The simplest atomistic model is the binary collision approximation (BCA), which simulates cascades as a series of atomic collisions. The ‘potential’ is then basically a hard sphere, with collisions either elastic or inelastic and the possibility of adding friction to describe an ion’s progress through an electron field. There is no binding energy, so the condensed phase is stabilized due to confinement by the boundary con­ditions. This is a poor approximation, since the struc­tures and energies of the equilibrium crystal and defects do not correspond to real material. However, it allows for quick calculation and the scaling of defect production with energy of the primary knock-on atom. The best-known code for this type of calculation is probably Oak Ridge’s MARLOWE.1

1.10.2 Pair Potentials

Pairwise potentials are the next level in complexity beyond BCA. They allow soft interactions between particles and simultaneous interaction between many atoms. Pair potentials always have some parameters that relate to a particular material, requiring fitting to experimental data. This immediately introduces the question ofwhether the reference state should be free atoms (e. g., in argon), free ions (e. g., NaCl), or ions embedded in an electron gas (e. g., metals).

The two classic pair potentials used for modeling are the LennardJones (LJ) and Morse potential. Each consists of a short-range repulsion and a long-range attraction and has two adjustable parameters.

The (y) 6 cohesion is on the basis of van der Waals interactions, while the e-ar is motivated by a screened — Coulomb potential. The repulsive terms were invented ad hoc.

Because they have only two parameters, all simu­lations using just LJ or Morse are equivalent, the values of e, s, or a , which simply rescale energy and length. Hence, these potentials cannot be fitted to other properties of particular materials.

Both LJ and Morse potentials stabilize close- packed crystal structures, and both have unphysically low basal stacking fault energies. Equivalently, the energy difference between fcc and hcp is smaller than for any real material. For materials modeling, this introduces a problem that the (110) dislocation structure is split into two essentially independent partials. For radiation damage, this means that con­figurations such as stacking fault tetrahedra are over­stabilized, and unreasonably large numbers of stacking faults can be generated in cascades, fracture, or deformation. If the energy scale is set by the cohe­sive energy of a transition metal, then the vacancy and interstitial formation energy tend to be far too large; if the vacancy energy is fitted, then the cohesive energy is too small.

For binary systems, these potentials can stabilize a huge range of crystal structures, even without explicit temperature effects; some progress has been made to delineate these, but it is far from complete.2 Once one moves to N-species systems, there are e and а parameters for each combination of particles, that is, N(N + 1) parameters. Now it is possible to fit to prop­erties of different materials, and the rapid increase in parameters illustrates the combinatorial problem in defining potentials for multicomponent systems.