Coupling between electronic and structural degrees of freedom in the triangular lattice conductor ${\mathrm{Na}}_x\mathrm{Co}{\mathrm{O}}_2$

The ambient temperature crystal structures of compounds in the ${\mathrm{Na}}_x\mathrm{Co}{\mathrm{O}}_2$ family, for $0.34<x⩽1.0$, determined by powder neutron diffraction, are reported. The structures consist of triangular $\mathrm{Co}{\mathrm{O}}_2$ layers with Na ions distributed in intervening charge reservoir layers. The shapes of the $\mathrm{Co}{\mathrm{O}}_6$ octahedra that make up the $\mathrm{Co}{\mathrm{O}}_2$ layers are found to be critically dependent on the electron count and on the distribution of the Na ions in the intervening layers, where two types of Na sites are available. Correlation of the shapes of cobalt-oxygen octahedra, the Na ion positions, and the electronic phase diagram in ${\mathrm{Na}}_x\mathrm{Co}{\mathrm{O}}_2$ is made, providing an example of how structural and electronic degrees of freedom can be coupled in electrically conducting triangular lattice systems.

Figure 1

The three hexagonal structure types found for ${\mathrm{Na}}_x\mathrm{Co}{\mathrm{O}}_2$. Layers of edge-shared $\mathrm{Co}{\mathrm{O}}_6$ octahedra are seen in a triangular lattice with Na ions occupying ordered or disordered positions in the interleaving planes. Three different Na ion sites are found. In the $H1$ phase, $0.3<x<0.75$, (with the exception of $x=0.5$) Na atoms partially occupy the Na(1) $2b$ and $\mathrm{Na}{\left(2\right)}^{\prime }$ $6h$ sites. In the $H2$ phase, $0.76<x<\sim 0.82$, the Na(1) and Na(2) $2c$ sites are occupied. In the $H3$ phase, $x=1$, only the $2c$ site sites are occupied.

Figure 2

Observed (crosses) and calculated (solid line) intensities for ${\mathrm{Na}}_{0.75}\mathrm{Co}{\mathrm{O}}_2$. Vertical lines indicate the Bragg peak positions for the phases $H2$ (bottom), $H1$ (middle), and $0.4\mathrm{wt}\%$ CoO impurity (top). Differences between the observed and calculated intensities are shown in the bottom of the figure. The inset shows a portion of the pattern illustrating that the (106) and (107) reflections are good indications of the different lattice parameters for the phases $H1$ and $H2$ in this sample with overall composition ${\mathrm{Na}}_{0.75}\mathrm{Co}{\mathrm{O}}_2$.

Figure 3

Selected structural components in ${\mathrm{Na}}_x\mathrm{Co}{\mathrm{O}}_2$. Upper figure: the triangular prismatic $\mathrm{Na}{\mathrm{O}}_6$ coordination polyhedra. The Na(1) ion ($2b$ site) triangular prisms share faces with the $\mathrm{Co}{\mathrm{O}}_6$ octahedra. The Na(2) ion ($2c$ site) regular triangular prisms share edges with the $\mathrm{Co}{\mathrm{O}}_6$ octahedra. The $\mathrm{Na}{\left(2\right)}^{\prime }$ ions randomly occupy one of the possible the $6h$ sites distributed around the $2c$ site, displaced from the center of the triangular prisms. If a particular Na(2) or $\mathrm{Na}{\left(2\right)}^{\prime }$ site is occupied, then the nearest Na(1) position is too close to be simultaneously occupied. Lower figure: detail of the $\mathrm{Co}{\mathrm{O}}_2$ layer.

Figure 4

The general structural characteristics and compositional stability regions of the four ${\mathrm{Na}}_x\mathrm{Co}{\mathrm{O}}_2$ phases, designated as $H1$, $H2$, $H3$, and $O1$. Upper panel, hexagonal crystallographic cell parameters. Lower panel, fractional occupancies of the two types of sodium sites: Na(1) shares faces with the $\mathrm{Co}{\mathrm{O}}_6$ octahedra, and $\mathrm{Na}{\left(2\right)}^{\prime }$ and Na(2) (plotted as one site) share edges with the $\mathrm{Co}{\mathrm{O}}_6$ octahedra. Above the panels, the sodium ion distributions in the four phases are shown schematically.

Figure 5

Upper panel, thickness of the $\mathrm{Na}{\mathrm{O}}_2$ layers (also the separation of the $\mathrm{Co}{\mathrm{O}}_2$ planes) in ${\mathrm{Na}}_x\mathrm{Co}{\mathrm{O}}_2$ as a function of Na content. Middle panel: thickness of the $\mathrm{Co}{\mathrm{O}}_2$ layer and variation in $\mathrm{O}\mathrm{Co}\mathrm{O}$ bond angle as a function of Na content. Lower panel: the corresponding variation in $\mathrm{Co}\mathrm{O}$ bond length.

Figure 6

Correspondence between structure and properties in ${\mathrm{Na}}_x\mathrm{Co}{\mathrm{O}}_2$. Upper figure: schematic of the Na ion distributions in the four ${\mathrm{Na}}_x\mathrm{Co}{\mathrm{O}}_2$ phases. Main panel: the electronic phase diagram. Lower panel: variation of the ratio of the observed $\mathrm{Co}{\mathrm{O}}_2$ layer thickness to the thickness of an ideal layer of octahedra.