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Multiscale methods for nanoengineering

By Kenny Jolley


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:

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  1. (2006). A bird's-eye view of density-functional theory, doi
  2. (2004). A bridging domain method for coupling continua with molecular dynamics, doi
  3. (2007). A continuum–atomistic simulation of heat transfer in micro- and nano-flows, doi
  4. (2005). A finite temperature dynamic coupled atomistic/discrete dislocation method, doi
  5. (1984). A molecular dynamics method for simulations in the canonical ensemble, doi
  6. (2005). A nonequilibrium molecular dynamics method for thermal conductivities based on thermal noise, doi
  7. (2008). A pseudo-atomistic model for nanoscale strain-controlled diffusion problems: the formation of heteroepitaxial alloyed quantum dot superlattices, (invited article)
  8. A review on the molecular dynamics simulation of machining at the atomic scale, doi
  9. (2004). A temperature equation for coupled atomistic/continuum simulations, doi
  10. (2003). Accelerated molecular dynamics with the bondboost method, doi
  11. (2004). An introduction and tutorial on multiple-scale analysis in solids, doi
  12. (2004). An introduction to computational nanomechanics and materials, doi
  13. (2004). An introductory overview of action-derived molecular dynamics for multiple time-scale simulations, doi
  14. (2007). Analytical and numerical study of coupled atomistic-continuum methods for fluids, doi
  15. (2007). and R.Yang, Effect of interface scattering on phonon thermal conductivity percolation in random nanowire composites, doi
  16. (2008). Atomistic basis for continuum growth equation: Description of morphological evolution of GaAs during molecular beam epitaxy, doi
  17. (2005). Atomistic simulation of incipient plasticity under Al(111) nanoindentation, doi
  18. (2003). Atomistic/continuum coupling in computational materials science, doi
  19. (2008). Atomistic/continuum models for multiscale heat conduction,
  20. (2006). Bridging scale methods for nanomechanics and materials, doi
  21. (2001). Can disorder induce a finite thermal conductivity in 1D lattices?, doi
  22. (2006). Coalescence and T-junction formation of carbon nanotubes: Action-derived molecular dynamics simulations, doi
  23. (2003). Coarse-grained stochastic processes and kinetic Monte Carlo simulators for the diffusion of interacting particles, doi
  24. (2002). Comparison of atomic-level simulation methods for computing thermal conductivity, doi
  25. (1967). Computer “Experiments” on Classical Fluids. doi
  26. (1990). Computer simulations of Liquids,
  27. (2000). Concurrent coupling of length scales in solid state systems, doi
  28. (1999). Concurrent coupling of length scales: Methodology and application, doi
  29. (2007). Concurrent Multiscale Kinetic Monte Carlocontinuum Models for the Evolution of Solids via Diffusion, Solid State Phenomena, doi
  30. (1964). Correlations in the Motion of Atoms in doi
  31. (1965). Cramming more components onto integrated circuits, doi
  32. (2001). Crystal, defects and microstructures – Modelling across scales, doi
  33. (2007). Diffraction limited phonon thermal conductance of nanoconstrictions, doi
  34. (1997). Diffusion of a Butanethiolate molecule on a Au{111} surface, doi
  35. Effect of strain on the thermal conductivity of solids, doi
  36. (1995). Effects of Deposition Rate on the Size of Self-Assembled InP Islands Formed on GalnP/GaAs(100) Surfaces, doi
  37. (1988). Empirical interatomic potential for carbon, with applications to amorphous carbon, doi
  38. (1998). Energy transport in anharmonic lattices close to and far from equilibrium, doi
  39. (2007). Equilibrium Distributions and the Nanostructure Diagram for Epitaxial Quantum Dots, doi
  40. (2006). Evaluation of momentum conservation influence in nonequilibrium molecular dynamics methods to compute thermal conductivity, doi
  41. (2000). Finite Thermal conductivity in 1D lattices, doi
  42. (2005). Finite-temperature quasicontinuum: Molecular dynamics without all the atoms, doi
  43. (2008). First principles surface thermodynamics of industrial supported catalysts in working conditions, doi
  44. (1995). Fracture simulations using large-scale moleculardynamics, doi
  45. (2002). Growth and characterization of GaAs and InAs nano-whiskers and InAs/GaAs heterostructures, doi
  46. (1999). Heat conduction in 2D nonlinear lattices, arXiv:chaodyn/9910034 v1,
  47. (2003). Heat conduction in one-dimensional lattices with on-site potential, Physical Review E, doi
  48. (2000). Heat conduction in one-dimensional nonintegrable systems, Physical Review E, doi
  49. (2006). How kinetics drives the two- to three-dimensional transition in semiconductor strained heterostructures: The case of InAs/GaAs(001), doi
  50. (2004). Introduction to Molecular Dynamics Simulation, Computational Soft Matter: From Synthetic Polymers to Proteins, Lecture Notes,
  51. (2005). Introduction to Solid State Physics doi
  52. (2002). Kinetic Monte Carlo Simulation of Chemical Vapor Deposition, doi
  53. (2000). Kinetic Monte Carlo simulation on patterned substrates, doi
  54. (2004). Langevin dynamics in constant pressure extended systems, doi
  55. (2007). Lattice thermal conductivity of nanoporous Si: Molecular dynamics study, doi
  56. (2005). Magnetic and structural properties of isolated and assembled clusters, Surface Science Reports, doi
  57. (1998). Mersenne Twister: A 623-Dimensionally Equidistributed Uniform Pseudo-Random Number Generator, doi
  58. (1989). Modeling solid-state chemistry: Interatomic potentials for multicomponent systems, doi
  59. Modelling Transient Heat Conduction at Multiple Length and Time Scales: A coupled Non-Equilibrium Molecular Dynamics/Continuum Approach, doi
  60. (2004). Molecular dynamics simulations, doi
  61. (1984). Molecular dynamics with coupling to an external bath, doi
  62. (2006). Multiscale diffusion Monte Carlo simulation of epitaxial growth, doi
  63. (2005). Multiscale Kinetic Monte-Carlo for Simulating Epitaxial Growth, arXiv:cond-mat/0504272v2, cond-mat.mtrl-sci, doi
  64. (2005). Multiscale modelling of the dynamics of solids at finite temperature, doi
  65. (2004). Multiscale plasticity modelling: coupled atomistic and discrete dislocation mechanics, doi
  66. (2004). Nanoscale heat transfer, Encyclopedia of Nanoscience and Nanotechnology (American Scientific publishers,
  67. (1988). New empirical approach for the structure and energy of covalent systems, doi
  68. (1986). New empirical model for the structural properties of silicon, doi
  69. (2000). Nosé-Hoover chain method for nonequilibrium molecular dynamics simulation, Physical Review E, doi
  70. (2008). On the existence of a critical perturbation amplitude for the Stranski-Krastanov transition, doi
  71. (1989). On the stability of surface of stressed solids, doi
  72. (1978). One-dimensional Kapitza conductance: Comparison of the phonon mismatch theory with computer experiments, doi
  73. (2007). Phonon-cavity-enhanced low temperature thermal conductance of a semiconductor nanowire with narrow constrictions, doi
  74. (2007). Quantum Thermal Transport from Classical Molecular Dynamics, doi
  75. (2006). Rapid thermal equilibration in coarse-grained molecular dynamics, doi
  76. (2005). Review of multiscale simulation in submicron heat transfer. doi
  77. (2000). Selforganized periodic arrays of SiGe wires and Ge islands on vicinal Si substrates, Physica E, doi
  78. (2002). Si/Ge nanostructures, doi
  79. (2001). Simple generic method for predicting the effect of strain on surface diffusion, doi
  80. (2004). Single-photon generation with InAs quantum dots, doi
  81. (1991). Solid state Physics second edition (J.
  82. (2005). Spatially adaptive grand canonical ensemble Monte Carlo simulations, doi
  83. (2004). Spatially adaptive lattice coarse-grained Monte Carlo simulations for diffusion of interacting molecules, doi
  84. (2003). Stacked low-growth-rate InAs quantum dots studied at the atomic level by cross-sectional scanning tunneling microscopy, doi
  85. (1975). Statistical Thermodynamics of Clean Surfaces, doi
  86. (1991). Stiffness of a solid composed of c60 clusters, doi
  87. (2004). Stochastic kinetic Monte Carlo algorithms for long-range Hamiltonians, doi
  88. (2006). Temporal acceleration of spatially distributed kinetic Monte Carlo simulations, doi
  89. (2004). The art of Molecular Dynamics Simulation, doi
  90. (1993). The embedded-atom method: a review of theory and applications, doi
  91. (2005). The surface of helium crystals, doi
  92. (2007). Thermal conductance across grain boundaries in diamond from molecular dynamics simulation, doi
  93. (2003). Thermal conductance through molecular wires, doi
  94. (2003). Thermal conduction in classical low-dimensional lattices, Physics reports 377, doi
  95. (2006). Thermal conduction in sub-100nm transistors, doi
  96. (2007). Thermal conduction simulations in the nanoscale. doi
  97. (2005). Thermal conductivity and temperature in solid argon by nonequilibrium molecular dynamics simulations, doi
  98. (2004). Time-reversible deterministic thermostats, doi
  99. (2006). Variational Boundary Conditions for Molecular Dynamics Simulations of Solids at Low Temperature, doi

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