Broader impact:

1. Modelling and Designing Ferroelectrics with Defects and in Two-dimensional Forms Laurent Bellaiche, University of Arkansas, DMR 0404335 • In ferroelectric nanostructures (FEN), three dielectric susceptibilities can be defined. An external (respectively, internal) susceptibility characterizes the response of the polarization to the external (respectively, internal) electric field. The third susceptibility (that is the intrinsic one) is associated with the material from which the FEN is made of. Our first-principles-based calculations of external (Fig. 1) and internal (Fig. 2) susceptibilities in ferroelectric films, nanowires and nanodots revealed that in FEN: • internal and external susceptibilities depend on the electrical boundary conditions (Figs 1-2); • external susceptibility is always positive and peaks at the point associated with transition from short-circuit-like to open-circuit-like boundary conditions (Fig. 2); • internal susceptibility is negative and diverges at some critical value of screening parameter (Fig2). • An analytical model is developed to explain these findings [Phys. Rev. Lett.99, 227601 (2007)]. Fig. 2.Internal dielectric susceptibility χint of a PZT60 film [part (a)], wire [part (b)], and dot [part (c)] vs the screening parameter β. The vertical lines characterize the transition from short-circuit-like conditions to open-circuit-like conditions. Note that χxx(yy)int = χxx(yy)ext in the film, while χzzint = χzzext in the wire - since no depolarizing field exists along these directions. These latter coefficients are already shown in Fig. 1. Fig. 1. External dielectric susceptibility χextof a PZT60 film [part (a)], wire [part (b)], and dot [part (c)] vs the screening parameter β. Left and right insets show the projections of the dipole patterns in the structures under open-circuit-like and short-circuit-like boundary conditions, respectively. The vertical lines characterize the transition from short-circuit-like conditions to open-circuit-like conditions.

2. Modelling and Designing Ferroelectrics with Defects and in Two-dimensional Forms Laurent Bellaiche, University of Arkansas, DMR 0404335 • Broader impact: • 6 graduate students (including two of female gender) and 6 research associates (including one of female gender) contributed to the works associated with this grant. • Emad Almahmoud and Saad Bin-Omran received their Ph.D. of Physics in Fall 2007 and Spring 2008, respectively. • Collaborations with international groups,s and strongly involving students and research associates, occurred. • The P.I. spent one day with students in an elementary school in Fall 2007. • The P.I.’s group and collaborators gave several invited talks at international conferences. • An invited review article on domains in ferroelectric nanostructures was written and published in a book.