(136e) Identification of Optimal Dopant Patterns in a Doped Perovskite Oxygen Carrier
AIChE Annual Meeting
Monday, October 29, 2018 - 1:46pm to 2:05pm
To that end, this work aims to formulate and solve a mathematical optimization model to identify doped perovskite lattices with optimal properties. To translate the search for a highly reducible perovskite into a mathematical optimization formulation, we first quantify the impact of dopant on the reducibility of the perovskite via a suitable metric, namely the oxygen excess energy, which is defined as the energy difference between the original lattice and the lattice with a particular oxygen removed. This quantity can be calculated accurately by Hubbard corrected density functional theory given a supercell with a particular arrangement of dopant around an oxygen atom in question [5,6]. In order to explore the impact that dopant has on the oxygen excess energy, a motif of relevant locations was defined and the set of possible configurations of dopant in a motif were enumerated. This resulted in 74 rotationally-unique ways to place dopant in the ten nearest sites near a given oxygen. The oxygen excess energy for each of these motifs was evaluated at T=0K and then additional free energy excess energy calculations were performed at process conditions.
Given a complete set of evaluations, we selected a subset of motifs with the lowest oxygen excess energy to consider as âtargetâ motifs to pack in an optimal material. A mathematical optimization model was formulated to relate the placement of dopant atoms in a supercell of the perovskite lattice to the number of oxygen sites that achieved one of the target motifs. Using binary variables and indicator constraints, we were able to model the problem as a mixed integer linear program. This modelling approach is generic in the sense that additional constraints, such as bounds on dopant concentration, fabricability, and stability of the material can be enforced to further restrict the search to materials of interest. In addition to the basic formulation, we derive several approaches to symmetry breaking that are able to improve the tractability of the model. A key advantage of casting our problem as a mathematical optimization model is the ability to rigorously guarantee the exploration of the entire search space and the ability to collect a list of the top designs for evaluation offline against secondary criteria.
Our optimal solutions demonstrate that a significant fraction of oxygen sites can display a target motif. By comparing the quality of our optimal designs against the baseline qualities of designs formed by random dopant placement, we show that nanostructured designs can significantly outperform unstructured materials. Furthermore, we can use our model of randomly doped perovskites to explain trends in the experimentally observed temperature of oxygen release. While the precise placement of dopant in the lattice may be currently impractical, the identification of ideal dopant patterns can serve to guide future development of synthesis methods and to establish rigorous upper bounds on the performance of doped perovskite materials.
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