## 3 Results and Discussion
At the same time, when the spectrum is excited by the 785 nm laser line, the intensities of the lines in the range of 900-2000 cm\({}^{-1}\) are higher by an order of magnitude or more (Figure 3). Sufficiently intense lines in the range of 900-2000 cm\({}^{-1}\), corresponding to the second-order Raman spectrum, were also observed in LiNbO\({}_{3}\):Tb(2.24 wt.%), LiTaO\({}_{3}\):Cr(0.2). Nd(0.45 wt.%), and LiNb\({}_{x}\)Ta\({}_{1-x}\)O\({}_{3}\)[43; 44; 45], characterized by a disordered cationic sublattice and distorted (compared to clusters of a congruent crystal) MeO\({}_{6}\) clusters, in the region above 1000 cm\({}^{-1}\). It should be noted that there are no lines in the recorded Raman spectra whose frequencies are greater than the precise value of the doubled frequency of the 4A\({}_{1}\)(z)LO mode (872 \(\times\) 2 = 1744 cm\({}^{-1}\)). For the LiNbO\({}_{3}\):Gd\({}^{3+}\)(0.003):Mg\({}^{2+}\)(0.65 wt.%) double doped crystal, we did not observe a low-intensity line with a frequency of 120 cm\({}^{-1}\) corresponding to two-particle states of acoustic phonons with a total wave vector close to zero, which is confidently observed in the scattering geometries involved \(x(zz,zy)\overline{x}\) and \(y(zz,zx)\overline{y}\) in the spectra of all nonstoichiometric LiNbO\({}_{3}\) crystals [2; 29; 27]. The absence of a 120 cm\({}^{-1}\) Raman line indicates that the R = [Li]/[Nb] value approaches unity, which is characteristic of a nominally net LiNbO\({}_{3}\) crystal of stoichiometric composition [2; 27; 46]. The appearance of this low-intensity line in the Raman spectrum indicates a strong anharmonic interaction of the lowest frequency fundamental A\({}_{1}\)(TO)-mode (quasi-soft mode) with the acoustic continuum [46]. In the Raman spectrum of the LiNbO\({}_{3}\):Gd\({}^{3+}\)(0.003):Mg\({}^{2+}\)(0.65 wt.%), we also did not find any lines corresponding to pseudoscalar vibrations of the A\({}_{2}\) symmetry type with frequencies of 209, 230, and 880 cm\({}^{-1}\), previously recorded in crystals of LiNbO\({}_{3}\) heavily doped with magnesium [30]. The appearance in the Raman spectrum of lines corresponding to pseudoscalar vibrations of the A\({}_{2}\) symmetry type is possible due to a decrease in the local point group of the symmetry of the crystal from C\({}_{3V}\) to C\({}_{3}\) due to the distortion of oxygen-octahedral MeO\({}_{6}\) clusters by dopant cations [2; 47]. The optical representation for the point symmetry group C\({}_{3}\) is 9A(z) + 9E(x, y) [2]. Thus, pseudoscalar vibrations of the A\({}_{2}\) symmetry type, forbidden in the Raman spectrum for C\({}_{3V}\) by the selection rules, pass into vibrations of the A\({}_{1}\)(z) symmetry type permitted by the selection rules for C\({}_{3}\). The fact that there are no lines in the Raman spectrum corresponding to A\({}_{2}\) vibrations of the symmetry type indicates an insignificant effect of the doping Gd\({}^{3+}\) and Mg\({}^{2+}\) cations on the geometry of oxygen-octahedral MeO\({}_{6}\) clusters in the LiNbO\({}_{3}\):Gd\({}^{3+}\)(0.003):Mg\({}^{2+}\)(0.65 wt.%) crystal. Figure 3 shows the Raman spectra of the LiNbO\({}_{3}\):Gd\({}^{3+}\)(0.003):Mg\({}^{2+}\)(0.65 wt.%) crystal obtained in the same backscattering geometries upon excitation by a laser line with a wavelength of 785 nm. From Figure 3, we can see that the Raman spectrum upon excitation by a laser line with a wavelength of 785 nm contains many more lines than are allowed by the selection rules, taking into account the LO-TO splitting for the space group R3c (\(C_{3V}^{6}\)), with two formula units in the unit cell [2]. The recorded spectra contain lines corresponding to the fundamental vibrations of the crystal lattice (<900 cm\({}^{-1}\)), as well as second-order Raman lines (in the range 900-2000 cm\({}^{-1}\)).