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Raman scattering was used to characterize the crystals. Room temperature Raman spectra for the as-grown and annealed wafer are shown in Fig. 3 a and Fig. 3 b, respectively. The spectra presented the typical bands corresponding to the normal vibration modes of XXX [22]. The maximum phonon energy of this crystal is 905 cm-1, which can be indexed to X-X stretching band. Linewidths (FWHM) for the line at 905 cm-1 of the as-grown and annealed wafers were fitted to be 8.2 and 6.8 cm-1, as shown in the insets of Fig. 3 a and Fig. 3 b, respectively. In the as-grown crystal, the dark brown color could be attributed to the partial reduction of X5+ ions, which are mainly source from the XX octahedron [17, 23]. It resulted in the change of the X-O stretching vibration, so that the band at 905 cm-1 broadened. The broadening of the Raman band at 905 cm-1 are mainly caused by the oxygen vacancies. After annealing, the oxidation state of Xions was in the same X+5 and X-O stretching vibration was more uniform, which resulted in a higher degree of order on the Nb and Mg sublattices [17]. Therefore, the color of the annealed crystal faded to light brownish and the linewideth at 905 cm-1 was narrowed. It indicates that the oxygen vacancies of the as-grown crystal can be eliminated by the annealing process in the oxygen atmosphere.
To determine the orientation of the as-grown XXX single crystal, XRD2 was conducted on the cross-section of the crystal (Fig. 4 a). It can be found that there is only one peak at 35.35° which can be indexed to (0 0 2) plane. It means that the XXX crystal grows along the c-axis direction. The cleavage plane parallel to the growth direction was also tasted by XRD2, as shown in Fig 4b. There are two peaks at 38.11° and 65.80°, which can be indexed to (0 6 0) and (0 10 0) plan, respectively. The above results suggested that the grown sample is a single crystal of high perfection.
The macroscopic defects, such as low-angle grain boundaries and inclusions of the as-grown crystal, were also checked by polarized-light microscopy in transmission configuration. Fig. 1 c shows a photograph of the wafer (Fig. 1 b) under polarized-light. Neither inclusionin nor low angle-grain boundaries were observed on the wafer.

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