Skip to main content

Abstract

This chapter describes one specific method for the configurational averaging of physical observables related to substitutionally random systems, the so-called coherent potential approximation (CPA). The calculation of such averages is greatly simplified by expressing them in terms of the Green function G(z). One of the main tasks of alloy theory is thus to find computational methods and approximations for the configurational average of G(z), 〈G(z)〉 ≡ Ḡ(z). Once 〈G(z)〉 is known the configurationally averaged one-electron observables can be calculated.

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 189.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 249.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 249.99
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. J.S. Faulkner and G.M. Stocks, Phys. Rev. B 21, 3222 (1980).

    Article  ADS  Google Scholar 

  2. J. Kudrnovskÿ and V. Drchal, Phys. Rev. B 41, 7515 (1990).

    Article  ADS  Google Scholar 

  3. J. Kudrnovskÿ, I. Turek, and V. Drchal, in Lectures on Methods of Electronic Structure Calculations, edited by V. Kumar, O.K. Andersen, and A. Mookerjee, (World Scientific Publishing Company, Singapore, 1994), p. 231.

    Google Scholar 

  4. J. Kudrnovskÿ, I. Turek, V. Drchal, and M. Sob, in Stability of Materials, edited by A. Gonis, P.E.A. Turchi, and J. Kudrnovskÿ (Plenum Press, New York, 1996), p. 237.

    Chapter  Google Scholar 

  5. P. Soven, Phys. Rev. 156, 809 (1967).

    Article  ADS  Google Scholar 

  6. D.W. Taylor, Phys. Rev. 156, 1017 (1967).

    Article  ADS  Google Scholar 

  7. B. Velickÿ, S. Kirkpatrick, and H. Ehrenreich, Phys. Rev. 175, 747 (1968).

    Article  ADS  Google Scholar 

  8. B.L. Gyorffy, Phys. Rev. B 5, 2382 (1972).

    Article  ADS  Google Scholar 

  9. G.M. Stocks and H. Winter, Z. Phys. B 46, 95 (1982).

    Article  ADS  Google Scholar 

  10. J. Kudrnovskÿ, V. Drchal, and J. Masek, Phys. Rev. B 35, 2487 (1987).

    Article  ADS  Google Scholar 

  11. R.J. Elliott, J.A. Krumhansl, and P.L. Leath, Rev. Mod. Phys. 46, 465 (1974); H. Ehrenreich and L.M. Schwarz, in Solid State Physics, vol. 31, edited by H. Ehrenreich, D. Turnbull, and F. Seitz (Academic Press, New York, 1976), p. 149.

    Google Scholar 

  12. J.S. Faulkner, Prog. Mater. Sci. 27, 1 (1982).

    Article  Google Scholar 

  13. P. Weinberger, Electron Scattering Theory for Ordered and Disordered Matter (Clarendon Press, Oxford, 1990).

    Google Scholar 

  14. A. Gonis, Green Functions for Ordered and Disordered Systems (North-Holland, Amsterdam, 1992).

    MATH  Google Scholar 

  15. J.A. Blackman, D.M. Esterling, and N.F. Berk, Phys. Rev. B 4, 2412 (1971).

    Article  ADS  Google Scholar 

  16. J. Masek and J. Kudrnovskÿ, J. Phys. Chem. Solids 49, 349 (1988).

    Article  ADS  Google Scholar 

  17. J. Kudrnovskÿ and V. Drchal, Solid State Commun. 17, 643 (1975).

    Article  ADS  Google Scholar 

  18. A.I. Liechtenstein, M.I. Katsnelson, V.P. Antropov, and V.A. Gubanov, J. Mag. Mag. Mat. 67, 65 (1987).

    Article  ADS  Google Scholar 

  19. J. Kudrnovskÿ, V. Drchal, I. Turek, and P. Weinberger, Phys. Rev. B 50, 16105 (1994).

    Article  ADS  Google Scholar 

  20. V. Drchal, J. Kudrnovskÿ, I. Turek, and P. Weinberger, Phys. Rev. B 53, 15036 (1996).

    Article  ADS  Google Scholar 

  21. R. Mills and P. Ratanavararaksa, Phys. Rev. B 18, 5291 (1978).

    Article  ADS  Google Scholar 

  22. A. Mookerjee, J. Phys. C: Solid State Physics 16, 1340 (1973).

    Article  ADS  Google Scholar 

  23. A. Mookerjee and R. Prasad, Phys. Rev. B 48, 17724 (1993).

    Article  ADS  Google Scholar 

  24. A. Gonis and J.W. Garland, Phys. Rev. B 16, 2424 (1977).

    Article  MathSciNet  ADS  Google Scholar 

  25. J. Banhart, P. Weinberger, and J. Voitländer, Phys. Rev. B 18, 12079 (1989).

    Article  ADS  Google Scholar 

  26. E. Suranyi and A. Gonis, Phys. Rev. B 45, 14371 (1992).

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

Copyright information

© 1997 Springer Science+Business Media New York

About this chapter

Cite this chapter

Turek, I., Drchal, V., Kudrnovský, J., Šob, M., Weinberger, P. (1997). Coherent Potential Approximation (CPA). In: Electronic Structure of Disordered Alloys, Surfaces and Interfaces. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-6255-9_4

Download citation

  • DOI: https://doi.org/10.1007/978-1-4615-6255-9_4

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-0-7923-9798-4

  • Online ISBN: 978-1-4615-6255-9

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics