Phonons from Powder Diffraction: A Quantitative Model-Independent Evaluation

We describe a model-independent approach for the extraction of detailed lattice dynamics information from neutron powder diffraction data, based on a statistical analysis of atomistic configurations generated using reverse Monte Carlo structural refinement. Phonon dispersion curves for MgO extracted in this way are shown to reproduce many of the important features found in those determined independently using neutron triple-axis spectroscopy. By means of molecular dynamics simulations, we quantify the extent to which the diffraction data are sensitive to lattice dynamics in this system.

Figure 1

(a) MgO phonon dispersion curves from INS experiments [17] (data points) and calculated using a shell lattice dynamical model [13] (solid lines). (b) Our analysis of RMC configurations derived from NPD data. The filled circles correspond to modes with predominantly longitudinal character and the open circles to those with transverse character. The lines are guides to the eye; each traces data with similar eigenvectors.

Figure 2

MgO phonon dispersion curves from our analysis of (a) MD configurations and (b) RMC configurations refined against MD-derived diffraction data. The filled circles correspond to modes with predominantly longitudinal character and the open circles to those with transverse character. The lines are guides to the eye; each traces data with similar eigenvectors.

Figure 3

RMC refinement of (a) neutron diffraction and (b) molecular dynamics $T(r)$ data. The dots are the experimental values and the solid lines are calculated from the refined RMC structural models described in the text. The lower trace in each plot shows the difference ($\mathrm{\text{measured}}-\mathrm{\text{calculated}}$), offset vertically by $-2$. The range of $r$ values differs between plots as a consequence of the corresponding difference in configurational box size.