Exploring Grain Boundaries and Phase Boundaries Through Monte Carlo Simulation Open Access
Guo, Ziwei (Spring 2019)
Abstract
Monte Carlo simulation methods such as grand canonical Monte Carlo (GCMC) and Gibbs Ensemble Monte Carlo (GEMC) use particle addition, removal, and exchange moves to equilibrate multiphase and/or multicomponent system. This dissertation focuses on the use of a recently developed GCMC variety called Solvent-repacking Monte Carlo (SRMC) and its extensions as applied to the grain boundaries of two-dimensional colloidal solids and the phase coexistences (vapor/liquid and liquid/solid) of size asymmetrical mixtures of Lennard-Jones particles. Using SRMC to model grain boundaries (GB) of 2-d solids formed from a monolayer of colloids represented as hard spheres, the stiffness of the grain boundary under varying GB angles was determined using the capillary fluctuation method and correlated with the rate of grain coarsening for grains with different misorientations. Further studies, inspired by experiments, show that when surface pressure is increased, the simple dependence of GB shrinking rate on the thermodynamic property of stiffness no longer holds. A complex dependence of GB dynamics on pressure, grain size, and method of preparation of misoriented grains can be traced to the geometries and mobilities of dislocation defects at the GB. Similarly, in hard sphere mixtures with size-asymmetrical impurities, simulated using an extension of SRMC named mixed repacking Monte Carlo (MRMC), affinity of a specific size of impurity for GB of varying misorientation was found to depend on packing details of the GB structure. We also extended our method to the quasi-2D case where spheres are confined to be near a flat surface by gravity, which enables the study of the presence of particles in an overlayer influence the ordering transition and the GB stiffness of the lowest layer. SRMC can also be used to simulate more complex 3D systems including the Lennard-Jones model. Extending the new SRMC approach to the Gibbs ensemble enables us to simulate the liquid-vapor phase coexistence boundaries of certain size-asymmetrical Lennard-Jones mixtures much more efficiently than existing methods. Lastly, we use GCMC and Gibbs-Duhem integration to map the solid-liquid phase coexistence of Lennard-Jones mixtures under conditions where solid-phase vacancies are occupied by multiple smaller impurities.
Table of Contents
Chapter 1 Introduction ........................................................................................................... 1
1.1 Colloidal particle and Grain boundary ........................................................................ 2
1.2 Lennard-Jones particle ................................................................................................ 6
1.3 The Monte Carlo Method ............................................................................................ 8
1.4 Outline of Dissertation .............................................................................................. 15
Chapter 2 Simulations of grain boundaries between ordered hard sphere monolayer
domains: orientation-dependent stiffness and its correlation with grain coarsening
dynamics… .............................................................................................................................. 16
2.1 Introduction ............................................................................................................... 16
2.2 Methods..................................................................................................................... 19
2.3 Results and Discussion ............................................................................................. 25
2.4 Conclusions ............................................................................................................... 35
Chapter 3 Partitioning of Size-mismatched Impurities to Grain Boundaries in 2-d Solid
Hard Sphere Monolayers ....................................................................................................... 37
3.1 Introduction ............................................................................................................... 38
3.2 Methods..................................................................................................................... 40
3.3 Results and Discussion ............................................................................................. 49
3.4 Conclusions ............................................................................................................... 63
Chapter 4 Dynamics of Grain Boundary Loops in 2-d Solid Hard Sphere Monolayers 65
4.1 Introduction ............................................................................................................... 65
4.2 Methods..................................................................................................................... 66
4.3 Results and Discussion ............................................................................................. 70
4.4 Conclusions ............................................................................................................... 79
Chapter 5 Ordering of colloidal hard spheres under gravity: From monolayer to
multilayer… ............................................................................................................................. 80
5.1 Introduction ............................................................................................................... 81
5.2 Methods..................................................................................................................... 84
5.3 Results and Discussion ............................................................................................. 93
5.4 Conclusions ............................................................................................................. 105
Chapter 6 Gibbs Ensemble Monte Carlo with Solvent Repacking: Phase Coexistence of
Size-asymmetrical Binary Lennard-Jones Mixtures ......................................................... 107
6.1 Introduction ............................................................................................................. 107
6.2 Methods................................................................................................................... 111
6.3 Results and Discussion ........................................................................................... 117
6.4 Conclusions ............................................................................................................. 128
Chapter 7 Size-asymmetrical Lennard-Jones solid solutions: Interstitials and
substitutions ........................................................................................................................... 129
7.1 Introduction ............................................................................................................. 130
7.2 Methods................................................................................................................... 132
7.3 Results and Discussion ........................................................................................... 138
7.4 Conclusions ............................................................................................................. 151
Conclusion. ............................................................................................................................ 153
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