Scaling and Pattern Formation in Condensed Matter Systems
Chan, Pak Yuen
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https://hdl.handle.net/2142/80547
Description
Title
Scaling and Pattern Formation in Condensed Matter Systems
Author(s)
Chan, Pak Yuen
Issue Date
2007
Doctoral Committee Chair(s)
Nigel Goldenfeld
Department of Study
Physics
Discipline
Physics
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Geophysics
Language
eng
Abstract
Finally, I study multiscale patterns in polycrystalline materials, with the phase field crystal (PFC) model. I first show that the complex amplitudes representation incorporates the correct form of nonlinear elasticity. I then analyze the plastic properties of the model by applying a shearing force. Dislocation avalanches, which resembling the scaling behavior in driven ferromagnetic, are observed. Critical exponents are extracted from power laws extending over 5 decades. I extend the PFC model to accommodate actual atomic configurations and vacancies. I use the extended PFC model to simulate a liquid and reproduce the correct form of the two-point correlation functions. Finally, I extend the PFC model to describing binary systems. The resulting theory describes both atomic hopping events on microscopic scales and diffusion on macroscopic scales. It also reproduces the activated Arrhenius form of the diffusion coefficient.
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