Nuclear Enhanced X-ray Maximum Entropy Method Used to Analyze Local Distortions in Simple Structures

We introduce a novel method for reconstructing pseudo nuclear density distributions (NDDs): Nuclear Enhanced X-ray Maximum Entropy Method (NEXMEM). NEXMEM offers an alternative route to experimental NDDs, exploiting the superior quality of synchrotron X-ray data compared to neutron data.
The method was conceived to analyse local distortions in the thermoelectric lead chalcogenides, PbX (X = S, Se, Te). Their extraordinary thermoelectric performance has caused huge research activity, but the mechanisms governing their unexpected low thermal conductivity still remain a controversial topic. It has been proposed to result from anharmonic phonon scattering or from local fluctuating dipoles on the Pb site.[1,2] No macroscopic symmetry change are associated with these effects, rendering them invisible to conventional crystallographic techniques. For this reason PbX was until recently believed to adopt the ideal, undistorted rock-salt structure.
NEXMEM employs a simple procedure to normalize extracted structure factors to the atomic form factors. The NDD is reconstructed by performing maximum entropy calculations on the normalized structure factors.
NEXMEM has been validated by testing against simulated powder diffraction data of PbTe with known displacements of Pb. The increased resolution of NEXMEM proved essential for resolving Pb-displacement of 0.2 Å in simulated data. The figure below shows Pb in the (100) plane for calculated MEM and NEXMEM densities, as well as the reference electron density. In addition, we have applied NEXMEM to multi-temperature synchrotron powder X-ray diffraction collected on PbX.
Based on powder diffraction data, our study demonstrates that NEXMEM successfully improves the atomic resolution over standard MEM. This new tool aids our understanding of the local distortions present in PbX. In the future it may be used for widespread characterization of subtle atomic features in crystals with unusual properties.