(9d) Designing Dopant Patterns in Indium-Doped Perovskite Oxygen Carriers

Doped perovskites are a highly versatile class of materials that exhibit tunable properties due to the choice and extent of doping in the lattice. In particular, some perovskites have found use as solid oxygen carriers for chemical looping applications [1,2]. These materials have promising properties such as rapid oxidation and reduction, tunable reduction temperature, and stability over a range of conditions [3]. As an example system, we study a BaFeO₃ perovskite doped with In for the purpose of rapid, tunable oxygen release in an oxygen carrier system. Since there are combinatorially many ways that dopant can arrange itself in a periodic lattice, it is generally impossible to rigorously to identify particular patterns of dopant that exhibit high performance for a target application. Fortunately, this combinatorial problem can be formulated and solved as a mathematical optimization problem.

The first step of translating the material design problem into a mathematical optimization model is the modelling of the material properties. To predict the reducibility of the doped perovskite, spin-polarized density functional theory (DFT+U) calculations were performed to identify the oxygen excess energy, the energy required to extract a particular oxygen from the lattice [4,5]. However, DFT calculations are computationally intensive and not tractable to be embedded in a mathematical optimization approach. To circumvent this, we propose to use a two-level approach predicated on a simplified structure-function relationship. First, we used DFT to generate a relevant training set of high-quality excess energy data. We then employed standard model identification tools to regress an algebraic model relating oxygen excess energy to some simple geometric descriptors of dopant placement.

The procedure of generating a simplified structure-function relationship was carried out by enumerating the possible conformations of dopant within a small neighborhood of a given lattice oxygen atom. These conformations were then screened to determine which motifs were actually unique with respect to rotational symmetry of the lattice. In this way, we were able to identify 47 conformations to evaluate via DFT that span the range of possible dopant loadings and placements. Geometric descriptors were tabulated using a combination of simple neighbor dopant-counting descriptors as well as descriptors to count the absolute value of the difference in dopant levels across a shared oxygen atom. This set of data points was then provided to ALAMO [6], a model identification tool, to determine the best algebraic model to represent the observed variance in oxygen excess energy with respect to our identified geometric descriptors.

Using the developed structure-function relationship, we were able to predict highly functional dopant patterns for a variety of target applications. To accomplish this, we formulated a mathematical optimization model with the structure-function relationship embedded in the algebraic constraints. Our approach is generic, enabling a variety of choices for objective function and constraints on the feasible design space.

The optimization model was used to generate a slate of designs that are optimal under various dopant loading levels and target values of oxygen excess energy. Our results highlight some distributions of In site reactivity that tend to be expressed when minimizing the overall oxygen excess energy of the lattice. These summary statistics on expressed site functionality can help elucidate the trends observed experimentally and will serve to guide the development of new materials. While the precise placement of dopant in the perovskite lattice is not possible with current experimental methods, these designs serve as a theoretical targets that can motivate further developments in synthesis methods.

References

[1] Adanez J., Abad A., Garcia-Labiano F., Gayan P., Diego L. F. De, “Progress in chemical-looping combustion and reforming technologies,” Progress in Energy and Combustion Science, 38(2):215–282, 2012.

[2] Rydén M., Lyngfelt A., Mattisson T., Chen D., Holmen A., Bjørgum E., “Novel oxygen-carrier materials for chemical-looping combustion and chemical-looping reforming; LaxSr1-xFeyCo1-yO3-d perovskites and mixed-metal oxides of NiO, Fe2O3 and Mn3O4,” International Journal of Greenhouse Gas Control, 2(1):21–36, 2008.

[3] Lekse J. W., Natesakhawat S., Alfonso D., Matranga C., “An experimental and computational investigation of the oxygen storage properties of BaLnFe2O5+d and BaLnCo2O5+d (Ln = La, Y) perovskites,” Journal of Materials Chemistry A, 2(7):2397–2404, 2014.

[4] Anisimov V., Aryasetiawan F., Lichtenstein A. I., “First-principles calculations of the electronic structure and spectra of strongly correlated systems: the LDA+U method,” Journal of Physics: Condensed Matter, 9:767–808, 1997.

[5] Kresse G., Furthmüller J., “Efficiency of ab initio total energy calculations for metals and semiconductors using a plane wave basis set,” Computational Materials Science, 6(1):15, 1996.

[6] Cozad A., Sahinidis N. V., Miller D. C., “Learning Surrogate Models for Simulation-Based Optimization,” AIChE Journal, 60(6):2211–2227, 2014.