Landau theory of second-order phase transitions in ferroelectric films - art. no. 144109

A detailed discussion is given of the predictions of the Landau-Devonshire theory for the behavior of thin ferroelectric films. It is assumed that the phase transition in the bulk is second order, and the theory is extended b y the inclusion in the free-energy density of a term proportional to \delP\ (2) together with a boundary condition involving an extrapolation length de lta. Expressions for the polarization profile P(z) are given in terms of Ja cobi elliptic functions; some of these are in a clearer and simpler form th an has been available previously. Interesting analytic results for the entr opy in terms of elliptic integrals and elliptic functions are also presente d. Graphical illustrations of the main results are included. Careful consid eration is given to the nature of the phase transition, and it is concluded that it is second order in all cases.