  We present a general parameter study, in which the abundance of interstellar
argonium (ArH$^+$) is predicted using a model for the physics and chemistry of
diffuse interstellar gas clouds. Results have been obtained as a function of UV
radiation field, cosmic-ray ionization rate, and cloud extinction. No single
set of cloud parameters provides an acceptable fit to the typical ArH$^+$,
OH$^+$ and $\rm H_2O^+$ abundances observed in diffuse clouds within the
Galactic disk. Instead, the observed abundances suggest that ArH$^+$ resides
primarily in a separate population of small clouds of total visual extinction
of at most 0.02 mag per cloud, within which the column-averaged molecular
fraction is in the range $10^{-5} - 10^{-2}$, while OH$^+$ and $\rm H_2O^+$
reside primarily in somewhat larger clouds with a column-averaged molecular
fraction $\sim 0.2$. This analysis confirms our previous suggestion that the
argonium molecular ion is a unique tracer of almost purely atomic gas.
