Synthesis of vacant graphitic carbon nitride in argon atmosphere and its utilization for photocatalytic hydrogen generation

Graphitic carbon nitride (C3N4) was synthesised from melamine at 550 °C for 4 h in the argon atmosphere and then was reheated for 1–3 h at 500 °C in argon. Two band gaps of 2.04 eV and 2.47 eV were observed in all the synthetized materials. Based on the results of elemental and photoluminescence analyses, the lower band gap was found to be caused by the formation of vacancies. Specific surface areas of the synthetized materials were 15–18 m2g−1 indicating that no thermal exfoliation occurred. The photocatalytic activity of these materials was tested for hydrogen generation. The best photocatalyst showed 3 times higher performance (1547 μmol/g) than bulk C3N4 synthetized in the air (547 μmol/g). This higher activity was explained by the presence of carbon (VC) and nitrogen (VN) vacancies grouped in their big complexes 2VC + 2VN (observed by positron annihilation spectroscopy). The effect of an inert gas on the synthesis of C3N4 was demonstrated using Graham´s law of ammonia diffusion. This study showed that the synthesis of C3N4 from nitrogen-rich precursors in the argon atmosphere led to the formation of vacancy complexes beneficial for hydrogen generation, which was not referred so far.

UV-vis diffuse reflectance spectroscopy. UV-Vis diffuse reflectance spectra (DRS) were recorded with a spectrophotometer Shimadzu UV-2600 (IRS-2600Plus, Japan) in the range of 220-1000 nm. The reflectance spectrum was transformed to the Kubelka-Munk function F(R) as follows: where R is the diffuse reflectance from a semi-infinite layer. The values of band gap energies (E g ) were determined according to well-known Tauc procedure 42 as follows: where ε is the molar extinction coefficient, hν is the energy of incident photons, C is a constant and p is a power depending on the type of electron transition. The power p = 2 and p = ½ are for direct and indirect semiconductors, respectively. In this work p = ½ 43 .
Photoluminescence spectroscopy. Photoluminescence (PL) and excitation spectra were recorded by a FLSP920 Series spectrometer (Edinburgh Instruments, UK) using an Xe900 arc non-ozone lamp 450 W (Steady State Lamp) and an R928P PMT detector. The PL spectra were measured in the range from 400 to 600 nm. X-ray diffraction analysis. The X-ray diffraction (XRD) analysis was carried out by means of a Rigaku SmartLab diffractometer (Rigaku, Tokyo, Japan) with a detector D/teX Ultra 250. A source of X-ray irradiation was a Co tube (CoKα, λ 1 = 0.178892 nm, λ 2 = 0.179278 nm) operated at 40 kV and 40 mA. XRD patterns were recorded between 5° and 90° of 2θ with the step size of 0.01° and the speed of 0.5 deg min -1 . The crystallite size L was calculated using Scherrer´s equation for broadening B (2θ) (in radians) at a half maximum intensity (FWHM) of a diffraction band as www.nature.com/scientificreports/ where λ is the wavelength of X-rays, θ is Bragg´s angle and K is the constant equal to 0.94 for cube or 0.89 for spherical crystallites. In this work K = 0.90.
Fourier transform infrared spectroscopy. Fourier transform infrared (FTIR) spectroscopy was performed using a Nicolet iS50 device (Thermo Scientific, Waltham, MA, USA). The samples were prepared by the KBr pellet technique. A small amount of sample was mixed and homogenised with KBr (approximately 200 mg) and pressed at the pressure of 20 MPa to obtain a transparent tablet. FTIR spectra were collected in the range of 500-4000 cm −1 with the resolution of 2 cm −1 . Each spectrum consisted of at least 64 scans lasting 1 s.
X-Ray photoelectron spectroscopy. Superficial elemental analysis was performed by means of an X-ray photoelectron spectrometer (XPS) ESCA 3400 (Kratos Analytical Ltd, UK) with the base pressure in the analysis chamber of 5.0 * 10 −7 Pa. Powdered materials were placed on top of a conductive carbon tape. Electrons were excited with Mg Kα radiation (hν = 1253.6 eV) generated at 12 kV and 10 mA. For all spectra, the Shirley background was subtracted. Peaks ascribed to sp 2 hybridized nitrogen (C=N-C) were set to 398.8 eV as a charge correction.
Physisorption of nitrogen. Specific  Photoelectrochemical measurements. Photoelectrochemical measurements were conducted using a photoelectric spectrometer equipped with a 150 W Xe lamp and coupled with a potentiostat (Instytut Fotonowy, Poland). Photocurrent responses were recorded using a classic three-electrode setup. Ag/AgCl and platinum wires were used as reference and counter electrodes, respectively. The working electrode was prepared as follows: 20 mg of powdered material was suspended in 150 µL drops of ethanol and ultrasonicated for 15 min. Afterwards, 45 µL of the suspension was deposited onto an indiumtin oxide (ITO) foil and a uniform layer was created using a film applicator (Elcomoter 3570). The foil with the layer was dried at 80 °C resulting in an adsorbed material on an ITO surface creating conductive connection. The 0.1 mol L −1 KNO 3 solution was used as an electrolyte. Photocurrent spectra were recorded within the range of 240-450 nm (with the step of 10 nm) in the presence of the external potential range of 0.2-1.0 V (step 0.1 V).

Mott-Schottky measurements.
Mott-Schottky measurements were performed using a Metrohm Autolab PGSTAT302 (Herisau, Switzerland) potentiostat. A glassy carbon electrode (GC), Ag/AgCl (3 mol L −1 KCl) electrode and a Pt sheet served as working, reference and counter electrodes, respectively. All electrodes were purchased from Metrohm. The Mott-Schottky measurements were performed twice with an AC signal having an amplitude of 10 mV and a frequency of 300 Hz. The validity of single-frequency Mott-Schottky measurement was checked by a more rigorous approach involving the determination of surface capacitances from a series of full electrochemical impedance spectra recorded at different potentials (for details refer to Supplementary material).
A thin layer of the materials was prepared on the GCE surface as follows. The powdered CN and CN-Ar materials, each in the amount of 10 mg, were added into 5 mL of deionized water, and then the mixtures were subjected to 30-min sonication in an ultrasonic bath. Then, 30 μL of the dispersion was dropped on the GC surface and dried at 85 °C for 3 h. The samples were measured in the 0.1 mol L −1 KCl aqueous solution, which was purged by nitrogen for 30 min before the experiment.
Photocatalytic experiments. The photocatalytic activity of the CN and CN-Ar materials was investigated in terms of hydrogen generation. The photocatalytic experiments were performed in a stirred batch photoreactor (stainless steel, volume 348 ml, Fig. 1S in Supplementary materials). The reaction mixture contained 100 mL of 50% methanol with a photocatalyst (0.1 g) and was saturated with helium to purge air and to saturate the solution. An 8 W Hg lamp (254 nm; Ultra-Violet Products Inc.) was used as an irradiation source and was placed on a quartz glass window on top of the photoreactor in horizontal position (Fig. 1S). The reactor was tightly closed and before the reaction started (switching on the lamp), a gaseous sample was taken (at time 0 h) through a septum with a syringe. All the gaseous samples were analysed by a gas chromatograph (Shimadzu Tracera GC-2010Plus) equipped with a barrier discharge ionization detector (BID). The reaction mixture was irradiated at certain time intervals (0-4 h) and samples were taken at 1, 2, 3 and 4 h for the GC analysis. Three reaction products were determined: hydrogen, methane, and carbon monoxide. A source contribution consisting of two components with lifetimes of ≈ 368 ps and ≈ 1.5 ns and corresponding intensities of ≈ 8% and ≈ 1% was always subtracted from the spectra. Decomposition of positron lifetime spectra into exponential components was performed using a dedicated code PLRF 45 .

Positron annihilation spectroscopy.
Ab-initio theoretical calculations of positron lifetimes were employed in order to identify defects in the CN and CN-Ar materials. Positron lifetimes were calculated using density functional theory within a so-called standard scheme 46 . In this approximation, the positron density is assumed to be vanishingly small everywhere and not affecting the bulk electron structure. At first, electron density n -(r) in the material was being solved without a positron. Subsequently, the effective potential for positron was constructed by the superposition of the Coulomb potential produced by the charge distribution of electrons and nuclei and the electron-positron correlation potential 47 . The ground state positron wave function Ψ + (r) was calculated by solving a single-particle Schrödinger equation for a positron in the effective potential. The positron lifetime was determined using an overlap of the electron and positron densities and positron density n + (r) = ψ + (r) 2 through the expression where r e is the classic electron radius, c is the speed of light, and γ denotes the electron enhancement factor describing the pileup of electrons at the positron site. The electron-positrons correlation, i.e. the correlation potential and the enhancement factor γ , were treated within the generalized gradient approximation (GGA) using the scheme developed by Barbiellini et al. 48,49 . C 3 N 4 tri-s-triazine (heptazine) ring-based layered structure was considered in the calculations 26 . Heptazine rings are cross-linked by triangular nitrogen atoms forming a two-dimensional honeycomb lattice. The interlayer distance between the heptazine layers is 3.19 Å 50 and the lattice parameter of 1 × 1 unit cell is 7.14 Å 51 . Ab-initio calculations were performed using 3594 atom-based supercells (consisting of 1536 C and 2048 N ions). Defects were modelled by removing the corresponding number of C or N atoms from the supercell. Convergence tests with respect to the supercell size revealed that the calculated positron lifetimes converged within ± 1 ps.  Table 1.

Results and discussion
By comparing these band gaps with the SSA changing from 15 to 18 m 2 g −1 (Table 1), it is indicated that no exfoliation occurred during the heating of CN-Ar0 for 1-3 h. If CN-Ar0 were exfoliated, the band gaps would have increased due to a quantum size effect, but it was not observed. The spectrum of the CN material used for comparison demonstrates only one absorption edge corresponding to the band gap of 2.65 eV. The new band gaps of 2.02-2.09 eV were also observed by several authors 29,33 due to the presence of structure defects. The light absorption extension in UV-Vis DRS spectra was also observed by Lv et al. 28 .
The second band gaps of the CN-Ar materials were very similar, that is, from 2.46 to 2.48 eV. On the contrary, the band gaps of the CN materials further heated in air increased from 2.72 to 2.77 eV due to its exfoliation. It www.nature.com/scientificreports/ was also documented by increasing their SSA values, see Table 1S and Fig. 4S. The CN-Ar materials were further studied by PL, XRD, FTIR and XPS.
Photoluminescence study. The photoluminescence spectra of the CN and CN-Ar materials were recorded, see Fig. 2. The broad CN band at around 480 nm (2.58 eV) corresponds to transition of photoinduced electrons from a conduction to valence band. The PL bands of the CN-Ar materials were red-shifted at about 500-510 nm (2.48-2.43 eV) and were broader than the PL band of CN. The PL maxima well agree with the band gap energies mentioned above. The red-shift, the band broadening and the PL intensity decrease can be explained by non-radiative transmission of excited electrons to mid-gap levels of N defects 29,30,33,34,[52][53][54] , from which they radiatively return to the valence bands. The PL effects mentioned above ascribed to the N vacancies were observed for C vacancies 55 as well. Moreover, another contribution to the band broadening and the red shift is the presence of the second band gap of 2.04 eV as a result of nitrogen defects. In addition, the PL intensity decreased with the increasing time of heating; the PL intensities of CN-Ar2 and CN-Ar3 were similar. This can be caused by the higher number of defects formed during the heating and, thus, the more non-radiative electron transitions. After 3 h of heating, the number of defects did not increase any more. It can be noted that a nitrogen loss of C 3 N 4 was observed as a result of its annealing 56 like in this study and due to electron beam irradiation 57 . The annealing of C 3 N 4 at 650 °C was also found to lead not only to the creation of N vacancies but also to the formation of new C=C bonds in heptazine units 35 but it was not observed in this work, see below.
The decreasing intensity and redshifts of the PL bands mentioned above are opposite to phenomena observed for the CN materials synthesised in air, see Fig. 5S. Their PL bands were blue-shifted, and their intensity increased with the heating time, which we already observed recently 33 . It could be explained by the decreasing number of defects in the CN ones.
Photoelectrochemical properties. Electric current generated after irradiation of the CN and CN-Ar materials was recorded in order for us to study the photoelectrochemical properties of these materials. The photocurrent generation measurement provides information about the amount of generated charge carriers. The dependence of the generated photocurrent on the wavelength is shown in Fig. 3. The whole measurements were conducted in the range of applied potentials from − 200 to 1000 mV (vs. Ag/AgCl) and in the range of wavelengths for each potential from 240 to 450 nm. The current responses were measured under the maximal applied potential of 1 V to suppress the recombination of photoinduced electrons and holes.
The maximal photocurrents were measured at about 380 nm within the range of 340-410 nm. The photocurrent records were evaluated based on their signal-to-noise (S/N). In general, when S/N is equal to 3.0 the presence of a significant signal is accepted 58  X-ray diffraction study. The XRD patterns of the CN and CN-Ar materials were recorded as shown in Fig. 4. The typical diffractions of (002) and (100) planes were observed. The (002) diffractions are attributed to interlayer stacking of C 3 N 4 planes and the (100) ones are attributed to the in-plane ordering of nitrogen-linked heptazine units 59 . Some basic characteristics were evaluated from the XRD patterns, see Table 2. The characteristics of all the CN-Ar materials were very similar and no exfoliation was observed in them. Only a little shift of the d(002)   www.nature.com/scientificreports/ spacings between CN and CN-Ar ones was calculated. The crystallite sizes L(002) of about 7 nm were similar for all the materials. One can conclude that no effect of the defects in the CN-Ar structures was observed. Similar diffraction patterns (Fig. 7S) were observed for the CN materials synthesised in air, as demonstrated by the basic XRD characteristics in Table 2S. The d(002) spacings were similar to those of the CN-Ar materials ( Table 2), and the crystallite sizes L(002) were a little smaller due to the thermal exfoliation providing nondiffracting nanosheets 33 .  In order for us to evaluate the changes of N-H stretching vibrations, the absorbances at 3163 cm −1 (primary amines) and 3435 cm −1 (secondary amines) were related to those at 1242 cm −1 and 1637 cm −1 concerning the C-N and C=N stretching vibrations, respectively. Since absorbance is a relative parameter depending on the concentrations of absorbing compounds the ratios of A 3163 /A 1242 and A 3163 /A 1637 calculated for the CN and CN-Ar materials can be comparable with each other, see Table 3. Both ratios of CN were lower likely due to the lower content of N-H species in relation to C-N and C=N ones. In other words, the CN-Ar materials had more N-H bonds than the CN one. A possible explanation is in oxidation of -NH 2 groups during the synthesis in air.
The FTIR spectra of the CN materials synthesised in the air for 1-3 h were recorded for comparison, see Fig. 8S. The typical band regions A and B and the band at 807 cm −1 were also observed. By analysis of absorbance at 3163 cm −1 , 1242 cm −1 , and 1637 cm −1 one can see that the content of N-H bonds decreased by the reheating in air due to their oxidation, see Table 3S. In addition, the content of C-N bonds in relation to the more stable C=N ones also decreased for the same reason.
Similar ratios of A 1242 /A 1637 indicate similar composition of heptazine units in the analysed materials. The findings concerning the ratios of A 3435 /A 1242 and A 3435 /A 1637 of the N-H vibrations of secondary amines are summarized in Table 4S and they also point out the lower content of N-H species in the CN sample. XPS analysis. The XPS analysis was performed in order for us to see changes in the surface composition and oxidation states of the CN and CN-Ar materials. Whole survey spectra were measured, however, no other element except C, N, and O was found. For deconvolution, detailed C 1s, N 1s and O 1s spectra were used. The  www.nature.com/scientificreports/ spectra of all the CN-Ar materials were similar, therefore, only one of CN-Ar0 is displayed in comparison with CN in Fig. 6. The spectra of the other CN-Ar materials are placed in the Supplementary materials; see Figs. 9S, 10S and 11S. For comparison, the additional N 1s spectra of CN synthesised in air and in argon are demonstrated in Fig. 7, see below.
The deconvolution of the C1s spectra provided no significant differences. These spectra were fitted by two peaks with the positions at 288.3 eV and 285.0-285.5 eV. The peak at 288.3 eV can be ascribed to sp 2 hybridized carbon (N-C=N). The second peak can be composed of several contributions, such as C-C (284.8 eV), C-O (286-287 eV) or C-N (286 eV). The origin of this peak can be ascribed either to oxidative changes in the CN-Ar materials or/and to adventitious carbon on the surface.
The deconvolution of the N 1s spectra (Fig. 6) showed four peaks positioned at 398.8, 400.0, 401.4 and 404.2 eV. These peaks can be ascribed to sp 2 hybridized nitrogen (C=N-C) also called two-coordination nitrogen (N C2 ), nitrogen of tertiary amine N-(C) 3 also called three-coordination nitrogen (N C3 ), the C-N-H bond, and to a π-π* (HOMO-LUMO) transition (shake-up line), respectively. Moreover, the band gap of about 2.04 eV (Table 1) can be explained by the presence of the nitrogen vacancies due to the preferential loss of N 2C compared to N 3C 29,61-63 . The energies for removing N atoms in N 2C and N 3C are 1.40 eV and 2.39 eV, respectively 29 . The oxygen O1s spectra did not provide data suitable for the deconvolution. Figure 7 provides the comparison of N 1s spectra of CN, CN-3, CN-Ar0, and CN-Ar3. The different intensities of peaks at 401.4 eV and 400.0 eV concerning N C3 and N C2 nitrogen atoms, respectively, are remarkable. The decrease of N C2 intensities in relation to N C3 ones in air and in argon implies the formation of N C2 vacancies with the heating time. Moreover, it is also visible that the CN-Ar materials contained a higher portion of N C2 than the CN ones synthesised in air. This can be explained by the preferential oxidation of amino groups (N C3 ).  Table 4. There are no significant changes in the surface composition of nitrogen and carbon of the CN and CN-Ar materials. Taking into account the experimental error of about 10%, the C/N ratios could be considered to be similar and, therefore, no significant differences in the surface composition of CN-Ar materials were found. However, there are differences in the content of oxygen between the CN and CN-Ar ones. The higher content of oxygen in CN can be explained by surface oxidation during its synthesis in air.
The surface analysis performed by XPS (Table 4) was compared with the bulk elemental analysis, see Table 5. The C/N value of the CN material was lower than the values of the CN-Ar ones (proved by the Dean-Dixon test and a box plot) likely due to the lower content of nitrogen as a result of nitrogen defects formed in the argon atmosphere. This is in consistency with the XPS analysis. The higher content of hydrogen in the CN-Ar materials agrees with the higher portion of > NH and -NH 2 groups indicated by FTIR.  www.nature.com/scientificreports/ It is interesting to see that the content of oxygen is similar in CN and CN-Ar materials, about 2 wt.%. There are questions (i) how oxygen could get in CN-Ar0 if it was synthesised in the argon atmosphere and (ii) why the content of oxygen did not increase when CN-Ar0 was further heated for 1-3 h in argon. A possible answer to the first question is that the incomplete polymerization of melamine could lead to the formation of structural defects, which were attacked with oxygen and water when CN-Ar0 came into contact with air. The second question can be answered by the high thermal stability of the CN-Ar0 structure, which was not changed by the repeated heating at 500 °C for 1-3 h, which is in contrast to the same procedure applied on C 3 N 4 in air when its exfoliation happed 12,33 . It indicates that the heating alone is not the only reason for exfoliation.
The bulk elemental analysis was also performed on the CN materials synthesised in air, see Table 5S. The content of oxygen increased due to direct oxidation with oxygen. The presence of oxygen attacking C 3 N 4 and forming its defective structure is natural. The C/N ratios were similar due to oxidation and consequent decarboxylation 33 . Texture and morphology study. The CN and CN-Ar materials were analysed in terms of SSA as mentioned above (Table 1) and pore size distribution. It is obvious that the SSA changed very little and the heating time in the argon atmosphere was not important. This is in line with our recent experiments of the C 3 N 4 synthesis under nitrogen 33 . Unlike the SSA, the pore size distribution plots showed some changes, see Fig. 8. In comparison with CN, the CN-Ar materials had fewer mesopores and more macropores with the radius above 200 nm. The CN mesopores were supposed to be created by erosion of the C 3 N 4 structure due to its oxidation and consequent decarboxylation in air.
The material morphology was studied by SEM. Figure 9 displays two micrographs of CN (left) and CH-Ar0 (right). Unlike the compact CN particles, the CN-Ar0 ones were composed of smaller fragments of various sizes and shapes with pores among them. The smaller fragments represent the smaller planes of C 3 N 4 with more terminating > NH and -NH 2 groups. The higher portion of these N-H species were observed by FTIR and the elemental analysis. The other CN-Ar materials resembled CN-Ar0 and are demonstrated in Figs. 12S and 13S.
Mott-Schottky measurements. Flat band potentials of the CN and CN-Ar materials were measured against the Ag/AgCl reference electrode (see Fig. 14S) and recalculated to be against the normal hydrogen electrode (NHE) as E vs. NHE = E vs. Ag/AgCl + 0.191 V + 0.059 (7 -pH) 64   www.nature.com/scientificreports/ From this figure one can see that the conduction band as well as valence band potentials of the CN-Ar materials are similar. The E VB values above 1.23 V indicate that these materials have the potential to be used in hydrogen generation by water splitting, see below.
Photocatalytic activity. The photocatalytic activity of the CN-Ar materials was tested in terms of the generation of hydrogen by water splitting: This reaction includes two redox chemical half reactions: Water oxidation half reaction and proton reduction half reaction   www.nature.com/scientificreports/ The photocatalytic water splitting is an energy-intensive reaction. Therefore, the experiments were performed in the presence of electron donors (sacrificial reagents), such as methanol, to avoid back-reaction 66 . Figure 11 shows the dependence of the hydrogen yields on the time (0-4 h) of irradiation (254 nm). A commercial TiO 2 photocatalyst Evonik P25 was used for comparison. The CN material showed lower yields of hydrogen (547 µmol g -1 ) after 4 h of irradiation-by about half compared to TiO 2 (1052 µmol g -1 ). On the other hand, all the CN-Ar materials generated more hydrogen than TiO 2 . Moreover, the highest yields of hydrogen were obtained in the presence of CN-Ar2 (1547 µmol g -1 ). Figure 12 shows the yields of produced hydrogen, methane and carbon monoxide (the CH 4 and CO yields were multiplied by 10 for better recognition), after 4 h of irradiation. Methane and CO 2 are typical intermediates of the photocatalytic decomposition of methanol 67 .
In general, the photocatalytic activity can be affected by several factors, such as phase composition, specific surface area, pore volumes, crystallite sizes, band gap energy, defects etc. The C/N ratio was found to play an important role. The elemental composition, which was determined by XPS, showed that the CN-Ar materials had a lower C/N ratio than CN that was prepared in air ( Table 4). The CN one was of the highest C/N and its photoactivity was the lowest (547 μmol g -1 of H 2 ), while CN-Ar2 and CN-Ar3 had the lowest C/N values and showed the highest photoactivity (1547 and 1482 μmol g -1 of H 2 , respectively). These findings indicate that the defects had a significant impact on the photocatalytic hydrogen generation.
Moreover, as shown in Fig. 2, CN exhibited the highest PL intensity, which means that the charge recombination was the highest and, therefore, less photogenerated charge carriers were available for the hydrogen generation. On the contrary, the lowest PL intensity was observed for the CN-Ar2 and CN-Ar3 ones, which had the highest photoactivity. This points out that the material defects confining the recombination of photoinduced   Fig. 13 one can conclude that the lifetime τ 1 = 316 ps measured in CN is not only longer than the bulk positron lifetime but is also longer than the lifetime of positrons trapped in either carbon (V C ) or nitrogen (V N ) single vacancies. So, the CN material contains defects with a larger free volume than monovacancies. The lifetime τ 1 = 316 ps measured in CN corresponds well to the calculated lifetime of positrons captured in V C + 3V N complexes. Considering nanocrystalline grain size of CN samples (see Table 2), which is more than an order of magnitude smaller than a typical positron diffusion length in solids 69 , a majority of positrons are annihilated at grain interfaces. Hence, V C + 3V N complexes are likely located at interfaces between crystallites.
The presence of a long component with the lifetime of τ 2 = 990 ps originating from the o-Ps pick-up annihilation indicates that the material contains nanoscopic pores. Using the Tao-Eldrup model 70,71 it is possible to estimate from the measured lifetime τ 2 the mean size of nanoscopic pores of 3.2 ± 0.2 nm. Figure 14 shows the lifetimes and intensities of the individual components measured in the CN and CN-Ar materials and their dependence on the annealing time in argon. In CN-Ar0, the lifetime τ 1 increased to ≈ 330 ps and with the increasing annealing time the lifetime increased further towards the value calculated for 2V C + 2V N complexes. Hence, the materials prepared in argon clearly contain larger defects and the size of these defects further increases during the heating in argon. It seems that V C + 3V N complexes (open volume of 4.89 nm 3 ) tend to form larger complexes 2V C + 2V N (open volume of 5.17 nm 3 ) containing two carbon vacancies. The lifetime τ 2 is nearly constant during annealing in argon, without significant changes. The I 2 intensity of the o-Ps component is smaller in CN-Ar0 than in CN and decreases slightly with heating. It follows from this that the CN-Ar materials contained a slightly lower concentration of nanoscopic pores.
For comparison, the lifetimes and intensities of the CN materials synthetized and further heated in air 33 are shown in Fig. 15 as well. Unlike the CN-Ar materials, these ones were exfoliated and one can see the opposite trends with respect to Fig. 14. The lifetime τ 1 gradually decreases during exfoliation from 316 ps corresponding to V C + 3V N towards the value calculated for V C + 2V N . At the same time, the intensity I 1 decreases as well. The lifetime τ 2 and the intensity I 2 gradually increase during the exfoliation. It points to a gradual increase of size and concentration of nanoscopic pores. Using the Tao-Eldrup model 70,71 one can estimate that the mean size of nanoscopic pores increased from 3.2 ± 0.2 nm to 4.6 ± 0.2 nm during the exfoliation for 3 h. This finding is in agreement with the loss of nitrogen during the repeated heating for 1-3 h observed by XPS. Unlike the C 3 N 4 synthesis and further heating in argon, the synthesis and heating in air are accompanied by reactions with  www.nature.com/scientificreports/ oxygen and, hence, the vacancy complexes are formed by different mechanisms, which are still unclear. The defect number reduction in CN and CN-1 to CN-3 observed by the PL spectrometry is likely a part of this process. The PAS analysis demonstrated that one cannot talk about either nitrogen or carbon single vacancies but about their complexes. The longer heating in argon resulted in the higher vacancy volumes (Fig. 13). This is in consistency with the C/N values as well as the increasing photocatalytic activity of the CN-Ar materials and it   Effect of inert gas on synthesis of C 3 N 4 . The synthesis of C 3 N 4 was based on the polycondensation of melamine forming heptazine and then melon units, which were mutually connected into the planes. This process is necessarily associated with the release of ammonia, which must be removed in order to shift the reaction equilibria toward the resulting C 3 N 4 in line with Le Chatelier's principle. During the synthesis, ammonia diffused out through the already formed porous C 3 N 4 and, at the same time, surrounding argon diffused in the opposite direction, see Fig. 15S. In general, this situation, when two gases of different molecular masses are diffusing in the opposite directions through a porous media, can be described by Graham´s law of gas diffusion as follows: where v NH3 and v Ar are the rates of diffusion of NH 3 and Ar, respectively; M NH3 and M Ar are the molar masses of NH 3 and Ar, respectively. Substituting for the molar masses M Ar = 40 g mol −1 , M NH3 = 17 g mol −1 and M N2 = 28 g mol −1 we can get from this relationship that the rate of NH 3 is 1.53 times higher than the rate of Ar and the rate of NH 3 is 1.28 times higher than that of N 2 .
The diffusion rates of gases can be expressed by means of their number of moles diffusing through a porous medium during the same time. The total number of diffusing NH 3 (n NH3 ) and Ar (n Ar ) moles is n = n NH3 + n Ar , which we can substitute in Eq. (9) as Then, we can calculate the molar fraction of NH 3 defined as Substituting for the molar masses of Ar and NH 3 we can get x NH3 = 0.61. Using the same equation for N 2 and NH 3 we can get x NH3 = 0.56. Thus, we can see that the number of moles of released NH 3 is higher in the argon than in nitrogen atmosphere.
Considering the reaction equilibria, it can be supposed that more ammonia released means more complete C 3 N 4 and less incomplete C 3 N 4 labelled as C x N y H z in Fig. 15S. In our previous work, the content of oxygen in C 3 N 4 synthesised under nitrogen was 7.52 wt. % 33 in contrast to 2.28 wt. % determined in this work ( Table 5). The incomplete C x N y H z is supposed to be more reactive with oxygen than C 3 N 4 due to various structural defects including vacancies. The higher content of the defects in C x N y H z was indicated by the higher C/N values of 0.686-0.700 (mol/mol) 33 , see Table 5 for comparison.
Equation (11) is an approximate calculation, which helps us to understand the beginning phase of the C 3 N 4 synthesis in an inert atmosphere. In a real process, it is also possible to consider the reaction rate of synthesis, which was changing with the increasing temperature, and complex geometry and a temperature field of resulting C 3 N 4 in a crucible.

Conclusion
Graphitic carbon nitride was synthesised at 550 °C for 4 h in the argon atmosphere and then heated for 1-3 h in argon again. The UV-Vis reflectance spectra revealed the two band gap energies of 2.04 eV (608 nm) and 2.47 eV (502 nm). The photoluminescence study indicated the formation of defects during the heating, which explains the band gap of 2.04 eV. Although the defects were formed, the regular C 3 N 4 structure was preserved as demonstrated by XRD and FTIR. The CN-Ar materials were not exfoliated by their heating; their SSAs were 15-18 m 2 g −1 . Macropores were formed in the CN-Ar materials as calculated by the BJH model and observed by SEM.
The bulk elemental analysis confirmed the presence of nitrogen defects likely due to the loss of the N 2C atoms. It was also observed that all the materials were photoactive because they were able to generate photoelectric current around the wavelength of 380 nm. Using the Mott-Schottky plots similar conduction band potentials of CN and CN-Ar materials were observed. The positions of valence band potentials indicated their capability of the photocatalytic water splitting, which was tested in terms of hydrogen generation in a water-methanol mixture. The best CN-Ar3 photocatalyst showed 3 times higher performance (1547 μmol g -1 ) compared to the CN photocatalyst (547 μmol g -1 ) and 1.5 higher compared to reference TiO 2 (1052 μmol g -1 ).
The PAS analysis showed the formation of the complexes of carbon and nitrogen vacancies. Big 2V C + 2V N and Vc + 3V N complexes were formed in argon in contrast to Vc + 3V N ones formed in air. The presence of the 2V C + 2V N complexes is assumed to affect the photocatalytic activity of C 3 N 4 . This positive effect resulted in higher hydrogen generation performance using CN-Ar materials in comparison to the CN one. Finally, the effect of an inert gas on the synthesis of graphitic carbon nitride from nitrogen-rich precursors was demonstrated based on Graham´s law of gas diffusion.  www.nature.com/scientificreports/ It was shown that not only the presence of vacancies, but also their size is the important factor of the C 3 N 4 photocatalytic activity for hydrogen generation. The research focused on vacancy complexes in C 3 N 4 will be performed in the future. The investigation based on theoretical calculations and material characterizations could lead to deeper understanding of the physico-chemical properties of C 3 N 4 structures for their prospective applications.

Data availability
The datasets used and/or analysed during the current study available from the corresponding author on reasonable request.