(476g) Identification of Stable Bimetallic Nanoclusters Via a Mathematical Optimization Framework
- Conference: AIChE Annual Meeting
- Year: 2019
- Proceeding: 2019 AIChE Annual Meeting
- Group: Particle Technology Forum
- Time: Wednesday, November 13, 2019 - 10:00am-10:18am
The cohesive energy of an NP accounts for the strength of its inter-metallic bonds . Therefore, we can deduce the structure of the most stable nanocluster of a given mass by maximizing its cohesive energy. Our work is based on a bond-centric cohesive energy model for bimetallic nanoclusters proposed by Zihao et al . This model relates a particleâs cohesive energy with the constituent atomsâ coordination numbers. In this work, we formalize the search for the most cohesive structure via a mathematical optimization model by introducing binary variables to indicate the presence or absence of certain type of atoms in design space. This leads to a Mixed-Integer Linear Programming (MILP) optimization model that can be solved to identify optimal structures using well-established numerical optimization techniques.
In order to improve the tractability of this design framework and be in position to address practically relevant sized NPs in reasonable computational time, we also propose a two-step âstructure-then-orderâ heuristic approach. First, we identify stable nanoparticle geometries using a monometallic nanocluster geometry optimization model that we have developed previously , and which results in a pool of nanocluster geometries that may be good candidates for bimetallic NPs. The pool can be further extended by local search based on a metaheuristic search framework such as simulated annealing and genetic algorithms. Then, we use a second MILP model for searching over the space of alloy compositions on a particular geometry. This second model possesses significantly reduced combinatorial complexity compared to the fully-flexible bimetallic structure optimization counterpart, and can thus be efficiently solved to guaranteed optimality for any particle size of interest. By iteratively solving many such alloy composition optimization models, we can obtain good solutions to the fully-flexible counterpart.
We have used this optimization framework to study a wide range of transition bimetallic systems. In many cases, our results reveal segregation patterns such as well-known core-shell structures, which are supported in the literature by both experimental and computational results. However, in some cases, unintuitive trends can be observed for certain bimetallic systems. These results will help us efficiently explore the bimetallic design space and gain a deeper understanding of relationships between structure, order and stability.
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