Strained tetragonal states and Bain paths in metals

Paths of tetragonal states between two phases of a material, such as bcc and fee, are called Pain paths. Two simple Pain 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 Letter 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.