(Color online) Emergence of ferroelectric trimerization-polarization domains in hexagonal . (a) Crystal at K with the unit cell (small diamond) and three possibilities for the trimerization at 1270 K (large diamonds). (b) Ferroelectric crystal with tripled unit cell. Sets of three bipyramids (triangles) tilt uniformly away from or toward a central ion, thus generating a spontaneous polarization ( or , respectively). The choice of the central ion determines the trimerization domain state as , , or . (c) Perspective view of the aforementioned tilt (black arrows) of the bipyramids in domains with . Along with the tilt, the central ion is pulled downward (down arrow), whereas the six surrounding ions are lifted up. (a) and (b): ions, z position in the unit cell; ions, local symmetry. (c): ions within the bipyramid, ions at the corners
Piezoresponse images recorded (a) on the z face and (b) on the x face of an crystal. In (c) the structure of the trimerization and polarization domains is depicted schematically.
Topography (a) and piezoresponse (b) recorded on the z face of a crystal polished mechanically with diamond paste. The two read-out channels of the scanning force microscope (topography and piezoresponse) are seen to be free of cross-talk: The scratches (depth nm) are not seen in the PFM image, and the domain pattern leaves no trace in the topographical image. The dust particle, which has a height of 20 nm and is indicated by an arrow, cannot be seen in the PFM image.
Topography (a) and piezoresponse (b) recorded on the z face of an crystal polished chemically-mechanically with Syton. The topography reflects the domain pattern with a step height of 10 nm.
Topography (a),(c) and piezoresponse (b),(d) on the z face of an crystal polished chemically-mechanically with Syton. Images were recorded before (a),(b) and after (c),(d) an annealing cycle in air in which a temperature of 1120 K was sustained for 1 h.
(Color online) Topography (a),(c) and piezoresponse (b),(d) on the z face of an unpolished crystal. Cleaning after crystal growth was obviously performed with a domain-selective etchant that imprinted the as-grown domain structure onto the sample topography (step height 10 nm). In a subsequent step, a () -sized area (dotted square) was poled by scanning with −94 V applied to the tip. Images (c) and (d) show the result of the local poling. In the bottom left corner of the poled area, the domain walls after poling are traced in the topographical and the PFM image.
(Color online) Topography (a) and piezoresponse (b) on the x face of an crystal. The cross with a depth of 350 nm was inscribed with a FIB. The implanted positive charge leads to an electric field in the vicinity of the cross (arrows), which sets the polarization of the crystal across a distance of about 10 .
Piezoresponse (a) on the x face of an crystal and cross section (b) obtained in the rectangle indicated in (a) by averaging over 12 scan lines. The PFM image exhibits three gray levels indicating a top layer of about in which the polarization was reversed as depicted in (c).
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