Skip to main content

Phase Correlation with Calculated Cosine Invariants for Routine Structure Analysis

  • Chapter
Theory and Practice of Direct Methods in Crystallography

Abstract

The sign correlation procedure, one of the oldest computer-oriented applications of the Σ2 relationship, was developed in the early sixties (Beurskens, 1964). At that time, the procedure was applicable only to centrosymmetric structures. The name “sign correlation procedure” will be used now only when referring explicitly to centrosymmetric structures; otherwise, the more general term “phase correlation procedure” will be used. The sign correlation procedure was programmed for the IBM 1620 computer (Beurskens, 1963) and applied successfully to several centrosymmetric structures (Sax et al., 1965). Thereafter, an automatic program was written in ALGOL-60 (Beurskens, 1965).

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 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight 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

  • Beurskens, P. T. (1963). “Technical Report on Sign Correlation by the Sayre Equation,” Crystallography Laboratory, University of Pittsburgh, Pittsburgh, Pennsylvania.

    Google Scholar 

  • Beurskens, P. T. (1964). Acta Crystallogr. 17, 462.

    Article  Google Scholar 

  • Beurskens, P. T. (1965). Thesis, University of Utrecht, Utrecht, The Netherlands.

    Google Scholar 

  • Beurskens, P. T., Beurskens, G., and van den Hark, Th. E. M. (1976). Cryst. Struct. Commun., 241.

    Google Scholar 

  • Germain, G., Main, P., and Woolfson, M. M. (1971). Acta Crystallogr. Sect. A 27, 368.

    Article  ADS  Google Scholar 

  • van den Hark, Th. E. M. (1976). Thesis, University of Nijmegen, Nijmegen, The Netherlands.

    Google Scholar 

  • van den Hark, Th. E. M., Beurskens, P. T., and Laarhoven, W. H. (1974a). J. Cryst. Mol. Struct. 4, 227.

    Article  Google Scholar 

  • van den Hark, Th. E. M., Hendriks, H. M., and Beurskens, P. T. (1974b). Cryst. Struct. Commun., 703.

    Google Scholar 

  • Hauptman, H. (1972). Crystal Structure Determination: The Role of the Cosine Seminvariants, Plenum Press, New York.

    Google Scholar 

  • Hauptman, H . (1974a). Acta Crystallogr. Sect. A 30, 472.

    Article  ADS  Google Scholar 

  • Hauptman, H . (1974b). Acta Crystallogr. Sect. A 30, 822.

    Article  ADS  Google Scholar 

  • Hauptman, H . (1975). Acta Crystallogr. Sect. A 31, 680

    Article  ADS  Google Scholar 

  • Hauptman, H., and Karle, J. (1953). Solution of the Phase Problem. I. The Centrosymmetric Crystal, American Crystallographic Association Monograph No. 3, Polycrystal Book Service, Pittsburgh, Pennsylvania.

    Google Scholar 

  • Hummelink-Peters, B. G. M. C., van den Hark, Th. E. M., Noordik, J. H., and Beurskens, P. T. (1975). Cryst. Struct. Commun., 281.

    Google Scholar 

  • Kanters, J. A., Kroon, J., Beurskens, P. T., and Vliegenthart, J. A. (1966). Acta Crystallogr. 21, 990.

    Article  Google Scholar 

  • Karle, J., and Hauptman, H. (1958). Acta Crystallogr. 11, 264.

    Article  Google Scholar 

  • Karle, J., and Hauptman, H. (1959). Acta Crystallogr. 12, 404.

    Article  Google Scholar 

  • Sax, M., Beurskens, P. T., and Chu, S. (1965). Acta Crystallogr. 18, 252.

    Article  Google Scholar 

  • Schenk, H . (1973). Acta Crystallogr. Sect. A 29, 77.

    Article  ADS  Google Scholar 

  • Schenk, H . (1974). Acta Crystallogr. Sect. A 30, 477.

    Article  ADS  Google Scholar 

  • Viterbo, D., and Woolfson, M. M. (1973). Acta Crystallogr. Sect. A 29, 205

    Article  ADS  Google Scholar 

  • de Vries, A . (1963). Thesis, University of Utrecht, Utrecht, The Netherlands.

    Google Scholar 

  • de Vries, A. (1965). Acta Crystallogr. 18, 473.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 1980 Plenum Press, New York

About this chapter

Cite this chapter

Beurskens, P.T., van den Hark, T.E.M. (1980). Phase Correlation with Calculated Cosine Invariants for Routine Structure Analysis. In: Ladd, M.F.C., Palmer, R.A. (eds) Theory and Practice of Direct Methods in Crystallography. Springer, Boston, MA. https://doi.org/10.1007/978-1-4613-2979-4_6

Download citation

  • DOI: https://doi.org/10.1007/978-1-4613-2979-4_6

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4613-2981-7

  • Online ISBN: 978-1-4613-2979-4

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics