A tangent formula derived from Patterson-function arguments. VII. Solutionof inorganic structures from powder data with accidental overlap

Accidental overlap constitutes one of the principal limitations for the sol ution of crystal structures from powder diffraction data, since it reduces the number of available intensities for direct-methods application. In this work, the field of application of the direct-methods sum function is exten ded to cope with powder patterns with relatively large amounts of accidenta l overlap. This is achieved by refining not only the phases of the structur e factors but also the estimated intensities of the severely overlapped pea ks during the structure solution process. This procedure has been specifica lly devised for inorganic compounds with uncertain cell contents and with p robable severe atomic disorder, a situation often found when studying compl ex minerals with limited crystallinity. It has been successfully applied to the solution of the previously unknown crystal structure of the mineral ti nticite. Finally, an estimation of the smallest ratio (number of observatio ns to number of variables) for the procedure to be successful is given.