Hostname: page-component-848d4c4894-4rdrl Total loading time: 0 Render date: 2024-06-17T08:55:32.040Z Has data issue: false hasContentIssue false
  • English
  • Français

Stationary States in Inhomogeneous Ordered Binary Alloys : Long-Period Superlattices

Published online by Cambridge University Press:  21 February 2011

M. Avignon  and
B.K. Chakraverty
M. Avignon
Affiliation:
Laboratoire d'Etudes des Propriétés Electroniques des Solides, C.N.R.S., B.P. 166, 38042 Grenoble Cedex, France
B.K. Chakraverty
Affiliation:
Laboratoire d'Etudes des Propriétés Electroniques des Solides, C.N.R.S., B.P. 166, 38042 Grenoble Cedex, France
Get access

Abstract

We examine the nature of all possible stationary states in an inhomogeneous ordered binary alloy. For this purpose, we use a development of the free energy in terms of the gradient of the non linear Euler equations is determined from the nature of its singular points. This method allows us to study these solutions for arbitrary expressions of the free energy of the homogeneous system as well as of the gradient coefficients. In general, periodic solutions which can be identified with long period superlattices are found. In specific cases, analytic solutions can be obtained. Fourier components are calculated and compared with experimental values determined for CuAu II.

Type
Research Article
Information
MRS Online Proceedings Library (OPL) , Volume 21: Symposium GREECE – Phase Transformations in Solids , 1983 , 259
Copyright
Copyright © Materials Research Society 1984

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

1. Muto, T. and Takagi, Y., Solid State Physics ed. by F. Seitz and D. Turnbull, Vol. 1, 193 (1955).Google Scholar
2. Guttman, L., Solid State Physics, ed. F. Seitz and D. Turnbull, Vol. 3, 174 (1956).Google Scholar
3. van Baal, C.M., Physica 64, 571 (1973).Google Scholar
4. Sato, H. and Toth, R.S. in ‘Allowing behavior and effects in concentrated solid solutions’ ed. Massalski, T.B., 295 (1963).Google Scholar
5. Johansson, C.H. and Linde, J.O, Annalen der Physik 25, 1 (1936).Google Scholar
6. Jehanno, G. and Perio, P., J. Phys. et Rad. 23, 854 (1962);Google Scholar
J. Phys. 25, 966 (1964).Google Scholar
7. Ogawa, S., J. Phys. Soc. Japan 17, Suppl. B11, 253 (1962).Google Scholar
8. Tachiki, M. and Teramoto, K., J. Phys. Chem. Solids 27, 335 (1966).Google Scholar
9. Villain, J., J. de Phys. et le Rad. 23, 861 (1962).Google Scholar
10. Avignon, M., J. de Phys. 38, Colloque C7–280 (1977).Google Scholar
11. Poincaré, H., Oeuvres, Vol. 1 Paris (1893);Google Scholar
J. de Math. 8, 251 (1882).Google Scholar
Davis, H.T. ‘Introduction to non-linear differential and integral equations’ Dover Publications Inc. N.Y. (1962).Google Scholar
12. Roberts, B.W., Acta Met. 2, 597 (1954).Google Scholar
13. Iwasaki, H. and Ogawa, S., J1. of Phys. Soc. Japan 22, 158 (1967).Google Scholar
14. Abramonitz, M. and Stegun, I.A., Handbook of Mathematical Functions, Dover Inc. N.Y. (1964).Google Scholar