Abstract
A matrix representation is developed for the solution of the Takagi–Taupin equations of x-ray diffraction. By the virtue of its unimodular property, the solution matrix substantially reduces the calculation time for the superlattice (SL) structure with a large periodicity. Also, the simplified form of the solution makes it easier to understand and quantify the inherent properties of the x-ray diffraction such as the interference fringes and the SL peaks.
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