Scaling and Pattern Formation in Condensed Matter Systems

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.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Physics

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2015

Author dc:creator

• Chan, Pak Yuen

Contributors dc:contributor

• Nigel Goldenfeld

• Geophysics

Language dc:language

eng

Identifier

(MiAaPQ)AAI3290194

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/80547