The changes in optical properties of bulk LiNbO 3 crystals were investigated depending on the diffusion depth. For this purpose the samples were isochronously annealed in hydrogen, subsequently the reduced samples were isochronously annealed in air. The investigations were held in different crystallographic directions. The experimentally determined distribution of depth-dependent additional absorption in reduced crystals was approximated basing on the oxygen vacancies diffusion model and solution of differential equations set describing the quasichemical reaction of bipolarons formation due to the oxygen loss in LiNbO 3 crystal.
IntroductionHigh temperature annealing of lithium niobate (LiNbO 3 , LN) in vacuum, reducing and oxidizing environments, in the presence of metal ions, in proton-rich liquids etc is one of the techniques, which is extensively used to create LN-based elements for acoustoelectronics, optoelectronics and integrated optics [1][2][3]. However such thermochemical treatments alter the optical and electrical properties of LN. These changes are based on ions diffusion processes out of the crystal into the environment and vice versa, that affect the chemical composition of LN and its defect subsystem state. The diffusion processes in LiNbO 3 are studied in a significant amount of works, for example [4][5][6][7][8][9][10][11][12][13].Since in most cases diffusion surface layers with several microns thickness are sufficient for practical applications, the changes in chemical composition of LN layers in depth (and, consequently, changes in their properties) caused by the diffusion processes, are mainly studied by mass spectroscopy of secondary ions (SIMS) (see. e.g. [5]). This technique allows determining the changes only in micron-range and the measurements are performed in the direction of diffusion. Only in [6,7] the changes in the optical properties of bulk congruent LN samples with about 3 mm thickness, treated by VTE technique, were investigated by means of second harmonic generation conditions analysis and spectrometry in the direction, perpendicular to the direction of diffusion.Therefore the targeted investigations of coloration changes in LN crystals, caused by redox annealing, depending on the distance from crystals surface (for a few millimeters deep into the crystal) were not performed. Thereby it is not known how the coloration processes occur at different temperatures in crystals volume during redox treatment.Furthermore, the diffusion mechanisms during thermochemical treatments are also not completely clear. In [8] it is considered that the main diffusion mechanism in congruent LiNbO 3 , which contains no impurity ions, is the diffusion of lithium and lithium vacancies. In [9] it is assumed that both lithium and niobium diffusion processes take place simultaneously. Authors in [10,11] consider the oxygen diffusion as the main mechanism and in [4,12] -the diffusion of oxygen and lithium. Moreover, the known data about anisotropy of the diffusion processes is also controversial. For exa...