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Nanoscale Momentum-Resolved Vibrational Spectroscopy

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Nanoscale Momentum-Resolved Vibrational Spectroscopy

Fredrik S Hage et al. Sci Adv.

Abstract

Vibrational modes affect fundamental physical properties such as the conduction of sound and heat and can be sensitive to nano- and atomic-scale structure. Probing the momentum transfer dependence of vibrational modes provides a wealth of information about a materials system; however, experimental work has been limited to essentially bulk and averaged surface approaches or to small wave vectors. We demonstrate a combined experimental and theoretical methodology for nanoscale mapping of optical and acoustic phonons across the first Brillouin zone, in the electron microscope, probing a volume ~1010 to 1020 times smaller than that of comparable bulk and surface techniques. In combination with more conventional electron microscopy techniques, the presented methodology should allow for direct correlation of nanoscale vibrational mode dispersions with atomic-scale structure and chemistry.

Figures

Fig. 1
Fig. 1. Sketch of the experimental scattering geometry and selected momentum-resolved spectra.
(A) By tilting the incident beam by an angle η, the forward scattered beam is effectively displaced with respect to the spectrometer entrance aperture (in momentum space) by a distance and direction given by a wave vector q′. (B) q as defined by the incident (k0) and scattered (k1) wave vectors, for q′→0. Sketch of the first Brillouin zone of (C) a 2D-projected hexagonal close-packed (HCP) crystal and (D) a 2D-projected face-centered cubic (FCC) crystal illustrating how effectively displacing the EELS entrance aperture (gray discs) by q′ with respect to the forward scattered beam results in EEL spectrum momentum selectivity. Selected momentum-resolved experimental (black) and simulated (in-plane polarization only, purple) EEL spectra for (E) hBN along Γ→K and (F) cBN along Γ→X. The magnitude of displacement in momentum space considered for each spectrum is given in black (experimental spectra, corresponding to the center of the displaced beam, estimated to one decimal place) and purple (modeled spectra).
Fig. 2
Fig. 2. Simulated (full curves) and experimental (blue discs) hBN and cBN phonon dispersions.
For in-plane polarization, only colored (red) modes are predicted to contribute to the EEL spectrum. Reported experimental Raman (pink circles) and infrared (green circles) values (16) (observed at q→0 only, showing the limitation of these optical techniques) are indicated.
Fig. 3
Fig. 3. Spatially resolved vibrational EELS of hBN for an electron beam incidence of 74.5° to the crystallographic c axis.
(A) Spatially resolved loss spectra acquired from a hBN particle in the regions indicated on the HAADF line profile in (B). A simulated spectrum (purple) is superimposed on the experimental aloof spectrum (distance, 55 nm). (C) Sketch showing the relative orientation of the incoming electron beam with respect to the hBN planes. The direction of the crystallographic c axis is indicated. (D and E) Simulated and experimental diffraction patterns of the hBN particle.

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