DDM Decomposition Procedure

The initial stages of powder diffraction structure analysis often require the decomposition of the powder pattern into individual Bragg components without reference to a structural model. The DDM-based decomposition procedure consists in finding additions to the calculated (or initially set) reflection intensities for minimizing the squared derivatives of the difference 

Considering the peak overlap, because of which several reflections may contribute to the same profile area, the addition 5 should be reduced by an appropriate overlap correction. Finally, the estimated observed reflection intensity is given by  

The result of the application of the DDM decomposition formula Equation (14) is similar to that of Rietveld s approximation for /obs except that it is DDM-oriented and thus does not require a background definition. In the DDM program the formula is also used for the Bragg R factor calculation. For single non-overlapped peaks or a set of peaks with the same position, the DDM decomposition directly gives the best estimate for /obs- For partly overlapped peaks it should be iterated to arrive at an optimized set of /obs similarly to the Le Bail method. The starting intensities f can either be calculated from an existing structure model or set arbitrarily when the model is absent. Notably, for fully overlapped peaks the DDM decomposition 

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