Structural properties of copper

First-principles total-energy calculations on the tetragonal states of bulk elemental copper have been made with a full-potential electronic structure program with both the local-density approximation (LDA) and the generalized gradient approximation (GGA). The unique path through tetragonal states produced by epitaxial strain on equilibrium stabs has been found. This path, called the epitaxial Bain path, shows that body-centered cubic Cu (at axial ratio c/a = 1) is unstable, but a shallow energy minimum exists for a body-centered tetragonal (bct) state with axial ratio c/a = 0.93. Structure parameters and elastic constants of both the face-centered cubic (fcc) ground state and the bct state are determined and the Ecc values are compared to experiment: the GGA results are better than the LDA results. The procedures for evaluating the three fee elastic constants and the six tetragonal elastic constants are described in detail. Tests of the stability of the bet phase at cia = 0.93 show that this phase, although stable with respect to tetragonal deformations, is unstable with respect to [110] shear in the (001) plane. A lower-energy body-centered orthorhombic phase is found that may be metastable.