  Ion-beam irradiation of an amorphizable material such as Si or Ge may lead to
spontaneous pattern formation, rather than flat surfaces, for irradiation
beyond some critical angle against the surface normal. It is observed
experimentally that this critical angle varies according to many factors,
including beam energy, ion species and target material. In this first part of a
set of papers, we consider a composite model of stress-free strain and
isotropic swelling with a generalized treatment of stress modification along
idealized ion tracks. We obtain a highly-general linear stability result with a
careful treatment of arbitrary depth-dependence profiles for each of the
stress-free strain-rate tensor, a source of deviatoric stress modification, and
isotropic swelling, a source of isotropic stress. We compare our theoretical
results with experimental measurements of angle-dependent deviatoric and
isotropic stresses for 250eV Ar+ on Si. Our analysis suggests that the presence
of angle-independent isotropic stress and the relationship between the
amorphous-crystalline and free interfaces may be strong contributors to
critical angle selection, while the influence of inhomogeneous stress
modification is seemingly non-existent in the idealized case of
diagonally-translated interface and stress generated entirely along a thin,
down-beam ion track. We also consider an opposing idealization: that of
interfaces defined by vertical translation, with stress modification along the
vertical regardless of beam orientation. The unacceptable variability in
predictions resulting from these two idealizations, both of which have appeared
in recent analyses, prompts modeling refinements discussed in subsequent papers
in this set. These refinements include the relationship between interfaces and
a more sophisticated treatment of the inhomogeneous stress field.

Materials Science;Soft Condensed Matter