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I twist and twist, I want to confuse: manipulations with two-layer graphene



In 2004, the scientific community first became acquainted with graphene in its physical form. For many decades, there have been many theories about this amazing material. Since the receipt of real graphene, we have learned a lot about it, but not all. Scientists from the University of Illinois at Urbana-Champaign (USA) decided to conduct rather unusual experiments with graphene plates. The study showed that the dimensions of graphene plates and the ambient temperature directly affect the stability of the structure, which can be used to obtain a structure of a certain shape, thereby changing its properties. How exactly were the experiments conducted, what new data on bilayer graphene were obtained, and how to put the knowledge into practice? We learn about this from the report of scientists. Go.

Study basis


As an object of study, it became not just graphene, but its two-layer version. As the name implies, such a structure consists of two graphene plates tightly adjacent to each other, the distance between which is about 1 nm. As a rule, in two-layer graphene, the lower plate is rotated 60 degrees relative to the upper one, due to which the sublattice A in the lower plate and the sublattice B in the upper are aligned vertically (AB configuration).


Examples of AA and AB plate configurations in bilayer graphene ( source ).

This version of a two-dimensional structure based on graphene is far from the only one. So, according to the example of scientists, there is a method of isolating graphene with graphite, which results in a completely new structure in terms of properties. But you can change the characteristics not only by changing the constituent elements, but also by changing their location.

Diffraction from the selected region and dark-field microscopy at one time confirmed the presence of rotated regions in bilayer graphene plates created by chemical vapor deposition.

Rolled bilayer graphene can exhibit a wide range of unusual properties, including superconductivity, ferromagnetism, and even increased lubricity. All these abilities are due to changes in interlayer communication due to the angle of rotation. An important parameter determining the interlayer coupling is the period of the unit cell, called the moiré superlattice, which changes strongly with small changes in the angle of rotation.

The study of the friction of rotated graphite flakes (plate parts) on graphite surfaces can undergo smooth sliding (increased lubricity), followed by a sudden cessation of sliding associated with the rotation of the graphene element back into its commensurate AB-packing. We also observed a transition from a commensurate (with the AB configuration) to an disproportionate (rotated) arrangement of graphene flakes with subsequent sliding.

Molecular studies have shown the existence of potential energy barriers to unwind graphene flakes, but the origin of these barriers with respect to the size of the flakes and its thermal stability has not yet been studied.

In the study we are considering today, scientists show that the effects of the final edges resulting from the truncation of periodic moire structures create many potential energy barriers to unwind the graphene plate at certain turning angles. The number and magnitude of these energy barriers scale with the size of the flakes and lead to size-dependent thermal stability of the rotational states.

Modeling


The rotational stability of twisted two-layer graphene was studied using large-scale molecular dynamics modeling based on LAMMPS software . Model structures of twisted two-layer graphene of a certain size were created by rotating graphene flakes in the AB configuration on a freely suspended endless graphene sheet with an initial misorientation angle * θ = 7.34 ° relative to the axis outside the plane ( 1a ).
Misorientation * - the difference in crystallographic orientation between two crystallites in a polycrystalline material.


Image No. 1 A

superposition of two rotated graphene gratings at this angle creates moire patterns with a periodicity of L p = 1.9 nm ( 1b ). Each unit moire cell consists of atoms with several different configurations - AB, AA, BA and SP ( 1 ).
Moire pattern * - a pattern obtained by superimposing on each other two periodic mesh patterns.
The graphene flakes were trimmed (top plate) to fit the size of the moire unit cell. This means that the graphene flake has exactly 1 moire period at θ = 7.34 ° and is called L1xL1.

Further, this unit cell was copied 2, 4, 6, and 32 times in planar directions to obtain graphene flakes L2xL2, L4xL4, L6xL6 and L32xL32 with dimensions of the rhombic edge 3.8, 7.6, 11.4 and 61.4 nm, respectively.

In the obtained model of bilayer graphene, in-plane CC bonds (covalent bonds between carbon atoms) are described by a reactive empirical bond model (REBO), and unbound interlayer interactions are represented by the Kolmogorov-Crespi potential, which correctly reflects the magnitude and anisotropy of the interlayer surface potential energy.

Calculations of packing fault energy * (SFE) of bilayer graphene in the AB configuration were also performed .
Packing defect * - violation of the normal sequence of packing of atomic planes in a close-packed crystalline structure.
The obtained SFE values ​​are approximately 2% different from those obtained in calculations based on the density functional theory (DFT) using the local density approximation, as well as DFT calculations that take into account Van der Waals interactions.

Research results


The rotated graphene flakes were thermally balanced at temperatures ranging from 300 to 3000 K using a Berendsen thermostat for 1 ns and then a Nose-Hoover thermostat for 3 ns (fixed time step 1 fs).


Image 2:

Graphs 2a - 2d show the change in the angle of rotation of the graphene flake L4xL4 during one equilibration period (4 ns) at different temperatures. At 300 K, the graphene flake rotates from its initial angle θ = 7.34 ° to θ = ∼8 ° ( 2a ). However, at 600 K, the graphene flake already rotates in the opposite direction to θ = ∼6.4 ° ( 2b) Higher temperature equal to 640 K, leads to a step change in the angle of repetition: first from θ = 7.34 ° to 6.4 ° at 0.25 ns, then to = 4.5 ° at 0.5 ns and to = 2.6 ° at 2.25 ns ( 2c ).

With a slight increase in temperature to 650 K, the graphene flake instantly unwinds, restoring its original configuration AB at θ = 0 ° ( 2d ). These distinct transitional turns of graphene flakes are accompanied by changes in the moire pattern and periodicity ( 2g ).

A curious feature of these turning changes is their dependence on the size of the flakes. So, for smaller graphene flakes L1xL1, instant untwisting to a stable AB configuration (θ = 0 °) occurs already at 300 K ( 2) But the large graphene flake L32xL32 shows slight changes in θ even at temperatures of 1000 K ( 2f ).

Then, scientists calculated the total potential energy E t θ relative to the global minimum energy E t AB when untwisting different graphene flakes.


Image No. 3

The existence of many energy barriers and local minima of potential energies was observed when graphene flakes are unwound from θ = ∼8 ° in order to reach an unrotated state, which is a global minimum at θ = 0 °. An increase in the size of the flakes increases the number of potential energy barriers for unwinding, as well as the magnitude of these energy barriers.

The smallest graphene flake L1xL1 has exactly one local minimum at θ = ∼8 ° with a low barrier energy of 0.052 eV ( 3a ), which is explained by spontaneous untwisting at room temperature ( 2e ). For the L2xL2 graphene plate, two local minima are currently developing at 8.51 ° and 5.81 ° with barrier energies of 0.17 and 0.31 eV, respectively ( 3b ).

For the graphene plate L4xL4, four locally stable rotation angles ( 3s ) were observed , corresponding to four transition states at 2a - 2d. The initial state at θ = 7.34 ° is energetically unfavorable, since it is near the local peak, as a result of which the graphene flake rotates another θ = 0.74 ° to its local minimum θ = 8.08 ° ( 2a ). The graphene flake has sufficient thermal energy to overcome both the first energy barrier (E b = 0.36 eV) at 600 K and all subsequent ones except the final energy barrier (E b = 0.74 eV) at 640 K. Slightly higher temperatures (650 K ) allow you to cross the final energy barrier to achieve the configuration of AB.

For larger graphene flakes L32xL32, 32 barriers were observed (each approximately in E b= 3 ... 6 eV) corresponding to 32 initial moire superlattices along each direction ( 3d ).

These numerous energy barriers ensure the stability of rotation of the L32xL32 graphene flake even at high temperatures (3000 K), which is comparable to the temperatures during the growth of graphene by chemical vapor deposition.

Using the Arrhenius equation * , the rate of transition from one rotation state (θ 1 ) to another (θ 2 ) can be expressed as k θ 1 → θ 2 = Ae - E b / k B T , where k B is the Boltzmann constant *.
* k T.

* (k) . k = 1380649 10-23 /.
Thus, barriers of potential energy E b1 were obtained for five graphene flakes of increasing size in the first stable state (θ 1 ) near the initial twist angle θ = 7.34 °.

Then, the temperature was gradually increased to obtain the value of the activation temperature (T) at which the graphene flake crosses E b 1 and untwists in a neighboring stable state (θ 2 ).

Scientists note that increasing the size of the flakes significantly increases E b1 and leads to a higher activation temperature T for the first case of unwinding. Due to the high E b1equal to 3.93 eV for the largest graphene flake L32xL32, we do not observe the spinning of the graphene flake even at a temperature of 3000 K.

Then, potential energy was calculated for completely periodic rotated two-layer graphene with moire superlattices scaled to the same number of atoms as in the flake L32xL32 for comparison.

As a result, the process of smooth decay of E t θ - E t AB (i.e., without energy barriers) with the unwinding of completely periodic moiré superlattices ( 3d) However, in rotated graphene flakes, moire superlattices are “cut off” near the edges, which ultimately leads to periodic fluctuations of potential energy during unwinding. Next, a quantitative determination was made of this incomplete periodicity of the moire superlattices on the edges r , as the remainder of the size of the flakes L over the moire period L p (θ).

The rotation angles at which r / L p sharply changes from 1 to 0 indicate the fully developed (not truncated) moire structure for the graphene flake, akin to fully periodic rotated bilayer graphene.

During unwinding, each graphene flake intersects many local minima of energy levels equal to the initial number of moire periods (4 for L4xL4; 32 for L32xL32, etc.).


Image No. 4

On 4a and 4b it is seen that the potential energies of each atom for both swirling graphene E θ and ABAB-configured graphene, the EAB value is much higher at the edges due to asymmetric cleavage of carbon bonds. To eliminate this edge effect, it was decided to take E θ - E AB as a measure of local change in energies ( 4c ). Therefore, the atoms in the configuration AB are already in the global minimal configuration and have E θ- E AB = 0, i.e. zero mismatch. The atoms in the BA configuration are also in the global minimum configuration. However, these atoms have maximum mismatch, since they have opposite atomic stacks compared to AB (stacking faults), as evidenced by the maximum differences in atomic energies (E θ - E AB = 13 meV).

Consequently, the magnitude of the excess potential energy of each atom compared to the energy in its non-rotating state (| E θ - E AB |) is a quantitative measure of the degree of mismatch of the atom. From this conclusion, we can classify atoms based on the range | E θ - E AB | (4d ): AB (0–2.2 meV); AA (2.2–3.7 meV and 10–11.5 meV); SP (3.7–10 meV) and BA (11.5–13 meV).


Image No. 5

The images above show the mismatch edges of the atoms of the graphene flake L4xL4 at rotation angles corresponding to local minima and saddle energy levels along the path of the minimum potential energy for 3 s . Fully periodic moire patterns ( 5a ) can now develop at saddle points , since the size of the flakes L is commensurate with the moire period L p . As a result, the barrier energy for interfacial slip becomes very low, since the configurations of atoms in the periodic geometry are independent of the translational motion of the graphene flake relative to the substrate.

In contrast, at rotation angles corresponding to local minima, the energies L and Lp become disproportionate and tend to minimize the total potential energy, contributing to the formation of AB rather than AA ( 5b ). Thus, small lattice shifts from this energy-minimized configuration can lead to large changes in the stacking sequence for an incomplete moire period at the edges, which will lead to high barrier energies for both rotation and interfacial slip.

For a more detailed acquaintance with the nuances of the study, I recommend that you look into the report of scientists .

Epilogue


The main conclusion of this study is that the effects of the final edges resulting from the trimming of the moire pattern control the rotation resistance of twisted two-dimensional materials. In particular, the changing periodicity of the moire during the unwinding of the two-layer material creates numerous barriers of potential energy due to the spatially varying degree of commensurability in the configurations of atoms. These boundary effects explain the mechanisms underlying the rotational transitions of such structures, as well as the dependence of such transitions on the sizes of the structures used and on temperature.

The bottom line is that rotated graphene always strives to return to its original state, since for it it is the most stable state and position of atoms. However, under certain conditions, stability is maintained even in the presence of rotation of the structure. The main factor in the presence of this stability is the rotation angles, as well as various temperatures, allowing the graphene structure to transition from one stable state to another.

In bilayer graphene, the layers that make up its structure are not tightly bound to each other. This feature, according to researchers, allows you to interpret the properties of the structure depending on the circumstances. Selecting certain conditions, you can get the same structure, but with different properties. Therefore, the range of applications of such a structure expands without the need to radically change it.

Thank you for your attention, stay curious and have a great weekend everyone, guys! :)

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