A First‐Principles‐Based Sub‐Lattice Formalism for Predicting Off‐Stoichiometry in Materials for Solar Thermochemical Applications: The Example of Ceria

Abstract

Theoretical models that reliably can predict off‐stoichiometry in materials via accurate descriptions of underlying thermodynamics are crucial for energy applications. For example, transition‐metal and rare‐earth oxides that can tolerate a large number of oxygen vacancies, such as CeO2 and doped CeO2, can split water and carbon dioxide via a two‐step, oxide‐based solar thermochemical (STC) cycle. The search for new STC materials with a performance superior to that of state‐of‐the‐art CeO2 can benefit from predictions accurately describing the thermodynamics of oxygen vacancies. The sub‐lattice formalism, a common tool used to fit experimental data and build temperature‐composition phase diagrams, can be useful in this context. Here, sub‐lattice models are derived solely from zero‐temperature quantum mechanics calculations to estimate fairly accurate temperature‐ and oxygen‐partial‐pressure‐dependent off‐stoichiometries in CeO2 and Zr‐doped CeO2. Physical motivations for deriving some of the “excess” sub‐lattice model parameters directly from quantum mechanical calculations, instead of fitting to minimize deviations from experimental and/or theoretical data, are identified. Important limitations and approximations of the approach used are specified and extensions to multi‐cation oxides are also suggested to help identify novel candidates for water and carbon dioxide splitting and related applications.

Factors Governing Oxygen Vacancy Formation in Oxide Perovskites

“…We find that SCAN+ U calculations are only modestly more computationally expensive (∼1.85–2.35×) for each self-consistent-field loop in comparison to those with PBE+ U (see Table S1 in the Supporting Information). We utilized the all-electron, frozen-core, projector augmented-wave (PAW) potentials , as in our prior work ,,, to describe the ion-electron interactions, along with including the nonspherical contributions related to the gradient of the electron density and the kinetic energy density within the PAW spheres for the XC evaluation. We used the Accurate “precision” mode in VASP to avoid aliasing errors when the fast-Fourier-transform and support grids were set, employed an additional support grid for more accurate evaluation of augmentation charges, and evaluated the projection operators in real space using VASP’s fully automatic optimization scheme.…”

“…We used the Accurate “precision” mode in VASP to avoid aliasing errors when the fast-Fourier-transform and support grids were set, employed an additional support grid for more accurate evaluation of augmentation charges, and evaluated the projection operators in real space using VASP’s fully automatic optimization scheme. We used a plane-wave kinetic energy cutoff of 520 eV, ,,, as this threshold converges total energies of oxide perovskites to within 1 meV/atom.…”

Exploring Ca–Ce–M–O (M = 3d Transition Metal) Oxide Perovskites for Solar Thermochemical Applications

“…G ABO 3 and G ABO 2.5 in eq 3 are the Gibbs energies of hypothetical pristine ABO 3 and defective ABO 2.5 perovskite phases, which are set to the calculated Gibbs energies of CeO 2 (G CeO 2 ) and CeO 1.5 (G CeO 1.5 ) in the fluorite structure. 52 Additionally, we set the enthalpy to form an oxygen vacancy (or the enthalpy of mixing oxygen vacancies with oxygen atoms; L 0 term in eq 3) to a constant value across all x, where the value used is identical to the DFT-calculated E f [Va O ] in CeO 2−δ at δ → 0 (= 3.98 eV/Va O ). 43,52,53 These approximations ensure that we capture the effect of entropy, while fixing ΔH red , T, and p O 2 .…”

“…52 Additionally, we set the enthalpy to form an oxygen vacancy (or the enthalpy of mixing oxygen vacancies with oxygen atoms; L 0 term in eq 3) to a constant value across all x, where the value used is identical to the DFT-calculated E f [Va O ] in CeO 2−δ at δ → 0 (= 3.98 eV/Va O ). 43,52,53 These approximations ensure that we capture the effect of entropy, while fixing ΔH red , T, and p O 2 .…”

Thermodynamic guiding principles of high-capacity phase transformation materials for splitting H2O and CO2 by thermochemical looping

“…When the metal oxide is reduced by increasing temperature, the chemical looping water splitting usually refers to two-step thermochemical water splitting. 30–35 Here a metal oxide (MO x , where M can be a combination of multiple metal cations) goes through two oxygen exchange reactions:Water splitting at a usually lower temperature T L : MO x * + ( x − x *)H 2 O → MO x + ( x − x *)H 2 …”