Supplementary Figure 1. Electron micrographs of graphene and converted h-bn. (a) Low magnification STEM-ADF images of the graphene sample before

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1 Supplementary Figure 1. Electron micrographs of graphene and converted h-bn. (a) Low magnification STEM-ADF images of the graphene sample before conversion. Most of the graphene sample was folded after the transfer onto the TEM grid. Quantitative analysis of the image intensity shows the unfolded areas are primarily monolayer graphene. (b) Low magnification TEM bright filed image of the converted h-bn, showing that large area continuous h-bn film can be obtained by this method. The inset is a typical electron diffraction pattern of h-bn. 1

2 Supplementary Figure 2. AFM characterization of the as-obtained h-bn film on silica substrates. (a) shows the AFM height topographies of a continuous h-bn film with size of ~5µm 12µm. The broken area is used to measure the thickness of h-bn. PMMA-assisted graphene transfer will lead to some broken areas where the graphene folded, as indicated by the white arrows. Such geometries will be retained after conversion. The double layered h-bn along the edges of this broken area is indicated by the arrow. Height profile, (b), shows thicknesses of ~ 0.3 nm, which confirms single-layer h-bn. 2

3 SiO 2 h-bnc Supplementary Figure 3. Characterization of h-bnc film with low BN concentration. (a) Optical image of h-bnc with low concentration BN (Fig. 3b). (b) Raman spectrum of the converted h-bnc films. c) XPS spectra of the converted h-bnc at the early stage. At the initial stage, only N signal is observed in the XPS spectra (black line, also illustrated in Fig. 3b). After a short time substitution, both B and N signals are found with an atomic ratio close to 1:1 (red line, Fig. 3c and 3d). (d) STEM bright field image of homogeneous h-bnc film and, (e) (g) the corresponding elemental mappings of carbon, boron and nitrogen, respectively, from the same area as shown in (d). (h) Typical EEL spectrum. 3

4 Supplementary Figure 4. Characterization of the h-bn nanodomains in the h-bnc film. The B and N substitution reaction happens at the carbon atoms functionalized by hydroxyl groups and defect sites. With a longer reaction, h-bn nanodomains are formed at these nucleated locations, as illustrated in Figure 3. Such morphologies are characterized by ADF-STEM imaging and elemental mapping via EELS. (a) ADF-STEM image of a typical h-bnc film. (b)-(d) Elemental maps of carbon, boron and nitrogen, respectively. (e) Overlap of boron and nitrogen maps. Regions 4 is highly dispersed B and N in graphene while regions 1-3 are BN nanodomains with a size of 5~20 nm. (f) The EELS fine structures from these two types of B-N-doped regions are quite different, indicating the bonding of B in these two types of regions are different. The B EELS spectra from regions 1-3 reproduce those from h-bn. It is noticed that the BN domains may have thickness larger than a monolayer which is possibly caused by the additional epitaxy growth of h-bn, during the lateral conversion process. 4

5 Supplementary Figure 5. Characterization of the micro-scale h-bn domains in h-bnc. BN nanodomains will rapidly coarsen into irregular shape by merging with neighboring domains by continually supplying BN sources and longtime reaction. The h-bn regions can be differentiated from the optical image, as shown in a. Region 1 and areas with the same color are h-bn domains; while region 2 and areas with the same color are graphene (may contain small h-bn domains). The Raman spectra from each region are represented in b and c. 5

6 Supplementary Figure 6. Characterization of the graphene domains within the converted h-bn film. The growth of h-bn domains will shrink the graphene lattice into quasi-one-dimension nanoroads (Fig. 3e). (a) ADF-STEM image showing the presence of a narrow gap, containing some bright impurity atoms, between two converted h-bn patches. This gap is more clearly shown in the elemental maps (b-d). Inset: FFT from the ADF image showing that the upper and lower h-bn domains have the same orientation, as one would expect from topological conversion of the same graphene grain. (b-d) B, C, and Si maps from the whole area shown in (a). Note that the carbon map shows both carbon signals in this h-bn gap and from the surface contaminations. There is a high concentration of Si impurities in the gap (d). Si is one of the most common substitutional impurities in CVD grown graphene 38,39 due to the chemical similarity between Si and C; however, substitutional Si is rarely observed in h-bn. These results thus suggest that the h-bn patches were converted independently from the same graphene film and that the conversion of graphene to BN pushes the Si impurities into the boundary regions through hopping of the Si atoms. 40 6

7 Supplementary Figure 7. The optical band-gap of converted BNC films with different BN concentrations. (a-e) The optical bandgap and their corresponding UV-vis absorption spectra of BNC films with 0%, 25%, 50%, 85%, and 100% BN, respectively. (f) Optical bandgap versus concentration of BN in the h-bnc films. 7

8 Supplementary Figure 8. Various graphene/h-bn in-plane heterostructure constructed by spatially controlled conversion. (a) Rice Owl demo of graphene/h-bn heterostructures. The Owl is synthesized by a photo-lithography mask of 200 µm in length. (b) A Rice Logo constructed by graphene ribbons embedded in h-bn lattice. (c) and (d) are the close-up look in the highlighted areas in (b). (e) Demonstrated devices transferred onto a flexible substrate. 8

9 Supplementary Figure 9. Vg versus resistance of graphene and h-bnc FETs. Plot of Vg vs R of graphene FETs (a) and the distribution of the mobility (b). Inset: I-V curves under the gating voltage of 0, -20 and 20V. (c, d) Plot of Vg vs R of h-bnc (~60% carbon in atomic concentration) FETs and the distribution of the mobility. Similar curves are measured at both sweeping direction and can be well repeated. Inset: I-V curves under the gating voltage of 0, 50 and 100 V. 9

10 Supplementary Figure 10. Comparison of the performance of h-bnc FETs with FETs based on other materials. The h-bnc FETs are perfect for the applications of flexible FETs with mobility 2~5 orders higher than the reported flexible FETs such as carbon nanotube networks (Mobility: 10~ 100; ON/OFF ratio: 10~10 7 ), p-si (mobility: ~100; ON/OFF ratio: 10 6 ), a-si (mobility: 1, ON/OFF ratio: 10 6 ~10 7 ) and organic FETs (mobility: 0.01 ~1; ON/OFF ratio: 10 6 ~ 10 7 ). 10

11 Supplementary Figure 11. Optimal pathway of nucleation of BN domains around an embedded N atom in a 4 4 graphene supercell. For each step, two C atoms forming a bond are substituted by a BN pair in sequence, following the labeled number. Increasing the supercell size can change substitution energies of some steps, but does not lead to essential change in the pathway. 11

12 G, H, -T S (KJ/mol) Bandgap (ev) a H G T S T (K) b Homogenous domains BN Concentration (%) Supplementary Figure 12. Thermodynamic estimation and bandgap versus BN concentration in the h-bnc films. (a) Reaction free energy (ΔG), enthalpy (ΔH) and entropy (-TΔS) involved in the proposed reaction formula as a function of reaction temperature. The conversion reaction becomes spontaneous (ΔG<0) at sufficiently high temperatures due to the entropic contribution to the total Gibbs free energy. (b) Band gap calculated by GGA as a function of BN concentration for both atomically homogenous h-bnc (like h-bc 2 N sheet, see Supplementary Reference 45) and h-bnc with domains (see Fig. 3). 12

13 Supplementary Tables Supplementary Table 1. E sub, for B, N, and BN pairs to substitute corresponding C atoms at various sites in graphene site E sub (ev) N B BN BNH 2 BNH 4 pristine hydroxyl GB vacancy embedded N embedded B

14 Supplementary Table 2. Calculated E sub for the recursive substitution of C-C bonds with BN pairs along the optimal pathway, in a sequence of 1, 2, as shown in Supplementary Fig. 11. N E sub (ev) N E sub (ev) N E sub (ev)

15 Supplementary Note Supplementary Note 1. UV-visible adsorption can be used to estimate the bandgap of different films. The h-bnc/h-bn samples (~ 1cm 1cm) were transferred onto quartz substrates. Before measurements, a blank quartz plate was used to determine the baseline of spectra. Insets in Supplementary Fig. 7a-e show the transmittance of the h-bnc with 0%, ~25%, ~50%, ~80% and 100% BN, respectively, in the range of 180 ~ 700 nm. The bandgap of each film, E g, could be derived from the Tauc s equation 2 2, where ε is the optical absorbance and ω is the angular frequency h E g of the incident radiation ( 2 /, and λ is the wavelength). The plots of ε 1/2 /λ versus 1/λ are shown in Supplementary Fig. 7a-e. The optical bandgap E g = hc/λ g can be calculated from the intersection point of ε 1/2 /λ with x axis. The optical bandgap for as-converted (Supplementary Fig. 7f) h-bn is ~ 5.6 ev, consistent with previous experimental results. 41,42 It is also in consistent with our previous study on the atomic-layered h-bn grown on Cu substrates. 15 For h-bnc films, two bandgaps locate at ~4 and 1~2 ev can be fitted from the UV adsorption spectra. We contribute them to the h-bn (~4 ev) and graphene nano-domains (1~2 ev), respectively. For h-bnc films, the h-bn and graphene exist in the form of nano-domains and are surrounded by each other. For h-bn, the energy levels between BN and graphene will have some offset, bringing them in contact will probably generate energy levels within the bandgap of BN. Therefore, it will effectively reduce the energy spacing with respect to pure h-bn. For graphene, the bandgap between 1 to 2 ev is found, which is confirmed by the ab-initio calculations. 43,44 15

16 Supplementary Discussion Proposed reaction formula. The substitution reaction can be proposed as: H 3 BO 3 + NH 3 + 2C = BN + CO 2 + H 2 O + CH 4 (1) The total reaction energy from the reactants to the products is 3.05 ev per reaction. We have also checked other products, such as CO, CH 2 O, but find that the corresponding reaction energies become much higher. Note that even CO 2 and CH 4 may not be the final products in our experiments, due to possible post-reactions between the products and reactants. In the main text we proposed a two-step mechanism for the conversion reaction from graphene into BN. First the substitution energy for embedding a single N atom (or B, or BN pair) into graphene is calculated as E sub = E GX+C -E G+X, where E G+X is the total energy of a graphene sheet with an adsorbed X (N or B) atom, and E GX+C is the energy of X-embedded graphene sheet plus a C atom kicked out. The calculated substitution energies are summarized in Supplementary Table 1, all over 1 ev, suggesting that such substitution is unlikely for a pristine graphene sheet. Considering our experimental conditions, hydroxyl groups can be continuously supplied from the feedstock and substrates to react with graphene. So we repeat our energy calculations for N (or B, or BN pair) to substitute the hydroxyl-adsorbed C atom. When the graphene sheet contains hydroxyl-adsorbed C atom, E G+X would be the energy of the sheet with the X atom adsorbed around the functionalized C atom. For the case of monovacancy, E sub is just the formation energy E f = E VX -(E V+X ), where E VX is the energy of the graphene sheet with its vacancy filled by X atom, and E V+X is the energy of the same system but with X atom adsorbed on the perfect graphene region 0.5 nm away from the vacancy. The corresponding substitution energies are provided in Supplementary Table 1. We find that N atoms are much more favorable to substitute the hydroxyl-adsorbed C atoms (substitution energy becomes -1 ev, see Supplementary Table 1), while B atoms energetically remain unfavorable. In addition to the hydroxyl-adsorbed sites, the vacancy defect, edges and grain boundaries 10 can also serve as additional nucleation sites, favoring both the N and B substitutions. Given the high quality of our graphene samples, the nucleation of BN domain should be dominated by the functionalized sites, which agrees with our experimental characterizations showing that the BN nucleation can be ubiquitous in graphene in the initial stage of conversion. Thermodynamic pathway of BN domain nucleation in graphene. Then, the embedded N atoms in the graphene sheet will serve as nucleation sites for further growth of BN domains in graphene. We thus turn to study the substitution of a B atom or a BN pair around the embedded N atom. It is shown that the presence of embedded N atom makes the subsequent substitution of adjacent C atoms much easier and favors the nucleation of BN domain (Supplementary Table 1). To simplify the picture, we take the BNH 4 group (produced by reaction between boric acid and ammonia) as an 16

17 example to investigate the thermodynamic growth of the BN domains in graphene. We calculate the substitution energies E sub of BN pairs at different sites and explore the optimal pathway. In this case, E E + E -E -E, where sub C n-2 (BN) m+1 C2H4 C n (BN) m BNH 4 E is the energy of graphene sheet with m+1 BN pairs embedded, C n-2 (BN) m+1 ECH 2 4 and E BNH 4 are the energies of the C 2 H 4 and BNH 4 molecules (again, the C 2 H 4 cannot represent the final side-product), respectively. The optimal conversion pathway around an embedded N atom in a 4 4 graphene supercell was marked in Figure S11, with the corresponding energetics of the recursive substitutions provided in Supplementary Table 2. All the substitution energies are less than 0.3 ev, rendering the nucleation of BN domains feasible under our experimental temperature. Note that the substitution energies can be further reduced if the C atoms near the BN-graphene interfaces were functionalized with hydroxyl groups. This is likely as the interface C atoms are more active than those in the bulk area. Since the phase mixing is kinetically controlled in the film growth, the true nucleation of BN domains does not necessarily follow the optimal thermodynamic pathway; our extensive calculations show that the thermodynamic path via graphene BC 2 N BN to form atomically homogenous h-bnc film is not impossible under the reaction conditions, as the calculated nucleation energies are higher than those in the domain scenario only by 0.1 ev. 45 Nevertheless, the revealed nucleation mechanism should still dominate the conversion of graphene to h-bn, at least during initial stages. To help understanding the nucleation of BN domains, we also calculate the zigzag and armchair graphene/bn interface energies. The graphene/h-bn interface energy can be estimated as E interface = E hybrid - E graphene - E BN, where E interface is the energy of a system containing a pair of complementary interfaces (spaced by at least 2 nm), and E graphene, and E BN are the energies of perfect graphene and BN sheet of the same atomic numbers as in the interface system, respectively. By extrapolating to large widths we estimate E interface,zz = 0.36 ev/å for the zigzag interface and E interface AC = 0.28 ev/å for the armchair interface. The positive interface energy implies that the system will tend to minimize the total graphene/h-bn interface length by forming triangle shaped h-bn domain initially and then coarsen into large area patches, instead of dispersing into small fragments or isolated BN centers. This behavior is supported by our experiments. The curves for evaluating the temperature dependent Gibb's free energy were calculated by the following formula ΔG =ΔH - T ΔS, where H and S are the enthalpy and entropy, which were taken directly from the experimental data. This estimation didn t consider the intermediate details of reaction pathways, but should still be useful to offer information on the reaction's free energy. According to the formula proposed above, we have 17

18 ΔS =S BN +S H2O + S CO2 + S CH4-2S C S NH3 S B(OH)3 ; ΔH =H BN +H H2O + H CO2 + H CH4-2H C H NH3 H B(OH)3 ; Here, we adopted the enthalpy and entropy of graphene and h-bn as the values of corresponding bulk materials. 18

19 Supplementary References 38 Zhou, W. et al. Direct determination of the chemical bonding of individual impurities in graphene. Phys. Rev. Lett. 109, (2012). 39 Zhou, W. et al. Atomically localized plasmon enhancement in monolayer graphene. Nat. Nano. 7, (2012). 40 Zhou, W. et al. Single atom microscopy. Microscopy and Microanalysis 18, (2012). 41 Kubota, Y., Watanabe, K., Tsuda, O. Taniguchi, T. Deep ultraviolet light-emitting hexagonal boron nitride synthesized at atmospheric pressure. Science 317, (2007). 42 Li, L. H. et al. Single deep ultraviolet light emission from boron nitride nanotube film. Appl. Phys. Lett. 97, (2010). 43 Zhao, R., Wang, J., Yang, M., Liu, Z. Liu, Z. BN-embedded graphene with a ubiquitous gap opening. J. Phys. Chem. C 116, (2012). 44 Son, Y.-W., Cohen, M. L. Louie, S. G. Energy gaps in graphene nanoribbons. Phys. Rev. Lett. 97, (2006). 45 Lu, P., Zhang, Z. H., Guo, W. L. Electronic structures of BC 2 N nanoribbons. J. Phys. Chem. C 115, (2011). 19