The Evaluation of n-Beam Dynamic Electron Diffraction Intensities by Matrix Method

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Abstract
On the basis of Fujimoto's1)n-beam matrix formulation, a computational method is given which allows very rapid and accurate estimation of electron diffraction intensities for largen-beam arrays. In its programmed form, the method consists of an array sort procedure which establishes the dispersion matrix. By applying the diagonalization routine of Jacobi to this matrix, the eigenvalues and eigenvectors can be very rapidly derived to six figure accuracy or more. Once this diagonalization has been achieved, no significant increase in computation time is encountered for the evaluation of diffraction intensities for any practical number of thickness levels within any thickness range. Examples of calculation are given for CuAu3. A beam reduction method is discussed, from which a practical criterion is established in regard to the number of beams to be considered in a given calculation.