Abstract
The atomic structures and formation energies and volumes of a copper crystal for a series of single and multiple point defects have been calculated by real-space computer modelling techniques. Stable and metastable defect configurations were obtained by iteratively minimizing the potential energy of the model crystal. The interaction between atoms was described by three new, short-ranged, central, 'non-equilibrium' pair-potentials. Each potential was derived in such a manner that they reproduce exactly the experimental lattice parameter, the three elastic constants c[11], c[12] and c[44] and the vacancy formation and intrinsic stacking fault energies. The potentials differ only at those separations which are less than the first nearest-neighbour distance in copper. Two types of single vacancies and nine different kinds of single interstitials were simulated with each of the potentials. The normal vacancy consisting of an empty lattice site is stable whilst the split vacancy comprising two nearest-neighbour vacant sites and an atom between them is unstable. The nine interstitial configurations studied are the octahedral, tetrahedral, crowdion, octahedral-tetrahedral, octahedral-crowdion, tetrahedral-crowdion, split , split and split types. For the softest potential all of the interstitials are equilibrium structures but for the other two the tetrahedral-crowdion is unstable. In each case the tetrahedral interstitial is the stable one. The stability of vacancy pairs and close-packed clusters of trivacancies and tetravacancies were studied using the potential in best agreement with experimentally determined single vacancy properties. All four of the possible clusters of trivacancies relax to equilibrium configurations. The stable trivacancy structure is formed from a tetrahedron of nearest-neighbour vacant sites enclosing at its centre an atom displaced from one of the empty sites. Of the twenty different tetravacancies clusters investigated six were either stable or metastable. The lowest energy configuration is derived from the square of tetravacancies which relaxes to an octahedral cage of six vacancies surrounding two interstitials lying on the long axis of the octahedron. The distance between the interstitials is close to the first nearest-neighbour separation in copper.