Electronic Structure, Phonon Dynamical Properties, and ${\mathrm{CO}}_2$ Capture Capability of ${\mathrm{Na}}_{2-x}{\mathit{M}}_x\mathrm{Zr}{\mathrm{O}}_3$ ($M=\mathrm{Li}$,K): Density-Functional Calculations and Experimental Validations

The electronic structural and phonon properties of ${\mathrm{Na}}_{2-\alpha }{\mathit{M}}_{\alpha }\mathrm{Zr}{\mathrm{O}}_3$ ($M=\mathrm{Li}$,K, $\alpha =0.0$,0.5,1.0,1.5,2.0) are investigated by first-principles density-functional theory and phonon dynamics. The thermodynamic properties of ${\mathrm{CO}}_2$ absorption and desorption in these materials are also analyzed. With increasing doping level $\alpha$, the binding energies of ${\mathrm{Na}}_{2-\alpha }{\mathrm{Li}}_{\alpha }\mathrm{Zr}{\mathrm{O}}_3$ are increased while the binding energies of ${\mathrm{Na}}_{2-\alpha }{\mathrm{K}}_{\alpha }{\mathrm{ZrO}}_3$ are decreased to destabilize the structures. The calculated band structures and density of states also show that, at the same doping level, the doping sites play a significant role in the electronic properties. The phonon dispersion results show that few soft modes are found in several doped configurations, which indicates that these structures are less stable than other configurations with different doping levels. From the calculated relationships among the chemical-potential change, the ${\mathrm{CO}}_2$ pressure, and the temperature of the ${\mathrm{CO}}_2$ capture reactions by ${\mathrm{Na}}_{2-\alpha }{\mathit{M}}_{\alpha }\mathrm{Zr}{\mathrm{O}}_3$, and from thermogravimetric-analysis experimental measurements, the Li- and K-doped mixtures ${\mathrm{Na}}_{2-\alpha }{\mathit{M}}_{\alpha }\mathrm{Zr}{\mathrm{O}}_3$ have lower turnover temperatures ($T_t$) and higher ${\mathrm{CO}}_2$ capture capacities, compared to pure ${\mathrm{Na}}_2\mathrm{Zr}{\mathrm{O}}_3$. The Li-doped systems have a larger $T_t$ decrease than the K-doped systems. When increasing the Li-doping level $\alpha$, the $T_t$ of the corresponding mixture ${\mathrm{Na}}_{2-\alpha }{\mathrm{Li}}_{\alpha }\mathrm{Zr}{\mathrm{O}}_3$ decreases further to a low-temperature range. However, in the case of K-doped systems ${\mathrm{Na}}_{2-\alpha }{\mathrm{K}}_{\alpha }\mathrm{Zr}{\mathrm{O}}_3$, although doping K into ${\mathrm{Na}}_2\mathrm{Zr}{\mathrm{O}}_3$ initially shifts its $T_t$ to lower temperatures, further increases of the K-doping level $\alpha$ causes $T_t$ to increase. Therefore, doping Li into ${\mathrm{Na}}_2\mathrm{Zr}{\mathrm{O}}_3$ has a larger influence on its ${\mathrm{CO}}_2$ capture performance than the K-doped ${\mathrm{Na}}_2\mathrm{Zr}{\mathrm{O}}_3$. Compared with pure solids ${\mathit{M}}_2\mathrm{Zr}{\mathrm{O}}_3$, after doping with other elements, these doped systems’ ${\mathrm{CO}}_2$ capture performances are improved.

Figure 1

The crystal structure of ${\mathrm{Na}}_2\mathrm{Zr}{\mathrm{O}}_3$. The $c$ axis is vertical. There are three types of Na atoms in the structure. By substituting these Na with $\mathit{M}$ ($M=\mathrm{Li}$,K) under different combinations, two types ($A$, $B$) of ${\mathrm{Na}}_{2-\alpha }{\mathit{M}}_{\alpha }\mathrm{Zr}{\mathrm{O}}_3$ ($\alpha =0.0$,0.5,1.0,1.5,2.0) are obtained.

Figure 2

The calculated cell volumes and total energies of the substituted systems with increasing concentration of the substituting elements.

Figure 3

The calculated band structures of ${\mathrm{Na}}_{1.5}{\mathit{M}}_{0.5}\mathrm{Zr}{\mathrm{O}}_3$ ($M=\mathrm{Li}$,K).

Figure 4

The calculated total density of states of ${\mathrm{Na}}_{2-\alpha }{\mathit{M}}_{\alpha }\mathrm{Zr}{\mathrm{O}}_3$ ($\alpha =0.5$,1.0,1.5). For comparison, the calculated total density of states of ${\mathit{M}}_2\mathrm{Zr}{\mathrm{O}}_3$ ($M=\mathrm{Li}$,Na,K) is also shown in the figure. (a) ${\mathrm{Na}}_{2-\alpha }{\mathrm{Li}}_{\alpha }\mathrm{Zr}{\mathrm{O}}_3$. (b) ${\mathrm{Na}}_{2-\alpha }{\mathrm{K}}_{\alpha }\mathrm{Zr}{\mathrm{O}}_3$.

Figure 5

The calculated partial density of states of ${\mathrm{Na}}_{1.5}{\mathit{M}}_{0.5}\mathrm{Zr}{\mathrm{O}}_3$.

Figure 6

Phonon dispersion curves of ${\mathrm{Na}}_{1.5}{\mathrm{M}}_{0.5}\mathrm{Zr}{\mathrm{O}}_3$ ($M=\mathrm{Li}$,K).

Figure 7

Total phonon density of states. (a) ${\mathrm{Na}}_{2-\alpha }{\mathrm{Li}}_{\alpha }\mathrm{Zr}{\mathrm{O}}_3$. (b) ${\mathrm{Na}}_{2-\alpha }{\mathrm{K}}_{\alpha }\mathrm{Zr}{\mathrm{O}}_3$, $\alpha =0.5$,1.0,1.5.

Figure 8

The calculated phonon free energies versus temperatures of ${\mathrm{Na}}_{2-\alpha }{\mathit{M}}_{\alpha }\mathrm{Zr}{\mathrm{O}}_3$, $M=\mathrm{Li}$,K, $\alpha =0.5$,1.0,1.5.

Figure 9

The calculated entropies versus temperatures of ${\mathrm{Na}}_{2-\alpha }{\mathit{M}}_{\alpha }\mathrm{Zr}{\mathrm{O}}_3$, $M=\mathrm{Li}$,K, $\alpha =0.5$,1.0,1.5.

Figure 10

The calculated thermodynamic properties of the reactions of ${\mathrm{Na}}_{2-\alpha }{\mathit{M}}_{\alpha }\mathrm{Zr}{\mathrm{O}}_3$ ($M=\mathrm{Li}$,K, $\alpha =0.5$,1.0,1.5) capturing ${\mathrm{CO}}_2$. (a) The heat of reaction versus temperature. (b) The entropy change of the reaction versus temperature. (c) Gibbs free-energy change versus temperature.

Figure 11

Contour plot of calculated chemical-potential changes versus ${\mathrm{CO}}_2$ pressures and temperatures of the reactions for ${\mathrm{Na}}_{2-\alpha }{\mathit{M}}_{\alpha }\mathrm{Zr}{\mathrm{O}}_3$ ($M=\mathrm{Li}$,K, $\alpha =0.5$,1.0,1.5) capture of ${\mathrm{CO}}_2$. The typical ${\mathrm{CO}}_2$ pressures for pre- and postcombustions are given in blue lines. The $y$ axis is plotted in logarithm scale. Only the $\mathrm{\Delta }\mu =0$ curve is shown explicitly. For each reaction, above its $\mathrm{\Delta }\mu =0$ curve, $\mathrm{\Delta }\mu <0$, which means ${\mathrm{Na}}_{2-\alpha }{\mathit{M}}_{\alpha }\mathrm{Zr}{\mathrm{O}}_3$ absorbs ${\mathrm{CO}}_2$ and the reaction goes forward, whereas below the $\mathrm{\Delta }\mu =0$ curve, $\mathrm{\Delta }\mu >0$, which means the ${\mathrm{CO}}_2$ starts to release and the reaction goes backward to regenerate the sorbents.

Figure 12

TGA measurements of ${\mathrm{CO}}_2$ capture by ${\mathrm{Na}}_{1.5}{\mathit{M}}_{0.5}{\mathrm{ZrO}}_3$ ($M=\mathrm{Li}$,K), compared to pure ${\mathrm{Na}}_2\mathrm{Zr}{\mathrm{O}}_3$.