*3.1. Crystal Growth*

It is well known that heavily doped LN:Mg crystals remarkably increase the laser damage threshold [37]. However, with the increase in the concentration of MgO, the heavily Mg-doped LN crystals used in optical devices have always been inhomogeneous with low production efficiency using the Czochralski method. Besides, many defects, such as scattering particles and inclusions, have been found in heavily doped LN:Mg crystals. In order to grow Ø2" optical grade heavily doped LN: Mg crystals with high homogeneity, more attention should be paid to its polycrystalline powders preparation, thermal field design, and growth technologies.

Normally, the LN:Mg polycrystalline powders are synthesized through solid reaction, which is mixing Li2CO3, Nb2O5, and MgO powders and then sintering at about 1100 ◦C [15]. Though the reaction of Nb2O5 with Li2O, discomposed by Li2CO3, could produce LN easily, MgO has very high melt point (2800 ◦C), weak reaction activity, and low diffusion velocity, which cause difficulties in preparing homogeneous LN:Mg polycrystalline powders and might induce macroscopic inclusions in crystals. Higher reaction temperature or heat preservation with a long time might improve the uniformity of dopant in the polycrystalline powders or melt. However, it is easy to cause the component deviation as the volatilization of Li2O. Thus, we chose the wet chemistry method with the advantage of low reaction temperature, which was helpful to avoid Li2O volatilization and enhance the composition homogeneity of LN:Mg. We tested the polycrystalline powders by an X-ray diffractometer, and the results are shown in Figure 1. Based on the PDF#74–2238, the XRD spectrum showed that the diffraction peaks and relative intensity of LN, LN: Mg3, and LN: Mg5 polycrystalline materials were very similar to those of lithium niobate without any obvious peak shift or second phase. That indicated that LN could be successfully prepared by the wet chemical method, and doping Mg2<sup>+</sup> had a negligible effect on diffraction data. Good quality of LN:Mg polycrystalline powders laid the foundation for crystal growth. Besides, most of doped LN crystals were grown by using pure LN crystals as seeds, but we used the Bridgman method to grow Ø1" LN crystals with different concentrations of MgO and then cut as seeds for growing Ø2" LN:Mg crystals.

**Figure 1.** XRD results of LN:Mg polycrystalline powders prepared by the wet chemical method. LN—lithium niobate.

A stable and suitable thermal field is crucial to growing Ø2" LN: Mg crystals with high quality. In the past, only Al2O3 powders were usually selected as insulation materials, but the heating time was long due to the low thermal conductivity of Al2O3 powders. In order to avoid the shortcomings, some mullite fiber was mixed with Al2O3 powders and served as insulation materials. About 35% of energy saving could be realized because of the higher thermal conductivity of mullite fiber compared to Al2O3 powders, which was also beneficial in keeping high stability of the thermal field. Moreover, with the excellent thermal insulation of mullite fiber mixed with Al2O3 powders, a small radial temperature gradient was obtained to avoid cracks caused by large thermal stress. The vertical temperature gradient ( <sup>∂</sup>*<sup>T</sup>* <sup>∂</sup>*<sup>Z</sup>* ) *<sup>s</sup>* above the solid-melt interface was designed as 1 ◦C/mm, which was smaller than other LN crystals with a small diameter [27]. The reason is that the vertical temperature gradient, as seen from Equation (4), should be controlled in a certain range and has an inverse relationship with the diameter of the crystal [29].

$$\frac{2\varepsilon\_b}{\alpha R^{3/2}} \bullet \left(\frac{2}{h}\right)^{1/2} \ge \left(\frac{\partial T}{\partial Z}\right)\_s \ge l - \frac{k\_l m V\_T (\mathbb{C}\_l(B)(1 - k^\*))}{D[k^\* + (1 - k^\*) \exp(v\_T \delta/D)]} + L\rho v\_T\}/k\_b\tag{4}$$

where α*a*, ε*b*, α,*R*, *h*,*ks*, and *vT* are the a-direction thermal expansion coefficient, fracture strain, thermal expansion coefficient, diameter, heat exchange coefficient, thermal conductivity, and falling rate (growth velocity of crystal), respectively; *kl* and *Cl*(*B*) are the thermal conductivity and bulk concentration of melt; *m*, δ,*D*, *k*∗ , *L*, and ρ are the liquidus slope, depth of solute boundary layer, diffusion coefficient, segregation coefficient at the interface, crystalline latent heat and density, respectively. Besides, the falling rate was optimizing from 1.5 mm/h–2.0 mm/h to 0.5 mm/h–0.8 mm/h at different growth stages. In the crystal growth experiment, we set the descending speed to 0.5 mm/h and extended the holding time to 8 h, which was more conducive to Mg2<sup>+</sup> entering the crystal lattice. The lower falling rate could provide enough time for the sufficient diffusion of Mg2<sup>+</sup> at the solid-melt interface and improving Mg2<sup>+</sup> distribution homogeneity in the crystal. The flat or slight convex shape was helpful to Mg2<sup>+</sup> diffused along the vertical and parallel direction of the solid-melt interface.

Based on the above improvements, colorless, transparent, crack-free, and inclusions free LN:Mg single crystals were grown. The cut and polished LN: Mg5 crystal with a length of 4 cm is shown in Figure 2. High-resolution X-ray rocking curves are widely used in checking the crystalline quality of single crystals. The narrower full width at half maximum (FWHM) of single crystals means higher crystalline quality. Here, the X-ray rocking curves for c-plates of LN:Mg3 crystal and LN:Mg5 crystal are given in Figure 3. The FWHM was measured to be 8" and 14" for (001) reflection of LN:Mg5 and LN:Mg3 crystal, respectively, which was better than the reported results [38]. It implied that they possessed high structural quality with few dislocations and thermal stress [39]. This proved that the Bridgman method could grow LN:Mg crystals with higher crystallinity.

**Figure 2.** Cut and polished LN: Mg5 crystal grew by the Bridgman method.

**Figure 3.** X-ray rocking curves of (001) reflection in LN:Mg crystals. (**a**) and (**b**) are for LN:Mg3 crystal and LN:Mg5 crystal, respectively.

#### *3.2. Characterization*

As we know, hydrogen ion can be introduced into LN crystals by means of water vapor during the growth of the crystals and forms as OH− exists in the lattice. As OH− is heavily sensitive to the surrounding environment, OH− spectra are usually used to investigate the composition and defect structures of LN. An infrared absorption band near 2.87μm (~3480 cm<sup>−</sup>1) in pure LN crystal was first reported by Smith et al. [40]. Herrington et al. demonstrated that the absorption band was caused by the stretching vibrations of OH− ions [41]. For doped LN crystals, it is well known that when the optical damage resistant dopants, such as Mg2<sup>+</sup>, In3+, and Hf4+, are doped with the concentration exceeding their threshold, the OH<sup>−</sup> absorption band shifts from the position at 3484 cm−<sup>1</sup> of pure LN to higher wavenumbers [42,43]. As shown in Figure 4, LN and LN:Mg3 crystals showed a broad OH<sup>−</sup> absorption band peak at approximately 3484 cm−1, while the OH<sup>−</sup> peak of LN:Mg5 crystal shifted to the higher wavenumber of 3534.7 cm<sup>−</sup>1. It was proposed that in LN:Mg crystals, Mg2<sup>+</sup> ions occupying Li-sites would push the NbLi<sup>4</sup><sup>+</sup> ions to the normal Nb-sites until all of the NbLi<sup>4</sup><sup>+</sup> were clean up when Mg concentration reached the threshold. Above the concentration threshold of Mg, additional Mg2<sup>+</sup> ions would occupy Nb-sites. The position of 3534.7 cm−<sup>1</sup> nearly coincided with the result of [42] and related to the OH<sup>−</sup> vibration formation in (MgNb<sup>2</sup>+- OH−) complex. It indicated that MgO was effectively doped into LN crystals, and 5 mol% had exceeded the threshold. Besides, as OH− absorption band peaks of different positions in different plates or the same plate were nearly centered at the same wavenumber, it reflected that MgO distributed homogenously in LN:Mg5 crystal.

**Figure 4.** The OH− spectroscopy of LN:Mg crystals.

Besides, the UV absorption edge of LN is also sensitive to defects [44]. Figure 5a shows that the UV absorption edge of LN:Mg3 and LN:Mg5 crystals was attributed to short wavelength compared to LN, especially the violet shift could be seen more obviously for LN:Mg5. The UV absorption edge of LN crystals has also been attributed to the presence of Li vacancies, actually of O2<sup>−</sup> ions in the vicinity of VLi<sup>−</sup>, forming as the defect of (VLi<sup>−</sup>- O2−) [45]. As mentioned above, for LN:Mg crystals, Mg2<sup>+</sup> ions pushed the NbLi<sup>4</sup><sup>+</sup> ions to the normal Nb-sites and formed MgLi<sup>1</sup><sup>+</sup>, until all of the NbLi<sup>4</sup><sup>+</sup> dismissed when the MgO concentration exceeded the threshold. Compared with NbLi<sup>4</sup><sup>+</sup> that needs four cationic vacancies VLi<sup>−</sup> for keeping the electric charge equilibrium [46], MgLi<sup>1</sup><sup>+</sup> only needs one VLi<sup>−</sup> for charge compensation. Thereby, the decrement of the (VLi<sup>−</sup>- O2−) defect concentration caused the observation of the UV absorption edge violet shift with the increment in MgO doping concentration. Especially, the NbLi<sup>4</sup><sup>+</sup> dismissal induced a more obvious violet shift in LN:Mg5 because of the MgO concentration exceeding the threshold. This result was also in accordance with the results of OH− spectra. We also compared the transmittance of the top and bottom parts for LN:Mg5, as shown in Figure 5b. It was clear that the two curves almost coincided throughout the 4 cm long crystal, indicating the crystal possessed a nice uniformity.

**Figure 5.** (**a**) is the UV absorption edge of LN:Mg crystals and (**b**) is the transmittance of the top and bottom plate in LN:Mg5 crystal.

High optical homogeneity is significant for the application of the nonlinear optical crystal. According to the high compositional homogeneity discussed above, LN:Mg5 crystal should also have high optical homogeneity. For the extraordinary refractive index ne is sensitive to the composition while the ordinary refractive index no is not, the gradient of the extraordinary refractive index δ ne was measured to examine the optical homogeneity of LN:Mg5 crystal. As listed in Table 1, the difference

between the average extraordinary refractive index δ ne of the top and bottom plate in LN:Mg5 crystal was 1 <sup>×</sup> 10−4. Since the distance of the two plates was about 4 cm, the gradient of the extraordinary refractive index δ ne was about 2.5 <sup>×</sup> <sup>10</sup>−5/cm, which exhibited high optical homogeneity of the crystal. The optical homogeneity was about two times higher than the reported high optical homogeneous LN:Mg crystal, of which δ ne was about 5.11 <sup>×</sup> <sup>10</sup>−5/cm [47].

**Table 1.** The extraordinary refractive index of the top and bottom plate in lithium niobate (LN):Mg5 crystal.

