<10$\bar{1}$0> Dislocation at a {2$\bar{1}$ $\bar{1}$0} low-angle grain boundary in LiNbO₃

Abstract

A LiNbO₃ bicrystal that contains a {2$\bar{1}$ $\bar{1}$0} low-angle grain boundary with both of 2° tilt misorientation and a slight twist misorientation was fabricated, and resulting dislocation structure at the boundary was analyzed by using transmission electron microscopy (TEM) and scanning TEM. The observations revealed that two types of dislocations of b = 1/3 <2$\bar{1}$ $\bar{1}$0> and b = <10$\bar{1}$0> are formed at the boundary. A 1/3 <2$\bar{1}$ $\bar{1}$0> dislocation, which dissociates into two partial dislocations with a {2$\bar{1}$ $\bar{1}$0} stacking fault in between, compensates only tilt misorientation of the boundary. On the other hand, it was found that a <10$\bar{1}$0> dislocation, which dissociates into three equivalent partial dislocations with b = 1/3 <10$\bar{1}$0>, has both edge and screw components in total. That is, the <10$\bar{1}$0> dislocations are formed to compensate the twist misorientation of the boundary, in addition to the tilt misorientation. It is interesting that the three partial dislocations from a <10$\bar{1}$0> dislocation are arranged in a zigzag pattern with left–right asymmetry. This special configuration is suggested to originate from the presence of stable stacking fault structure on the {2$\bar{1}$ $\bar{1}$3} plane in LiNbO₃.

Appendices

Appendix 1: Twist misorientation at the boundary

The grain boundary fabricated in this study has a 2° tilt misorientation owing to +1° and −1° inclinations of the crystallographic orientation of the original two single-crystal plates. In addition, a slight twist misorientation is also introduced at the boundary due to a misalignment in the fabrication process. In investigating the twist misorientation, convergent beam electron diffraction (CBED) analyses are useful because they can provide accurate information on crystallographic orientations in TEM samples. In fact, CBED analyses have been successfully performed for the samples of LiNbO₃ [33,34,35]. However, it is not easy to apply the CBED analyses to local regions near the fabricated boundary because LiNbO₃ is very sensitive to electron beam irradiation. Therefore, selected area diffraction (SAD) patterns were taken from around the boundary to analyze the twist misorientation.

Figure 8a shows a TEM bright field image of the boundary for this analysis. Figure 8b, c show SAD patterns from the lower and upper grains in Fig. 8a, respectively, which were taken approximately along the [0$\bar{1}$10] zone axis. Here, note that these SAD patterns were acquired by changing the position of the SA aperture on the same field of view without moving the specimen in the TEM. As can be seen in the SAD pattern from the lower grain (Fig. 8b), diffraction spots in the left half part are slightly brighter than ones in the right half part. Meanwhile, in the case of the SAD pattern from the upper grain (Fig. 8c), diffraction spots in the right half part are brighter than ones in the left half part, although it appears that the specimen is observed almost along the [0$\bar{1}$10] zone axis. This suggests the [0$\bar{1}$10] axes of the upper and lower grains are deviated from each other in the lateral direction [32]. Thus, it was found that the crystallographic orientations of these two grains are slightly rotated around the [2$\bar{1}$ $\bar{1}$0] axis each other, corresponding to twist misorientation of the grain boundary. As a result, the direction of twist misorientation can be uniquely determined. Actually, as shown in Fig. 2, the upper grain was rotated in clockwise direction with respect to the lower grain when viewed from above.

Figure 8

a A bright field TEM image of the boundary. b, c Selected area diffraction patterns obtained from the lower and upper grains, respectively

Appendix 2: Direct characterization of polar atomic configuration in ferroelectric LiNbO₃

LiNbO₃ has a crystal structure with the R3c symmetry, and the [0001] and [2$\bar{1}$ $\bar{1}$0] directions differ from the [000$\bar{1}$] and [$\bar{2}$110] directions, respectively. On the HAADF-STEM images in Figs. 3 and 4, the bright spots represent the projection of the Nb atomic columns along [0$\bar{1}$10]. Here, configuration of the bright spots has a mirror symmetry with respect to the [0001] and [2$\bar{1}$ $\bar{1}$0] directions (or the [000$\bar{1}$] and [$\bar{2}$110] directions). As a result, it is impossible to identify the [0001] and [2$\bar{1}$ $\bar{1}$0] directions from usual HAADF-STEM images. Therefore, we performed additional analyses to uniquely identify crystallographic orientation relationship of the observed specimen being a (0$\bar{1}$10) thin foil as below.

Figure 9a, b show an annular bright field STEM (ABF-STEM) image [36] of the bulk region in the specimen taken using JEOL ARM-200F and the corresponding schematic illustration of crystal structure in LiNbO₃, respectively. In case of the ABF-STEM image, the O atomic columns can be obviously observed in addition to the Nb atomic columns. For understanding the positions of the Nb and O atomic columns perpendicularly to the [0001] direction, the blue and red lines are also drawn along the Nb and O atomic columns, respectively. It can be seen that the separation distance between particular neighboring blue line and red line is different from that between another neighboring red line and blue line due to the polar atomic configuration of Nb and O along [0001] in LiNbO₃. On the basis of the difference of the separation distances, the [0001] direction in LiNbO₃ has been uniquely identified. That is, we succeeded in direct imaging of polar atomic columns along [0001] using the ABF-STEM, which makes it possible to determine the polarization direction along [0001] in LiNbO₃ with high resolution. Here, it should be mentioned that the polar [0001] direction in LiNbO₃ has also been determined by CBED analyses [33,34,35].

Figure 9

a ABF-STEM image of the bulk region in the LiNbO₃ crystal. b Schematic illustration showing the crystal structure of LiNbO₃. The red and blue lines indicate the location of the O and Nb atomic columns, respectively

For identifying the [2$\bar{1}$ $\bar{1}$0] direction, subsequently, the specimen was rotated in situ by ±30° with respect to the [0001] axis in TEM. In this case, it follows that the specimen was viewed along the [$\bar{1}$ $\bar{1}$20] (or [$\bar{1}$2$\bar{1}$0]) axis. From the image along the [$\bar{1}$ $\bar{1}$20] view, the [1$\bar{1}$00] direction can be easily distinguished since the diffraction pattern makes a parallelogram with unequal sides. Additionally, LiNbO₃ has threefold symmetry around the [0001] axis. By combining the obtained information on the [1$\bar{1}$00] direction with the crystallographic consideration, the [2$\bar{1}$ $\bar{1}$0] direction along [01$\bar{1}$0] view on the original HAADF images in Figs. 3 and 4 also has been uniquely identified. Thus, we demonstrated that it is possible to determine the crystallographic orientations with the polar atomic configuration in LiNbO₃.