Surface state on first-order ferroelectrics
In the presence of a surface the Landau-Devonshire equations of ferroelectricity must be extended to include a boundary condition. For a ferroelectric with a second-order transition in the case when the polarization p(z) increases at the surface, it is well known that a surface state occurs in a ran...
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| Main Authors: | , , , , , |
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| Format: | Article |
| Published: |
2006
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| Subjects: | |
| Online Access: | http://eprints.um.edu.my/8221/ http://link.springer.com/content/pdf/10.1140%2Fepjb%2Fe2006-00271-1.pdf |
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| Summary: | In the presence of a surface the Landau-Devonshire equations of ferroelectricity must be extended to include a boundary condition. For a ferroelectric with a second-order transition in the case when the polarization p(z) increases at the surface, it is well known that a surface state occurs in a range of temperature above the bulk critical temperature t(CB) . Here we explore the corresponding effect for a first-order ferroelectric. We show that a surface state can occur, but only if the surface effect is sufficiently strong. Analytic expressions are derived and illustrated for p(z), the surface value p(S) =p(0) and the free energy. The transition from the paraelectric state (p=0) to the surface state is first order, and for completeness we establish the dependence of the three critical temperatures (supercooling, thermodynamic and superheating) on a boundary-condition parameter y. In a final section, we derive and illustrate expressions for p(z)in the temperature range t < t(CB) . |
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