Molecular neutron spectroscopy techniques applied to ceramics $α$-SiC and $β$-Ga$_2$O$_3$

Abstract

Neutron spectroscopy is a powerful technique for determining the vibrational states of matter. Instruments with fixed geometry may measure inelastic scattering at a limited set of angles, producing a 1-D spectrum $S(ω)$. Such measurements are usually simulated in a DOS-like semi-analytic incoherent approximation, well-established for study of bending/stretching modes in molecular crystals. In this work we empirically test the simulation method for two ceramics with industrial electronic applications that act as "worst-case" systems. The phonon scattering from $α$-SiC and $β$-Ga$_2$O$_3$ is coherent, depends on momentum transfer $Q$ and sits in frequencies below the typical "fingerprint" range of molecular spectroscopy. Inelastic neutron-scattering measurements of powders were performed with two contrasting spectrometers at cryogenic and elevated temperatures, and simulations performed using a variety of density-functional approximations. We find that for 1-D powder spectra from a compact instrument, the approximate simulations are easily comparable with experimental spectra and give similar results to a more computationally-intensive numerical sampling of the coherent spectrum. Given the success with these systems, the approximate method appears to be suitable for modelling inelastic neutron scattering by harmonic phonons of almost any powder sample with this technique. When a $Q$-resolved instrument is used to collect the 2-D dynamical structure factor $S(Q,ω)$, numerical averaging is still required to capture phonon features. Our simulations of inelastic scattering from $α$-SiC in the 6H polytype using the PBEsol functional gave good agreement with the experiments. By contrast, the RSCAN functional gave the best agreement with the measured spectra of $β$-Ga$_2$O$_3$ and is recommended for future work on the lattice dynamics of this material.