Green-function method for lattice statics

Abstract

This article gives a review of the Green-function method for the calculation of the static properties of lattices with point defects. This method, based upon the Born-von Kármán model of a lattice, uses the zero frequency limit of the phonon Green function which gives the static response of the lattice to an applied force. The method is quite general and is applicable to most kind of defects but the attention in this review is restricted to point defects in cubic Bravais lattices. The Green-function method is shown to be formally equivalent to the Kanzaki method but is more powerful and computationally more convenient.

For the purpose of illustration the Green-function method has been applied to a vacancy in the Rosenstock-Newell model of a solid. Although the model is physically unrealistic, it has the advantage of yielding results in closed analytic forms which are very useful for qualitative discussions. The applications of the Green-function method to some real systems—vacancies and interstitials in f.c.c. and b.c.c. lattices—have also been described. Finally the Green-function method is generalized to account for a regular array of point defects and its application to super lattices of voids and gas interstitials in certain metals is discussed.

Additional information

Notes on contributors

V.K. Tewary

On attachment from the University of Surrey.