Observation of Regular Energy Patterns in Finite Systems of Low-Dimensional Ionic Crystals

Invention of novel nanofabrication techniques has made possible the realization of stable finite systems of almost perfect low-dimensional ionic crystals consisting of regular arrays of alternating positive and negative ions. For example, it has been successfully demonstrated that certain cations and ions can be trapped and aligned alternately inside a carbon nanotube forming a nearly ideal finite one-dimensional ionic crystal. In this work we consider a simple model of a finite one-dimensional ionic crystal and study its properties. We calculate the energy for ion for various finite systems consisting of an arbitrary number of ions that interact with a standard Coulomb interaction potential. The results give a fairly accurate picture of how the energy of this finite one-dimensional ionic crystal evolves towards the bulk value as the size of the system increases. The results obtained show some interesting regular patterns of the energy per ion as a function of the parity (even or odd) of the total number of ions in the crystal. Possible extensions of this approach to other finite low-dimensional ionic crystals are discussed.