A modified lattice-statics formalism is developed which allows anharmonic forces to be applied in determining the displacements of host atoms close to a point defect in a cubic lattice. The method is applied to determine the atomic relaxations in the vicinity of an octahedral carbon interstitial in $\alpha$-iron and a single vacancy in $\alpha$-iron. The displacements obtained for first and second neighbors to the vacancy are extremely close to those obtained by the semidiscrete method. The nearest neighbor to the carbon interstitial is displaced by an amount midway between the corresponding lattice-statics and semidiscrete values. The relaxation energy for the carbon interstitial is found to be -1.71 eV.

• Received 13 December 1971

DOI:https://doi.org/10.1103/PhysRevB.6.1176