SUPPLEMENTARY INFORMATION

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1 Methods and supplementary materials Materials and sample preparation Bulk hexagonal boron nitride (h-bn) powders were provided by Saint-Gobain Advanced Ceramics Lauf GmbH. The stated chemical composition was >98% h-bn, <1.5% O 2, <0.5% B 2 O 3. N-Methyl-2-Pyrrolidone (NMP) was purchased from Sigma-Aldrich and used as received. Commercially available NMP typically contains sodium in the order of about 100 ppb and amine impurities at about 12 ppm. The as-received powders were dispersed in NMP at a concentration of 1 mg/ml by sonicating in a low power sonic bath (Model Ultrawave U50, 100W, 42 khz) for 30 minutes 27. The resultant dispersion was centrifuged using a SIGMA 1-6 centrifuge for 30 minutes at 500 rpm. TEM grids were prepared by drop casting from the dispersion onto holey and lacey carbon grids (400 mesh size) and drying in air. At the microscope site, the grids were loaded into sample cartridges, and the cartridges were baked, prior to their introduction into the electron microscope, in clean vacuum at 140 C for 8 hours, to drive off or immobilize hydrocarbon contaminants. The cartridges were cooled by venting the baking chamber to argon, and transferred while still warm into the microscope. Image acquisition Monolayer areas of the BN flakes that extended over holes in the support film were examined in a Nion UltraSTEM100 scanning transmission electron microscope 28, with a C3+C5 aberration corrector that had Nion s third-generation power supplies. The operating voltage was 60 kv and the beam current, measured on the microscope s Ronchigram CCD camera, was typically 50 pa. The microscope used a cold fieldemission electron gun. The resolution was limited principally by a total chromatic aberration coefficient of 1.3 mm (arising mainly from the objective lens, corrector and the first condenser lens), an energy spread of 0.35 ev, and the finite brightness of the electron source. The incident electron probe half-angle was selected to be 31 mr, as an optimum compromise between the best obtainable spatial resolution and the absence of 1

2 probe tails caused by chromatic aberration. In the limit of zero probe current, the theoretical resolution worked out using formulas given in reference S1 was 0.96 Å, with the finite source size needed to deliver 50 pa into the electron probe, it became 1.14 Å. This was in good agreement with the size of the electron probe obtained in practice: about 1.2 Å full-width at half-maximum, but with a sharp-enough central maximum to transfer spatial frequencies down to 1.09 Å into the image. The imaging detector was a medium-angle annular dark field detector (MAADF), with the accepted half-angles spanning from 58 mr to about 200 mr. The detector used a YAP single-crystal scintillator and a Hamamatsu R1924 photo-multiplier tube (PMT). Its detective quantum efficiency (DQE) has been measured close to 1 at the intensity levels used for the present imaging. Its gain was set by the user, by adjusting the PMT voltage via the microscope s software. The PMT electronics was designed to keep the gain linear to better than 1% at the signal levels used here. The pixel size in the image of Fig. 1 was Å, i.e. the image was over-sampled with about 20 pixels per resolution element. The per-pixel dwell time was 64 µs. With 50 pa of beam current, the incident dose was therefore 6x10 6 electrons per Å 2. The same perpixel time was used for images S1 and S3a, whose pixel size was 2x larger. All images were acquired in the line-synched mode, in which the start of each new line was synchronized with the AC mains. Identifying single atoms by the strength of their ADF signal in a scanning transmission electron microscope requires high stabilities of many parameters, including 1) the beam current, which should not vary by more than about 1% r.m.s. across the image; 2) the probe position, which must not jitter at random frequencies by more than 0.2 Å peak-to-peak; 3) the microscope imaging parameters, especially the defocus and first-order (two-fold) astigmatism, which must be stable enough so that the probe does not change shape while scanning over the image; and 4) the sample chamber vacuum, which must be clean enough so that hydrocarbon 2

3 contamination does not settle on the sample and also that no water condenses on it, causing chemically-induced etching under the beam. The results presented in this paper demonstrate that the microscope we used had sufficiently precise control over all these parameters: the beam current r.m.s. variation was < 1% in images taken with up to 64 second acquisition time, the probe position was stable to about 0.1 Å peak-to-peak, the imaging parameters were stable over tens of minutes, and the sample level vacuum was such that initially clean samples neither contaminated nor etched under the beam. The effort needed to get to this level of performance was comparable to the effort required to produce the microscope s aberration-corrected optics. An unprocessed lower-magnification image of the area shown in Fig. 1 of the main paper, recorded 2 minutes earlier, is shown in Fig. S1. The area imaged at high magnification in Fig. 1 is marked by a white rectangle. The whole monolayer area was surrounded by thicker areas of multilayer boron nitride and some curled-up BN, other material that was amorphous and consisted of amorphous carbon (identified by EELS) and some hydrocarbons, and several heavier adatoms. The number of the BN layers in various parts of the image was checked by comparing their average ADF intensity to the monolayer area, and is shown in the figure. Monolayers surrounded by thicker material were typically more stable under the electron beam than monolayers going all the way to the flake s edge, and were therefore preferred for high resolution imaging. Image processing and analysis Unprocessed ADF images are a convolution of the true sample structure with the electron probe, which was ~1.2 Å wide in the present work and which almost certainly also had a non-gaussian tail. As described in the main text, the tail created a serious problem for image quantification, especially at the three nearest neighbours located 1.45 Å away from each atom. A clear indication that the effect was important was seen in histograms of image maxima in smoothed, but otherwise unprocessed ADF images. The histogram for the N sites showed three well-separated peaks approximately equally spaced, with the 3

4 central peak the strongest. These were identified as a central N peak plus weaker C and O side peaks. The histogram for the B sites showed a major and a minor peak, spaced by a similar amount, and these were identified as B and C. When the two histograms were combined, however, there was a major offset between the intensities from the two sites, which caused the B-site C peak to overlap the N-site N peak, and the N-site C peak to overlap the B-site B peak. Another indication of the tail strength was provided by the intensity at the center of the hexagonal rings in single layer images. This should have been zero, but it was in fact typically around 50% of the average ring intensity in our unprocessed ADF images. It came from the 6 atoms of the hexagonal ring that were 1.45 Å distant from the ring s center, the 6 second nearest neighbours 2.5 Å away, the 12 third nearest neighbours, etc. The intensity at the center of the rings was used to measure the strength of the probe tail experimentally, i.e. to determine the intensity contributions of each atom to its nearest neighbours. When these contributions were subtracted and the histogram of atomic intensities computed again, the maximum intensities of the carbon atoms on the two different sites merged into a single histogram peak that did not overlap the B or the N peaks. The atomic assignments then became the same as those made using the deconvolution procedure described below. The image of Figure 1b, on which the histogram analysis shown in Fig. 2 was carried out, was obtained by using the Fast Fourier Transform (FFT) short-cut to deconvolution. The FFT of an undistorted version of the image shown in Figure 1a was multiplied by the filter of Fig. S2a and the inverse FFT was computed. The filter was a sum of a broad positive smoothing Gaussian that cut out high spatial frequencies from the image, and a narrower negative sharpening Gaussian that enhanced intermediate spatial frequencies at the expense of low frequencies. Figure S2b shows a profile through the image of an isolated atom modeled by a Gaussian peak 1.1 Å wide, filtered in the same way as Figure 1a was. It shows that the smoothing component of the deconvolution had not broadened the image of the atom visibly, and that the deconvolution added a negative skirt to the atom, extending from about 0.9 Å to about 1.8 Å radius. The strength of the negative 4

5 skirt was adjusted to give zero average intensity in the center of the BN holes at 1.45 Å from the 6 atoms of each ring. This also reduced the tail of the experimental atom images close to zero at the nearest neighbours, exactly the same distance away. In the histogram analysis, the B and N peaks, for which there were more atoms and hence the statistics were better than for the C and O peaks, had standard deviations of 5.7% and 4.5% of their mean values, respectively. We extrapolated these widths to the C and O distributions, and modeled them by Gaussians with standard deviations of 5% and 4% respectively. The imaged atoms could have had adatoms lying on top of them and modifying the image intensity. Helium was not a likely adatom, and adatoms with Z > 2 would have been easily identified by the added intensity. H would have contributed about 7 % of the B signal, which means that it would have added about one standard deviation to the intensity of an underlying B, C or N atom in the histogram of Fig. 2b. This is not enough to distinguish H adatoms in the present case. However, the additional signal would have shifted the intensity of an atom with hydrogen over it to the right side of the histogram peak, and this may have in fact happened for the C atom whose intensity was the closest to the N peak. Had the image statistics been about 6x better (which would have needed a 36x greater electron dose), and had the H adatoms remained stationary, they would have been detectable using the present methodology. Similar arguments apply to heavy atoms on light substrates. Signal from a single C atom will amount to about 70% of the difference between Pt (Z=78) and Au (Z=79), and will make the atomic identification unreliable unless the relative separation of the histogram peaks is much better than the one obtained here. High-resolution tomographic reconstruction 24, S2 should in principle be able to sort out which part of the signal came from the single heavy atom, and which part came from the sample background. The above discussion implies that image intensities added up linearly for overlapping atoms, i.e., that the images were incoherent. This was checked both experimentally, by 5

6 comparing intensities of double layers of BN and also graphene to those of single layers, and computationally. Nonlinearities due to a coherent image component were found to be negligible at the statistical precision level used here. The image un-distortion was done by using linear ramps to remove an image stretch probably caused by the sample not being precisely perpendicular to the electron beam, plus sinusoidal terms to remove a small (0.4 Å peak-to-peak) distortion caused by external 60 Hz stray magnetic fields (0.3 mg r.m.s.) deflecting the electron probe. As a final operation carried out on the image of Figure 1b, the image gain was scaled to give average peak intensity for the boron atoms of 1. Distances between the atomic images were determined by using the following steps: a) re-sampling the filtered image onto a 4x finer mesh (with pixel spacing of 1.5 pm), using DigitalMicrograph s scaling function that s based on cubic spline interpolation, b) finding the maximum of each atomic peak using the find maxima and minima function of DigitalMicrograph, and c) computing the distances between the atomic maxima of interest. Using the positions of the maximum of the image peaks avoided difficulties with separating the not very well resolved near-neighbour atomic peaks. The reliability of the method was checked by using it to determine the variation in the distance between B and N atomic neigbours in the BN-only parts of the image. This showed that the r.m.s. variation of the BN distance measurements relative to the mean value of 1.45 Å was 0.10 Å. The variation was largely statistical, and this was confirmed by the fact that in images acquired with twice the pixel spacing and thus an electron dose that was 25% of the one used for Fig. 1, the displacements were about 2x higher. An increase was expected for random displacements due to finite image statistics, whereas other random influences such as sample or probe movements would have been expected to decrease in an image acquired 4x faster. In order to improve the statistical precision of the measured atomic distances around the 2 available O atoms, 6

7 the measurements were averaged over all their near neighbours, as described in the main paper. Identifying atoms of different Z s by ADF histogram analysis. Because the intensity I of the images of individual atoms increases as a Z 1.64, where a is a constant, the separation of the histogram peaks for adjacent elements will increase as ΔI/ΔZ = 1.64 a Z The width of the histogram peaks in an image whose SNR is limited by the finite statistics due to the limited electron dose will increase as a 0.5 Z 0.82, which means that the relative separation of the histogram peaks (the absolute separation divided by the width of the peaks) for adjacent elements will decrease as Z This is a rather weak dependence: the relative separation of Pt (Z=78) and Au (Z=79) histogram peaks will be about (78/6) = 63% of the relative separation of C and N peaks. Provided that no influences other than the finite image statistics limit the precision with which individual atomic intensities can be measured, distinguishing isolated Pt atoms from Au ones with high confidence level will therefore be possible with an electron dose that is (1/0.63) 2 = 2.5x times higher than the one used here (i.e., at about 2x10 7 electrons per Å 2 ), and distinguishing iridium (Z=77) from Au will be possible with a slightly smaller dose than used here. Another requirement would be that atoms of a known and similarly high Z be imaged at the same time, so that Z-dependence data such as acquired here for a range of ΔZ of just 3 would not have to be extrapolated to very different Z s. Extending the SNR considerations towards lighter elements shows that individual atoms of all elements lighter than B are identifiable by ADF imaging with a slightly smaller dose than the one used in this work, provided that they remain stationary while the electron beam is scanning over them. Origin of the atomic substitutions A likely mechanism for the observed atomic substitutions is documented in Fig. S3, which compares the same sub-area of the image of Fig. 1a (shown as Fig. S3b) with the corresponding region of an unprocessed image recorded 2 minutes earlier (Fig. S3a, also 7

8 shown at a much lower magnification as Fig. S1). The earlier image was taken at half the magnification and the same dwell time per pixel, i.e. at ¼ of the electron dose per unit area. The statistical precision of the image was therefore 2x worse, but it can still be seen that the two oxygen impurity atoms identified in Fig. 3 were already incorporated into the lattice, in the same places as where they were 2 minutes later, and even that the four C impurity atoms that were separate from the C ring were also present. Most revealingly, the image shows a 3-atom hole in the sample precisely where the six carbon atoms were about to be incorporated. An image recorded prior to Fig. S3a did not show the same hole, but showed another hole roughly where the right O atom and four C atoms were observed in S3a and S3b. An image recorded even earlier showed no holes and no substitutional atoms. This indicates that small holes opened up and then filled in with carbon and occasionally also oxygen atoms rather than B and N. A source of non-bn atoms was available nearby in the carbon-containing layers near the hole. Since the threshold for knock-on damage in BN is 78 kev 19, the holes most likely did not arise by direct collisions of incident beam electrons with the atoms in the BN sheet, but rather by a hydrogen-mediated, impedance matched knock-on damage mechanism S3, whose threshold energy is 3.7x lower. Atomic-size holes in single layer BN are readily created by an electron beam whose primary energy is higher than the knock-on damage threshold Å-level control of the atomic substitutions should therefore be achievable if the holes are drilled by a beam deliberately focused on a specific site, with the desired substitutional atoms present in mobile molecules attached to the thin sample. Density Functional Theory Modeling Density functional theory S4, S5 (DFT) calculations were performed using a plane-wave basis within the projector-augmented-wave method S6 and generalized-gradient approximation as implemented in the Vienna ab initio simulation package (VASP) code S7. A periodic supercell containing a single layer of boron nitride consisting of 60 atoms was constructed using the B-N nearest neighbor separation of 1.45 Å. The out of plane dimension of the supercell was set to 12 Å. Carbon atoms were substituted for the 8

9 B and N atoms of one of the boron nitride rings, and an O atom substituted for a N atom neighbouring the carbon ring. The structure was then relaxed using an energy cutoff of 400 ev and up to a 3x3x3 Monkhorst-Pack k-point mesh centered at the Γ-point. The resulting supercell was then doubled in each of the inplane directions and filled with additional single layer BN and the extra C and O substitutional impurities identified by the histogram analysis. The resultant 240 atom supercell was relaxed using only the Γ- point in k-space and an energy cutoff of 400 ev. References S1. Krivanek O.L., et al., Advances in Aberration-Corrected Scanning Transmission Electron Microscopy and Electron Energy-Loss Spectroscopy, in: Aberration- Corrected Electron Microscopy, Advances in Imaging and Electron Physics 153 (Hawkes P.W., ed. Elsevier, Amsterdam) (2008). S2. Midgley P. A. et al., Nanoscale scanning transmission electron tomography, J. Micr. 223, (2006). S3. Bond G.M., Robertson I.M., Zeides F.M., Birnbaum H.K., 'Sub-threshold' electron irradiation damage in hydrogen charged aluminum, Phil Mag A55, (1987). S4. Hohenberg P. & Kohn W., Inhomogeneous Electron Gas, Phys. Rev., 136, B864- B871 (1964). S5. Kohn W. & Sham L. J., Self-Consistent Equations Including Exchange and Correlation Effects, Phys. Rev., 140, A1133-A1138 (1965). S6. Blöchl P. E., Projector augmented-wave method, Phys. Rev. B 50, (1994). S7. Kresse G. & Furthmüller J., Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set, Phys. Rev. B, 54, (1996). 9

10 Figure S1: Lower magnification image of the sample area of Fig. 1, recorded 2 minutes earlier. The area shown in Fig. 1 is marked by a white rectangle. Different numbers in the image mark the number of BN layers in that image area. 0 indicates the vacuum beyond the sample edge. 10

11 Figure S2: Details of the deconvolution procedure applied to the image of Figure 1a. a) Profile of the rotationally symmetric Fourier filter used on the unprocessed image. The spatial frequencies of the two principal reflections due to the BN lattice are also shown. The three major effects of the filter were (1) to lower the DC level of the image, (2) to enhance the contribution of diffuse scattering due to non-periodic features, and (3) to eliminate high spatial frequencies due to image shot noise. b) Profile through the image of an isolated atom, modeled by a Gaussian with a 1.1 Å full with at halfmaximum, processed with the filter. 11

12 Figure S3: Two images taken serially that document the likely cause of the atomic substitutions. a) Unprocessed ADF image recorded 2 minutes prior to the image of Figure 1, at double the pixel size of the latter image, b) The corresponding area of the image of Figure 1. The white arrows point to O atoms identified by the histogram analysis. The yellow circle marks a hole in the first image that preceded the hexagonal carbon ring of the second image. The two short horizontal streaks (about 1.5 Å wide) visible in the hole in (a) are due to mobile atoms which were present for some scan lines but not for others. 12