Location of Repository

This thesis is presented in two sections. Two different multiscale models are developed in order to increase the computational speed of two well known atomistic algorithms, Molecular Dynamics (MD) and Kinetic Monte Carlo (KMC).\ud In Section I, the MD method is introduced. Following this, a multiscale method of linking an MD simulation of heat conduction to a finite element (FE) simulation is presented. The method is simple to implement into a conventional MD code and is independent of the atomistic model employed. This bridge between the FE and MD simulations works by ensuring that energy is conserved across the FE/MD boundary. The multiscale simulation allows for the investigation of large systems which are beyond the range of MD. The method is tested extensively in the steady state and transient regimes, and is shown to agree with well with large scale MD and FE simulations. Furthermore, the method removes the artificial boundary effects due to the thermostats and hence allows exact temperatures and temperature gradients to be imposed on to an MD simulation. This allows for better study of temperature gradients on crystal defects etc.\ud In Section II, the KMC method is introduced. A continuum model for the KMC method is presented and compared to the standard KMC model of surface diffusion. This method replaces the many discrete back and forth atom jumps performed by a standard KMC algorithm with a single flux that can evolve in time. Elastic strain is then incorporated into both algorithms and used to simulate atom deposition upon a substrate by Molecular Beam Epitaxy. Quantum dot formation due to a mismatch in the lattice spacing between a substrate and a deposited film is readily observed in both models. Furthermore, by depositing alternating layers of substrate and deposit, self-organised quantum dot super-lattices are observed in both models

Topics:
Molecular dynamics, Kinetic Monte Carlo, Finite Element Method, boundary conditions, heat transfer, multiscale modelling, atomistic/continuum coupling

Publisher: University of Leicester

Year: 2009

OAI identifier:
oai:lra.le.ac.uk:2381/7809

Provided by:
Leicester Research Archive

Downloaded from
https://lra.le.ac.uk/bitstream/2381/7809/1/2009jolleykphd.pdf

- (2006). A bird's-eye view of density-functional theory,
- (2004). A bridging domain method for coupling continua with molecular dynamics,
- (2007). A continuum–atomistic simulation of heat transfer in micro- and nano-flows,
- (2005). A finite temperature dynamic coupled atomistic/discrete dislocation method,
- (1984). A molecular dynamics method for simulations in the canonical ensemble,
- (2005). A nonequilibrium molecular dynamics method for thermal conductivities based on thermal noise,
- (2008). A pseudo-atomistic model for nanoscale strain-controlled diffusion problems: the formation of heteroepitaxial alloyed quantum dot superlattices, (invited article)
- A review on the molecular dynamics simulation of machining at the atomic scale,
- (2004). A temperature equation for coupled atomistic/continuum simulations,
- (2003). Accelerated molecular dynamics with the bondboost method,
- (2004). An introduction and tutorial on multiple-scale analysis in solids,
- (2004). An introduction to computational nanomechanics and materials,
- (2004). An introductory overview of action-derived molecular dynamics for multiple time-scale simulations,
- (2007). Analytical and numerical study of coupled atomistic-continuum methods for fluids,
- (2007). and R.Yang, Effect of interface scattering on phonon thermal conductivity percolation in random nanowire composites,
- (2008). Atomistic basis for continuum growth equation: Description of morphological evolution of GaAs during molecular beam epitaxy,
- (2005). Atomistic simulation of incipient plasticity under Al(111) nanoindentation,
- (2003). Atomistic/continuum coupling in computational materials science,
- (2008). Atomistic/continuum models for multiscale heat conduction,
- (2006). Bridging scale methods for nanomechanics and materials,
- (2001). Can disorder induce a finite thermal conductivity in 1D lattices?,
- (2006). Coalescence and T-junction formation of carbon nanotubes: Action-derived molecular dynamics simulations,
- (2003). Coarse-grained stochastic processes and kinetic Monte Carlo simulators for the diffusion of interacting particles,
- (2002). Comparison of atomic-level simulation methods for computing thermal conductivity,
- (1967). Computer “Experiments” on Classical Fluids.
- (1990). Computer simulations of Liquids,
- (2000). Concurrent coupling of length scales in solid state systems,
- (1999). Concurrent coupling of length scales: Methodology and application,
- (2007). Concurrent Multiscale Kinetic Monte Carlocontinuum Models for the Evolution of Solids via Diffusion, Solid State Phenomena,
- (1964). Correlations in the Motion of Atoms in
- (1965). Cramming more components onto integrated circuits,
- (2001). Crystal, defects and microstructures – Modelling across scales,
- (2007). Diffraction limited phonon thermal conductance of nanoconstrictions,
- (1997). Diffusion of a Butanethiolate molecule on a Au{111} surface,
- Effect of strain on the thermal conductivity of solids,
- (1995). Effects of Deposition Rate on the Size of Self-Assembled InP Islands Formed on GalnP/GaAs(100) Surfaces,
- (1988). Empirical interatomic potential for carbon, with applications to amorphous carbon,
- (1998). Energy transport in anharmonic lattices close to and far from equilibrium,
- (2007). Equilibrium Distributions and the Nanostructure Diagram for Epitaxial Quantum Dots,
- (2006). Evaluation of momentum conservation influence in nonequilibrium molecular dynamics methods to compute thermal conductivity,
- (2000). Finite Thermal conductivity in 1D lattices,
- (2005). Finite-temperature quasicontinuum: Molecular dynamics without all the atoms,
- (2008). First principles surface thermodynamics of industrial supported catalysts in working conditions,
- (1995). Fracture simulations using large-scale moleculardynamics,
- (2002). Growth and characterization of GaAs and InAs nano-whiskers and InAs/GaAs heterostructures,
- (1999). Heat conduction in 2D nonlinear lattices, arXiv:chaodyn/9910034 v1,
- (2003). Heat conduction in one-dimensional lattices with on-site potential, Physical Review E,
- (2000). Heat conduction in one-dimensional nonintegrable systems, Physical Review E,
- (2006). How kinetics drives the two- to three-dimensional transition in semiconductor strained heterostructures: The case of InAs/GaAs(001),
- (2004). Introduction to Molecular Dynamics Simulation, Computational Soft Matter: From Synthetic Polymers to Proteins, Lecture Notes,
- (2005). Introduction to Solid State Physics
- (2002). Kinetic Monte Carlo Simulation of Chemical Vapor Deposition,
- (2000). Kinetic Monte Carlo simulation on patterned substrates,
- (2004). Langevin dynamics in constant pressure extended systems,
- (2007). Lattice thermal conductivity of nanoporous Si: Molecular dynamics study,
- (2005). Magnetic and structural properties of isolated and assembled clusters, Surface Science Reports,
- (1998). Mersenne Twister: A 623-Dimensionally Equidistributed Uniform Pseudo-Random Number Generator,
- (1989). Modeling solid-state chemistry: Interatomic potentials for multicomponent systems,
- Modelling Transient Heat Conduction at Multiple Length and Time Scales: A coupled Non-Equilibrium Molecular Dynamics/Continuum Approach,
- (2004). Molecular dynamics simulations,
- (1984). Molecular dynamics with coupling to an external bath,
- (2006). Multiscale diffusion Monte Carlo simulation of epitaxial growth,
- (2005). Multiscale Kinetic Monte-Carlo for Simulating Epitaxial Growth, arXiv:cond-mat/0504272v2, cond-mat.mtrl-sci,
- (2005). Multiscale modelling of the dynamics of solids at finite temperature,
- (2004). Multiscale plasticity modelling: coupled atomistic and discrete dislocation mechanics,
- (2004). Nanoscale heat transfer, Encyclopedia of Nanoscience and Nanotechnology (American Scientific publishers,
- (1988). New empirical approach for the structure and energy of covalent systems,
- (1986). New empirical model for the structural properties of silicon,
- (2000). Nosé-Hoover chain method for nonequilibrium molecular dynamics simulation, Physical Review E,
- (2008). On the existence of a critical perturbation amplitude for the Stranski-Krastanov transition,
- (1989). On the stability of surface of stressed solids,
- (1978). One-dimensional Kapitza conductance: Comparison of the phonon mismatch theory with computer experiments,
- (2007). Phonon-cavity-enhanced low temperature thermal conductance of a semiconductor nanowire with narrow constrictions,
- (2007). Quantum Thermal Transport from Classical Molecular Dynamics,
- (2006). Rapid thermal equilibration in coarse-grained molecular dynamics,
- (2005). Review of multiscale simulation in submicron heat transfer.
- (2000). Selforganized periodic arrays of SiGe wires and Ge islands on vicinal Si substrates, Physica E,
- (2002). Si/Ge nanostructures,
- (2001). Simple generic method for predicting the effect of strain on surface diffusion,
- (2004). Single-photon generation with InAs quantum dots,
- (1991). Solid state Physics second edition (J.
- (2005). Spatially adaptive grand canonical ensemble Monte Carlo simulations,
- (2004). Spatially adaptive lattice coarse-grained Monte Carlo simulations for diffusion of interacting molecules,
- (2003). Stacked low-growth-rate InAs quantum dots studied at the atomic level by cross-sectional scanning tunneling microscopy,
- (1975). Statistical Thermodynamics of Clean Surfaces,
- (1991). Stiffness of a solid composed of c60 clusters,
- (2004). Stochastic kinetic Monte Carlo algorithms for long-range Hamiltonians,
- (2006). Temporal acceleration of spatially distributed kinetic Monte Carlo simulations,
- (2004). The art of Molecular Dynamics Simulation,
- (1993). The embedded-atom method: a review of theory and applications,
- (2005). The surface of helium crystals,
- (2007). Thermal conductance across grain boundaries in diamond from molecular dynamics simulation,
- (2003). Thermal conductance through molecular wires,
- (2003). Thermal conduction in classical low-dimensional lattices, Physics reports 377,
- (2006). Thermal conduction in sub-100nm transistors,
- (2007). Thermal conduction simulations in the nanoscale.
- (2005). Thermal conductivity and temperature in solid argon by nonequilibrium molecular dynamics simulations,
- (2004). Time-reversible deterministic thermostats,
- (2006). Variational Boundary Conditions for Molecular Dynamics Simulations of Solids at Low Temperature,

To submit an update or takedown request for this paper, please submit an Update/Correction/Removal Request.