On computer simulation methods for calculating `exactʹ surface formation free energies of steps and (1 × 2) missing row reconstructions

Recently we have examined λ-integration paths for the calculation of `exactʹ surface free energies of `idealʹ and disordered surfaces using λ-integration simulation cell transformations of the type, bulk to `idealʹ surface and bulk to disordered surface. In this work we show how these methods can be used in conjunction with a relabelling/displacement of surface atoms and/or a rotation of the simulation cell, to find exact formation free energies of certain surface defects such as steps or the (1 × 2) missing row (MR) reconstruction, via transformations of the type, bulk to defect surface. We also introduce λ-integration paths of the type, ideal surface to defect surface, and show these paths to be valid and accurate for calculating the above defect formation free energies directly, i.e. in a single λ-integration. As a test and demonstration of these procedures we find the fcc(1 1 0) (1 × 2) MR reconstruction free energies, as a function of temperature, for the elements Au, Pt, Al, Ag, Cu, Ni, Pb and Pd using embedded atom method (EAM) and Glue potentials. As a further example we calculate the [1 0 0] surface step free energy for an Fe(1 0 0) bcc EAM system. All direct calculations of the type ideal surface to defect surface where found to be reversible at low temperatures and in agreement with the bulk to defect surface paths. The method has advantages in simplicity over other methods but is limited in applicability to certain surface defects which can be constructed via a relabelling/displacement of surface atoms and/or cell rotations.