High-temperature Phonon Dispersion at the Nanometer Scale by Electron Energy-Loss Spectroscopy

The advent of monochromated aberration-corrected scanning-transmission-electron microscopy (MAC-STEM) has led to spatially resolved and millielectronvolt-scale energy resolution in electron-energy-loss spectroscopy (EELS) of phonons. The versatility of MAC-STEM also allows for the trading of spatial resolution for momentum resolution, leading to measurements of phonon dispersions. Here, we report momentum-resolved EELS in layered, hexagonal boron nitride at three temperatures 300 K, 800 K and 1300 K across and beyond the first Brillouin zone. The EELS measurements allow the extraction of anharmonic effects in the phonon modes, reflected by meV-scale phonon energy shifts. Density-functional-theory calculations incorporating anharmonic effects in phonon self-energies are consistent with observed energy shifts and allow the identification of contributing mechanisms. Available phonon-EELS theories that treat a crystal as a collection of atoms fail to reproduce the EEL spectra at large momentum transfers and high temperatures. Umklapp processes are likely to be the dominant issue in the case of large momentum transfer.