The basic lattices formed by condensed ions that we consider are composed of (a) paired ions forming dipole arrays at the boundaries between stripes, or system , and (b) stripe-centered ionic arrays, or system type . The shadow regions comprise the unit cell of the respective lattices. Panel (c) shows the bare surface with alternating charged stripes and sets our axis notation. The white and gray regions have opposite uniform charge density.
Panels (a) and (b) show the geometric structures of lattices deformed away from the basic and arrangements. Panel (c) shows a plot of the ratio of Madelung constants . The minima of the ratio correspond in all cases to the undeformed case at .
Steps in the construction of the phase diagram of the system. The top panel (a) shows the regions where the three basic phases: Dipolar, stripe centered, and no adsorption, are preferred. These regions are modified by structural instabilities: Panel (b) shows the subregion of the dipolar case that is unstable against the addition of a single ion, while panel (c) shows the region of instability of the stripe-centered charge case against the inclusion of the dipole. The schemes at the right show the basic structure of the phases and their perturbations. Results are presented for a fix ratio , in a plane with axes proportional to the charge density and the chemical potential .
The dependence of the condensed ion density vs the surface charge density for both types of lattices, dipolar and stripe centered , evaluated along the coexistence line. The charge density axis coincides with that of Fig. 2.
The final phase diagram for values for the system, for the same parameter values of Fig. 3.
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