Single-atom electron energy loss spectroscopy of light elements

Light elements such as alkali metal (lithium, sodium) or halogen (fluorine, chlorine) are present in various substances and indeed play significant roles in our life. Although atomic behaviours of these elements are often a key to resolve chemical or biological activities, they are hardly visible in transmission electron microscope because of their smaller scattering power and higher knock-on probability. Here we propose a concept for detecting light atoms encaged in a nanospace by means of electron energy loss spectroscopy using inelastically scattered electrons. In this method, we demonstrate the single-atom detection of lithium, fluorine, sodium and chlorine with near-atomic precision, which is limited by the incident probe size, signal delocalization and atomic movement in nanospace. Moreover, chemical shifts of lithium K-edge have been successfully identified with various atomic configurations in one-dimensional lithium compounds.

(a-d) line profiles of ADF images (black line) and the corresponding EELS signals (red line) for Cs, Cl atoms in a CsCl chain, a Ce atom inside a C 82 1 and a Li atom inside a C 60 , respectively. Line profiles are taken along the white lines in the insets. In the case of Cs, Cl and Ce atoms, the EELS profiles are broadened than ADF profiles. The difference is attributed to the EELS delocalization. Although there is no visible ADF contrast for the Li atom inside the C 60 molecule, the fact that the EELS profile is wider than ADF profile of the C 60 molecule reflects the contribution of the EELS delocalization for the Li atom.

Supplementary note 1. Ionic atomic chains including "invisible" atoms
Supplementary Figures 1a-d present STEM annular dark-field (ADF) images of NaI, CsF, CsCl, and CsI atomic chains inside DWNTs. Although the ADF contrast profiles along the chains ( Supplementary Fig. 1e) do not produce clear peaks for Na, F, and Cl atoms, there is sufficient space for those light atoms between two neighbouring Cs or I atoms, considering the atomic distance of CsI atomic chains. The average distance between two neighbouring Cs or I atoms is ordered according to CsF < NaI < CsCl < CsI, which simply reflects the sums of ionic radii for cation (Na + (102 pm), Cs + (170 pm)) and anion (F -(133 pm), Cl -(181 pm), and I -(220 pm)). However, in the all cases presented here, the length between two neighbouring Cs or I atoms are shorter than twice the sums of ionic radii for cation and anion in bulk crystals. The fact suggests the shorter bond length of the ionic atomic chains than the bulk crystals.

Supplementary note 2. Single-atom spectroscopy of fluorine
Supplementary Figure 2 shows an atomic chain of CsF in a DWNT. Similar to the other cases (NaI and CsCl), the CsF atomic chain is supposed to be alternatingly aligned inside of the DWNT (Supplementary Fig. 2a). Supplementary Figure 2b-c shows the ADF image of CsF and corresponding elemental maps of Cs and F, based on Cs M-edge and F K-edge spectra. From those maps, it is clear that the F atoms are located exactly in the middle of two Cs atoms. However, the F map is not sophisticated to the extent like the Cl map, as shown in Fig. 3 of the main text. While some pixels have strong signals, others, especially those below pixels with high F K-edge intensity have weak or almost no signal. This means that fluctuations of the F atoms are induced by the electron irradiation and, finally, they are kicked out even from such a highly confined space during scanning.
The fine structure of the F K-edge is also affected by the coordination number, like the Li K-edge, as shown in Fig. 5 of the main text. The main peak of the F K-edge of CsF atomic chains is located at lower energy than in case of the 2 × 2 structure, as shown in Supplementary Fig. 2e. The electron affinity of the F atoms in CsF atomic chains should be higher than in the 2 × 2 structure because of the weaker Coulomb repulsion among nearest neighbouring F atoms. Thus, the lower binding energy of the F 1s electrons in CsF atomic chains causes the red shift in the F K-edge.

Supplementary note 3. Confidence level of invisible-atom detection
To consider the accuracy of our measurements, we estimated the signal-to-noise ratio (SNR) of our experimental data. We adopted the following expression for SNR in EELS, developed by Egerton 2 .
and are integration regions of the core-loss signal and the background ( Supplementary Fig. 4a), respectively. ℎ is a dimensionless parameter defined as ℎ = [ + ( )]⁄ and represents the error caused by the background extrapolation. For our experiments, SNR for the Li K-edge corrected for even a single atom ( Supplementary Fig. 4a) can be estimated to be approximately 8 (h = 10) by choosing the background fitting and integration region (г and Δ in Supplementary Fig. 4a, respectively) carefully to avoid a large value of ℎ.
In addition, the obtained signal of the Li K-edge is located sufficiently above the noise level. Supplementary Figure 4c shows the colour variation of the Li elemental map as a function of the standard variation of the signal noise σ, measured from the vacuum area far from the sample. In this map, the zigzag area has the intensity of more than 4σ. These values demonstrate a high confidence level of our results.

Supplementary note 4. Estimation of the delocalization distance
The broadening of EELS profile can be expressed by a distance between the incident beam and the target atom, called the impact parameter b. In the classical theory, the delocalization distance L is defined as the maximum value of b in which the dynamic screening does not take place and roughly determined by the velocity of incident electron and the angular frequency of an atomic electron ; = / 3 . If we simply assume the absorption energy to excite the atomic electron as ∆ = (ℎ/2π) , L is inversely proportional to the absorption energy. In addition, by introducing the following relation 0 = ℎ/λ (de Broglie relation) in which λ, 0 , and ℎ denote the wave length, effective electron mass, and Plank's constant, respectively, is written as where is the characteristic scattering angle defined by = 0 2 ⁄ . For practical usage, 50 in which 50% of the inelastically scattered electrons are contained, is commonly used to estimate the degree of delocalization. 50 can be derived by adding cutoff functions to , which is then approximated by Supplementary Figure 8 presents the 50 values as function of the energy loss at the accelerating voltages of 30 (broken line) and 60 (solid line) kV. Much more detailed discussion has been reported by Egerton, Muller and Silcox 3-5 , for example.

Supplementary note 5. Origin of localized EELS detectable area in 1D ionic crystals.
In Table 1 in main text, the experimentally measured EELS detectable distance for Li or Na atoms in 1D ionic crystals is much smaller than one for a Li atom inside a C 60 molecule, even though the theoretically estimated EELS delocalization are larger due to the different acceleration voltages used (60 kV instead of 30kV). One of the reason for this discrepancy can be simply explained by the difference in the atomic motion. Light elements in 1D ionic crystal should be more confined (0.4nm) because of the robust ionic interaction between neighboring counter ions, while a Li atom inside C 60 molecule can move rather freely in a larger space (0.7nm). A strong screening effect of the heavier atoms aside in 1D crystal may also contribute to reduce the delocalization effect of low-lying EELS edge.