Skip to main content
SpringerLink
Log in

Lattice statics Green’s function method for calculation of atomistic structure of grain boundary interfaces in solids: Part II. Anharmonic theory

  • Articles
  • Published:
Journal of Materials Research Aims and scope Submit manuscript

Abstract

The lattice statics Green’s function method for calculation of the atomistic structure of grain boundary interfaces in solids as described in Part I is extended to include anharmonic effects. It is shown that the ‘anharmonic’ response of a solid to ‘anharmonic’ forces can be represented in terms of the ‘harmonic’ response of the solid to an effective anharmonic force. The Green’s function method then requires solving a finite order nonlinear matrix equation, which is done by using standard numerical methods. For the purpose of illustration, the method is applied to calculate the atomistic structure of a ∑5 tilt boundary in fec copper.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. V. K. Tewary, E. R. Fuller, Jr., and R. M. Thomson, J. Mater. Res. 4 (2) 309 (1989).

    Article  Google Scholar 

  2. A. G. Crocker, M. Doneghan, and K. W. Ingle, Phil. Mag. 41A, 21 (1980).

    Article  Google Scholar 

  3. A. G. Crocker and B. A. Faridi, Acta Metall. 28, 549 (1980).

    Article  CAS  Google Scholar 

  4. A. A. Maradudin, E. W. Montroll, G. H. Weiss, and I. P. Ipatōva, “Theory of Lattice Dynamics in the Harmonic Approximation”, edited by H. Ehrenreich, F. Seitz, and D. Turnbull, Solid State Phys. Suppl. 3, II edition (Academic Press, New York, 1971).

  5. A. Ralston and P. Rabinowitz, First Course in Numerical Analysis (McGraw-Hill, New York, 1978).

    Google Scholar 

  6. V. K. Tewary, Adv. in Phys. 22, 757 (1973).

    Article  CAS  Google Scholar 

  7. V. K. Tewary and R. Bullough, J. Phys. F (Metal. Phys.) 1, 554 (1971).

    Article  CAS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. The Ohio State University, Ohio, Columbus, USA

    V. K. Tewary

  2. Fracture and Deformation Division, National Institute of Standards and Technology, Colorado, 80303, Boulder, USA

    V. K. Tewary

  3. Institute for Materials Science and Engineering, National Institute of Standards and Technology, Maryland, 20899, Gaithersburg, USA

    V. K. Tewary & E. R. Fuller Jr.

Authors
  1. V. K. Tewary
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. E. R. Fuller Jr.
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Tewary, V.K., Fuller, E.R. Lattice statics Green’s function method for calculation of atomistic structure of grain boundary interfaces in solids: Part II. Anharmonic theory. Journal of Materials Research 4, 320–326 (1989). https://doi.org/10.1557/JMR.1989.0320

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1557/JMR.1989.0320

Search

Navigation