Density-functional studies of tungsten trioxide, tungsten bronzes, and related systems

Tungsten trioxide adopts a variety of structures which can be intercalated with charged species to alter the electronic properties, thus forming “tungsten bronzes.” Similar effects are observed upon removing oxygen from $\mathrm{W}{\mathrm{O}}_3$. We present a computational study of cubic and hexagonal alkali bronzes and examine the effects on cell size and band structure as the size of the intercalated ion is increased. With the exception of hydrogen (which is predicted to be unstable as an intercalate), the behavior of the bronzes are relatively consistent. $\mathrm{Na}\mathrm{W}{\mathrm{O}}_3$ is the most stable of the cubic systems, although in the hexagonal system the larger ions are more stable. The band structures are identical, with the intercalated atom donating its single electron to the tungsten $5d$ valence band. A study of fractional doping in the ${\mathrm{Na}}_x\mathrm{W}{\mathrm{O}}_3$ system $(0⩽x⩽1)$ showed a linear variation in cell parameter and a systematic shift in the Fermi level into the conduction band. In the oxygen-deficient $\mathrm{W}{\mathrm{O}}_{3-x}$ system the Fermi level undergoes a sudden jump into the conduction band at around $x=0.2$. Lastly, three compounds of a layered $\mathrm{W}{\mathrm{O}}_4\bullet \alpha ,\omega$-diaminoalkane hybrid series were studied and found to be insulating, with features in the band structure similar to those of the parent $\mathrm{W}{\mathrm{O}}_3$ compound that relate well to experimental UV-visible spectroscopy results.

Figure 1

The structure of cubic (left) and hexagonal (right) tungsten oxide and bronzes. The unit cell is indicated in each case.

Figure 2

Calculated energies of formation per $\mathrm{W}{\mathrm{O}}_3$ unit for cubic and hexagonal tungsten bronzes, relative to cubic $\mathrm{W}{\mathrm{O}}_3$.

Figure 3

The density of states as calculated for cubic (a) and hexagonal (b) $\mathrm{W}{\mathrm{O}}_3$.

Figure 4

Calculated density of states for cubic tungsten bronzes, $M\mathrm{W}{\mathrm{O}}_3$, near the Fermi level: (a) $\mathrm{W}{\mathrm{O}}_3$, (b) $\mathrm{H}\mathrm{W}{\mathrm{O}}_3$, (c) $\mathrm{Li}\mathrm{W}{\mathrm{O}}_3$, (d) $\mathrm{Na}\mathrm{W}{\mathrm{O}}_3$, (e) $\mathrm{K}\mathrm{W}{\mathrm{O}}_3$, (f) $\mathrm{Rb}\mathrm{W}{\mathrm{O}}_3$, (g) $\mathrm{Cs}\mathrm{W}{\mathrm{O}}_3$. The Fermi level is indicated in each case.

Figure 5

(a) Calculated and experimental values of the cell parameter for cubic ${\mathrm{Na}}_x\mathrm{W}{\mathrm{O}}_3$ with variable $x$. (b) Band gap and Fermi level of ${\mathrm{Na}}_x\mathrm{W}{\mathrm{O}}_3$. The lines are given as a guide.

Figure 6

The volume-averaged cubic cell parameter for calculated and experimental substoichiometric “cubic” $\mathrm{W}{\mathrm{O}}_{3-x}$ systems. The curve is given as a guide.

Figure 7

Density of states for the $\mathrm{W}{\mathrm{O}}_{3-x}$ system, all with the valence band set at zero. Arrows show the position of the Fermi level. Inset: Position of the Fermi level relative to the top of the valence band.

Figure 8

(Color online) Calculated structure of methylamine in bridging (left) and apical (right) configurations.

Figure 9

Calculated structures of diaminoethane (DA2) in bridging (left) and apical (right) configurations.

Figure 10

Calculated density of states for W-DA2 (bottom), W-DA4 (middle), and W-DA6 (top). The Fermi level is located at $E=0$.