EMPIRICAL POTENTIAL-ENERGY FUNCTION FOR CALCIUM SOLIDS AND CLUSTERS

An empirical potential-energy function, consisting of two- and three-body terms, has been derived for the study of calcium solids and clusters. With a single set of parameters, this potential reproduces the phonon frequencies and elastic constants of both the low-temperature fee and the high-temperature bcc crystalline phases to a high degree of accuracy. It also gives a sensible energy profile for the tetragonal (Bain path) interconversion of the two structures, which are both minima along the path. The potential predicts that the fee and hcp solids have almost equal cohesive energies, with that of the bcc phase being 0.02 eV lower. Other cubic phases and various two-dimensional and one-dimensional structures have lower cohesive energies. The potential leads to the conclusion that the most stable clusters tend to be polytetrahedral, leading to icosahedral packing, thereby maximizing coordination number.