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Zhang et al. Microstructures 2023;3:2023046 https://dx.doi.org/10.20517/microstructures.2023.57 Page 5 of 11

Type 2 domain structures with a checkerboard feature in the topography are shown in Figure 2. The
alternating yellow and brown quadrilateral patterns [Figure 2A], with an average base/height of 1.5/3 mm,
can only be observed in a minority of the sample regions embedded in the matrix of type 1 domain
configurations. The OOP phase image shows the same alternating checkerboard domains in comparison
with the topography, exhibiting distinct 180° phase differences [Figure 2B]. The optical image shows a
consistent checkerboard pattern [Figure 2G]. Two sets of IP PFM images with different tip-sample
orientations, i.e., 0° and 90°, were measured to determine the polarization vectors [Figure 2C and E]. Based
on the binarized IP phase values [Figure 2D and F], the reconstructed four polarization vectors with both
upward and downward directions are shown in the schematic in Figure 2H. The IP polarization projections
are denoted in corresponding domains in Figure 2C. Compared to the type I domain structure, 71° domains
are non-existent, but 109° domain walls emerge (m1+ and m3+, m1- and m3-) in addition to the 180°
domain walls that are present in both type 1 and type 2 domain structures. The existence of 180° domain
walls in both type 1 and 2 domain structures is due to the allowed polarization states in both upward and
downward directions.

Type 3 domain structures have a prominent horizontal long stripe domain arrangement along [010], as
shown in Figure 3A. The stripes have a typical width of around 1-2 mm. Not all stripe domains are
continuous, as some of them terminate or merge to form larger stripes. The OOP phase also demonstrates a
clear 180° phase difference between adjacent stripe domains, as shown in Figure 3B. The optical image also
shows a consistent structure, as shown in Figure 3C. It should be noted that the type 3 domain only emerges
at certain regions that are adjacent to the sample edge, as denoted by the red dashed boxes in
Supplementary Figure 8. The same rotational experiments were done and are shown in Figure 3D-G. The
0° rotational IP phase signals [Figure 3D and E] show the same phase contrast as the OOP phase
signal [Figure 3B]. The 90° rotational IP phase signals [Figure 3F and G], by contrast, present a
uniform bright phase contrast. This indicates that the polarization components perpendicular to the
cantilever from all variants now have the same direction with respect to the cantilever. The reconstructed
polarization vectors with only two allowed directions, sharing the same m1+ and m3+ variants as
compared to the type 2 domain, are shown in the schematic in Figure 3H. In this domain
configuration, only non-charged 109° domain walls exist due to the existence of only two polarization
variants.

A PMN-xPT system is a well-known relaxor ferroelectric system, and the hierarchy of domain structures is
known to vary on length scales from nanometer to millimeter with different Ti concentrations. PMN is a
pure relaxor with short-range-ordered polar nano regions (PNRs), while PT is a classical ferroelectric with
4+
long-range-ordered large domain structures. The introduction of Ti increases the off-center displacement,
and the distortion inside the PNRs results in a mechanical mismatch between regions with different
polarization orientations. To accommodate the generated mechanical strain or minimize the elastic energy,
the small PNRs tend to amalgamate into larger domains of micrometer sizes, such as the observed stripe
domains or checkboard patterns, following their macroscopic symmetries . The observed domain
[31]
configurations in all three types of domains show macroscopic domain structures, which is consistent with
previous studies [3,21,31,32] . On a close inspection, type 1 and 2 domain structures, while both showing a clear
four-variant domain configuration, are slightly different from the commonly reported ones [3,21,32] . A very
typical four-rhombohedral domain configuration after DC or AC poling will have four allowed polarization
orientations only in the OOP directions [3,21] , either upward or downward. A checkerboard domain structure
along [110] directions and alternating long stripe domains along [010] directions are presented for the OOP
and IP domain structures, respectively. The coexistence of 71° and 109° domains and the absence of 180°
domains are seen. By comparison, a type 1 domain shows zigzag and checkboard domain structures in the
OOP and IP images, respectively, with a coexistence of 71° and 180° domains. Type 2 does show a