Strain mediated tri- and quattro- interactions of adatoms

Lateral interactions of oxygen adatoms derived from first-principles calculations of the O-Pd(100) system had been claimed to include trio- and quattro terms beside pair interactions. This paper is dedicated to extend an earlier model for substrate strain mediated interactions between adatom pairs to include trio- and quattro terms. While monomers (sitting on high symmetric sites) are supposed to create isotropic stress on the substrate, dimers would create anisotropic stress. The requirement of mechanical equilibrium allows to formulate the elastic energy as a sum of pair-, trio- and quattro terms, solved by respective an eigenvalue problems. Resulting interactions are strongly angle dependent and also reflect the elastic anisotropy of the substrate. A continuum elastic model supports the long range character of the elastic interaction but should also describe some short range features. For the elastically isotropic tungsten substrate a closed solution for quattro interactions is presented, for trio inter cations numerical values are given.