Lattice resolution of vibrational modes in the electron microscope

Systematic Absences of Optical Phonon Modes in Phonon Dispersion Measured by Electron Microscopy

Phonon dispersion relations are widely used to elucidate the vibrational properties of materials. As an emerging technique, momentum-resolved vibrational spectroscopy in scanning transmission electron microscopy offers an unparalleled approach to explore q-dependent phonon behavior at local structures. In this study, we systematically investigate the phonon dispersion of monolayer graphene across several Brillouin zones (BZs) using momentum-resolved vibrational spectroscopy and find that the optical phonon signals vanish at the Γ points with indices (hk0) satisfying h+2k=3n (n denoted integers). Theoretical analysis reveals that the observed phenomena arise from the complete destructive interference of the scattered waves from different basis atoms. This observation, corroborated by the study of diamond, should be a general characteristic of materials composed of symmetrically equivalent pairs of the same elements. Moreover, our results emphasize the importance of multiple scattering in interpreting the vibrational signals in bulk materials. We demonstrate that the systematic absences and dynamic effects, which have not been much appreciated before, offer new insights into the experimental assessment of local vibrational properties of materials.

Nanoscale Localized Phonons at Al2O3 Grain Boundaries

Nanoscale defects like grain boundaries (GBs) would introduce local phonon modes and affect the bulk materials' thermal, electrical, optical, and mechanical properties. It is highly desirable to correlate the phonon modes and atomic arrangements for individual defects to precisely understand the structure-property relation. Here we investigated the localized phonon modes of Al2O3 GBs by combination of the vibrational electron energy loss spectroscopy (EELS) in scanning transmission electron microscope and density functional perturbation theory (DFPT). The differences between GB and bulk obtained from the vibrational EELS show that the GB exhibited more active vibration at the energy range of <50 meV and >80 meV, and further DFPT results proved the wide distribution of bond lengths at GB are the main factor for the emergence of local phonon modes. This research provides insights into the phonon-defect relation and would be of importance in the design and application of polycrystalline materials.

Single-atom vibrational spectroscopy with chemical-bonding sensitivity

Correlation of lattice vibrational properties with local atomic configurations in materials is essential for elucidating functionalities that involve phonon transport in solids. Recent developments in vibrational spectroscopy in a scanning transmission electron microscope have enabled direct measurements of local phonon modes at defects and interfaces by combining high spatial and energy resolution. However, pushing the ultimate limit of vibrational spectroscopy in a scanning transmission electron microscope to reveal the impact of chemical bonding on local phonon modes requires extreme sensitivity of the experiment at the chemical-bond level. Here we demonstrate that, with improved instrument stability and sensitivity, the specific vibrational signals of the same substitutional impurity and the neighbouring carbon atoms in monolayer graphene with different chemical-bonding configurations are clearly resolved, complementary with density functional theory calculations. The present work opens the door to the direct observation of local phonon modes with chemical-bonding sensitivity, and provides more insights into the defect-induced physics in graphene.

Localized Phonon Densities of States at Grain Boundaries in Silicon

Since it is now possible to record vibrational spectra at nanometer scales in the electron microscope, it is of interest to explore whether extended defects in crystals such as dislocations or grain boundaries will result in measurable changes of the phonon densities of states (dos) that are reflected in the spectra. Phonon densities of states were calculated for a set of high angle grain boundaries in silicon. The boundaries are modeled by supercells with up to 160 atoms, and the vibrational densities of states were calculated by taking the Fourier transform of the velocity–velocity autocorrelation function from molecular dynamics simulations with larger supercells doubled in all three directions. In selected cases, the results were checked on the original supercells by comparison with the densities of states obtained by diagonalizing the dynamical matrix calculated using density functional theory. Near the core of the grain boundary, the height of the optic phonon peak in the dos at 60 meV was suppressed relative to features due to acoustic phonons that are largely unchanged relative to their bulk values. This can be attributed to the variation in the strength of bonds in grain boundary core regions where there is a range of bond lengths.

Advances and Applications of Atomic-Resolution Scanning Transmission Electron Microscopy

Although scanning transmission electron microscopy (STEM) images of individual heavy atoms were reported 50 years ago, the applications of atomic-resolution STEM imaging became wide spread only after the practical realization of aberration correctors on field-emission STEM/TEM instruments to form sub-Ångstrom electron probes. The innovative designs and advances of electron optical systems, the fundamental understanding of electron–specimen interaction processes, and the advances in detector technology all played a major role in achieving the goal of atomic-resolution STEM imaging of practical materials. It is clear that tremendous advances in computer technology and electronics, image acquisition and processing algorithms, image simulations, and precision machining synergistically made atomic-resolution STEM imaging routinely accessible. It is anticipated that further hardware/software development is needed to achieve three-dimensional atomic-resolution STEM imaging with single-atom chemical sensitivity, even for electron-beam-sensitive materials. Artificial intelligence, machine learning, and big-data science are expected to significantly enhance the impact of STEM and associated techniques on many research fields such as materials science and engineering, quantum and nanoscale science, physics and chemistry, and biology and medicine. This review focuses on advances of STEM imaging from the invention of the field-emission electron gun to the realization of aberration-corrected and monochromated atomic-resolution STEM and its broad applications.

Role of Convergence and Collection Angles in the Excitation of Long- and Short-Wavelength Phonons with Vibrational Electron Energy-Loss Spectroscopy

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.

Theory of Atomic-Scale Vibrational Mapping and Isotope Identification with Electron Beams

Transmission electron microscopy and spectroscopy currently enable the acquisition of spatially resolved spectral information from a specimen by focusing electron beams down to a sub-angstrom spot and then analyzing the energy of the inelastically scattered electrons with few-meV energy resolution. This technique has recently been used to experimentally resolve vibrational modes in 2D materials emerging at mid-infrared frequencies. Here, on the basis of first-principles theory, we demonstrate the possibility of identifying single isotope atom impurities in a nanostructure through the trace that they leave in the spectral and spatial characteristics of the vibrational modes. Specifically, we examine a hexagonal boron nitride molecule as an example of application, in which the presence of a single isotope impurity is revealed through changes in the electron spectra, as well as in the space-, energy-, and momentum-resolved inelastic electron signal. We compare these results with conventional far-field spectroscopy, showing that electron beams offer superior spatial resolution combined with the ability to probe the complete set of vibrational modes, including those that are optically dark. Our study is relevant for the atomic-scale characterization of vibrational modes in materials of interest, including a detailed mapping of isotope distributions.