From Ferroionic Instability to Domain Patterns at an Exposed Surfaces of Multiaxial Ferroelectrics

Abstract

We analyze the formation of domain structures in multiaxial ferroelectrics with an open, electrochemically compensated surface. The model combines vector polarization, surface electrochemistry, electrostatics, compatible strain, and competitive adsorption on common sites. We construct homogeneous phase maps and analyze polarization instabilities, first assuming perturbations that are uniform through the film thickness and then allowing depth-dependent polarization profiles. Nonlinear continuation follows the growth of these modulations into developed domains. Optimization of their period and tests of their stability establish how the initial instability wavelength relates to the preferred spacing of an established domain structure. We also consider surface ordering above a stable, weakly anisotropic bulk as a constitutive limit relevant to ferroelectric relaxors, providing insight into possible origins of their periodic surface modulations. Surface energies with the same quadratic terms can produce the same initial instability but favor different developed states, including periodic domains and uniform in-plane polarization. This analysis provides a procedure for connecting the initial development of ferroelectric modulations to amplitude selection, wavelength adjustment, and the subsequent evolution of the resulting domain structures.