Atomistic Modelling and Simulation of Transmission Electron

Microscopy Images: Application to Intrinsic Defects of Graphene

Cyril Guedj

, Léonard Jaillet

, François Rousse

and Stéphane Redon

Univ. Grenoble Alpes, CEA, LETI, 38000 Grenoble, France

Univ. Grenoble Alpes, Inria, CNRS, Grenoble INP*, LJK, 38000 Grenoble, France

Institute of Engineering Univ. Grenoble Alpes

https://www.minatec.org/fr, http://www.leti-cea.fr/cea-tech/leti, https://www.samson-connect.net

Keywords: Atomistic, Atomic, Modelling, Electron Microscopy, STEM, TEM, Microscopy, Graphene, Defects,

Vacancy, Microstructure, Image, Simulation, Materials, Characterization, Brenner, Samson.

Abstract: The characterization of advanced materials and devices in the nanometer range requires complex tools, and

the data analysis at the atomic level is required to understand the precise links between structure and

properties. This paper demonstrates that the atomic-scale modelling of graphene-based defects may be

performed efficiently for various structural arrangements using the Brenner module of the SAMSON

software platform. The signatures of all kinds of defects are computed in terms of energy and scanning

transmission electron microscopy simulated images. The results are in good agreement with all theoretical

and experimental data available. This original methodology is an excellent compromise between the speed

and the precision required by the semiconductor industry and opens the possibility of realistic in-silico

research conjugated to experimental nanocharacterisation of these promising materials.

1 INTRODUCTION

Digitals tools are more and more required to study,

design and prototype nano-objects, although the

underlying physics is so complex that the quest for a

universal tool is still far from being over. With the

increase of the computational power and the

improvement of the simulation methods, new

possibilities are offered by these tools and even

more shall be expected in the future. The increasing

pace of the semiconductor industry requires rapid

and efficient simulation and modelling strategies to

analyse the results and improve the technological

performances of various nano-devices, sensors or

actuators. In many systems, the optical or electronic

properties are driven by interfacial or by defect-

engineered phenomena. In order to understand the

links between structure and properties, the

nanocharacterisation of materials and devices is

advantageously combined with atomistic modelling

studies. The equilibrium positions of all atoms

provide the necessary basis to simulate the relevant

physical properties, which are measured with

increasing precision and sensitivity. The

combination of experiments conducted in parallel of

simulations is particularly relevant in the field of

transmission electron microscopy (TEM), because

the correlation between the measured image and the

actual arrangement of atoms is not straightforward in

general. Like most characterizations (TEM, X-ray or

electron diffraction, spectroscopic ellipsometry,

scanning tunnelling microscopy, etc.), the precise

simulation of TEM images is usually mandatory to

interpret the experimental results at the atomic scale.

With developments in aberration-corrected

transmission electron microscopy, it is now possible

to characterize vacancy defects in graphene

(Novoselov et al., 2004) at atomic resolution,

enabling the direct comparison between theoretically

predicted structures and experiment. This paper

provides an optimised methodology to perform

atomic-scale modelling of high resolution scanning

transmission electron microscopy (HRSTEM)

experiments of graphene-based defects. For this, it

uses relaxed structural models obtained with the

Brenner module of the Software for Adaptative

Modeling and Simulation Of Nanosystems

(SAMSON) developed by the NANO-D group at

INRIA (www.samson-connect fr). The case of

graphene-based defects is extremely interesting,

Guedj C., Jaillet L., Rousse F. and Redon S.

Atomistic Modelling and Simulation of Transmission Electron Microscopy Images: Application to Intrinsic Defects of Graphene.

DOI: 10.5220/0006829200150024

In Proceedings of 8th International Conference on Simulation and Modeling Methodologies, Technologies and Applications (SIMULTECH 2018), pages 15-24

ISBN: 978-989-758-323-0

because this is a 2D material with outstanding

mechanical (Geim and Novoselov, 2007), (Lee et al.,

2008), (Chen et al., 2008), (Pei et al., 2010), (Scarpa

et al., 2009), and electronic (Park et al., 2012); (Lee

et al., 2010) properties. Hence, graphene belongs to

a family of 2D materials which generates huge

expectations in terms of possible applications (Allen

and Kichambare, 2007), (Sorkin and Zhang, 2011)

(Qureshi et al., 2009), (Joh et al., 2013), (Yao et al.,

2009), (Stankovich et al., 2006). The high mobility

of graphene makes it advantageous in the

perspective of post-silicon electronics, but the

defectivity remains a recurrent critical issue. A wide

variety of deviations from a perfect crystal might

occur during the processing of graphene, either due

to the growth conditions or to various sources of

degradation, such as knock-on interactions, electron

or ionic collisions, plasma damage, chemical

reactions, etc. The link between the defectivity and

the electronic, magnetic, optical and mechanical

properties is critical for the device performance.

Thus, the defect engineering is certainly the key of

the possible industrial viability of this material. In

this paper, we study the defects in graphene in terms

of structure and energy. The methodology used to

build the systems and to simulate TEM images is

explained before presenting simulated graphene-

based defects that are compared to available data

from the literature.

2 METHODOLOGY

Many methods exist to simulate hydrocarbon

systems, such as molecular dynamics, Monte Carlo

and the many proposed variants of these approaches.

Typically, these simulations come with ab-initio

quantum-chemistry computations. Therefore,

computational studies of complex defects in

graphene are often limited by a number of atoms

larger than the current first-principle methods can

handle. In all cases, these methods require an initial

structural model consisting in the description of all

atoms in terms of position and chemical nature. In

the case of pure crystals, the 3D periodicity helps in

calculating all the atom positions for large systems

(i.e. more than 50 000 atoms), but in case of

localised asymmetrical defects, this task is much

more tedious or even completely unfeasible in the

worst cases. Hence, a computational tool that is fast

enough to handle physically-relevant calculations

with tens of thousands atoms is highly desirable. The

SAMSON platform and its Brenner module appear

to be ideally suited to this task, since they can handle

complex models and simulate big systems in a

timescale typically less than a day, which is

compatible with the feedback delay required by most

research teams in nanomaterial characterization.

This module appears as an interactive tool for

performing predictive modelling, particularly

adapted to the very sustained pace of

experimentalists and convenient to use, as it is

embedded in a user-friendly software platform.

2.1 SAMSON Software

SAMSON is a software platform for computational

nanoscience developed by the NANO-D group at

Inria and distributed on SAMSON Connect at

https://www.samson-connect.net. SAMSON has an

open architecture, and users customize their

installation with SAMSON Elements, i.e. modules for

SAMSON that may contain apps, editors, builders,

force fields, optimizers, visualizations, etc.

SAMSON Elements are developed with a

provided Software Development Kit, and distributed

on SAMSON Connect as well.

At the time of writing, about fifty SAMSON

Elements are available on SAMSON Connect, for a

number of application domains, including materials

science (e.g. Brenner model, graphene generator,

Universal Force Field, Crystal creator, graphene

TEM image analyser, etc.) and drug design

(GROMACS force fields, AutoDock Vina,

Interactive Ramachandran plots, Normal Modes

Analysis, PEPSI-SAXS, etc.).

Users may mix and match SAMSON Elements

to design their own processes and workflows, and

may use Python scripting to perform modelling and

simulation tasks.

2.2 Brenner Model

To simulate the structure of defects in graphene, the

atomic positions are computed from energy

minimization using the well-known bond-order

Brenner interatomic potential (Brenner, 1990),

(Brenner, 2000), (Brenner et al., 2002), (Dyson and

Smith, 1996), (Los and Fasolino, 2003), (Stuart, et

al., 2000), (Brenner et al., 1996). This is a

parametrized version of Tersoff’s potential which

includes terms to correct for the overbindings of

radicals. Brenner potential is ideally suited to the

interactive digital modelling (virtual nano-

engineering) of complex hydrocarbon structures like

carbon nanotubes (Sinnott et al., 1999), fullerene

(Brenner et al., 1991), or defective single layered

graphene (Lehtinen et al., 2010). We detail below

how the energy and forced can be described from

this potential.

2.2.1 Energy

The Brenner interatomic potential is particular in the

sense that it mostly focuses on covalent bonds (i.e. it

does not consider long-range interaction). Therefore

the potential energy 



of the bonding interactions is

a sum over interacting atoms (i.e. separated by less

than 0.2 nm):





=[







−













]

(1)

The details are given in the original reference

(Brenner et al., 2002). Since bonds are defined

dynamically via a bond-order function evolving with

the interatomic distances, this potential has the

ability to describe chemical reactions: it is reactive.

The potential also includes angular and dihedral

terms, radical energetics and the influence of π

bonds (Bosson et al., 2012).

To overcome the lack of long-range interactions,

a non-bonded interaction potential term is added. It

consists in a sum of pairwise potential contributions.

For simplicity, the approach of Los and Fasolino is

chosen (Los and Fasolino, 2002) and the Van der

Waals potential term is added:









=

(

−





)

−









−



(2)

to adjust the precision, using b=3224.9 eV, c

35.995 nm

-1

, =0.01396 eV and σ=0.344 nm.

2.2.2 Forces

The force terms can be calculated from the gradient

of the potential . More specifically, the Force 



applied on atom  at position 



can be written:





=−







=−  









,(,)∈













(3)

where r

is the distance between atoms i and j, and β

is the set of all pairs of atoms involved in the

interaction:

=

(

,

)

,



<









(4)

with 





 being a threshold distance depending on

the atom types.

2.2.3 Adaptive Brenner

An adaptive version of the Brenner potential has

been implemented in SAMSON (Bosson et al.,

2012). Its interest is that it relies on an algorithm

which incrementally updates the forces and the total

potential energy.

It basically consists in an incremental dynamical

update of the set of interacting atoms and all

information related to one, two, three or four atoms.

Bonds are divided into 4 types: bond with a relative

motion, bonds with a change in potential, bond with

a change in conjugate number, and bonds without

any change in potential. After initialization, all terms

with relative motions are updated incrementally and

after a first level and second level potential update,

the forces are henceforward updated. This allows the

algorithm to linearly scale with the number of

updated bonds. Therefore the computational cost is

decoupled from the number of atoms in the system

and physically-based editing becomes markedly

faster.

To take advantage of adaptive Brenner, an

adaptive mechanism is proposed in SAMSON to

update when minimizing a system. Such an

approach in Cartesian coordinates consists in

deciding for each atom if it might move or be frozen

in space. This decision is made by comparing the

norm of its potential displacement with a threshold

value, either automatically deduced from the system

state or by a manual choice fixed by the user. This

implementation is an extension of the internal

coordinates and articulated bodies simulation

(Redon et al., 2005).

This efficient update mechanism allows

continuous minimization of the system energy

during the edition of the system, which helps to

build realistic structures in a very convenient

manner. The user action step

(creating/moving/deleting atoms) alternates with the

adaptative minimization steps to parallelize the

structure editing and the energy minimization.

2.3 Simulation of Microscopy Images

Once the structure is fully relaxed, it is possible to

compute the corresponding high-resolution scanning

transmission microscopy image by using the

QSTEM software (Koch, 2002). This program

allows accurate image simulations including fully

dynamic calculations. QSTEM computes the true 3D

potential distribution and numerically integrates

every slice of the potential map. This enables a

thickness reduction without limitations in the

multislice calculation. In addition, it is possible to

explore a wide range of experimental setups in order

to evaluate the best conditions to observe the

defects. Here the images are simulated using a

typical voltage of 80 kV, a C3 spherical aberration

of 0.001 mm, a Cc chromatic aberration of 1 mm, an

energy spread of 0.16 eV and a convergence angle

of 20 mrad, which are reasonable values to compare

with high-resolution scanning transmission electron

microscopy (HRSTEM) experiments from an

aberration-corrected microscope. The detectors

collection angle are chosen between 50 mrad and

200 mrad for realistic high-angle annular dark field

(HAADF) conditions. In this conditions of Z-

contrast imaging, the contrast scales with the atomic

number with a power-law dependence (Crewe et al.,

1970). In addition, the HRTEM images are also

calculated with QSTEM using a voltage of 80 kV,

all aberration coefficients equals to zero except for

the chromatic aberration of 1 mm, a spherical

aberration of 5 µm and a vibration of 3 nm in all

directions. In these conditions, the HRTEM

contrasts are usually comparable to HRSTEM, and

the superimposition of the atomic model to the

(S)TEM image provides an efficient method of

validation. To outlines the most striking features, we

have used suitable look-up tables (LUT) to colorize

the experimental TEM and the simulated STEM

images.

3 RESULTS AND DISCUSSION

In the following, we illustrate the cases of typical

defects induced by electron-beam damage during

TEM observation. The probability to observe these

defects is therefore relatively high, for instance

when the electron beam energy is set up above the

threshold for knock-on damage in sp

-bonded

carbon structures (i.e. > 100 keV) (Banhart et al.,

1999), (Smith et al., 2001). These defects could also

be obtained by other interactions, such as ionic or

mechanical or by plasma damage, for instance if the

technological processing steps are inappropriate. We

focus the analysis on simple topological defects,

vacancies and adatom, but the same conclusion

applies to all defects we have studied so far

(dislocations, novel phases, extended defects, etc.),

based on available published data.

In the following figures, colorization of

experimental images is obtained with Fiji

(Schindelin et al., 2012) using 16 colors LUT. The

various atomistic models correspond to flake system

of 1308 atoms with flat borders, built in SAMSON

and optimized thanks to the Brenner module. The

clear advantage of the Brenner approach compared

to ab-initio is a ∼ 4 orders of magnitude

improvement in terms of simulation speed.

Moreover, as we will see, the precision achieved is

sufficient to match the experimental results and we

obtained similar findings for all the graphene-based

defects we found in literature, without apparent

limitation, and even for systems with tens of

thousands of atoms. In the following, all

experimental data already published are used with

permissions.

3.1 Stone-Wales Defect

Graphene has the ability to form nonhexagonal

rings, and the simplest example is the Stone-Wales

(SW) defect (Stone et al., 1986) in which four

hexagons are transformed into two pentagons and

two heptagons [SW(55-77) defect] by an in-plane

90° rotation of two carbon atoms with respect to the

midpoint of the C-C bond (Figure 1).

Figure 1: Left: atomistic ball and stick model of the

unstable flat SW(55-77) defect in graphene. Black balls

represent carbon atoms. Right: Corresponding HRSTEM-

HAADF simulated image.

In pure graphene, the C-C bond distance is 0.142

nm according to Pauling (Pauling, 1960), which is

the exact value provided by our code. The

simulation also matches very well previous

experimental results (Meyer et al., 2008), (Kotakoski

et al., 2011) and the corresponding ab-initio

simulations (Li et al., 2005), (Ma et al., 2009).

The planar configuration is unstable and may

relax in the 3D sinelike or cosinelike configuration.

In our case, the minimum energy configuration of 6

eV is obtained for the sinelike configuration (Figure

2), in reasonable agreement with the configuration

and the energy of 5.82 ± 0.03 eV obtained by

quantum Monte Carlo (Ma 2009) and the value of

5.9 eV obtained by DFT-LDA (Jensen et al., 2002).

An absolute comparison with the exact and

precise value of the formation energy is difficult

because of the significant dispersion of formation

energies published in the literature, depending on the

DFT options (LDA, GGA, PW91, PBE, PBE0,

B3LYP, M06-L, vdW-DF, DFT-D, etc.) or the size

of the supercell for instance (Ma et al., 2009), (Li et

al., 2005), (Zhang et al., 2016), (Trevethan et al.,

2014), (Skowron et al., 2015). Meanwhile, the

buckling

height value of 0.156 nm is very close to

the value of 0.161 nm obtained by DFT for the

biggest cell (11 x 11) of Ma et al. (Ma et al., 2009).

The SW defects are not simple planar defects but

rather involve 3D displacements. Our simulation

provides realistic 3D positions of all atoms from a

2D TEM image.

Figure 2: Atomistic model of the lowest energy

configuration SW(55-77) sinelike defect in graphene, with

bond distances, superimposed with the experimental

HRTEM image of Kotakoski (Kotakoski et al., 2011).

Colorization has been added to help the interpretation.

3.2 Monovacancy (V

Defects)

3.2.1 Case V

(5-9)

The removal of one carbon atom from the graphene

network results in the formation of a single vacancy,

which has been studied both theoretically and

experimentally (Ma et al., 2009), (Li et al., 2005),

(Kotakoski et al., 2011), (Gass et al., 2008), (Meyer

et al., 2008), (Girit, 2009).

Our simulated model matches precisely the

experimental HRTEM images published in the

literature (Figure 3, Figure 4 and Figure 5). We

obtained a formation energy of 5.45 eV, which is

less than the range of [7.6, 7.9] eV obtained by DFT

(Skowron et al., 2015). The symmetric

monovacancy (s-MV) is known to exhibit a Jahn

Teller distortion, and may reconstruct into a closed

five- and nine-membered pair of rings. The

reconstructed monovacancy (r-MV) arrangement

lowers the energy of the symmetrical vacancy

structure in agreement with ab-initio calculations

(El-Barbary et al., 2003).

Figure 3: Left: atomistic model of the V

(5-9) defect

superimposed to the colorized experimental HRTEM

image (Kotakoski et al., 2011). Right: simulated

HRSTEM-HAADF image.

Figure 4: Atomistic model of the V

(5-9) defect

superimposed to the experimental HRTEM image

published by Robertson (Robertson 2013). Left: r-MV

(also labelled C

). Right: s-MV (also labelled D

Another comparison with HRTEM experiment

(Figure 4) shows that the best agreement between

experiment and simulation is obtained for the

reconstructed model r-MV, in expected agreement

with our lowest computed energy. Hence, our

methodology provides a convenient and realistic

approach to model the HRTEM images at the atomic

scale for this case.

Figure 5: Atomistic model of the V

(5-9) defect r-MV

superimposed to the experimental HRTEM defect image

entitled “SALVE-III-project-HRTEM-graphene-vacance-

foreign-atoms-defects-zoom.png” obtained by the SALVE

III project (Salve, 2018).

We found similar findings for all the cases we

have studied, without any exception. In general, the

precise comparison with experiment must include

the possible extrinsic contamination by

oxycarboneous species, by hydrogen or by water for

instance to be fully significant, therefore a relevant

comparison should take all these effects into

account.

3.2.2 Case V

(5-5)

The V

(5-5) state (Figure 6) may be considered as

intermediary between the V

(5-9) r-MV and s-MV

(Trevethan et al., 2014). Our calculations predicts a

formation energy of 5.01 eV, which means that such

defect should be observable in principle.

Figure 6: Left: atomistic model of the V

(5-5) defect

superimposed to the simulated HRSTEM image. Right:

model superimposed to the experimental HRSTEM image

(Lehtinen et al., 2013).

The simulated HRSTEM-HAADF of Figure 6 is

so close to the image of pure graphene that it might

not be identified in most cases, except perhaps in

ultra-low doses quantitative experiments to

minimize the knock-on energy provided by the

incident electrons and at very low temperatures to

freeze the thermal motion. In the supplementary

movie provided by Lehtinen (Lehtinen et al., 2013),

a pattern similar to the

(5-5) is possibly obtained,

just prior to the formation of a more extended defect.

Although the contrasts are very rapidly changing,

the

(5-5) is presumably a reactive seed for more

complex defect growth.

This type of defect has been observed

experimentally with the central 4-fold atom being

substituted by silicon (Ramasse et al., 2013).

3.3 Divacancy (V

Defects)

3.3.1 Case V

(5-8-5)

When two individual diffusing mono-vacancies meet

they will coalesce into a nearest-neighbour di-

vacancy defect (equivalent to removing a carbon

dimer from the lattice). This process results in the

formation of the stable pentagon–octagon– pentagon

(5–8–5) structure, which has been widely observed

in high-resolution transmission electron microscopy

(HRTEM) images (Kotakoski et al., 2011), (Warner

et al., 2012), (Lehtinen et al., 2013) (Robertson and

Warner 2013). Our calculation provides a formation

energy of 7.29 eV, not far from 7.59 eV by DT-LDA

(Saito et al., 2007) and 7.52 eV by Tight Binding

(Xu et al., 1993), (Dettori et al., 2012).

Figure 7: Left: atomistic model of the V1 (5-8-5) defect

superimposed to the colorized experimental HRTEM

image (Kotakoski et al., 2011). Right: simulated

HRSTEM-HAADF image.

The comparison with experiment (Figure 7) is

once again very positive, with a nearly perfect match

with published experimental TEM results.

The

(5-8-5) defects may mutate into the V

(555-777) and V

(5555-6-7777) states due to

electron beam irradiation for instance, and these

transitions were observed by HRTEM (Robertson,

2012), (Kotakoski et al., PRL 2011), (Kotakoski et

al., PRB 2011).

3.3.2 Case V

(555-777)

The structure of the V

(555-777) divacancy is

displayed in Figure 8, showing an excellent

agreement between experiment and simulation.

Figure 8: Left: atomistic model of the V

(555-777) defect

superimposed to the colorized experimental HRTEM

image (Kotakoski et al. 2011). Right: simulated

HRSTEM-HAADF image.

The calculated formation energy is 7.14 eV, in

reasonable agreement with the value of 7.41 eV

obtained by DFT-PBE/DNP (Wu et al., 2013).

Hence the

(555-777) state should be more stable

than the

(5-8-5), in agreement with all DFT

results published (Skowron et al., 2015).

3.3.3 Case V

(5555-6-7777)

The divacancy state V

(5555-6-7777) is represented

in Figure 9, superimposed to the experimental

HRTEM image attributed to this defect by

Kotakoski. Surprisingly, the matching is not perfect

and the TEM image appears asymmetrical as

opposed to the simulated image.

Figure 9: Left: atomistic model of the V

(5555-6-7777)

defect superimposed to the colorized experimental

HRTEM image (Kotakoski et al., 2011). Right: simulated

HRSTEM-HAADF image.

The computed formation energy is 7.45 eV, close

to the DFT value of 7.08 eV (Wu et al., 2013).

According to our simulation, this defect should be

less stable than the

(5-8-5), whereas Wu predicts

the opposite conclusion.

To understand this apparent contradiction, we

have tried to obtain a better match to the

experimental results, because we believe that

ultimately Nature is never wrong. This corresponds

to the trivacancy case as reported below.

3.4 Trivacancy (V

Defects)

3.4.1 Case V

(5555-666-77)

A set of studies is devoted to the structure and

energetics of trivacancies in graphene obtained by

structure reconstruction rearrangements after

removing 3 carbon atoms (Dai et al., 2011), (Faccio

et al., 2012), (Saito et al., 2007). Experimentally, the

trivacancy state may be obtained for instance by

bombardment with energetic particles (Wang et al.,

2012). The

(5555-666-77) structure has not been

studied to our knowledge, yet it apparently provides

the best agreement (Figure 10) with the experimental

image tentatively attributed to the

(5555-6-7777)

by Kotakoski et al., (2011).

This novel defect structure has a formation

energy of 12.54 eV. We therefore suggest that this

trivacancy may occur during e-beam irradiation.

This case highlights particularly well the interest of

our methodology which offers a new way to explore

in-silico novel types of defects, perhaps

unpublished, and yet observed experimentally by

HRTEM or HRSTEM.

Figure 10: Left: atomistic model of the V3 (5555-666-77)

defect superimposed to the colorized experimental

HRTEM image tentatively attributed to the V2 (55555-6-

7777) defect (Kotakoski et al., 2011). Right: simulated

HRSTEM-HAADF image.

3.5 Carbon Adatom

The healing (self-repair) of various graphene defects

by migration of adatoms has been observed by

HRTEM (Song et al., 2011), (Robertson et al.,

2012). The result of our calculation is displayed in

Figure 11.

Figure 11: Left: atomistic model of the 1C adatom defect

superimposed to the colorized experimental HRTEM

image extracted from the supplementary movie 6 provided

in (Lehtinen et al., 2013). Right: corresponding simulated

HRSTEM-HAADF image.

DFT studies usually gives three stable positions

of the adatom on graphene (Tsetserisa and

Pantelides, 2009). The bridge position is predicted to

be the most stable and was observed by HRTEM

(Hashimoto et al., 2004) and by HRSTEM ( Bangert

et al., 2009). We obtain a formation energy of 2.69

eV, therefore such defect should form easily during

processing of a graphene-based nanodevice. The

DFT method provides a value of the order of 1.5-2

eV for the binding energy of the carbon adatom (Lee

et al., 1997); (Lehtinen et al., 2003). The

perpendicular distance of the adatom to the graphite

surface is ∼ 0.222 nm, not too far from the value of

0.187 nm previously obtained by ab-initio

calculations for 50 atoms (Lehtinen et al., 2003). In

our case, we find that the 5

nearest neighbours

around the carbon adatom are vertically displaced,

therefore a simulation box of 50 atoms is certainly

too small to simulate the full relaxation of the

structure. Indeed, we obtained that 192 atoms are

vertically displaced by more than 0.005 nm around

the carbon adatom. Our methodology therefore

provides extended strains and stresses over long

distances, which is not possible with other methods

restricted to a limited number of atoms.

3.6 Extended Edge Defect (88-7-5555)

A severe test to assess the validity of a structural

model consists in considering a complex defective

structure with a large number of atoms. Hence, we

have used an extended defect and the excellent

spatial resolution obtained by the Salve project

(Salve, 2018) to check our methodology. The double

correction of chromatic and spherical aberrations

provides information transfer until 71 pm, which is

probably the best result ever obtained for an image

of graphene. The comparison is depicted in Figure

12. As usual, a nearly perfect agreement between

simulation and experiment is obtained.

Figure 12: Left: atomistic model of the extended defect

88-7-5555 defect superimposed to the experimental

HRTEM image entitled “SALVE-III-project-HRTEM-

graphene-vacancy-characteristic-defects.png” (Salve,

2018). Right: corresponding simulated HRTEM image.

The simulation also provides the distortion maps

for all bonds, in 3D and with picometric spatial

resolution. The positions of all atoms in the system

are therefore extracted and are readily available for

further ab-initio calculations in order to get all the

physical properties (electronic, optical, mechanical,

magnetic, etc.).

4 CONCLUSIONS

Using the Brenner module of the SAMSON

platform, we have precisely matched the

experimental high resolution transmission electron

microscopy experiments of various graphene-based

defects. We have also shown that a good agreement

is obtained with more complex ab-initio simulations

in terms of structure and energy. This methodology

opens the pathway to more extensive in-silico

exploration of all forms of phases or defects in

carbon-based materials, like diamond-like carbon

(DLC), amorphous carbon, nanotubes, fullerenes,

pentaheptite (Crespi et al., 1996), or other novel

phases or defects. Apparently, there is virtually no

limit in the number of structural arrangements of

graphene-based defects that can be simulated with

the Brenner module of SAMSON, in good matching

with experimental results. Finally, this methodology

is therefore a reliable approach to obtain 3D

atomistic models from 2D experimental TEM

images.

In the future, we would like to extend such a

methodology to study in detail the possible

transitions between different types of defects.

ACKNOWLEDGEMENTS

The invaluable contribution from the platform of

nanocharacterization (PFNC) at MINATEC,

Grenoble, France is respectfully acknowledged

(https://www minatec.org/en/). We would like to

gratefully acknowledge funding from the European

Research Council through the ERC Starting Grant

No. 307629.

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