  The destruction of quasi-long range crystalline order as a consequence of
strong disorder effects is shown to accompany the strict localization of all
classical plasma modes of one-dimensional Wigner crystals at T=0. We construct
a phase diagram that relates the structural phase properties of Wigner crystals
to a plasmon delocalization transition recently reported. Deep inside the
strictly localized phase of the strong disorder regime, we observe
``glass-like'' behavior. However, well into the critical phase with a plasmon
mobility edge, the system retains its crystalline composition. We predict that
a transition between the two phases occurs at a critical value of the relative
disorder strength. This transition has an experimental signature in the AC
conductivity as a local maximum of the largest spectral amplitude as a function
of the relative disorder strength.
