Application of the Method of Lattice Statics to Carbon Interstitials in α -Iron

The method of lattice statics has been applied to determine the strain-field displacements about single octahedral and tetrahedral carbon interstitials in α-iron as well as the strain-field interaction energies between pairs of octahedral interstitials. A comparison of the exact lattice-statics displacements to the corresponding results of an asymptotic lattice-statics calculation indicates that elasticity theory is not valid closer than $25a$ from the octahedral interstitial in either the [100] or [011] direction in the lattice, where a is half of a cubic unit-cell side. The lattice-statics displacements have also been compared to analogous results obtained from a direct-space calculation, and some differences between the two sets of results are apparent. Relaxation energies have been calculated for the two types of carbon interstitial, and the octahedral configuration is found to be the more stable of the two. Assuming the tetrahedral configuration to be the saddle point for interstitial migration, the migration energy is found to be 0.27 eV.