Ion Implantation and Synthesis of Materials - Studium

2 Particle Interactions2.1 IntroductionThe manner in which the potential energy of a two-particle system varies with thedistance separating the two centers determines both the equilibrium properties ofan assembly of atoms and the way that energetic particles interact with a lattice ofstationary atoms. The scattering probability of an ion–atom collision is intimatelyrelated to the interaction forces between atoms.2.2 Interatomic ForcesWe start our discussion with the concept that atoms are comprised of a central nucleusand orbital electrons, and we consider the forces when one atom interactswith another atom. The nucleus is effectively a solid body of diameter ∼10−12 cmwith a positive charge, Z, which is dependent on the number of protons present. Ifthere were no orbital electrons, the force between two nuclei separated by a distancer would be Coulombic, of the form21 2Fr () = Z Ze ,2r(2.1)where Z 1 and Z 2 are the numbers of protons contained in the nucleus, ande 2 = 1.44 eV nm (1.8).For most purposes, the force between two atoms is expressed in terms of aninteratomic potential, which depends primarily on the separation, r, between theatoms or other charged particles. If the dependence of the potential on other coordinatesis neglected (central force approximation), then the force, F(r), and thepotential, V(r), are related bydF( r) =− [ V( r)].dr(2.2)11