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Theory of Complex Lattice Quasicontinuum and Its Application to Ferroelectrics


Kowalewsky, Olga (2005) Theory of Complex Lattice Quasicontinuum and Its Application to Ferroelectrics. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/rb0c-9534.


Complex lattice Quasicontinuum theory is developed and applied to the description of ferroelectric phenomena. Quasicontinuum theory is a multiscale theory that provides a unified description of materials by combining atomistic and continuum approaches. It provides a seamless transition between atomistics and continuum, but the description of the material is derived directly from the underlying atomic structure, using the computationally expensive atomistics only where needed, at the location of phenomena of atomistic origin.

Complex Lattice Quasicontinuum theory can be applied to complex lattice crystals consisting of many kinds of atoms. One highlight of it is treatment of each component lattice as separately and independently as possible. The component Quasicontinua are coupled through the microscopic forces within nodal clusters, making the complex atomistics of the heterogeneous lattice the basis of the description.

Ferroelectrics are especially suited to the application of Quasicontinuum theory. The nature of defects in ferroelectric materials is atomistic, but their influence over the material is long ranged due to induced elastic fields. Many different ferroelectric phenomena involving the perovskite ferroelectrics Barium Titanate and Lead Titanate are investigated and simulated. For Barium Titanate: the 180 degree domain wall structure and quasistatic crack under load. For Lead Titanate: the 180 degree domain wall structure and a domain wall step.

The results for the domain walls show that the domain wall thickness is atomistically small, of the order of few lattice constants, which is in agreement with recent ab initio molecular dynamics simulations, but we also observe long range effects resulting from the presence of the wall. During crack loading in the sample of Barium Titanate we observe polarization changes around the crack tip which are consistent with experimental observations of an increase of fracture toughness. The quasicontinuum study of a domain wall step gives an atomistical view into the equilibrium structure of the step.

Quasicontinuum is able to model these phenomena with atomistic precision around the defects and non-homogeneities, and also capture the influence of long-ranging effects in the samples. These studies could also give valuable modeling input for larger scale continuum approaches.

Item Type:Thesis (Dissertation (Ph.D.))
Subject Keywords:domain walls; ferroelectrics; multiscale modeling; Quasicontinuum
Degree Grantor:California Institute of Technology
Division:Engineering and Applied Science
Major Option:Aeronautics
Minor Option:Computer Science
Thesis Availability:Public (worldwide access)
Research Advisor(s):
  • Ortiz, Michael
Thesis Committee:
  • Bhattacharya, Kaushik (chair)
  • Ravichandran, Guruswami
  • Beck, James L.
  • Ortiz, Michael
  • Lapusta, Nadia
Defense Date:11 November 2004
Record Number:CaltechETD:etd-12202004-182638
Persistent URL:
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:5084
Deposited By: Imported from ETD-db
Deposited On:21 Dec 2004
Last Modified:16 Apr 2021 22:20

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