Since its discovery, the direct methods origin-free modulus sum function S [Rius (1993) Acta Cryst. A49, 406-409] has been used for solving some complex crystal structures from powder X-ray diffraction data. In these applications, phase refinement was normally carried out by maximising function S with a modified tangent formula. However, further progress in the powder diffraction field was hampered by the complexity of combining the tangent formula refinement that makes explicit use of triple-phase sums, with the introduction of constraints in real space necessary to counterbalance the information loss produced by peak overlap in powder diffraction. In this connection the recently developed S-FFT phasing algorithm that maximises S by means of the FFT algorithm (thereby considering the triple-phase sums implicitly [Rius, Crespi, Torrelles (2007) Acta Cryst A63, 131-134]) is considerably simpler, completely general and can represent a source of progress in powder diffraction. It will be shown how the application of the S-FFT algorithm according to the SnB philosophy can treat powder diffraction data more effectively due to the easy introduction of real-space constraints. This has been implemented in the new version of the direct methods program XLENS (Rius, 2008) distributed through the Fullprof suite of programs (Rodríguez-Carvajal, 2008). 

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1. Crystal structure refinement of Fe³⁺-rich aerinite from synchrotron powder diffraction and Mössbauer data