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Nonequilibrium Statistical Mechanical and Coarse-Grained Modeling King C Chemistry Publications Chemistry 6-4-2019 Reshaping, Intermixing, and Coarsening for Metallic Nanocrystals: Nonequilibrium Statistical Mechanical and Coarse-Grained Modeling King C. Lai Iowa State University and Ames Laboratory, [email protected] Yong Han Iowa State University and Ames Laboratory, [email protected] Peter M. Spurgeon Iowa State University, [email protected] Wenyu Huang Iowa State University, [email protected] Patricia A. Thiel IFoowlalo Swta tthie Usn iaverndsit ay ddandit Aionmeals L waborkoratso rayt, :pthiehttps://[email protected] tate.edu/chem_pubs Part of the Materials Chemistry Commons, Metallurgy Commons, and the Nanoscience and See next page for additional authors Nanotechnology Commons The ompc lete bibliographic information for this item can be found at https://lib.dr.iastate.edu/ chem_pubs/1131. For information on how to cite this item, please visit http://lib.dr.iastate.edu/ howtocite.html. This Article is brought to you for free and open access by the Chemistry at Iowa State University Digital Repository. It has been accepted for inclusion in Chemistry Publications by an authorized administrator of Iowa State University Digital Repository. For more information, please contact [email protected]. Reshaping, Intermixing, and Coarsening for Metallic Nanocrystals: Nonequilibrium Statistical Mechanical and Coarse-Grained Modeling Abstract Self-assembly of supported 2D or 3D nanocrystals (NCs) by vacuum deposition and of 3D NCs by solution- phase synthesis (with possible subsequent transfer to a support) produces intrinsically nonequilibrium systems. Individual NCs can have far-from-equilibrium shapes and composition profiles. The free energy of NC ensembles is lowered by coarsening which can involve Ostwald ripening or Smoluchowski ripening (NC diffusion and coalescence). Preservation of individual NC structure and inhibition of coarsening are key, e.g., for avoiding catalyst degradation. This review focuses on postsynthesis evolution of metallic NCs. Atomistic- level modeling typically utilizes stochastic lattice-gas models to access appropriate time and length scales. However, predictive modeling requires incorporation of realistic rates for relaxation mechanisms, e.g., periphery diffusion and intermixing, in numerous local environments (rather than the use of generic prescriptions). Alternative coarse-grained modeling must also incorporate appropriate mechanisms and kinetics. At the level of individual NCs, we present analyses of reshaping, including sintering and pinch-off, and of compositional evolution in a vacuum environment. We also discuss modeling of coarsening including diffusion and decay of individual NCs and unconventional coarsening processes. We describe high-level modeling integrated with scanning tunneling microscopy (STM) studies for supported 2D epitaxial nanoclusters and developments in modeling for 3D NCs motivated by in situ transmission electron microscopy (TEM) studies. Disciplines Materials Chemistry | Metallurgy | Nanoscience and Nanotechnology Comments This document is the unedited Author’s version of a Submitted Work that was subsequently accepted for publication in Chemical Reviews, copyright © American Chemical Society after peer review. To access the final edited and published work see DOI: 10.1021/acs.chemrev.8b00582. Posted with permission. Authors King C. Lai, Yong Han, Peter M. Spurgeon, Wenyu Huang, Patricia A. Thiel, Da-Jiang Liu, and James W. Evans This article is available at Iowa State University Digital Repository: https://lib.dr.iastate.edu/chem_pubs/1131 Reshaping, intermixing, and coarsening of metallic nanoclusters: Non-equilibrium statistical mechanical and coarse-grained modeling King C. Lai,1,2 Yong Han,1,3 Peter Spurgeon,4 Wenyu Huang,4 Patricia A. Thiel,3,4,5 Da-Jiang Liu,2 and James W. Evans1,2 1Department of Physics & Astronomy, Iowa State University, Ames, Iowa 50011 2Division of Chemical & Biological Sciences, Ames Laboratory – USDOE, Iowa State University, Ames, Iowa 50011 3Division of Materials Science & Engineering, Ames Laboratory – USDOE, Iowa State University, Ames, Iowa 50011 4Department of Chemistry, Iowa State University, Ames, Iowa 50011 5Department of Materials Science & Engineering, Iowa State University, Ames, Iowa 50011 ABSTRACT Self-assembly of ensembles of supported 2D or 3D nanoclusters (NCs) by surface deposition, and of unsupported 3D NCs by solution-phase synthesis, produces intrinsically non- equilibrium systems. Individual nanoclusters can have far-from-equilibrium shapes and composition profiles. The free energy of the ensemble can be lowered by coarsening which can involve Ostwald ripening or Smoluchowski ripening (NC diffusion and coalescence). Preservation of individual NC structure and inhibition of coarsening is key for, e.g., avoiding catalyst degradation. In this review, we focus on crystalline metallic NCs. Atomistic-level modeling of equilibration processes typically utilizes stochastic lattice-gas models to access appropriate time- and length-scales. However, predictive modeling requires incorporation of realistic rates for relaxation mechanisms, e.g., periphery diffusion and intermixing, in numerous local environments (rather than the use of generic prescriptions). Alternative coarse-grained modeling must also incorporate appropriate mechanisms and kinetics. At the level of individual NCs, we present analyses of reshaping, including sintering and pinch-off, and of compositional evolution. We also discuss modeling of coarsening including diffusion and decay of individual NCs, and unconventional coarsening processes. We describe high-level modeling integrated with STM studies for 2D epitaxial NCs, and developments in modeling for supported and unsupported 3D NCs motivated by in situ TEM studies. CONTENTS 1. Introduction 2. Synopsis of self-assembly and coarsening for metallic NC systems 2.1. Basics of NC self-assembly 2.2. Self-assembly 2D and 3D supported NCs via surface deposition 2.2.1. Ensemble-level features 2.2.2. Individual NC structure 2.3. Post-assembly coarsening pathways for supported NCs 2.4. Solution-phase self-assembly and coarsening of 3D unsupported NCs 3. Overview of atomistic-level stochastic modeling strategies 3.1. Stochastic lattice-gas modeling of equilibrium NC structure 3.2. Generic and refined lattice-gas modeling of kinetics for individual NCs 3.3 Application to 2D epitaxial nanoclusters 3.3.1. Conventional Formulations 3.3.2. Refined Formulations 3.4 Application to 3D unsupported (and epitaxial supported) nanoclusters 3.5. Stochastic lattice-gas modeling with ab-initio based kinetics 3.5.1. 2D epitaxial NCs 1 3.5.2. 3D fcc NCs 3.5.3 Concerted many-atom processes 3.6 Off-lattice atomistic-level stochastic modeling for supported NCs 4. Overview of coarse-grained continuum modeling and coarsening theories 4.1. Coarse-grained continuum modeling of reshaping for individual NCs 4.1.1. Shape evolution of 2D epitaxial NCs 4.1.2. Shape evolution of 3D NCs 4.2. Incorporating fluctuations into coarse-grained modeling for individual NCs 4.3 Other continuum formulations for NC shape evolution 4.3.1. Continuum multi-field formulations 4.3.2. Evolution of faceted NCs 4.3.3. Multilayer step dynamics 4.3.4. Eulerian versus Lagrangian dynamics 4.4. Post-assembly coarsening of ensembles of supported NCs 4.4.1. Ostwald ripening (OR) 4.4.2. Smoluchowski ripening (SR) 4.4.3. General issues for OR and SR including crossover 4.5. Solution-phase self-assembly and coarsening of 3D unsupported NCs 5. Shape evolution of single-component 2D epitaxial NCs 5.1. Reshaping for convex 2D epitaxial NCs: fcc(111) homoepitaxial systems 5.2. Reshaping for convex 2D epitaxial NCs: fcc(100) homoepitaxial systems 5.3. Coalescence of pairs of 2D epitaxial NCs: fcc(111) homoepitaxial systems 5.4. Coalescence of pairs of 2D epitaxial NCs: fcc(100) homoepitaxial systems 5.5. Evolution for extreme shapes of 2D epitaxial NCs 5.5.1. Irregular NCs 5.5.2. Elongated nanorods 6. Shape evolution of single-component 3D fcc NCs 6.1. Atomistic modeling for initial convex shapes of unsupported 3D NCs 6.2. Experiment and modeling of coalescence of pairs of unsupported 3D NCs 6.3. Evolution of unsupported 3D nanorods 6.4. Shape evolution for supported 3D NCs: Wetting and de-wetting 6.5. Sintering and breakup of supported 3D NCs. 7. Compositional evolution of 2D and 3D multi-component NCs 7.1. Vacancy-mediated intermixing: Basic theory 7.1.1. Mechanisms for intermixing and voiding 7.1.2. Theoretical formulation for vacancy-mediated intermixing 7.1.3. Ab-initio kinetics for vacancy-mediated intermixing 7.2. Evolution of 2D epitaxial core-ring NCs 7.3. Evolution of unsupported 3D core-shell and sandwich or multi-shell NCs 8. Coarsening of ensembles of 2D and 3D NCs 8.1. Diffusion of 2D epitaxial NCs: Smoluchowski Ripening 8.2. Decay of 2D epitaxial NCs: classic and unconventional Ostwald Ripening 8.2.1. OR for Ag/Ag(111) 8.2.2. Anomalous OR for Ag/Ag(110) 8.2.3. General comments 8.3. Diffusion and SR for supported 3D NCs 8.4. Coarsening for supported and unsupported 3D NCs 8.5. Accelerated complex-mediated Ostwald Ripening 9. Summary 2 1. INTRODUCTION Nanostructured materials, and specifically crystalline nanoclusters or ensembles thereof, can have unique and desirable properties relative to macroscale crystals.1,2 However, these systems tend to be intrinsically unstable which can limit their utility for applications including catalysis, plasmonics, and energy storage and conversion. The lack of stability derives from two features. First,
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