  Paths of tetragonal states between two phases of a material, such as bcc and
fcc, are called Bain paths. Two simple Bain paths can be defined in terms of
special imposed stresses, one of which applies directly to strained epitaxial
films. Each path goes far into the range of nonlinear elasticity and reaches a
range of structural parameters in which the structure is inherently unstable.
In this paper we identify and analyze the general properties of these paths by
density functional theory. Special examples include vanadium, cobalt and
copper, and the epitaxial path is used to identify an epitaxial film as related
uniquely to a bulk phase.
