In this work, we will present an alternative explanation of the success of non-stoichiometric oxides from a performance perspective. In particular, we first illuminate the importance of entropy as a key driver in the efficiency of the two-step redox cycle. The entropy change ÎSrxn of the MOox â MOred + O2 reaction is a gauge of the effect of the temperature swing between Step 1 and Step 2: the higher ÎSrxn, the lower the ÎT = Tred â Tox needed to thermodynamically switch between Step 1 and Step 2. Because sensible heating between Tred and Tox constitutes the major energy loss in the cycle, minimizing ÎT is key to maximizing efficiency. In this light, maximizing ÎSrxn can be seen as a first step towards finding an optimal redox material.
Stoichiometric most metal/oxide pairs, for example SnO2 â Sn + O2, suffer from an inherent flaw: the reduced metal is typically more ordered than its oxide counterpart. The thermodynamic significance of this is paramount. The reaction entropy is ÎSrxn = SMOred + SO2â SMOox = Sss + SO2, where Sss = SMOredâ SMOox is the entropy change in the solid state and SO2 is the entropy associated with the liberated oxygen. In this reaction ÎSrxn will be a positive quantity, and here we would like to maximize it. Now SO2 is fixed by the temperature and partial pressure of the system. Holding those operating parameters constant, the only way we can increase ÎSrxn is by making Sss positive and as large as possible. However, recall that for a typical stoichiometric pair the reduced metal is more ordered (lower entropy) than its oxide. Therefore, for most stoichiometric pairs Sss is negative, and so contributes negatively to ÎSrxn.
For a non-stoichiometric pair, for example CeO2 â CeO1.8 + 0.1O2, the above analysis procedure remains the same, but the result can be starkly different. Oxygen liberation in a non-stoichiometric oxide is concomitant with oxygen vacancy formation in the crystal. Therefore, reduced non-stoichiometric oxides are less ordered than their oxidized counterpart, which can be attributed to the configurational entropy associated with vacancy formation in the lattice. Because of this, Sss can be positive for non-stoichiometric pairs, thereby giving them the unique capability of boosting to ÎSrxn above that of SO2.
In this work, the above phenomenon is investigated from an empirical and statistical thermodynamic approach. In particular, we investigate the potential to maximize ÎSrxn through the appropriate choice of non-stoichiometric material, and nonstoichiometry, Î´, endpoints for both the reduction and oxidation step. We then explore how this unique property of non-stoichiometric can be exploited to maximize the theoretical conversion efficiency of two-step thermochemical water and CO2 splitting. Ultimately, we hope that this works will shed some light on the role of entropy in redox cycles based on non-stoichiometric oxides, and may pave a path to new materials discovery, guided by a principle of maximizing the solid-state entropy change.