Room temperature single-crystal diffuse scattering and ab initio lattice dynamics in CaTiSiO5

The modulated low-temperature structure of malayaite, CaSnOSiO4

The crystal structure of the mineral malayaite has been studied by single-crystal X-ray diffraction at a temperature of 20 K and by calculation of its phonon dispersion using density functional perturbation theory. The X-ray diffraction data show first-order satellite diffraction maxima at positions q = 0.2606 (8)b*, that are absent at room temperature. The computed phonon dispersion indicates unstable modes associated with dynamic displacements of the Ca atoms. The largest-frequency modulus of these phonon instabilities is located close to a wavevector of q = 0.3b*. These results indicate that the malayaite crystal structure is incommensurately modulated by static displacement of the Ca atoms at low temperatures, caused by the softening of an optic phonon with B_g symmetry.

Ultrafast calculation of diffuse scattering from atomistic models

Diffuse scattering is a rich source of information about disorder in crystalline materials, which can be modelled using atomistic techniques such as Monte Carlo and molecular dynamics simulations. Modern X-ray and neutron scattering instruments can rapidly measure large volumes of diffuse-scattering data. Unfortunately, current algorithms for atomistic diffuse-scattering calculations are too slow to model large data sets completely, because the fast Fourier transform (FFT) algorithm has long been considered unsuitable for such calculations [Butler & Welberry (1992). J. Appl. Cryst. 25, 391-399]. Here, a new approach is presented for ultrafast calculation of atomistic diffuse-scattering patterns. It is shown that the FFT can actually be used to perform such calculations rapidly, and that a fast method based on sampling theory can be used to reduce high-frequency noise in the calculations. These algorithms are benchmarked using realistic examples of compositional, magnetic and displacive disorder. They accelerate the calculations by a factor of at least 10², making refinement of atomistic models to large diffuse-scattering volumes practical.

Computation of diffuse scattering arising from one-phonon excitations in a neutron time-of-flight single-crystal Laue diffraction experiment

A methodology is presented to compute diffuse scattering arising from one-phonon excitations in a time-of-flight neutron single-crystal Laue diffraction experiment from density functional theory results. This methodology is illustrated using NaCl as an example.

Direct phonon excitation in a neutron time-of-flight single-crystal Laue diffraction experiment has been observed in a single crystal of NaCl. At room temperature both phonon emission and excitation leave characteristic features in the diffuse scattering and these are well reproduced using abinitio phonons from density functional theory (DFT). A measurement at 20 K illustrates the effect of thermal population of the phonons, leaving the features corresponding to phonon excitation and strongly suppressing the phonon annihilation. A recipe is given to compute these effects combining DFT results with the geometry of the neutron experiment.