Eigenstrains and the elastic field of an adatom

A harmonic lattice model for an adatom at the (001) surface of a cubic crystal is developed, based on the concept of eigenstrains. In this context, eigenstrains represent the distortion introduced by the adatom, affecting the substrate atoms in its vicinity. The distortions which model the relaxations associated with an adatom are obtained directly using embedded atom method (EAM) potentials. The eigenstrains are translated into a set of forces which, in the case of second-neighbor interactions, are applied to five 'substrate' atoms in the immediate vicinity of the adatom. Four of these atoms are located at the surface and one in the first layer below the surface. The resulting set of forces is self-equilibrated as expected by the nature of the adatom. The elastic field of the adatom is described and the limitations of the continuum theory are discussed. Calculations of the interaction energy between adatoms indicate agreement with existing, long-range results. The strength of the leading singularity of the interaction energy changes, however, when the adatoms are closely spaced. Anisotropy plays a significant role in this process; in certain directions, identical adatoms actually attract each other. Independent simulations using EAM potentials clearly demonstrate the accuracy of the elastic field produced by the eigenstrain model. The restrictive assumptions regarding the adatom/force system found in existing models are removed in this distortion-based model. The eigenstrain approach can also be used to represent surface steps and vacancies.