Determination of three-dimensional orientations of ferroelectric single crystals by an improved rotating orientation x-ray diffraction method

X-ray diffraction (XRD) techniques are widely used in determining crystallographic orientations. In this paper we describe a two-step method to determine the three-dimensional orientations of ferroelectric single crystals based on an improved rotating orientations XRD method. This method could be readily carried out on standard x-ray laboratory equipment. Taking into account the geometric relationship in crystallography, we obtain an equation to find the expected crystallographic plane and simplify the determining process. The application of this method to LiNbO₃ and xPb (Mg_1/3 Nb_2/3) O³ - (1-x) PbTiO₃ ferroelectric single crystals demonstrates that it is a fast, flexible, and waste-free method for crystallographic orientation. Explanations of the scanning diffraction patterns and evaluation of the determining accuracy are presented. This method is also applicable to other nonferroelectric single crystal systems and would benefit the orientation-related issues.