Strategies for solving neighboring-element problems: a case study using resonant X-ray diffraction and pulsed neutron diffraction to examine Sr₈Ga₁₆Ge₃₀

The distribution of gallium and germanium over the available framework sites in the type-I clathrate Sr₈Ga₁₆Ge₃₀ (Pmn) has been determined by powder diffraction using several different combinations of resonant scattering data sets, collected at energies close to both the Ga and Ge K-edges, and time-of-flight (TOF) neutron diffraction data. Based on a combined refinement using three X-ray data sets and a composition restraint, the fractional occupancies of the 6c, 16i and 24k sites by gallium are estimated to be 0.705 (5), 0.181 (3) and 0.376 (2), respectively. The required resonant scattering factors were determined by Kramers-Kronig transformation from X-ray absorption spectra. The results from refinements using single data sets and various combinations of data sets are compared. The high degree of scattering contrast that resonant diffraction can provide leads to very precise site occupancies. However, systematic errors in the resonant diffraction intensity data can considerably degrade the accuracy of the results. The use of a carefully chosen multiple-data-set strategy can minimize bias in the refinement results by reducing the correlations between site occupancies, atomic displacement parameters and histogram scale factors. The effect of errors in the resonant scattering factors on the refinement results was also examined.