Single-crystal diffuse scattering data have been collected at room temperature on synthetic titanite using both neutrons and high-energy X-rays. A simple ball-and-springs model reproduces the observed diffuse scattering well, confirming its origin to be primarily due to thermal motion of the atoms. Ab initio phonons are calculated using density-functional perturbation theory and are shown to reproduce the experimental diffuse scattering. The observed X-ray and neutron scattering patterns are consistent with a summation of mode frequencies and displacement eigenvectors associated with the entire phonon spectrum, rather than with a simple, short-range static displacement. A band gap is observed between 600 and 700 cm-1 with only two modes crossing this region, both associated with antiferroelectric Ti-O motion along a. One of these modes (of Bu symmetry), displays a large LO-TO mode-splitting (562-701.4 cm-1) and has a dominant component coming from Ti-O bond stretching and, thus, the mode-splitting is related to the polarizability of the Ti-O bonds along the chain direction. Similar mode-splitting is observed in piezo- and ferroelectric materials. The calculated phonon dispersion model may be of use to others in the future to understand the phase transition at higher temperatures, as well as in the interpretation of measured phonon dispersion curves.
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