Direct observation and catalytic role of mediator atom in 2D materials

Mediator atoms catalyse bond formation and breaking in graphene and its defects.

, frame 6-8, Here, we analyse the blurry images which are not related to mediator atoms mechanism. The analysis of images related to mediator atom mechanism is shown in Fig. 2 of main manuscript. In A, we suspect whether there is an undercoordinated atom at same position from 1 to 5 as indicated by green arrows. We put the atom in the structure of 3 as shown in c and performed force relaxation by DFT calculation. In this calculation, we found the structure is unstable and changed into other structure without energy barriers as shown in C.
Therefore, the structure with the under-coordinated atom as shown from 1 to 5 is unstable and could not be observed in TEM. Therefore, we suggest the structural analysis in B for the structures from 1 to 5.
We found that the blurry image which can be misunderstood as the existence of under-coordinated atom is due to the softness of bonding with nearby atoms as shown in D. When we calculate the energy for the shift from the optimized position of the atom, the energy is lower than the atom in pristine part for the same shift by 1 eV. Therefore, the atom indicated by an blue arrow in D is very flexible under electron irradiation and gives blurry image. For the another under-coordinated atom indicated by green arrows in 6, 7, and 8, the energy barriers for its mediating roles is found to be 1.7 eV and 1.8 eV which is much higher (H and I) than the energy barrier (0.4 eV) of the mediating role (G) of mediator atom in yellow circles. So, under the electron irradiation, the atom indicated by yellow circles play a mediating role first as shown in G and the atom indicated by an blue circle does not play a mediating role during the observation. Therefore, we determine the structures for 6, 7, and 8 as annotations in F. We analyse more the role of mediator atom in Fig. 2 with annotated structures in B and F.

Switching Rate from Scattering Cross-Section under Electron Irradiation
An analytic approximation of the cross section for Coulomb scattering between an incident electron and a nucleus 24,25 was employed to address the energy transfer rate to carbon atoms during experimental imaging conditions. The scattering cross section for the events when energy or higher is transferred can be written as where is the atomic number of the target atoms, is the electron mass, = v/c (electron velocity divided by the speed of light c), max is the maximum transferred energy in the scattering event. max

Switching Rate from Thermal Activation
The switching rate from thermal activation is calculated from the first order Arrhenius relation, where is the attempt frequency, E b is the energy barrier, k B is Boltzmann constant, T is temperature.
We take here to be the Debye frequency, ~10 13 Hz.
The overall switching rate is determined by the summation of effects ( ( ) and ℎ ( )) from electron scattering and thermal activation. When we consider the AC-TEM performed at room temperature (293 K) and 700°C (973 K), the overall switching rate is shown in Fig. 4.
At room temperature, when the barrier height is below 0.8 eV, thermal activation will dominate over electron scattering as shown in Fig. 4a. In Fig. 2 the maximum calculated energy barrier for structural change is 1.2 eV and most barriers are ~ 0.8 eV or less. For individual processes contributing to the overall mechanism to occur within the experimental image exposure time (3 sec), their switching rates must be above 0.33 sec -1 . This is marked as a blue region in Fig. 4a, which corresponds to an activation barrier of 0.83 eV or below. Therefore, mediator atom mechanism processes with barriers below 0.83 eV occur faster than the single exposure time and result in the blurry image in our AC-TEM due to the fast structural change. For comparison the energy barrier associated with STW bond rotations (~ 5 eV) will only be e-beam activated and occurs on average 2.79×10 -2 times per second, i.e. the barrier will be overcome once every 36 seconds, much longer than the exposure time.
When we consider the AC-TEM performed at 700 °C (973 K) shown in Fig. 4b, max increases to 18.8 eV. At this temperature, for energy barrier less than 2.74 eV, thermal activation will dominate over electron scattering. The energy barriers for kink motion of dislocations in graphene are below 2.20 eV from our DFT calculations, and therefore at this temperature thermal activation will dominate the kink motion. From the calculation of switching rate, hopping events will occur faster than 40 times per second. This means that over a single image experimental exposure time (3 sec), there is sufficient time for all the processes from Fig. 3b to Fig. 3c to occur. In this way we can explain the abrupt change of dislocation kink in AC-TEM as shown in Fig. 3. For the comparison, the STW bond rotation (energy barrier: ~ 5eV) occurs on average 3.00×10 -2 times per second at 700 °C, i.e. the barrier will be overcome once every 33 seconds. However, as we mentioned in the main text, the structural change from Fig. 3b to 3c requires at least five STW type bond rotations, which will take over 150 seconds. It is much longer  108, 196102, doi:10.1103108, 196102, doi:10. /PhysRevLett.108.196102 (2012.

Supplementary Discussion 2 : Consideration of Electron Impact under AC-TEM
In this discussion, we consider the electron impact under AC-TEM. As we mention in Supplementary Discussion 1 about the switching rate theory from electron scattering cross section and thermal activation, much of mediator atom mechanism belongs to the region governed by thermal activation rather than the effect of electron irradiation. However, since our TEM images are acquired from AC-TEM, we need to consider the electron impact. In order to study the electron impact, we have performed ab initio molecular dynamics simulation (AIMD) simulation considering momentum transfer corresponding to energy 15 keV to perpendicular direction to graphene plane. We choose various atoms as the objective atom of momentum transfer as denoted by red circles in fig. S4 and it is found that the AIMD results are almost the same as our TBMD results obtained by thermal activation. Especially, we performed it for the structural changes shown in Fig. 2B and 2D (See fig. S4, Movie S5 and Movie S6) and it shows almost same results as shown in Fig. 2B and 2D (See also Movie S1 and S3 in our manuscript). From the Movie S5 and S6, we can find that the mediator atom mechanism can be observed by the fluctuation of the graphene plane or by the change of strain even in the case of electron impact to carbon atoms which are not mediator atoms. Therefore, in case of a high energy barrier of 5 eV, which corresponds to the STW bond rotation, the electron irradiation situation should be considered.
However, the mediator atom mechanism, which corresponds to an energy barrier below 0.8 eV at room temperature (energy barrier below 2.2 eV at 700 °C), can be sufficient for thermal activation regardless of electron irradiation conditions. Therefore, in the analysis of mediator atom mechanism, the result considering electron irradiation is not significantly different from the result of thermal activation.

Mediator Atom
As an under-coordinated atom, the mediator atom usually bonds with two carbon atoms. We may suspect the mediator atoms as N or O atoms because those atoms can form bonds with two carbon atoms.
Here, we would like to discuss the possibility of N or O atoms for mediator atoms in Fig. 2A frame 2, frame 6 and frame 8. There is no mediator atom in Fig. 2A frame 1 and the number of carbon atoms in the white line is 113 as shown in Fig. 2. We consider all atoms in Fig. 2A frame 1 as carbon atoms because there is no under-coordinated atom. As shown in Fig. 2A frame 2, one atom is added so that the number of atoms in the white line increases to 114. One added atom in Fig. 2A frame 2 can be assumed as N (or O) atom. In this case, the other two under-coordinated atoms will be carbon atoms because three under-coordinated atoms are found in Fig. 2A frame 2. When we perform the DFT calculation for the structure, two carbon atoms always make a bond to each other as shown in fig. S8 (Although fig. S8 is studied for the analysis of Fig. 2A frame 3, the important part noted by dotted yellow circles is same as that in Fig. 2A frame 2) and the structural change does not occur likely to that of Fig. 2B. Therefore, the simulated TEM image is not same as Fig. 2A frame 2 as shown in fig. S8. We can also consider the case that three under-coordinated atoms are all N (or O) atoms. In this case, the simulated TEM images can be same as Fig. 2A frame 2 but two carbon atoms should be replaced by two incoming N atoms because only one N atom can be added from Fig. 2A frame 1 to Fig. 2A  atoms become all N atoms, the structure of three N atoms are quite stable and the structure cannot be changed into the structure in Fig. 2A frame 4 because at least two N atoms should be replaced by two carbon atoms again on the way to the structure of Fig. 2A frame 4.
We also consider the possibility of N (or O) atoms as the under-coordinated atoms in Fig. 2A frame 6 and frame 8. For the structural change from frame 6 to frame 8, we can consider the most favorable pathway ( fig. S9) from the DFT search of various pathways. Because the energy barriers (2.5eV ~ 3.5 eV) for the process are very high compared to mediator atom mechanism by carbon atoms, it is very difficult to achieve the complex process in a short exposure time. When we consider the switching rate in Fig. 4, the process takes over 10 sec which was longer than one exposure time (3 sec). Furthermore, the process of the structural change cannot explain the TEM image as shown in fig. S9. Therefore, the possibility that the under-coordinated atoms can be N or O atoms in Fig. 2  We also performed electron energy loss spectroscopy (EELS) for some images in STEM image series of defect change containing STEM images in Fig. 5F. The EELS mapping for those STEM images is shown in fig. S10. In this EELS mapping, we did not find any signal from other element such as N or O.