Off-lattice self-learning kinetic Monte Carlo: application to 2D cluster diffusion on the fcc(111) surface

We report developments of the kinetic Monte Carlo (KMC) method with improved accuracy and increased versatility for the description of atomic diffusivity on metal surfaces. The on-lattice constraint built into our recently proposed self-learning KMC (SLKMC) (Trushin et al 2005 Phys. Rev. B 72 115401) is released, leaving atoms free to occupy 'off-lattice' positions to accommodate several processes responsible for small-cluster diffusion, periphery atom motion and heteroepitaxial growth. This technique combines the ideas embedded in the SLKMC method with a new pattern-recognition scheme fitted to an off-lattice model in which relative atomic positions are used to characterize and store configurations. Application of a combination of the 'drag' and the repulsive bias potential (RBP) methods for saddle point searches allows the treatment of concerted cluster, and multiple- and single-atom, motions on an equal footing. This tandem approach has helped reveal several new atomic mechanisms which contribute to cluster migration. We present applications of this off-lattice SLKMC to the diffusion of 2D islands of Cu (containing 2-30 atoms) on Cu and Ag(111), using the interatomic potential from the embedded-atom method. For the hetero-system Cu/Ag(111), this technique has uncovered mechanisms involving concerted motions such as shear, breathing and commensurate-incommensurate occupancies. Although the technique introduces complexities in storage and retrieval, it does not introduce noticeable extra computational cost.