Site-selective determination of coordination symmetries by anisotropic anomalous X-ray scattering

Based on an experiment of Kirfel and Petcov on rutile (136) P4₂/mnm, which verified anisotropic anomalous scattering (AAS) by measuring ‘Forbidden Reflection near Edge Diffraction’ (FRED), we aimed to extend the results with allowed reflections to extract more tensor symmetries of the Ti scattering factor tensor f _ij by fitting the model of AAS to the experimental data. Results from DFT calculations will also be presented. Furthermore we intended to study possible restrictions for atomic site occupation of unknown structures in an identified space group due to these local symmetry relations exemplary for this model structure.

Experiments were carried out at DESY/HASYLAB BL C using a Si (111) double crystal monochromator tuned to an energy of 4985eV. An automated optimization and Y-scan routine for a sample setup with rotating degree of freedom assured AAS measurements at the reflection maxima. The rutile samples investigated were 10x10x1mm³ wafers in (001), (110) and (111) orientation and Y-scans were measured for the reflections 001, 220, 110 and 111.

Ti occupies Wyckoff site 2a, its tensor symmetry must follow the local symmetry m.mm leaving 3 complex elements f ₁₁, f ₁₂, f ₃₃. Simulations showed dependencies: 001 to f ₁₂, 220 to f ₁₁- f ₃₃, 110 to f ₁₁- f ₃₃, 111 to f ₁₂. For the 001 reflection intensity real and imaginary part correlate, but the 111 intensity displays asymmetric influence so the ambiguity is separable.

The measured data show clear evidence of AAS and the 001 FRED and 111 intensities could be fitted:

f ’ _Ti d ’ ₁₂ = -5.44 _* 0.5(8)

f ” _Ti d ” ₁₂ = 3.98 _* 1.4(2)

Since f ₁₃ and f ₂₃ were refined to zero, the positioning of Ti in the unit cell would by inverse symmetry arguments only be consistent with respect to site symmetry on Wyckoff sites a, b, e, f, g (out of k ).