First-principles thermodynamic framework for the evaluation of thermochemical ${\text{H}}_2\text{O}$- or ${\text{CO}}_2$-splitting materials

We present an analysis of the equilibrium thermodynamics of two-step metal oxide-based water and carbon dioxide-splitting cycles. Within this theoretical framework, we propose a first-principles computational approach based on density-functional theory (DFT) for evaluating new materials for these cycles. Our treatment of redox-based gas-splitting chemistry is completely general so that the thermodynamic conclusions herein hold for all materials used for such a process and could easily be generalized to any gas as well. We determine the temperature and pressure regimes in which the thermal reduction (TR) and gas-splitting (GS) steps of these cycles are thermodynamically favorable in terms of the enthalpy and entropy of oxide reduction, which represents a useful materials design goal. We show that several driving forces, including low TR pressure and a large positive solid-state entropy of reduction of the oxide, have the potential to enable future, more promising two-step gas-splitting cycles. Finally, we demonstrate a practical computational methodology for efficiently screening new materials for gas-splitting applications and find that first-principles DFT calculations can provide very accurate predictions of high-temperature thermodynamic properties relevant to gas splitting.

Figure 1

(Color online) Temperature and pressure ranges in which TR and GS are thermodynamically favorable, neglecting solid-state entropy [from Eq. (11)]. The window in which both TR and GS are favorable is restrictive from experimental and materials standpoints.

Figure 2

(Color online) Temperature ranges in which TR (at 1 atm pressure) and GS are thermodynamically favorable, for a set of reasonable $\Delta S_{reduction}=S^{M{\text{O}}_{x-1}}-S^{M{\text{O}}_x}$ values. This solid-state entropy delta can, if it is large and positive, broaden the window in which TR and GS are both favorable.

Figure 3

(Color online) Regions of favorable TR (below indicated TR line) and GS (above indicated GS lines) thermodynamics plotted in terms of materials properties $\Delta S_{reduction}$ and $\Delta H_{reduction}$, assuming TR at 2000 K and GS at 1000 K. The thermodynamics of 105 elemental oxide cycles are calculated at an intermediate temperature of 1500 K (or the next-highest available temperature in 100 K increments) from the SSUB3 database at 1 bar (Ref. 24) or in the case of Fe and its oxides from NIST (Ref. 28). Labeled cycles have generated significant interest in the literature. Brackets on those materials’ points indicate the small effects of changing the assumed 1500 K temperature by $\pm 200\text{K}$ (exceptions due to limited data: ${\text{Fe}}_3{\text{O}}_4$ range 1300–1600 K, CdO range 1200–1400 K, and ZnO range 1300–1600 K). All the indicated materials except ${\text{CeO}}_2$ move left at higher temperatures.

Figure 4

Enthalpies and entropies of reduction for four selected gas-splitting cycles. Scale is identical to that of Fig. 3. (a) Experimental and first-principles calculated values for the highest possible temperature (in 100 K increments; indicated next to the data points) before either member of each pair undergoes a phase transition. (b) Experimental and first-principles values, all at 1500 K, directly comparable to Fig. 3.