Ni films were evaporated by Molecular Beam Epitaxy (MBE) in a UHV chamber (residual pressure less than 10⁻⁹ mbar) equipped with a RHEED. Ni atoms were evaporated with an electron gun (10 kW) from a Ni ingot in a crucible (purity 99.999%; Root Mean Square roughness (RMS) 2.29 nm) with a working pressure of around 10⁻⁸ mbar. The internal walls were continuously cooled down to 77 K. During the growth the Ni films thickness was measured by a quartz balance and ex situ checked by Rutherford Backscattering Spectrometry (RBS). The deposition rate was estimated to 0.03 nm∙s⁻¹. MgO(111) (10 × 10 × 0.5 mm³) samples were purchased from Crystal GmBH. They were preliminary cleaned with an ultrasonic bath filled with acetone and isopropanol. Each operation was repeated two times for 10 min. Then the substrate is set on a rotating Molyblock substrate holder into the UHV chamber and subsequently cleaned at 773 K (12 hours) and 1023 K (1 hour) according to [24] . The temperature was measured by contacting a thermocouple settled on the backside of the substrate holder. The growth was monitored by RHEED with 20 kV electrons. RHEED observations along the azimuth of MgO have been monitored at the different steps of the growth, i.e. preparation of the MgO substrate, germi- nation, growth, coalescence and final annealing. The main characteristics of the samples prepared are summa- rized in Table 2.

^aAfter carbon implantation at 300 K.

Samples, further named as Ni/MgO_X (1 ≤ X ≤ 6), were prepared by a four step process including a common cleaning step, a germination step at 605 K (X = 1 - 2) or 635 K (3 ≤ X ≤ 6) followed by a growth step at 873 K (X = 4 - 6) and a final annealing at 1015 K (X = 5) or 1173 K (X = 6). This last step was achieved in a UHV furnace (base pressure 2 × 10⁻⁹ mbar) equipped with a silica reactor. Therefore the annealing was achieved at three temperatures: 1) during ion implantation at 873 K (X = 1 - 4); 2) Post-thermal treatments at 1015 K (X = 5) and 3) at 1173 K (X = 6) after room temperature implantation. Each preparation included two samples. The first sample was used solely for the steps of the process and carefully stored in a desiccator meanwhile. The second one was devoted to characterization studies (EBSD, SEM, RBS, NRA,…) between each step of the process. The reason for this doubling was that deposition of surface hydrocarbon and carbon incorporation as impurity might occur during handling and characterization studies. However, unless otherwise stated, we did not find significant differences in carbon content between the two sets of samples. Finally, as we want to minimize the thickness of the nickel films, the overall thickness of the samples does not exceed 420 nm.

The Ni/MgO samples were implanted with ¹³C ions at a fluence of 1.4 × 10¹⁶ at∙cm⁻² from a ¹³CO source (EURISO-TOP, purity 99%), corresponding to around 4 equivalent graphene monolayers (EGM), as one EGM is quoted to 3.6 × 10¹⁵ at∙cm⁻² for a graphene surface. The implantation was carried out at a vacuum pressure of 2 × 10⁻⁶ mbar and at 873 K for Ni/MgO_X samples (1 ≤ X ≤ 5) using a heated substrate holder in Inconel alloy. The duration of the implantation process was around 1 hour. The heating and cooling rates were around 20 K/min for the implantation occurring at 873 K. The temperature at the sample surface was calibrated by using both a thermocouple settled on the back of the substrate holder and an extinction pyrometer in front of the sam- ple. The sample Ni/MgO_6 was implanted with 4 EGM at room temperature (however the true temperature during the carbon implantation was estimated to around 350 K) followed by a UHV thermal annealing at 1173 K.

Ion Beam analyses were performed using the 4 MV Van De Graff accelerator facility of ICube. RBS and NRA were carried out either in a random or in a channeling mode. In the last case, the samples were settled on a go- niometer to accurately tune the angle θ for which the backscattered ions can be channeled with a resolution of the order of 10 keV.

RBS experiments were carried out with 2 MeV incident alpha particles (1 × 1 mm²), a 10 nA intensity current, and a 160˚ scattering angle. The pressure inside the analysis chamber during the analysis was around 10⁻⁶ mbar. The thicknesses of the Ni films were determined by RBS in the random mode before and after the implantation and/or thermal post-treatments. RBS in the channelling mode was used to determine the crystallisation level of the Ni films.

Moreover, to determine the evolution of ¹²C (as impurity), ¹³C and O concentrations after each treatment, Nuclear Reaction Analyses (NRA) were performed. The ¹²C(d, p)¹³C, ¹³C(d, p)¹⁴C, ¹⁶O(d, p₁)¹⁷O and ¹⁶O(d, p₀)¹⁷O reactions were recorded with a 900 keV deuterons beam on a 1 × 1 mm² area. A 150 mm² silicon surface barrier detectors was mounted at an angle of 150° to the beam direction resulting in a total solid angle of Ω―60 msr. An absorber of 11.8 μm Mylar foil was attached above the detector to stop the alpha particles generated by the ¹⁶O(d, α)¹⁴N reaction and the backscattered deuterons particles. The experimental spectra were calibrated by using bare SiO₂ and SiC samples for oxygen and carbon nuclear reactions, respectively, and the spectra were then simulated with the SIMNRA software [30] . Due to the weak depth resolution of the NRA, it is not possible to differentiate surface or interface carbon from bulk carbon. Therefore this technique is allowed to determine only the overall carbon amount.

To characterize the surface of the implanted samples, SEM observations were carried out using a Scanning Electron Microscope (JEOL 6700F-2001) provided with a field emission gun in the Secondary Electron Image mode at low voltages (1 - 3 kV) more sensitive to the chemical contrast. The pressure in the analysis chamber was determined at around 10⁻⁶ mbar. The electron backscattered diffraction (EBSD) diagrams were acquired us- ing a TESCAN (Vega II XMU) scanning electron microscope, provided with a tungsten electron gun and equipped with an EDAX-TSL EBSD package, operating at 30 kV and a working distance of 23 mm. The pres- sure in the observation chamber was around 10 Pa. EBSD patterns (i.e. Kikuchi lines) were calibrated using a Si single crystal (space group Fm3m with a lattice spacing a = 5.431 Å). Kikuchi diagrams had been clearly ob- served at 30 kV and point analyses with more than 100 points were performed to check the orientation of the nickel plans. Data were processed with an OIM analysis (TSL/EDAX) software. Typical EBSD images are re- ported in Supplementary Material 1 (SM1).

The Atomic Force Microscopy (AFM) measurements were performed on a NT-MDT Stand Alone SMENA set-up used in the resonant mode AFM Semicontact. Non-Contact Mikro Mash NSC 18 cantilever scanning probes were used with a minimum scanning step of 0.012 nm. Root Mean Squares (RMS) are determined on full images of size 100 μm².

Raman spectroscopy was carried out using a Horiba spectrometer LabRam at 532 nm equipped with a CCD camera. Spectra and images were recorded using a ×100 magnification, with a power energy of 0.9 mW and a fluence of 2.25 mW∙µm⁻² in order to avoid damages to the graphene film.

X-ray photoemission spectra were recorded with a 150 mm hemispherical detector VSW with an overall res- olution of 0.65 eV under a base pressure of 5 × 10⁻⁹ mbar using a monochromatic AlK_α source. Energy refer- ences are set using the HOPG C1s core level at 284.6 eV.

The Figure 2 displays one characteristic set of RHEED patterns recorded at different steps of the preparation process on Ni/MgO_5 sample. Previous RHEED observations highlight the importance to distinguish a germi- nation step at a rather low temperature increasing the grain density from a growth step at higher temperature promoting the coarsening and the coalescence of the oriented grains. Moreover in agreement with literature [25] [31] , an annealing step at higher temperature has been added after the growth step in order to improve the sur- face morphology.

In Figure 2(A) the RHEED pattern of MgO(111) substrate after in situ pretreatment at 1023 K displays rather wide bars. This broadening is likely due to some charge effects. This diagram is characteristic of a (111) surface without reconstruction, the bars displaying intensity modulations due to some surface roughness. Indeed the RMS of MgO(111) have been quoted to 1.6 ± 0.1 nm. The Figure 2(B) recorded after 100 nm Ni deposition at 635 K shows the RHEED diagram characteristics of an epitaxy of Ni on MgO(111) according to the orientation relationships Ni(111) //MgO(111). The form of the diagram undergoes only few evolutions, whe- reas the distance between the bars has increased. Ni and MgO have the same fcc structure, but with a different surface (111) lattice spacings of 0.249 nm and 0.298 nm, respectively (Table 1). Taking as a reference the bar spacing of MgO(111) in Figure 2(A), one can evaluate the lattice parameter of the nickel deposited, from the interval distance between the bars, at 0.353 nm, a value close with 0.35239 nm expected for bulk nickel. The difference is beyond 1% and may be attributed to the uncertainty of the measurements. Furthermore the intensity modulations of the bars are due to the nature of the growth which is of 3D type with the germination of oriented dots. Subsequent 300 nm growth at 873K shows less intensity modulations of the RHEED bars (Figure 2(C)), as the Ni islands become larger and coalesce. The accuracy of the RHEED patterns however is limited. There-

fore the 3D diffraction cannot clearly distinguish the twin formation, i.e. whether a single or a two-domain <111> oriented film is formed corresponding to the ABC or the ACB stacking modes, each of them turned by 180˚ from the other one around [111], respectively. One illustration of these growth modes is displayed in Sup- plementary Material 2 (SM2).

The Figure 3(A), Figure 3(B) and Figure 3(D)-(F) show the SEM and AFM images of samples Ni/MgO_3-5, respectively. These samples are obtained with different temperatures of ultimate growth or post-treatment at 635 K (Figure 3(A), Figure 3(D)), 873 K (Figure 3(B), Figure 3(E)) and 1023 K (Figure 3(C), Figure 3(F)), respectively. After deposition at 635 K it can be seen that small grains of some µm² size are not fully coalesced with the presence of dark pit sat boundaries, and also some protrusions whose origin is not known (Figure 3(A)). After subsequent growth at 873 K only few holes still exist as stitches, testifying that the coalescence is almost but not completely achieved (Figure 3(B)). After further annealing at 1015 K with a thicker film of 420 nm the holes have now completely disappeared and the morphology is now a film completely covering the surface, even if some roughness is apparent due to the plug of the remaining pits (Figure 3(C)). This is confirmed by the AFM images, as well as by the RMS measured on the surface of typical grains reported in Table 2. A high RMS is obtained on the sample Ni/MgO_1 due to the presence of large pits between the grains. We also note that the thickness is around 200 nm with the lowest deposition temperatures instead of 300 nm or more for the other samples. More AFM images on samples Ni/MgO_1-2 are displayed in Supplementary Material 3 (SM3).

The determination of the orientation of the nickel domains has been achieved by EBSD with an indexed dif- fraction figure (Figure 4(C)). The Figure 4(B) displays the pole figures obtained on a 300 nm Ni film deposited at 635 K with one single orientation by contrast with the growth performed at 605 K (Figure 4(A)). Then the double orientation within a 180˚ rotation around the 111 pole normal to the surface is present with similar intensities. This is rather in good agreement with the literature data that state that a transition between a two-domain to a single domain nickel film occurs between 473 K and 573 K [25] . The reasons for this transition are not com- pletely clear but are probably due to long range interactions between the first Ni layer and MgO subshells that promote favorable orientation of the nuclei [31] .

The true thicknesses of the metallic films have been determined by RBS (Table 2). The Figure 5 shows typi- cal RBS spectra recorded on the Ni/MgO_1 sample, one set in Figure 5(A) before (black) and after (red) carbon implantation, and another set in Figure 5(B) after carbon implantation in the channeling mode (black) and in the random mode (red), respectively. In addition to Ni, Mg and O are also detected. The surface and interface

levels are rather steep before and after carbon implantation with an energy range ΔE_Ni corresponding to 186 nm in both cases. This reveals that the effect of surface Ni sputtering by implantation of carbon ions is negligible. When the beam of α-particles is channeled along the [111] direction, the beam is much less backscattered as in- dicated by the notable decrease of the RBS signal of nickel in the channeling mode. The small signal, around 15% of the random signal, is relied therefore to defects in the Ni monocrystalline array due to local backscattering. This signal increases along the deepness of the Ni film with a crystallinity factor estimated as where I_channel and I_random are the RBS intensities in the channeling and in the random modes at a given deepness, respectively. This result strongly confirms the good crystallization and the [111] orientation of the Ni films. The thicknesses of the Ni films determined by RBS reported in Table 2 are in rather good agreement with the measured ones by quartz microbalance.

Previous works [23] have shown that many carbon impurities are incorporated into the Ni films during the Ni growth as well as during the carbon implantation process, leading to an excess of carbon. To disentangle be- tween the true carbon coming from the implantation process and the pollution carbon incorporated at any step of the process, we have used the ¹³C isotope, which is only 1.07% of natural carbon.

Figure 6 shows the near-gaussian profile of the ¹³C distribution after implantation at 20 and 50 keV simulated by SRIM software. At these energies the carbon is implanted only into the nickel film whose thickness is at least 185 nm. The mean implantation depths (projected ranges R_p) are 24 nm and 58 nm and the longitudinal straggles (ΔR_p, almost half width at half maxima) are 19 and 37 nm for carbon implantation energy of 20 keV and 50 keV, respectively.

The ¹³C isotope with a fluence of 1.4 × 10¹⁶ at/cm² corresponding to 4 EGM have been implanted at 873 K and room temperature. The implantation at a high temperature induces concomitantly carbon atoms diffusion into the nickel film. As the carbon solubility in Ni decreases when temperature is decreasing the carbon atoms segregate towards the surface also when cooling after the implantation. The diffusion towards the interface Ni/MgO is unlikely considering the projected ranges and the longitudinal straggles used (Figure 6).

The Figures 7(A)-(C) display SEM images of the samples Ni/MgO_2-4 after carbon implantation, respectively. At low thickness corresponding to sample Ni/MgO_1, the nickel film is not stable during carbon implantation (see Supplementary Material 4 (SM4)). However an evolution of the morphology with the thickness of the film and the implantation energy can be noted. On samples Ni/MgO_2 and Ni/MgO_3 the implantation energy is the same (20 keV), but the thickness of the Ni film is changing from 275 to 325 nm. Dark fragments corresponding to TLG with sizes ≤ 2 µm² are located mainly around grain boundaries and are not very well-defined. On both samples TLG fragments are mainly relied to the presence of grain boundaries and other point defects, as for polycrystalline Ni films [23] . Preferential nucleation occurs due to preferential carbon diffusion along these grain boundaries or defects. Their presence could be related to an uncompleted coalescence of the oriented nickel particles at around 300 nm thick, but also to the damages created by the implantation process, especially at rather low implantation energy of 20 keV. As seen in the simulation profile of Figure 6 a large amount of carbon is let at the surface at low implantation energy, creating nucleation centers for further growth of TLG from carbon implanted into the bulk diffusing to the surface. Contrasts in the TLG fragments are due to variations of the thickness of the graphitic layers.

By contrast on sample Ni/MgO_4, prepared with implantation energy of 50 keV with similar thickness, the surface sample is relatively seamless with no preferential location of the TLG fragments (Figure 7(C)). The ger- mination density is far less dense, and the TLG fragments exhibit now clear 6-fold symmetry with size up to 5 µm². The edge facets exhibit angles multiple of 60˚, corresponding to the hexagonal graphite structure. Again some grey level contrasts suggest thickness variations, even inside a single fragment. On Ni/MgO_4-6 samples, the TLG are larger and better facetted than TLG grown on polycrystalline Ni/SiO₂ samples (see Figure D of Supplementary Material 4).

The AFM images (Figure 7(E), Figure 7(F)) confirm the increase of the grain sizes and the roughness on the surface of a Ni grain. Thus RMS of 3.9 nm and 6.2 nm are measured after implantation on Ni/MgO_4 and Ni/MgO_3 samples, respectively, instead of 3.1 nm and 2.4 nm before implantation, respectively. The overall roughness generally increases with the carbon implantation at 873 K (Table 2). Many physical phenomena oc- curring during heated implantation can explain this behavior: 1) diffusion of activated Ni atoms that promotes a

restructuration of the Ni grain surface but also a separation between the grains not completely coalesced; 2) cre- ation of defects by sputtering of the surface with impinging carbon atoms. However the absence of any RMS change on Ni/MgO_6 sample, after carbon implantation but before heat treatment at 1173 K, indicates that Ni sputtering by ion implantation can be neglected. The TLG fragments density strongly decrease with the TLG mean area (see Supplementary Material 5 in the case of Ni/MgO_3 sample), suggesting a unique and fast path- way of carbon diffusion inside Ni films.

The polar figure of the Ni films determined by EBSD (see Supplementary Material 6 (SM 6) completed with SEM images) before and after the carbon implantation reveals no modification on the crystallographic orienta- tion, even if the surface are more disturbed after carbon implantation.

The NRA experiments have been performed at each step of the overall process described in Figure 1 in order to determine the origin of ¹²C carbon impurities in addition to the implanted carbon ¹³C, the concentration and the localization of carbon inside Ni films. The Figure 8(A) shows NRA spectra in the random mode obtained on Ni/MgO_1 sample before and after the ¹³C implantation at 873 K with a fluence of 4 EGM. The ¹⁶Op₀, ¹⁶Op₁, ¹²Cp and ¹³Cp signals at 1140 keV, 1970 keV, 2760 keV et 5740 keV are due to the nuclear reactions ¹⁶O(d, p₀)¹⁷O, ¹⁶O(d, p₁)¹⁷O ,¹²C(d, p₀)¹³C and ¹³C(d, p₀)¹⁴C, respectively. The NRAs involving oxygen are included to ascertain the stability of the data collection, as the oxygen concentration is assumed unchanged by the implanta- tion. The results are summarized in Table 3 where the carbon concentrations determined with the software SIMNRA are given in EGM. It can be seen that ¹²C is incorporated into the film both during the nickel deposi- tion (black curve of the ¹²C(d, p₀)¹³C inset) as well as during the implantation itself (red curve of the ¹²C(d, p₀)¹³C inset). This has been already shown with polycrystalline nickel films evaporated on SiO₂/Si [23] . The raw signals must be corrected by the NRA cross-sections which are 25.9 mb/sr [32] and 2.36 mb/sr [33] for ¹²C(d, p)¹³C and ¹³C(d, p)¹⁴C reactions, respectively. Thus the error bars are estimated to around 1 and 2 EGM, respec- tively. Moreover we are not able to differentiate between the carbon surface and the carbon diluted into the Ni layer, as NRA is a bulk-sensitive technique. Within these limitations, it can be inferred from the results of Table 3 that:

1) The overall ¹³C concentration is in the range 20% - 25% of the overall carbon concentration.

2) ¹²C incorporation as impurity occurs both during the Ni sample preparation, and mainly during the ¹³C im- plantation. This is bulk pollution inside the nickel film as Raman investigations fail to evidence any carbon sig- nal on the Ni surface before the annealing at 873 K.

The incorporation of ¹²C has been discussed in greater details elsewhere [23] .

In addition we have determined by NRA in the channeling mode the localization of each carbon isotope into the metallic matrix (Figure 8(B)). In both cases the NRA signal due to carbon remains unchanged. This infers that the carbon is randomly located outside the channels of the [111] direction, rather than in interstitial sites of the Ni cfc structure.

The Figure 9(C), Figure 9(D), Figure 9(H), Figure 9(I) and Figure 9(M), Figure 9(N) show the Raman mappings of the G and 2D bands on the Ni/MgO_3, Ni/MgO_4 and Ni/MgO_6 samples, recorded in the 1100 - 1750 cm⁻¹ and 2695 - 2800 cm⁻¹ ranges, respectively. The mappings are recorded on an area of 10 µm² with an increasing intensity scale from dark to bright. Moreover, to illustrate the chemical contrast between the dark and the bright zones observed on the optical images of Figure 9(A), Figure 9(F) and Figure 9(K), several individual Raman spectra are displayed on Figure 9(B), Figure 9(G) and Figure 9(L), respectively.

Similar results have been obtained on Ni/MgO_1, Ni/MgO_2 and Ni/MgO_5 samples. The optical images (Figure 9(A), Figure 9(F) and Figure 9(K)) show dark TLG fragments formed during implantation/surface segregation. The contrast is however weaker in Figure 9(K) of Ni/MgO_6 sample. These TLG fragments display variable sizes, up to 4 µm² for sample Ni/MgO_3 and up to 10 µm² for sample Ni/MgO_4, but more than 100 µm² on Ni/MgO_6 sample. Corresponding typical Raman spectra (Figure 9(B), Figure 9(G) and Figure 9(L)) are collected on the edge or inside the TLG fragments at locations labelled in the images (Figure 9(A), Figure 9(F) and Figure 9(K), respectively). As expected the Raman spectra exhibit a G band at around 1565 - 1580 cm⁻¹ and 2D band at around 2670 - 2700 cm⁻¹. The G band is the one-mode Raman vibration characteristic of graphitic carbon [34] . The 2D band is a multiple step mode of carbon vibration whose intensity, shape and wave

number are sensitive to the interaction with the substrate, to the thickness of the graphene layers, to the ordering within the graphene layers in the direction c normal to the graphene planes and to the presence of either impurities or doping atoms, or vacancies, or functionalized molecules [35] . The detection of such 2D band is a strong indication that the ordering of the graphene planes starts to occur. Furthermore as soon as graphitic domains display either structural defects or size-limited dimensions a D band at around 1360 cm⁻¹ will appear [36] . Finally on sample Ni-MgO_3 a D’ band around 1615 - 1620 cm⁻¹ as a shoulder of the G band can be seen that is due to rolling, wrapping or rippling of the TLG sheet. Contrasts from different fragments or within the same TLG fragment are probably due to variable thickness as indicated by the variable intensity of the G band (Figure 9(F), Figure 9(G) and Figure 9(K), Figure 9(L) for Ni/MgO_4 and Ni/MgO_6 samples, respectively).

The mappings show rather steady intensity of the G and 2D bands on the large TLG fragment of the Ni/MgO_4 sample, while the distribution is more variable with the small TLG fragments of the Ni/MgO_3 sam- ple and on the large TLG fragment of Ni/MgO_6 sample.

Some other Raman characteristics of the Ni/MgO_X samples are reported in Table 4. The strong intensity of the 2D band on Ni/MgO(111)_6 sample, as well as the narrowing of all the D, G and 2D bands, compared to any other Ni/MgO sample confirm an ordering of the graphene plans in the c direction and an advanced graphitiza- tion due to the high pretreatment temperature. The ratio I_D/I_G is sensitive to the structural disorder as well as the size limitations of the films [37] . Among samples implanted at high temperatures, the ratio I_2D/I_G is increasing with Ni/MgO_4 sample, whereas the Full Widths at Half maximum (FWHM) of G and 2D bands are decreasing, as expected from a better ordering of the graphene layers.

On Figure 9(E), Figure 9(J) and Figure 9(O) Raman mappings of the ¹³C concentration on TLG fragments are displayed. The ¹³C concentrations c are calculated from the downshift of the G band wavenumber Dω_i according to Equation (1), assuming random isotope distribution and equal bond force constants [38] :

where ω₀ is the frequency of the given Raman mode G in the ¹²C implanted sample (ω₀(G) = 1581 cm⁻¹), C₀ is the ¹³C concentration in the ¹²C samples (¹³C natural abundance = 0.0107). The isotopic distributions are rather uniform on a single fragment, around 30% - 40%, 40% - 50%, and 40% - 50% on Ni/MgO_3, Ni/MgO_4 and Ni/MgO_6 samples, respectively. Thus the ¹³C concentrations determined by Raman spectroscopy are stronger than the ¹³C concentrations determined by NRA (Table 3). However it should be reminded that the later probe is both a bulk- and surface-sensitive probe, whereas the former one is only a surface-sensitive probe. Moreover the downshift of the 2D or G wavelengths can also be sensitive to other parameters, such as the thickness of the graphitic fragment, the occurrence of either impurities, or doping, or vacancies or functionalized adsorbents. However these last effects infer rather weak amplitude of the shift compared to the ¹³C isotopic effect, so that the main conclusions may be still valid.

Finally we have estimated the mean thickness of surface carbon concentration by angular XPS measurements on the Ni/MgO_3 sample (Figure 10). The XPS carbon signal C1s obtained on this signal I_Gene is continuously recorded along with the C1s signal of the HOPG graphite I_Gite taken as reference.

Assuming that the mean free path of the inelastic process of carbon λ_C is the same on both samples and that the surface is continuously covered by a carbon layer of thickness e, e can be extracted from the ratio of the C1s signal. Indeed I_Gene can be expressed as [22] :

where θ is the angle between the normal to the sample surface and the electron detector, A is a constant geome- tric factor, σ_C1s is the C1s photoelectron cross section, N_Gene and λ_Gene are the carbon atomic density and the mean free path of photoelectron in the graphene layers. On a HOPG reference, the C1s signal with infinite carbon layer I_Gite is expressed as:

Taking the ratio from Equations (2) and (3) and assuming that the mean free path of the inelastic process on C1s level is around the same on both samples, ie, and the atomic densities are identical on graphene layers and graphite, ie, the thickness e can be extracted by the following re- lation (4):

The mean thickness is thus extracted from the slope of the plot of Equation (4) (Figure 10(B)) by varying θ with λ_C = 2.1 nm [39] . The mean thickness extracted is quoted to 5 ± 0.5 EGM. This value is in rather good agreement with the dose of implanted carbon (around 3.3 EGM), but lower than the measured amount of carbon by NRA estimated to 13.2 EGM (Table 3). However, we must remind that NRA encompasses both surface and bulk carbon. Therefore, it is presumed that carbon remains diluted into the Ni matrix, e.g. EGM for Ni/MgO_3 sample.