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The dynamical theory was used to model X-ray diffraction by the YZ-cut of an LiNbO3 crystal modulated by surface acoustic waves (SAWs). It includes both the calculation of the crystal lattice deformation, induced by a surface wave of Rayleigh type, and the simulation of X-ray wavefields in the crystal based on Takagi-Taupin equations. A detailed discussion is included on the effect of peak splitting occurring at high acoustic amplitudes. The developed theory entirely describes this effect and proves to be a powerful tool for understanding X-ray diffractometry and topography measurements by SAW-modulated crystals. [ABSTRACT FROM AUTHOR]