Skip to main content

Part of the book series: Springer Series in Materials Science ((SSMATERIALS,volume 47))

  • 569 Accesses

Abstract

This chapter briefly describes basic notions of the theory of crystal symmetry and space groups. They will be repeatedly referred to in subsequent discussion of the structure of nonstoichiometric compounds, alteration of symmetry and properties of these compounds during ordering.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 129.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 169.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. E. S. Fedorov: Elements of the study of figures, Zapiski Imper. S.-Petersburg. Mineralog. Obshestva, Second Seriya, Part 21, 1–289 (1885) (in Russian)

    Google Scholar 

  2. E. S. Fedorov: Studies in analytical crystallography. Second scetch, Gornyi Zhurnal 1, 395–425 (1886) (in Russian)

    Google Scholar 

  3. E. S. Fedorov: Symmetry of regular systems of figures, Zapiski Imper. S.-Petersburg. Mineralog. Obshestva, Second Seriya, Part 28, 1–147 (1891) (in Russian). (Engl. Transi.: The Symmetry of Regular Systems of Figures, in E. S. Fedorov: Symmetry of Crystals, ACA Monograph No. 7, Amer. Crystallographic Association, New York 1971, pp. 50–131 ).

    Google Scholar 

  4. E. S. Fedorov: Theorie der Kristallstruktur. Einleitung. Regelmässige Punktsysteme, Z. Kristallogr. Min. 24, 209–252 (1895)

    Google Scholar 

  5. E. S. Fedorov: Theorie der Kristallstruktur. I. Mögliche Structurarten (mit über-sichtlicher graphischer Darstellung der Symmorphen Structurarten), Z. Kristallogr. Min. 25, 113–124 (1895)

    Google Scholar 

  6. E. S. Fedorov: Reguläre Plan-und Raumverteilung, Abhandlungen der K. Bayer Akademie der Wissenschaft, Math.-Phys. Cl., (München) XX, 465–588 (1899–1900)

    Google Scholar 

  7. E. S. Fedorov: Symmetry and Structure of Crystals ( Nauka, Moscow 1949 ) 630 pp. (in Russian)

    Google Scholar 

  8. E. S. Fedorov: Tiling of Plane and Space ( Nauka, Leningrad 1979 ) 272 pp. (in Russian)

    Google Scholar 

  9. E. S. Fedorov: Symmetry of Crystals, ACA Monograph No. 7 (Amer. Crystallographic Association, New York 1971 ) 315 pp.

    Google Scholar 

  10. A. Schönflies: Über reguläre Gebietstheilungen des Raumes, Nachrichten der Gesellschaft der Wissenschaft zu Goettingen No 9, 223–237 (1889)

    Google Scholar 

  11. A. Schönflies: Über Gruppen von Transformationen des Raumes in sich, Mathemat. Annalen. 34, 172–203 (1889)

    Article  Google Scholar 

  12. A. Schoenflies: Krystallsysteme und Krystallstructur (Teubner, Leipzig 1891) 638 SS.

    Google Scholar 

  13. A. Schoenflies: Theorie der Kristallstruktur (Gebrüder Borntraeger, Berlin 1923) 556 SS.

    Google Scholar 

  14. T. Hahn (Ed.): International Tables for X-ray Crystallography A, Space group symmetry 4th revised edn ( Kluwer Academic Publishers, Dordrecht-Boston-London 1995 ) 878 pp.

    Google Scholar 

  15. G. B. Bokii: Introduction to Crystal Chemistry ( US Atomic Energy Commission, Office of Technical Information, Oak Ridge, Tennessee 1960 ) 528 pp.

    Google Scholar 

  16. O. V. Kovalev: Irreducible Representations of the Space Groups ( Gordon und Breach, New York 1965 ) 210 pp.

    Google Scholar 

  17. O. V. Kovalev: Irreducible and Induced Representations and Corepresentation of Fedorov Groups ( Nauka, Moscow 1986 ) 368 pp. (in Russian)

    Google Scholar 

  18. W. Ludwig, C. Falter: Symmetries in Physics ( Springer, Berlin-Heidelberg 1988 ) 461 pp.

    Book  Google Scholar 

  19. Yu. A. Izyumov, V. N. Naish, R. P. Ozerov: Neutron Diffraction of Magnetic Materials ( Consultants Bureau, New York 1981 ) 339 pp.

    Google Scholar 

  20. M. Wagner: Gruppentheoretische Methoden in der Physik (Spriger, Berlin-Heidelberg 1998) 461 SS.

    Google Scholar 

  21. R. L. Flurry: Symmetry Groups: Theory and Chemical Applications ( Prentice - Hall Inc., Englewood Cliffs 1980 ) 356 pp.

    Google Scholar 

  22. Yu. A. Izyumov, V. N. Syromyatnikov: Phase Transitions and Symmetry of Crystals ( Nauka, Moscow 1984 ) 248 pp. (in Russian)

    Google Scholar 

  23. A. I. Gusev, A. A. Rempel: Structural Phase Transitions in Nonstoichiometric Compounds ( Nauka, Moscow 1988 ) 308 pp. (in Russian)

    Google Scholar 

  24. D. Shechtman, I. Blech, D. Gratias, J. W. Chan: Metallic phase with long-range orientational order and no translational symmetry, Phys. Rev. Lett. 53, 1951–1953 (1984)

    Article  CAS  Google Scholar 

  25. R. D. Field, H. L. Fraser: Precipitates possessing icosahedral symmetry in a rapidly solidified Al-Mn alloy, Mater. Sci. Eng. 68, L17 — L21 (1984)

    Google Scholar 

  26. L. V. Azaroff, M. J. Buerger: The Powder Method in X-ray Crystallography ( McGraw-Hill, New York-London 1958 ) 342 pp.

    Google Scholar 

  27. A. J. C. Wilson (Ed.): International Tables for X-ray Crystallography C, Mathematical, Physical and Chemical Tables ( Kluwer Academic Publishers, Dordrecht-BostonLondon 1992 ) 883 pp.

    Google Scholar 

  28. C. Giacovazzo, H. L. Monaco, D. Viterbo, F. Scordari, G. Gilli, G. Zanotti, M. Catti: Fundamentals of Crystallography ( Oxford University Press, Oxford 1992 ) 654 pp.

    Google Scholar 

  29. M. von Laue: Röntgenstrahlinterferenzen ( Akademische Verlagsgesellschaft Becker und Erler Korn.-Ges., Leipzig 1941 ) 367 pp.

    Google Scholar 

  30. R. W. James: The Optical Principles of the Diffraction of X-rays (G. Bell and Sons Ltd., London 1954 ) 624 pp.

    Google Scholar 

  31. M. A. Krivoglaz: Theory of X-ray and Thermal-Neutron Scattering by Real Crystals ( Plenum Press, New York 1969 ) 405 pp.

    Google Scholar 

  32. M. Bee: Quasielastic Neutron Scattering: Principles and Applications in Solid State Chemistry, Biology, and Materials Science ( Adam Hilger, Bristol — Philadelphia 1988 ) 437 pp.

    Google Scholar 

  33. Yu. Z. Nozik, R. P. Ozerov, K. Hennig: Structural Neutron Diffraction ( Atomizdat, Moscow 1979 ) 344 pp. (in Russian)

    Google Scholar 

  34. M. A. Krivoglaz, A. A. Smimov: The Theory of Order—Disorder in Alloys ( American Elsevier, New York 1964 ) 427 pp.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

Copyright information

© 2001 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Gusev, A.I., Rempel, A.A., Magerl, A.J. (2001). Crystal Symmetry. In: Disorder and Order in Strongly Nonstoichiometric Compounds. Springer Series in Materials Science, vol 47. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-04582-4_2

Download citation

  • DOI: https://doi.org/10.1007/978-3-662-04582-4_2

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-07524-7

  • Online ISBN: 978-3-662-04582-4

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics