Localized defects in an elastically isotropic continuum

For localized defects in a solid, it has been customary to treat the elastic-continuum model in terms of point-body forces. More detailed lattice calculations have demonstrated that this point-force model fails to duplicate the actual complexities of the elastic displacement field. By introducing a more realistic distribution of body forces based upon interatomic forces into the continuum model, the present results essentially duplicate the pattern of displacements obtained by the lattice calculations. Comparisons are given between the lattice and continuum calculations for vacancies in aluminum and tungsten. While quantitative disagreements remain, the improvement over the point-force model is very substantial. The modified continuum model also predicts a volume dilatation and vacancy interaction energy that varies as $R^{-5\mathrm{}}$ in elastically isotropic media, a result which agrees with work by Siems and by Hardy and Bullough.