  We study formation of the nanowires formed after deposition of Pt on a
Ge(001) surface. The nanowires form spontaneously after high temperature
annealing. They are thermodynamically stable, only one atom wide and up to a
few hundred atoms long. Ab initio density functional theory calculations are
performed to identify possible structures of the Pt-Ge (001) surface with
nanowires on top. A large number of structures is studied. With nanowires that
are formed out of Pt or Ge dimers or mixed Pt-Ge dimers. By comparing simulated
scanning tunneling microscopy images with experimental ones we model the
formation of the nanowires and identify the geometries of the different phases
in the formation process. We find that the formation of nanowires on a
Pt-Ge(001) surface is a complex process based on increasing the Pt density in
the top layers of the Ge(001) surface. Most remarkably we find the nanowires to
consist of germanium dimers placed in troughs lined by mixed Pt-Ge dimer rows.
