Microstructure of Ferroelectric Domains in ${\mathrm{BaTiO}}_3$ Observed via X-Ray Microdiffraction

X-ray microdiffraction utilizing Fresnel zone plate focusing optics has been used to study microstructural properties of individual 90° ferroelectric domains in ${\mathrm{BaTiO}}_3$. Diffraction measurements at a microfocused spot resolution of $0.3\mu \mathrm{m}$ over domain widths of $\sim 10\mu \mathrm{m}$ unambiguously reveal features of lattice buckling, rotation, and strain near domain boundaries. Our results may be understood within the context of bound residual strain due to lattice mismatch and elastic interactions between neighboring domains.

Figure 1

Ferroelectric 90° domain walls found in ferroelectric ${\mathrm{BaTiO}}_3$. For the $[100]$ oriented crystal the domain boundaries fall away at 45° to the surface normal. The scattering geometry and microfocused spot on the sample are indicated. As the microdiffracted x-ray scattering volume is moved relative to the sample (along $\mathbf{z}$), diffracted intensity is collected from both the (002) and the (200) reflections.

Figure 2

Integrated microdiffracted x-ray intensity from ${\mathrm{BaTiO}}_3$ ferroelectric domains taken as a function of sample position. (a) A map of the (002) diffraction peak intensity from a $50\mu \mathrm{m}\times 50\mu \mathrm{m}$ region at $0.5\mu \mathrm{m}$ steps. The periodic domain structure in the $\mathbf{z}$ direction is clearly evident as the $\mathbf{c}$ axis undergoes 90° rotations at $\sim 10\mu \mathrm{m}$ intervals. (b) An overlay plot of integrated intensity from both (002) and (200) domains. The registry of these scans shows the alternating $\mathbf{c}$-axis–$\mathbf{a}$-axis–$\mathbf{c}$-axis pattern. At each point complete crystallographic data were recorded for both the (002) and the (200) diffraction peaks—this specifies lattice rotation and expansion along the surface normal in both domains. The solid black lines are a two-component model of the active scattering volume following Fig. 3c. A single component model shown by the red line is inadequate to describe the data.

Figure 3

This figure is a summary of detailed crystallographic data taken on the (002) reflection as a function of beam spot position across a single ${\mathrm{BaTiO}}_3$ domain. Two approximate reference points are marked in all panels—the intersection of domain walls with one x-ray attenuation length from the surface (dotted blue line), and the surface–domain wall intersection (solid red line). (a) A schematic showing the active diffracting volume (domain boundary positions and pitch) resulting from our two-component fit. (b) Integrated intensity of the rocking curve. (c) The relative strain along the surface normal mapped directly from the $2\Theta$ position of the $[002]$ peak. (d) The rocking curve width in $\theta$ diverges as the scattering volume approaches zero. (e),(f) The lattice vector exhibits a marked rotation in $\theta$ (e) and $\chi$ (f) about points of strain maxima and minima [compare to Fig. 3b].