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In practical application of crystals in optoelectronics and laser technology it is necessary to know the direction of optical axes and types of oscillatory centers, which is a relevant and necessary condition. In this paper, the infrared spectra of transmission and absorption of hexagonal crystals of lithium iodate α-LiIO3, grown by open evaporation in H2O and D2O solutions, as well as natural lamellar crystals of phlogopite and muscovite monoclinic crystal are investigated. The band gap width of the investigated crystals is determined by transmission spectra. In the absorption spectra there were determined activation energy and wavelength of the oscillatory centers that are associated with the vibrations of protons, hydronium ions Н3О+, protium H+, OH groups and molecules HDO. The good correlation of the parameters of infrared spectra with the spectra of thermally stimulated depolarization currents and NMR spectra has shown. The possibility of diagnostics of types of oscillatory centers by means of infrared spectra is considered, which also allows to find out the direction of optical axes. The obtained results allow to use IR spectra to determine not only the types of vibrational centers, but also the presence of anisotropy of the crystal lattice of the studied crystals.