Density functional theory study of the relaxation and energy of iron surfaces

The relaxations and energies of the (1 0 0), (1 1 0) and (1 1 1) surfaces of (bcc) Fe have been calculated using density functional theory. A plane-wave pseudopotential method was employed. The results demonstrate that for the (1 0 0) surface a contraction of the first (outer) layer is observed while the second and third layers expand perpendicular to the surface plane; for the (1 1 0) surface, the displacements are the same, however, the magnitude of the relaxations is much smaller, showing the surface to be basically bulk terminated; for the (1 1 1) surface the first two layers contract while the third expands, with the magnitude of the relaxations being much larger than for the other surfaces. The surface energy values for the relaxed and unrelaxed surfaces were determined showing the (1 0 0) and (1 1 0) surfaces to have almost identical surface energies with the (1 0 0) being slightly higher followed by the (1 1 1) surface. Our results are compared to other experimental and computational studies and generally show good agreement with experiment; an explanation is provided for any differences. The surface models used in this study provide a good basis for future work examining the adsorption of impurities on the surface and the effect of relaxation on adhesion.