Tight-binding calculations of stacking energies and twinnability in fcc metals

We calculate the material properties needed to evaluate the tendency of a face-centered-cubic (fcc) metal to plastically deform by forming crystallographic twins as opposed to dislocation-mediated slip. We refer to this property as the twinnability of the metal. We use a formulation for twinnability derived from a coupling of continuum mechanics with an atomistic stress-slip relation. The essential quantities for evaluating the twinnability are elastic constants, which are measurable experimentally, and energies for various stacking sequences of the fcc (111) planes. These stacking sequences include the intrinsic stacking fault configuration as well as the unstable-stacking energy and unstable-twinning energy configurations which can only be determined computationally. We use a tight-binding model to evaluate the necessary stacking energies, as well as the extrinsic stacking fault energy and twin-boundary energy, for eight fcc metals. The accuracy of the tight-binding parameters is established by comparing them with first-principles values obtained through an extensive study of the literature. The results of the literature survey are included in the paper as a resource for the reader. We show that the ranking of these metals in order of twinnability agrees with available experimental results. We reproduce the low incidence of deformation twinning in Al, and explain it in terms of the material parameters using an approximation to the twinnability expression. We also predict that Pd, which has not been studied experimentally, should twin as easily as Cu.