Imaging of isotope diffusion using atomic-scale vibrational spectroscopy (2024)

a, EEL spectrum at bright field without samples. b, c, Linear- and log-scaled EEL spectra at dark field on ¹³C graphene. The natural width of the zero-loss peak in the ideal on-axis condition has been shown. As an instrumental function, the zero-loss half-width is 18 meV, whereas it is 45 meV in the off-axis condition (with sample). The zero-loss peak in the off-axis is an ambiguous concept and cannot be detected without a sample.

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a, Comparison of the optical modes (H-peak) in the vibrational spectra of all the samples including 1L graphene shown in Fig. 1. The energy shift of approximately 7–8 meV between isotopes was found in 2L as in the case of 1L. The H-peak in 2L consists of two components due to possible contributions from the TO mode due to LO–TO splitting or the high-energy component of the LA mode. b, Line shape analysis of the vibration spectra obtained from 2L samples, where a rough component analysis by Voigt function is possible as in the case of 1L shown in Fig. 1. In this case, four components were used for the fittings: the L-peak, which is mainly the contribution of acoustic phonons, the two H-peaks mentioned above, and the peak that appears between them, which is considered to be the contribution of out-of-plane ZO mode.

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The signal is almost identical regardless of the position of the EELS collection aperture (green, red and black); therefore, the in-plane orientation of graphene hardly affects the fitting parameters. The lattice defects in graphene also do not affect these parameters, except for the acoustic vibration mode in the lower peak, which is considered negligible.

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The phonon dispersion (left) and PDOS (right) of ¹²C and ¹³C graphene obtained by DFPT calculations in Quantum Espresso. The energy difference between ¹²C and ¹³C graphene is 7.7 meV at the highest energy peak in PDOS corresponding to the LO mode and 6.7 meV at the second highest energy peak which is mainly contributed from the LO/TO mode. The interatomic force constants calculated from DFPT is, for instance, 52.4 eV Å⁻² for the in-plane direction at Γ. This calculation was performed to estimate the energy shift of the PDOS of ¹²C and ¹³C with the simple model. To reproduce the experimental spectra, full calculation considering the charge modulation in the higher-order Brillouin Zone is necessary, although such calculation is beyond the scope of this study and is not addressed here.

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a, Comparison of probe and pixel size with graphene lattice. When the electron beam is fixed on an atom with our probe condition in which the probe size is increased to gain the current, the resulting spectrum contains the signal of the nearest three atoms in addition to that of the atom at the centre of the probe. Thus, a single spectrum roughly consists of the average signal of four atoms. The momentum space was also integrated up to 3.5 Å^–1. Therefore, the spatial resolution was influenced by the integration effect in both real and momentum space. Based on a study by Hage et al. using silicon single atoms on graphene, when the probe size is sufficiently small, a localized signal at the single atom level can be obtained in the dark-field EELS condition¹. b, Isotope combinations of the four atoms. The colour distribution at the top in b corresponds to that used in Figs. 3, 4. The corresponding vibrational energies of the LO/TO mode at Γ are calculated by DFPT and shown on the bottom line in b. When all four atoms are ¹²C or ¹³C, the energy difference of the H-peak between them is the largest and detectable with more than 90% of confidence level. If any one or two of the four atoms belong to different isotopes, the peak positions are between them. In this case, there are six possible configurations, as shown in b.

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a, b, The isotope colour map in Fig. 3 before and after median filtering, respectively.

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The residual gases include hydrocarbons such as CH_x and C₂H_x.

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a, TEM image of ¹³C graphene involving a grain boundary. The grain boundary extends from the top right to the bottom left of the image. The crystal orientation is rotated by approximately 16° across the grain boundary comprised of 5–7 membered rings, as indicated by the yellow lines. b, Annular dark-field image obtained by performing a STEM-EELS two-dimensional scan at the same position as in a. c, Colour map of the high-energy peak positions corresponding to b. d, The EEL spectra taken from positions 1–3 in b are shown. The H-peaks in all three spectra are almost identical.

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a, b, TEM image of initial ¹²C graphene including a crack and the same position after the nanodomain growth, respectively. The newly grown domain contains prolific defects involving 5–7 membered rings, as shown in c. d, Annular dark-field image obtained by performing a STEM-EELS two-dimensional scan at the same position as in b. e, Colour map showing the position of the high-energy peak without noise filtering. The peak positions are almost uniform over the whole area, including the newly grown region.

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a, b, The variation of the measured vibrational peak positions for line scans with an exposure time of 1 s per pixel on ¹²C and ¹³C graphene, respectively. The standard deviations σ for 500 data points are 2.1 meV for ¹²C and 2.0 meV for ¹³C graphene, which is three times smaller than the energy shift S between ¹²C and ¹³C graphene ~8 meV. Because the standard deviations of the measured points are based on fitting and contain errors, then the confidence intervals cannot be directly measured around those data points. This statical analysis, however, simply proves the high detection level of ¹²C atoms in case of 4 atoms and will give a standard for future experiments. Note that the purities of these samples are both over 99%, and thus, the peaking data points may be attributed to 1% of the isotopes in the samples. c, The variation of the measured vibrational peak positions on ¹³C graphene (corresponding to Fig. 4a) shows a σ of 3.0 meV at an exposure time of 0.5 s. Note that the data points at the crack are excluded.

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