynoch Press, Birmingham, 1952, vol. I.
26. International Tables for Crystallography, ed. Th. Hahn, Kluwer Academic Publishers, London, 2002, vol. A.
27. The SARAH program suite enables non-specialist users to perform the calculations of representational analysis and to refine magnetic structures using the output; A. S. Wills, Physica B, 2000, 276, 680; program available in the supporting information and from ftp:// ftp.ill.fr/pub/dif/sarah/.
28. L. D. Landau and E. M. Lifshitz, Course on Theoretical Physics, Butterworth-Heinemann, Oxford, 2002, vol. 3.
29. F. A. Cotton, Chemical Applications of Group Theory, John Wiley & Sons, Chichester, 1990.
30. P. Czapnik and W. Sikora, program available from http:// www.ftj.agh.edu.pl/zffs/staff/sikora/program/mody.zip.
31. J. Rodriguez-Carvajal, program available from juan@llb.saclay. cea.fr.
32. J. M. Perez-Mato, M. I. Aroyo, J. Hlinka, M. Quilichini and R. Currat, Phys. Rev. Lett., 1998, 81, 2462.
33. A. S. Wills, C. Detlefs and P. C. Canfield, Philos. Mag, 2003, 83, 1227.
34. B. Fåk, N. H. van Dijk and A. S. Wills, Phys. Rev. B, 2002, 66, 216401.
35. Y. Taguchi, T. Sasaki, S. Awaji, Y. Iwasa, T. Tayama, T. Sakakibara, S. Iguchi, T. Ito and Y. Tokura, Phys. Rev. Lett., 2003, 90, 257202.
36. S. Onoda and N. Nagaosa, Phys. Rev. Lett., 2003, 90, 196602.
37. T. Katsufuji, H. Y. Hwang and S.-W. Cheong, Phys. Rev. Lett., 2000, 84, 1998.
38. D. D. Awschalom, M. E. Flatté and N. Smith, Sci. Am., 2002, 67.
39. S. T. Bramwell and M. J. P. Gingras, Science, 2001, 294, 1495 and the references therein.
40. D. R. Parker, M. A. Green, S. T. Brarnwell, A. S. Wills, J. S. Gardner and D. A. Neumann, J. Am. Chem. Soc., 2004, 126, 2710.