Advances in X-ray diffraction based on two-dimensional diffraction theory. Derivation of the basic equation in orientation analysis

Information on the orientation of thin-sheet samples can be obtained with a conventional Bragg–Brentano diffractometer based on the two-dimensional X-ray diffraction theory because a set of general mathematical models has been constructed that includes a general diffracted-intensity equation, an azimuthal-angle equation of the observed crystal planes and a common scan mode. These are developed for both surface Bragg reflection and for transmitted reflection cases. These are of benefit for solving orientation problems. Three independent angular variables, besides θ and α, are used to describe the position of the specimen; in the present paper, an angle φ is introduced in addition to a reasonable derived azimuthal angle ψ. All of these may be used to define the relative positions of the observed crystal planes with indices (hkl) in space. Equations for orientation analysis are derived. Discussions of the relationship with quantitative phase analysis and the pole-figure method are included.