Skip to main content

Theory of simulation methods for lattice and defect energy calculations in crystals

  • Section A: Techniques
  • Chapter
  • First Online:
Computer Simulation of Solids

Part of the book series: Lecture Notes in Physics ((LNP,volume 166))

Abstract

The methodsdescribed in this section enable us to perform accurate and reliable calculations of the properties of perfect and defective lattices where good potential models of the pair-wise type may be derived. The limitation of the type of potential model which may be effectively used in the calculations has tended to confine their application to the study of ionic and semi-ionic materials; the types of model appropriate for covalent and metallic systems are discussed in Chapters (11) and (19). Additional restrictions follow from the omission of any direct representation of quantum mechanical effects which excludes the applications of the methods to metals and semi conductors. (Treatments of defects in these systems are discussed in Chapters (13) and (14). However, in spite of these limitations, the methods we have described in this chapter have had possibly the greatest degree of quantitative success of any similar procedure in solid state studies - a feature which should become apparent in later chapters.

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

Access this chapter

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Catlow, C.R.A. and Norgett, M.J. AERE Harwell Report M.2763 (1978).

    Google Scholar 

  2. Born, M. and Huang, K., Dynamical Theory of Crystal Lattices (Oxford University Press), 1954.

    Google Scholar 

  3. Lidiard, A.B. and Norgett, M.J. In ‘Computational Solid State Physics’ 1972. Ed. F. Herman, N.W. Dalton and T.R. Koehler, p.385 (Plenum Press, New York).

    Google Scholar 

  4. Norgett, M.J., AERE Harwell Report R.7015 (1972).

    Google Scholar 

  5. Norgett, M.J., AERE Harwell Report R.7650 (1974a).

    Google Scholar 

  6. Norgett, M.J., AERE Harwell Report R.7780 (1974b).

    Google Scholar 

  7. Mackrodt, W.C. J, Comp, Phys.-in press (1981).

    Google Scholar 

  8. Catlow, C.R.A., James, R., Mackrodt, W.C. and Stewart, R.F., Phys. Rev. B25, 1006, (1982).

    Google Scholar 

  9. Mackrodt, W.C., Stewart, R.F., Campbell, J.C. and Hillier, I.H., J. de Physique C7, 64 (1980).

    Google Scholar 

  10. Davidon, W.C., AEC Report ANL-5990 (Rev) (1959).

    Google Scholar 

  11. Fletcher, R. and Powell, M.J.D., Computer J. 6, 16 (1963).

    Google Scholar 

  12. Norgett, M.J. and Fletcher, R., J. Phys. C3, L190 (1970).

    Google Scholar 

  13. Powell, M.J.D., AERE Harwell Report TP372, 1969.

    Google Scholar 

  14. Broyden, C.G., J. Inst. Maths. Appl. 6, 222 (1970).

    Google Scholar 

  15. Shanno, D.F., Math. Computing 24, 647 (1970).

    Google Scholar 

  16. Kendrick, J., I.C.I., Corporate Laboratory Report, CL-R/81/1640 (1981).

    Google Scholar 

  17. Ewald, R.P., Ann. Physik [4] 64, 253 (1921; Gottinger Nechr., Math.-Phys. K1. 113, 55 (1937).

    Google Scholar 

  18. Catlow, C.R.A. and Norgett, M.J., AERE Harwell Report M

    Google Scholar 

  19. Catlow, C.R.A., Cormack, A.N. and Parker, S.C. To be published.

    Google Scholar 

  20. Lesley, M. and Smith, W., Daresbury Laboratory Report-To be published.

    Google Scholar 

  21. Catlow, C.R.A., Parker, S.C. and Saunders, M.J. Nature-in press.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

C. R. A. Catlow W. C. Mackrodt

Rights and permissions

Reprints and permissions

Copyright information

© 1982 Springer-Verlag

About this chapter

Cite this chapter

Catlow, C.R.A., Mackrodt, W.C. (1982). Theory of simulation methods for lattice and defect energy calculations in crystals. In: Catlow, C.R.A., Mackrodt, W.C. (eds) Computer Simulation of Solids. Lecture Notes in Physics, vol 166. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0017928

Download citation

  • DOI: https://doi.org/10.1007/BFb0017928

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-11588-5

  • Online ISBN: 978-3-540-39347-4

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics