  We consider the crystallization problem for a finite one-dimensional
collection of identical hard spheres in a periodic energy landscape. This issue
arises in connection with the investigation of crystalline states of ionic
dimers, as well as in epitaxial growth on a crystalline substrate in presence
of lattice mismatch. Depending on the commensurability of the radius of the
sphere and the period of the landscape, we discuss the possible emergence of
crystallized states. In particular, we prove that crystallization in
arbitrarily long chains is generically not to be expected.
