Semiempirical Angular-Force Method for BCC Transition Metals


An angular-force method for bcc transition-metals is obtained by generating a functional form via a quantum-mechanical analysis, and subsequently fitting the parameters in this form to experimental and ab-initio theoretical inputs. The quantummechanical analysis uses a four-moment treatment of the electronic density of states (DOS) in a d-band tight-binding model. Calibration of the method gives excellent results for the bcc-fcc energy difference and the vacancy-formation energy in W. The method is used to treat relaxation and c(2×2) reconstruction on the W (100) surface. The relaxation energy is primarily due to two-body terms, while the reconstruction requires the angular terms. Agreement with ab-initio results is obtained for reasonable values of the parameters in the model. However, the energy difference between the reconstructed surface and the optimally relaxed surface is quite sensitive to the details of the implementation of the method.

This is a preview of subscription content, access via your institution.


  1. 1.

    M. S. Daw and M. I. Baskes, Phys. Rev. B 29, 6443 (1984).

    CAS  Article  Google Scholar 

  2. 2.

    M. W. Finnis and J. Sinclair, Phil. Mag. A 50, 45 (1984); Phil. Mag. 53, 161 (1986).

    CAS  Article  Google Scholar 

  3. 3.

    A. E. Carlsson, in Solid State Physics; Advances in Research and Applications, Volume 43, edited by H. Ehrenreich and D. Turnbull (Academic, New York, 1990), p. 1.

    CAS  Google Scholar 

  4. 4.

    J. Moriarty, Phys. Rev. B 38, 3199 (1988).

    CAS  Article  Google Scholar 

  5. 5.

    R. B. Phillips and A. E. Carlsson, Phys. Rev. B 42, 3345 (1990).

    CAS  Article  Google Scholar 

  6. 6.

    J. A. Moriarty and R. B. Phillips, Bull. Am. Phys. Soc. 35, 283, Abstract C8-4, (1990).

    Google Scholar 

  7. 7.

    F. Ducastelle and F. Cyrot-Lackmann, J. Phys. Chem. Solids 32, 285 (1971).

    CAS  Article  Google Scholar 

  8. 8.

    K. Hirai and J. Kanamori, J. Phys. Soc. Jpn. 50, 2265 (1981).

    CAS  Article  Google Scholar 

  9. 9.

    A. E. Carlsson, P. A. Fedders, and C. W. Myles, Phys. Rev. B 41, 1247 (1990).

    CAS  Article  Google Scholar 

  10. 10.

    These are usefully summarized in W. A. Harrison, Electronic Structure and the Properties of Solids, (Freeman, New York, 1980).

    Google Scholar 

  11. 11.

    H. L. Skriver, The LMTO Method, (Springer, New York, 1984).

    Google Scholar 

  12. 12.

    T. Felter, R. A. Barker, and P. J. Estrup, Phys. Rev. Lett. 38, 1138 (1977).

    CAS  Article  Google Scholar 

Download references


We are grateful to Murray Daw, Steven Foiles, and Rob Phillips for enlightening conversations. This work was supported by the Department of Energy under Grant No. DE-FG02-84ER45130.

Author information



Corresponding author

Correspondence to A. E. Carlsson.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Carlsson, A.E. Semiempirical Angular-Force Method for BCC Transition Metals. MRS Online Proceedings Library 209, 165–170 (1990).

Download citation