Difference Patterson functions at 3 or 4 wavelengths

Abstract

Difference Patterson functions from data sets measured at 3 or 4 selected wavelengths around the absorption edge of an anomalous scatterer, are used for solving crystal structures. Wavelength selection for each pair of measurements is made such that for the first pair /' is equal, with f" being as much different as possible. For the second pair, f" has little (or no), f a large difference. The two pairs of wavelengths can be reduced to three single ones, with some loss of contrast due to smaller Af" for λι, λ 2 and Af for λ 2 , λ 3 respectively. The real part of the first difference Patterson essentially contains the self-convolution of the anomalous scatterers (e-atoms). The imaginary part, added to the real part of the second difference Patterson, consists of the vectors from the e-atoms to all other ("normal") atoms (e->w vectors), the reverse w-»e vectors being suppressed. The solution of the «-atom structure, e.g. by a minimum function, is straight-forward in its "true" space group (including the correct enantiomer and/or polarity), provided the e-atom arrangement can be found from the first difference Patterson. Because the result of applying the minimum function consists of the (slightly modified) electron density distribution of the normal scatterers, atomic resolution for them is not a prerequesite. Determination of single reflection phases is neither necessary for, nor a direct result of this "lambda technique": it circumvents the phase problem for the «-atoms. For the e-atoms, the phase problem is separated and therefore to be solved more easily. The "lambda technique" has been put to a praxis test: re-determination of the pseudosymmetric (ferroelectric) KNb0 3 structure.