  A tetragonal (Bain path) distortion of a metal with an fcc (bcc) ground state
will initially cause an increase in energy, but at some point along the Bain
path the energy will again decrease until a local minimum is reached. Using a
combination of parametrized tight-binding and first-principles LAPW
calculations we show that this local minimum is unstable with respect to an
elastic distortion, except in the rare case that the minimum is at the bcc
(fcc) point on the Bain path. This shows that body-centered tetragonal phases
of these materials, which have been seen in epitaxially grown thin films, must
be stabilized by the substrate and cannot be free-standing films.
