Structure determination without Fourier inversion. Part VI: High resolution direct space structure information from one-dimensional data obtained with two wavelengths

Abstract

Abstract A method for locating in an unknown one-dimensional structure (or structure projection) a resonant scattering atom from reflection intensities measured at two wavelengths is presented in terms of the parameter space concept. Even with rather few one-dimensional data the method permits high resolution (well beyond that of Fourier or Patterson calculations). In presence of some hundred ‘light’ atoms, a resonant scattering ‘heavy’ atom can be retrieved from a small number of proposed positions, even if reflection intensities with maximum relative errors of up to 20 or 30% are used. The same applies to structures composed of up to about 50 ‘normal’ atoms with scattering powers similar to that of the resonant scatterer. Further, the method allows for combining the results from sub-sets of a harmonic reflection data sequence, and there is no need to include the lowest reflection orders. Results for some hypothetical model structures both with and without inversion centre are presented and discussed. Also, the advantage of the technique compared to conventional one-dimensional difference Patterson calculations is illustrated and possible applications of the method and extensions to several resonant scatterers are adressed.