Ion Implantation and Synthesis of Materials - Studium

142 Particle Interactions(a)V(r)r 0r∆E(b)FFmaxTension(+)F =dV(r)drrHooke's Law(Linear Elastic Region)(c)-Compression(-)+Repulsion-AttractionAtomFig. 2.1. (a) Interatomic potential function, V(r), plotted against interatomic distance, r. (b)Interatomic force plotted as a function of r. (c) A schematic showing the force neighboringatoms experience as a function of separation (Tu et al. 1992)and compressing the spacing produces a repulsive force. This data shows thatthere are no forces acting on atoms at a spacing of r 0 . (The directions of the forcesthat an atom near the minimum experiences due to a neighboring atom located atr = 0 are indicated in Fig. 2.1c.) If the atoms are displaced toward each other, a repulsiveforce acts to increase the interatomic distance back to r 0 . On the otherhand, if the distance between atoms is increased, an attractive force acts to decreasethe interatomic distance.For crystalline solids, the equilibrium interatomic distance, r 0 , can be estimatedfrom knowledge of lattice site separation distances and is typically expressed assome fraction of the lattice parameter a c . Aluminum forms a face-centered-cubic(fcc) lattice, with lattice parameter a c = 0.405 nm. Since the densest packing direcction is along the face diagonal, i.e., along the 〈110〉 direction, the equilibriuminteratomic distance in Al is 2a /2= 0.29nm. We can also calculate the distanceapproximately from the atomic volume Ω , where Ω is the reciprocal of the atomicvv