Graphite forms via annihilation of screw dislocations

Carbonisation and graphitisation has been extensively studied for decades, however, the precise atomistic mechanism remains unknown. In 1965, Brooks and Taylor first observed under polarised light how disc-shaped aromatic molecules within graphitising carbons align during carbonisation, forming a liquid crystal mesophase below 1000 ^∘C [Brooks1965]. Further heating leads to extensive crosslinking between these aromatic regions as heteroatoms such as hydrogen, chlorine or oxygen are thermally driven off. X-ray diffraction revealed significant disorder in the structure at this stage with the distance between the layers significantly larger than that of graphite (3.4 versus 3.35 Å), misalignment twist between the layers away from ideal ABA stacking called turbostratic disorder [Puech2019] and broad reflections suggesting small regions of stacking and hexagonal ordering. This disorder is only removed between 2000–2500 ^∘C when graphitisation occurs.

In the 1970s, Oberlin and coworkers extensively studied this transformation at the nanoscale using electron microscopy [Oberlin1984]. Dark field transmission electron microscopy images revealed small regions of aligned stacked layers called basic structural units that initially are misaligned. Further details were found using phase contrast or high resolution imaging where dark and light fringes are formed by small aromatic regions at Bragg angle from the electron beam. Figure 1 shows these fringes that are misaligned by $\sim$10^∘ forming a zig-zag texture. During the transformation fringes align into columnar texture where fringes are interdigited and shifted by half a layer (c/2), then as the fringes enlarge a wavy texture follows before finally the fringes become ordered graphite. In dark field TEM Moiré fringes can be seen as the graphenic regions extend and align forming the ABA stacked ordering. Most recently, Ouzilleau et al. demonstrated that graphitisation follows a second order structural phase transition that occurs with a critical temperature of $T_{c}=2250^{\circ}$C [Ouzilleau2016]. These authors suggest stable topological defects that require these extreme temperatures to anneal.

Many defects have been suggested to inhibit graphitisation. Defects involving non-hexagonal rings, specifically 5775 dislocation dipole (otherwise known as a Diene or Stone-Wales defect), were suggested in the work of Ouzilleau et al. [Ouzilleau2016]. Indeed non-hexagonal rings have been directly imaged in disordered carbons [Harris2008, Guo2012]. These would provide the wavy textures seen and would limit the size of the graphenic regions. Isolated pentagonal rings provide positive disclinations (fullerene-like or bowl-shaped structures) that have been suggested to inhibit graphitisation [Harris2013]. Heptagonal rings provide negative disclinations (schwarzite-like or saddle-shaped structures). These heptagonal rings have been suggested to interconnect graphite layers, forming wormholes that inhibit graphitisation [Margine2007]. Other interconnects have been suggested such as interstitial atoms pinning the rotation of sheets or isolated layers that restructure into ’ruck-and-tuck’ [Heggie2011], ramps/messanines [Trevethan2013] or Y/T junctions [McHugh2022].

Recently, modelling of self-assembled disordered carbon structures using image reconstruction [Leyssale2012] and our recent annealed molecular dynamics simulations [Martin2019d] have demonstrated the significant role of screw dislocations, which we have previously studied in ideal graphite [Suarez-Martinez2007]. Screw defects are well known in graphite with 1952 imaging showing superscrew dislocations across many layers at concentrations of 10^2–4 cm^–2 [Horn1952] as well as screws with a single layer (elemental screws) later found in 1965 at concentrations of 10^6–8 cm^–2 [Patel1965, Hennig1965]. Recently, they have been directly imaged using atomic force microscopy [Rakovan2002]. All of these interplanar defects discussed have been shown to provide wavy and offset fringes seen in HRTEM [Sun2011, Trevethan2013]. However, critically the defect(s) involved in the graphitisation transition have yet to be observed and related to a mechanistic understanding of the process, inhibiting efforts to enhance graphite formation. What is needed is the ability to probe defects during graphitisation.

In order to probe the defects responsible, partially graphitised material needs to be prepared, however, attempts have been hampered by the need to rapidly heat and cool samples within seconds. Graphite furnaces can provide uniform heating but require hours to heat up meaning they can only probe equilibrium state of carbon materials [Chung2002]. While laser heating have been shown to rapidly heat samples but are unable to uniformly heat a sample to a defined temperature and also suffer from ablation [Abrahamson2018]. Recently, we have developed a pulsed graphite furnace that allows us to heat samples to 3000 ^∘C within seconds and maintain temperature for less than a minute (see Figure 1) [Putman2018, Fogg2020]. This provides us the opportunity of preparing uniformly heated partially graphitised material while observing the defects involved.

In this letter, a pulsed high-temperature furnace is used to observe the change in defective structures during graphitisation using X-ray diffraction and high resolution transmission electron microscopy. Molecular dynamics simulations and simulated microscopy images identify the critical defect as screw dislocations. The movement and annihilation of screws is also described.

X-ray diffraction provides insights into the kinetics of graphitic (stacking order) and graphenic (hexagonal order) crystallites during graphitisation with the pulsed furnace. These structural metrics can be measured from the X-ray diffraction pattern shown in Figure 2 a) (with the inset providing an interpretation of the crystallites with a molecular structure). The graphitic crystallite comes from the stacking of the layers providing the low angle {002} reflection. From the peak position the average distance between layers can be determined $d_{\{002\}}$ and the width of the peak provides insight into the size of the regions of stacking $L_{c\{002\}}$. During graphitisation the $d_{\{002\}}$ is found to change between 2000^∘C and 2800^∘C approaching the value for graphite of 3.35Å. The $L_{c\{002\}}$ is also found to continuously change during heating. The graphenic structure comes from small regions where hexagonal rings of carbon atoms in the same plane provides higher angle reflections such as the {110} reflection. The peak width then gives an average size of the graphenic crystallites, $L_{a\{110\}}$.

Figure 2 b) shows that after a single 10 s pulse the $d_{\{002\}}$ is shifted to a higher critical temperature of $T_{c}\sim 2500{\circ}$C. This demonstrates the system after 10 s pulse is out of equilibrium and further pulses will progress the material towards the thermodynamic equilibrium. Figure 2 d) shows that $L_{a\{110\}}$ follows the $d_{\{002\}}$ only increasing after 2400^∘C. However, all three parameters were found to continuously transform during graphitisation after a single pulse at different temperatures.

The pulsed approach also provides a means of probing this phase transition at a fix temperature over time. For a given set of temperatures multiple pulses can be applied and the system is seen to converge to the equilibrium value of the $d_{\{002\}}$ for that temperature, as does the $L_{a\{110\}}$. However, surprisingly the $L_{c\{002\}}$ is not found to change instead being constant to within the experimental uncertainty. This shows that $L_{c\{002\}}$ is in thermodynamic equilibrium and is not involved in the second order phase transition of graphite. A barrier for graphitisation can be computed using the $d_{\{002\}}$ values from a starting value before graphitisation at 2000 ^∘C in a similar manner to Ouzilleau et al. [Ouzilleau2016]. The barrier was found to be 6$\pm$1 eV (kJ/mol). Pulsed experiments reveal a non-equilibrium system where $L_{a\{110\}}$ and $d_{\{002\}}$ change dependently while $L_{c\{002\}}$ is found to be independent.

Further insights can be gleaned from imaging the partially graphitised material at the fixed temperature of 2400 ^∘C as it equilibrates. Low electron intensities were used and short exposure times to not disturb the structure and increasing beam intensities were found to increase the amorphous fraction in the material suggesting the ordering is solely due to the high temperature treatment. Figure 3 shows the phase contrast images from the HRTEM as well as skeletonised fringes. With the aid of the cold field emission gun, which enable higher resolution than previously achievable, interlayer defects could also be imaged and seen as vertical skeletonised fringes. For a single pulse a series of fringes appear in the misaligned zig-zag texture described earlier [Oberlin1984]. After 60 seconds an alignment of interplanar defects and fringes is seen. This has been called a columnar structure again by Oberlin and colleagues [Oberlin1984]. Finally, after 200 seconds the fringes were found to elongate and the interplanar defects significantly decreased. A wavy texture was found during this phase. During imaging it was found that the regions of interplanar defects have a short focal depth coming into and out of focus within a couple of angstroms. These results reveal the presence of interplanar defects aligning into columns after which they annihilate forming more extended graphitic structures.

To consider what defects could be present, annealed molecular dynamics simulations were performed. Figure 4 a) shows the initial configuration for the simulations with aligned aromatic coronene and benzene fragments to mimic the aligned mesophase formed during carbonisation of graphitising carbons. Molecular dynamics simulations were performed using the EDIP forcefield capable of accurately describing the bond forming and breaking in carbon materials as demonstrated in disordered carbons [Martin2019d, DeTomas2016]. An elevated temperature of 3200 K was used to ensure dynamics on the simulation timescales of picoseconds. Figure 4 b) shows the structure after the first ten picoseconds. A variety of non-hexagonal rings are formed, however, no stacking order was found. After 100 ps Figure 4 c) shows stacking and small regions with screw-like structures. At this stage extended hexagonal regions were also formed. By 1000 ps the main interplanar defect seen are screw dislocations with alignment of screw along the entire length of the box (Fig. 4 d)). These simulations reveal that screw dislocations can form from an ordered phase of carbon resembling the mesophase.

The high resolution TEM image of a screw dislocation in ideal AA stacked graphite can be simulated and compared with the experimental fringes. Figure 4 e) shows a molecular model of the cylindrical core of a screw dislocation in AA graphite. The ramped structure connecting the layers together can be seen. Figure 4 f) shows the simulated HRTEM images at focus as well as infront and behind. At focus the interdigited fringes offset by c/2 can be seen. Compared with the experimental HRTEM image for the 200s at 2400^∘C sample (Figure 4 g) a close resemblance can be seen. By defocusing by only 0.2 nm the interdigited structure disappears and a ramped structure is seen either to the left or to the right depending on the chirality of the screw. This short depth of field also match what is seen experimentally and eliminates attribution to other extended defects such as prismatic edge dislocations (or reconstructions of them) that can also provide the fringes offset by half a layer but would have a larger depth of field in the microscope or would shift predictably with focal depth. The Supplementary information shows many screws in a sample revealing a wavy texture when the interscrew distances are greater than $\sim$2 nm. This matches one of the last textures seen as graphite forms a series of wavy fringes. The multislice HRTEM simulations of screw dislocations match the experimentally seen interplanar defects, depth of focus and wavy texture [Oberlin1984] providing a reasonable assignment for the defect involved in graphitisation at high temperatures.

To understand how screw dislocations can be removed further molecular dynamics simulations were performed at an increased heating rate. Similar simulations were performed as previously described, however, a slightly higher temperature was used of 3500 K enabling the screw glide to occur on picosecond timescales. Figure 5 a) to c) shows a slice of the molecular structure with screw dislocations highlighted and with an arrow in the direction of the Burger’s vector. At 739 picoseconds the two screws in the top left form a dislocation loop with two prismatic edge dislocations in the plane of the graphite layers. Figure 5 b) shows the glide of the topmost screws happening before 994 picoseconds reducing the length of the screw by one layer. Figure 5 c) shows the structure after the pair annihilation of the two topmost screws dislocation. The removal of these defects is identical to that previously studied computationally for the ramp or mezzanine defect  [Trevethan2013, Vuong2017a, Vuong2017b]. This was found to be annihilated with a barrier of 3.24 eV in AA stacked graphite [Martinez2007]. This is a similar energy found for barrier for screw dislocation gliding in an similar system of 2.8 eV per layer. However, it should be noted in the case of the mezzanine defect only six carbon atoms are displaced so this energy is perhaps too low compared with an extended screw dislocation undergoing pair annihilation. Using an Arrhenius argument the temperatures used can be scaled to experimental timescales (see Supplementary Information). This provides temperatures close to the critical temperature seen if 30 s is considered the time scale. Providing a barrier for graphitisation of 8 eV close to that measured in this study. These simulations reveal that screw dislocations can glide and when two of the opposite sense meet can annihilate providing insights into the kinetics and barriers involved in graphitisation.

How are the graphenic crystallites impacted by the annihilation of screw dislocations? These crystallites or $L_{a\{110\}}$, can be approximately tracked in the simulations by considering the hexagonal rings that are connected and aligned to within 3^∘. Figure 5 d) to f) shows the crystallites colour coded according to their size as well as the histogram of size plotted g) to i). At the beginning of the time series a significant fraction of the structure are between 0 and 24 Å in size. After the top layers are freed from a screw defect the total area is increased from 83–94 nm² and the regions of extended hexagonal regions grow up to 40 Å. These screw dislocations appear to pin the in-plane growth in a similar manner to how dislocation can inhibit growth of grain boundaries in metals \textcolorredref Irene\? Nigel?. These simulations therefore provide evidence that the annihilation of screw dislocations allow for the growth of the $L_{a\{110\}}$ thus connecting this defect with the crystallographic ordering seen in X-ray diffraction.

Due to the limited size of the simulations they could no capture other features of the screw formation but some insights can be gained from comparison with other studies. Due to the periodic approximation used, screws can only grow to the extent of the simulation box and the alignment of multiple columns was not observed. This could suggest that the annealing of a particular density of interplanar defects gives rise to ordered columns a set distance apart, which could perhaps be inferred from the size of the aromatic regions in the precursor material during carbonisation. The small size also means that the long range dispersion forces would not have contributed significantly. Screw defects are known to provide a small misalignment angle between layers due to the small negative curvature present in the screw. This provides an increased $d_{\{002\}}$ distance and could explain the turbostratic ordering seen. These misalignment angles could have interesting electronic properties with magic angle graphene having superconducting properties at low temperature [Cao2018]. Some preliminary experimental work looking at Moiré patterns seen along the basal plane suggest these misalignments are present [Boi2021]. Screw formation and controlled annihilation may provide a path for creating these regions in partially graphitised materials. However, there are other ways that lattice mismatch can occur such as in multiwalled nanotubes, carbon fullerene onions or stacked nanocones. So these conclusions only apply for highly ordered graphitising carbons.

What about the ABA stacking structure? As the screws are removed and larger regions of $L_{a\{110\}}$ are formed dispersion will provide a considerable torque between hexagonal regions to pull the layers into ideal ABA stacking alignment. But we hypothesis this can only occur after the majority of screw dislocations are annihilated. This has previously been shown by the strong correlation between $L_{a\{110\}}$ and $d_{\{002\}}$. In the current work these two parameters are time dependent while $L_{c\{002\}}$ is not. Some interesting work on XRD peak shape has suggested a progressive model of alignment where pairs of layers begin to align before complete graphitisation [Puech2019]. This would be interesting to explore in the light of the screw annihilation mechanism presented.

These findings also provide possible routes for improving the production of synthetic and discovery of natural graphite. In particular previous simulations of disordered carbons [Martin2019d] provide a comparison to highlight what is different with graphitising carbons. Both graphitising and non-graphitising materials possess non-hexagonal rings as well as screw defects. But in non-graphitising carbons bent wavy structures still persist after screw annihilation, which have long been seen experimentally [Heidenreich1968]. Our simulations suggest these could be due to the presence of disclinations as we found an excess of negative curvature in all disordered carbons simulated [Martin2019d] but not in the graphitising models shown. These could provide a possible non-annealable topological defect that cannot be removed via screw dislocation pair annihilation. Therefore our first suggestion for improving graphtisation is to form a well ordered mesophase so that no bent regions with disclinations can form.

Mechanical approaches have been extensively studies to align the structure during carbonisation. For example elongational shear in carbon fibre manufacture, stress to form highly oriented pyrolytic graphite [Blackman1962] or shear in diamond anvils [Wong2019]. These all appear to encourage large regions of local molecular orientation. This may also explain the success of using templating approaches to form graphite from non-graphitising materials by enforcing a 2D orientation [Nishihara2012]. While the mesophase alignment is critical it is interesting to consider how mechanical shear, twist or stress could lower the barrier to screw dislocation annihilation providing potential new mechanical routes to graphite. It is also interesting to note that in pyrolytic graphite an even number of left handed and right handed screws have been found [Hennig1965], whereas in natural graphite many superscrews can be seen to form [Rakovan2002]. This suggests that natural graphite with very large crystals forms from a spiral growth mechanism which has yet to be synthetically replicated.

Finally, chemicals can be used to catalyse graphitisation. Intercalating metals have been extensively employed [Oya1979] and could provide strain in the interplanar region that could aid in screw dislocation gliding. Non-carbon atoms such as silicon that more readily form sp³ bonds could also lower the barrier for screw dislocation migration. It is interesting to consdier the Acheson process which uses SiC as a precursor that produces industrial scale graphite at significantly lower temperatures of 1700–2500 ^∘C. These results could also suggest that using graphitic crystallites as a temperature probe in geology could also be challenging if impurity in the material could accelerate graphitisation at a lower temperature. It is also unclear how the addition of shear in geological rock would further modify the graphitisation process as discussed previously [Bonijoly1982]. Chemical or mechanical approaches that specifically target screw dislocation migration could therefore provide new routes for making synthetic graphite and predicting where natural graphite forms underground.