On the Ordering of Na$^+$ Ions in Na$_x$CoO$_2$

TL;DR

This paper investigates how electrostatic interactions influence sodium ion ordering in Na$_x$CoO$_2$, using Monte Carlo simulations and diffraction experiments, revealing stable vacancy clusters and their impact on electronic properties.

Contribution

It provides a theoretical model supported by experimental data that explains sodium ion ordering and vacancy clustering in Na$_x$CoO$_2$.

Findings

Small vacancy clusters are stable at large x.

Ordered superstructures form at commensurate fillings.

Experimental diffraction data confirm the model's predictions.

Abstract

The influence of electrostatic interactions on the ordering of sodium ions in Na$_x$CoO$_2$ is studied theoretically through Monte-Carlo simulations. For large $x$ small di- or tri-vacancy clusters are stable with respect to isolated Na vacancies. At commensurate fillings these small clusters order in triangular superstructures. These results agree with recent electron diffraction data at $x=1/2$ and 3/4. We have performed neutron La\"ue diffraction experiments at higher $x$, which confirm the predictions of this simple model. The consequences on the properties of the electronic charges in the Co layers are discussed.