Configurational Thermodynamics of Alloyed Nanoparticles with Adsorbates

Abstract

Changes in the chemical configuration of alloyed nanoparticle (NP) catalysts induced by adsorbates under working conditions, such as reversal in core-shell preference, are crucial to understand and design NP functionality. We extend the cluster expansion method to predict the configurational thermodynamics of alloyed NPs with adsorbates based on density functional theory data. Exemplified with PdRh NPs having Ocoverage up to a monolayer, we fully detail the core-shell behavior across the entire range of NP composition and O-coverage with quantitative agreement to in situ experimental data. Optimally fitted cluster interactions in the heterogeneous system are the key to enable quantitative Monte Carlo simulations and design. ABSTRACT: Changes in the chemical configuration of alloyed nanoparticle (NP) catalysts induced by adsorbates under working conditions, such as reversal in core−shell preference, are crucial to understand and design NP functionality. We extend the cluster expansion method to predict the configurational thermodynamics of alloyed NPs with adsorbates based on density functional theory data. Exemplified with PdRh NPs having O-coverage up to a monolayer, we fully detail the core−shell behavior across the entire range of NP composition and O-coverage with quantitative agreement to in situ experimental data. Optimally fitted cluster interactions in the heterogeneous system are the key to enable quantitative Monte Carlo simulations and design.

Using density functional calculations to elucidate atomic ordering of Pd-Rh nanoparticles at sizes relevant for catalytic applications

“…There are several levels of the computational modelling ap-proaches to address surface restructuring of bimetallic NPs caused by interactions with adsorbates present in reactive environments. A rigorous approach, albeit too computationally intensive for routine applications to particles larger than 1 nm, is an extension of the cluster expansion method to DFT treatment of bimetallic particles with adsorbates [21]. The TOP approach used in the present work was also employed to evaluate surface segregation effects induced by adsorbates in quite large bimetallic NPs [34,37].…”

“…State-of-the-art modelling atomic ordering of alloy particles combines DFT calculations [19] with cluster expansion method [20]. Extension of this sophisticated approach to treat bimetallic particles with adsorbates allowed Wang et al [21] to comparatively study bare and oxygen-covered cuboctahedral 55-atomic Pd-Rh particles at various Pd : Rh compositions. Bare NPs were shown to exhibit a simple alloying behavior and strong Rh-core/Pd-shell preference.…”

Thermodynamics of nanoalloys

“…An interesting extension of the cluster expansion method was recently made toward ligand-coated Pd-Rh nanoparticles. 59 Such nanoalloys have been experimentally shown to be enriched in rhodium under oxidizing conditions, while being enriched in palladium under reducing conditions. 60 While this behavior can be qualitatively explained by the stronger interaction of oxygen with rhodium relative to palladium, much more insight can be obtained from dedicated modeling.…”

“…60 While this behavior can be qualitatively explained by the stronger interaction of oxygen with rhodium relative to palladium, much more insight can be obtained from dedicated modeling. In their computational study of 55-atom clusters, Wang and coworkers 59 considered the possibility for surface atoms to be bound to external atomic oxygen, in addition to the normal alloying variables. All oxygen atoms were restricted to sit on specific lattice sites, and the model was parametrized further to take into account the adsorption energies of oxygen over various possible sites.…”

icet - A Python library for constructing and sampling alloy cluster expansions

“…2,3 The CE approach has been widely and very successfully adopted to analyze for example phase diagrams in metallic 4,5 and semiconducting alloys, [6][7][8] including surfaces [9][10][11][12][13][14][15] as well as nanoparticles. [16][17][18][19][20][21][22][23] CEs have also been applied to study the temperature and composition dependence of ordering in various materials. [24][25][26][27][28] The CE approach is not limited to the mapping of total and mixing energies but can also be applied to model for example activation barriers, 29 vibrational properties, 30,31 chemical expansion, 26 or transport properties.…”