A rate-dependent two-dimensional free energy model for ferroelectric single crystals

Stefan Seelecke, Sang Joo Kim, Brian L. Ball, Ralph C. Smith

Research output: Contribution to journalArticlepeer-review

23 Scopus citations


The one-dimensional free energy model for ferroelectric materials developed by Smith et al. [29-31] is generalized to two dimensions. The two-dimensional free energy potential proposed in this paper consists of four energy wells that correspond to four variants of the material. The wells are separated by four saddle points, representing the barriers for 90°-switching processes, and a local maximum, across which 180°-switching processes take place. The free energy potential is combined with evolution equations for the variant fractions based on the theory of thermally activated processes. The model is compared to recent measurements on BaTiO3 single crystals by Burcsu et al. [8], and predicitions are made concerning the response to the application of in-plane multi-axial electric fields at various frequencies and loading directions. The kinetics of the 90°- and 180°-switching processes are discussed in detail.

Original languageEnglish
Pages (from-to)337-350
Number of pages14
JournalContinuum Mechanics and Thermodynamics
Issue number4
StatePublished - Dec 2005


  • 2-D free energy model
  • Ferroelectric materials
  • Hysteresis
  • Rate-dependent effects


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