Phase Field of Ferroelectic and NonConserved Order Parameters

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Phase Field of Ferroelectic and Non-Conserved
Order Parameters

• R. Edwin García
• redwing_at_purdue.edu

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The Cahn-Hilliard Equation
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Two for the Price of One
Surface Tension, Included
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Conceptual Implications

• Global equilibrium is reached when every volume
  element of material stops evolving in time
• Phase separation can be represented by a PDE that
  includes the (measurable) thermodynamic
  properties of the system
• Interfacial Effects ARE included
• The question remains Can this be applied to
  describe other types of phase transformations?

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A More Detailed Picture The Structure of
Interfaces
TEM images courtesy of Prof. Jian Luo, Clemson
University, 2005
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Diffuse Interface Models Concept
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Conserved and Non-Conserved Quantities
Conserved Quantities
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Conserved and Non-Conserved Quantities
Non-Conserved Quantities
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Kinetics of Ferroelectric Materials
2 µm
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Free Energy Description of Ferroelectric Materials
f
P
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Ferroelectric Kinetics
S. Choudhury et al. Phase-field simulation of
polarization switching and domain evolution in
ferroelectric polycrystals. Acta Materialia 53,
(2005) 5313-5321.
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The Allen-Cahn Equation
(for non-conserved quantities)