Fig. 2. Pair distribution function (PDF) measured using neutron diffraction.

a Measured PDF (G(r)) for several temperatures (top) and a breakdown of the pair distribution function (PDF) by atomic pairs for the 100 K refinement (bottom). The first few nearest neighbor distances are indicated. Since Ti has a negative neutron scattering length, the Ti-X peaks are negative. The nearest neighbor Ti-S peak is asymmetric and lacks temperature dependence. Note that other peaks that appear to lack temperature dependence actually consist of both positive and negative peaks as shown in the bottom panel, in contrast to the first Ti-S peak. b Measured PDF (blue circles) and best fit (red line) at 300 K. The residual difference between the measurements and fit is also shown (green line). Anisotropic distribution ellipsoids for 90 percent probability from the fit to PDF at c 100 K and d 300 K from different perspectives. The Ti distributions along the c axis (stretched blue ellipsoids) decrease in size with increasing temperature, the opposite of what is expected for thermal vibrations. e Derived atomic displacement parameters versus temperature. Note that the Ti-U₃₃ parameter decreases with increasing temperature. The inset shows a schematic for the bimodal distribution of Ti atoms residing in shallow potential wells.