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Theoretical Modeling of Epitaxial Graphene Growth on the Ir(111) Surface
Holly Alexandra Tetlow
Verlag Springer-Verlag, 2017
ISBN 9783319659725 , 192 Seiten
Format PDF, OL
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Supervisor’s Foreword
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Abstract
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Parts of this thesis have been published in the following journal articlesGrowth of epitaxial graphene: Theory and experiment, H. Tetlow, J. Posthuma de Boer, I.J. Ford, D.D. Vvedensky, J. Coraux, L. Kantorovich, Physics Reports, 542 (2014) 195–295.Ethylene decomposition on Ir(111): Initial path to graphene formation, Holly Tetlow, Joel Posthuma de Boer, Ian J. Ford, Dimitri D. Vvedensky, Davide Curcio, Luca Omiciuolo, Silvano Lizzit, Alessandro Baraldi, and Lev Kantorovich, Physical Chemistry Chemical Physics 18 (2016) 27897–27909.A free energy study of carbon clusters on Ir(111): Precursors to graphene growth, H. Tetlow, I. J. Ford, and L. Kantorovich, Journal of Chemical Physics 146 (2017) 044702.Hydrocarbon decomposition kinetics from first principles H. Tetlow, L. Kantorovich, In Progress.
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Acknowledgements
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Contents
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1 Review of Epitaxial Graphene Growth
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1.1 Epitaxial Graphene Growth
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1.1.1 Experimental Techniques
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1.2 The Graphene Growth Process
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1.2.1 Producing a Carbon Source
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1.2.2 Forming Carbon Clusters
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1.2.3 Graphene Formation on Ir(111)
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1.2.4 Graphene Substrate Interaction
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1.2.5 Removing Defects
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References
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2 Theoretical Modelling Methods
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2.1 Density Functional Theory
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2.1.1 Formalism
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2.1.2 The Exchange-Correlation Functional
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2.1.3 Van der Waals Forces in DFT
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2.2 Basis-Sets
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2.2.1 K-Point Sampling
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2.3 Pseudopotentials
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2.4 The Nudged Elastic Band Method
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2.4.1 Climbing Image NEB
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2.5 Lattice Dynamics
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2.5.1 Vibrational Free Energy
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2.6 Core Level Binding Energies
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2.7 Kinetics
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2.7.1 Transition State Theory
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2.7.2 Rate Equations
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2.7.3 Kinetic Monte Carlo
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2.7.4 Lattice-Based kMC
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2.8 Molecular Dynamics
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2.8.1 Canonical Ensemble: NVT
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2.8.2 Langevin Thermostat
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2.9 Ir(111) Surface Parameterisation
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2.9.1 Bulk Lattice Constant
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2.9.2 Ir(111) Surface
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2.9.3 Plane Wave Cutoff Energy
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References
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3 Producing a Source of Carbon: Hydrocarbon Decomposition
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3.1 Theoretical Method Outline
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3.2 Decomposition Reaction Scheme
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3.3 Hydrocarbon Species
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3.4 Hydrogen
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3.5 Photoemission Experiments
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3.5.1 Binding Energy Calculations
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3.5.2 Interpretation of XPS Data
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3.6 Reaction Energy Barriers
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3.7 Rate Equations
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3.8 Conclusions
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References
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4 Hydrocarbon Decomposition: Kinetic Monte Carlo Algorithm
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4.1 Method
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4.2 Surface Lattice Grid
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4.3 Hydrocarbon Species
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4.4 Reactions
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4.4.1 Hydrogenation and Dehydrogenation Reactions
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4.4.2 H2 Desorption Reaction
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4.4.3 C-C Breaking and C-C Recombination Reactions
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4.4.4 Isomerisation Reactions
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4.4.5 Diffusion
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4.4.6 Product Species Fitting
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4.5 Time Step Calculation
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4.6 kMC Efficiency
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4.7 Conclusions
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5 Thermal Decomposition in Graphene Growth: Kinetic Monte Carlo Results
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5.1 Temperature Ramping Programmed Growth
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5.1.1 kMC Results
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5.1.2 Comparison with Experimental Results
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5.1.3 Energy Barrier Tuning
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5.1.4 Comparison with Rate Equations
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5.2 Fixed Temperature Programmed Growth (kMC)
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5.3 Ethylene Decomposition on Pt(111)
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5.3.1 Energy Barriers
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5.3.2 kMC Results
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5.4 Chemical Vapour Deposition
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5.4.1 Ethylene
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5.4.2 Methane
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5.5 Conclusions
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References
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6 Beginnings of Growth: Carbon Cluster Nucleation
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6.1 Classical Nucleation Theory
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6.1.1 Derivation of ??(N)
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6.2 Carbon Clusters
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6.2.1 Rotational Multiplicity
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6.3 Zero-Temperature Formation Energy
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6.4 Temperature Dependence of the Work of Formation
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6.5 Vibrational Free Energy Dependence on Cluster Type
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6.6 Cluster Isomerisation During Growth
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6.7 Conclusions
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References
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7 Removing Defects: Healing Single Vacancy Defects
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7.1 Theoretical Method Outline
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7.2 Single Vacancy Defects
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7.3 Langevin Thermostat
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7.3.1 Computation of Phonon DOS
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7.3.2 Choice of the Damping Parameter
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7.4 Molecular Dynamics Simulations of Defect Healing
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7.4.1 System Configuration
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7.4.2 Initialisation
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7.4.3 Ethylene Molecule Deposition
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7.4.4 Ethylene Molecule Starting Position
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7.4.5 Simulation Results
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7.4.6 Conclusions from the MD Simulations
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7.4.7 Final States
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7.5 NEB Healing of the Single Vacancy Defect
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7.6 Conclusions
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References
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8 Final Remarks
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8.1 Conclusions
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8.2 Limitations and Further Work
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References
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Appendix A Hydrocarbon Decomposition
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A.1 Lowest Energy Hydrocarbon Geometries
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A.1.1 NEB Reaction Profiles
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A.1.2 Core Level Binding Energy Calculations
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A.1.3 Convergence of Energy Barriers with Number of Layers
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A.1.4 H2 Desorption
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A.1.5 Pre-exponential Factors
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A.1.6 Vibrational Frequency Calculations and Coverage Effects
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A.1.7 Rate Equations
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Appendix B Carbon Clusters and Their Formation Energy at T=0
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Reference
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