  Ion-beam irradiation of an amorphizable material such as Si or Ge may lead to
spontaneous pattern formation beyond some critical angle of the beam versus the
surface. It is known from experimental results that this critical angle varies
according to beam energy, ion species and target material. However, most
prevailing theoretical analyses predict a critical angle of $45^{\circ}$
independent of energy, ion and target, disagreeing with experiment. In this
second part of a set of papers, we consider the influence of the relationship
between the upper and lower interfaces of the amorphous thin film (the
``interface relation"). From our previous work, we are motivated to derive from
a geometric argument closed-form expressions describing the interface relation
in terms of the collision cascade shape. This feature leads to a refined
characterization of the influence of ion-, target- and energy-dependence on
critical angle selection.
