Current generation electron monochromators employed as attachments to scanning transmission electron microscopes (STEM) offer the ability to obtain vibrational information from materials using electron energy-loss spectroscopy (EELS). We show here that in crystals, long- and short-wavelength phonon modes can be probed simultaneously with on-axis vibrational STEM EELS. The long-wavelength phonons are probed via dipole scattering, while the short-wavelength modes are probed via impact scattering of the incident electrons. The localized character of the short-wavelength modes is demonstrated by scanning the electron beam across the edge of a hexagonal boron nitride nanoparticle. It is found that employing convergence angles that encompass multiple Brillouin zone boundaries enhances the short-wavelength phonon contribution to the vibrational energy-loss spectrum much more than that achieved by employing collection angles that encompass multiple Brillouin zone boundaries. Probing short-wavelength phonons at high spatial resolution with on-axis vibrational STEM EELS will help develop a fundamental connection between vibrational excitations and bonding arrangements at atomic-scale heterogeneities in materials.

The equilibrium structures of cubic, tetragonal and orthorhombic phases of magnesium silicate perovskite are found from first principles electronic structure calculations. Zone centre and zone boundary phonons of each phase are also calculated from ab initio forces from finite displacments, and phase transitions between the phases are analysed in terms of phonon instabilities, and coupling between modes. Both the cubic and tetragonal phases have strongly unstable modes dominated by rotation of the SiO6 octahedra, which freeze in to ultimately form the orthorhombic phase. First priniciples molecular dynamics simulations at finite temperatures are used to further investigate the stability of the intermediate tetragonal phase and the coupling between participating phonon modes. The implications for a transition temperature between orthorhombic and tetragonal phases are discussed.