Grain Boundary Engineering via TEM

October 15, 2024 - Researchers from Ulm University, the Institute for Quantum Optics, and Leiden University have studied the formation of grain boundaries in nanocrystalline carbon monolayers under different electron beam conditions. Using a transmission electron microscope with spherical and chromatic aberration correction, they explored how electron beam energy affects defect formation and structural dynamics at the atomic level. Their findings suggest that precise manipulation of grain boundaries is possible, enabling future applications in nanotechnology and materials science.

Observing, manipulating, and precisely constructing structures at the atomic scale open new possibilities in nanotechnology, particularly when precise control over individual atoms is achieved.¹–³ These atom-by-atom studies have only become possible with the development of spherical (CS) aberration correctors,⁴,⁵ monochromators,⁶–¹⁰ and chromatic (CC) hardware aberration correction,¹¹,¹² enabling imaging at accelerating voltages of 80 kV, 60 kV, 40 kV, and even lower. When a sample is exposed to a broad 100 kV electron beam, which exceeds graphene’s knock-on threshold of ~86 kV,¹³ an increasing number of defects are introduced into the monolayer until it transitions into a disordered state.¹⁴ However, graphene’s self-healing properties can be exploited to reduce the defect density through thermal treatment.¹⁵ Additionally, a high-dose 80 kV electron beam has been shown to transform amorphous carbon into nanocrystalline graphene.¹⁶

Structural changes as subtle as the introduction of individual defects can significantly alter the properties of materials, highlighting why carbon monolayers with minimal long-range order—such as nanocrystalline graphene or amorphous carbon monolayers—exhibit vastly different characteristics compared to pristine graphene. These variations can endow the material with new functionalities.¹⁷,¹⁸ Notably, the incorporation of seven- and eight-membered rings can enhance the proton permeability of an otherwise pristine carbon monolayer¹⁹,²⁰ while maintaining its impermeability to larger atoms and molecules. Grain boundaries, primarily composed of five- and seven-membered rings,²¹ are of particular interest due to their composition and the variability in their sequence, which depends on the angular mismatch between adjacent grains.²² These boundaries have also been successfully utilized to fabricate simple circuitry for sensing applications.²³

As a type of extended defect, grain boundaries have a significant impact on the structural,²⁴ chemical,²⁵ and electronic²⁶ properties of carbon sheets. They have been the focus of extensive theoretical and experimental research.²⁷,²⁸ Moreover, the structure of grain boundaries can evolve under electron beam illumination. When sufficient energy is provided to overcome activation barriers, a grain boundary may transition into a more energetically favorable configuration.²⁸,²⁹ Consequently, grain boundaries in graphene can be modified by electron beam exposure. Through this process, small grains may be entirely removed as they integrate into the surrounding pristine carbon structure.²⁸ The interaction mechanisms between the electron beam and the sample in transmission electron microscopy (TEM) are diverse. These include elastic interactions, often referred to as knock-on damage, in which individual atoms are displaced from their lattice sites. Inelastic interactions, such as bond rotations, radiolysis, ionization, and chemical etching, can also occur and modify the specimen under investigation.³⁰ The knock-on threshold for graphene has been determined both experimentally and theoretically to be slightly above 80 kV.¹³ Additionally, graphene’s high electrical conductivity helps mitigate the effects of radiolysis.

However, the knock-on threshold for carbon atoms in defective carbon rings and at edge sites is significantly reduced.³¹ For instance, in the presence of dangling bonds, the knock-on threshold can drop to as low as 56 kV.³²,³³ At high defect concentrations, this threshold decreases further and can be below 40 kV for free-standing, thin amorphous carbon.³⁴ Additionally, the energy required to move an atom within the lattice is lower in defective structures. For example, the energy needed to rotate bonds in a carbon monolayer is approximately 10 eV,³⁵ compared to 17 eV required to remove a carbon atom from pristine graphene.³⁶ According to the McKinley-Feshbach formalism, these energies correspond to electron beam energy thresholds of ~<52 kV and <86 kV, respectively. Consequently, extensive examination of nanocrystalline graphene and other defective carbon monolayers at 80 kV in high-resolution HRTEM mode can induce structural changes, promote hole growth,³⁷,³⁸ and ultimately lead to the degradation of the layer. Furthermore, single vacancies exhibit high formation energies (7.5 eV) and rapidly merge with other vacancies,³⁹ accelerating hole formation during TEM imaging.

80 kV Experiments
When an area of the sample is observed for the first time at high resolution, it initially appears completely covered by contamination, obscuring the individual atomic positions. Over time, small holes (1–3 nm in diameter) in the contamination layer allow individual carbon atoms or atomic rings to become visible (~0–3 holes per 3,300 nm², Fig. 1a). As imaging continues, the amorphous contamination dissipates, revealing the underlying nanocrystalline material. Composed of small grains, a significant portion of the NCG monolayer consists of grain boundaries. Due to its lower knock-on threshold compared to pristine graphene, holes form and expand, rapidly degrading the monolayer. Consequently, no large monolayer regions remain visible at any given time, with the diameters of any exposed monolayer seldom exceeding 5 nm (see Fig. 1b).

To further investigate the samples' behavior under the electron beam, the electron dose rate was drastically increased. Two key observations emerged from the high-dose-rate experiment. First, the elevated dose rate naturally led to an increased damage rate. However, by shifting the beam away from an area as soon as the onset of hole formation was detected, damage to the material could be minimized. This approach was feasible because, under these conditions, only part of the field of view was illuminated. Consequently, despite the higher damage rate compared to experiments conducted at normal dose rates, more of the monolayer could be revealed. Second, as progressively larger monolayer regions became visible, their structural evolution during the experiment could be studied in detail. The researchers employed a neural network⁴⁰,⁴¹ to differentiate between monolayer and contamination, as well as to identify the positions of carbon atoms. The carbon rings were mapped, clearly displaying the positions and composition of the grain boundaries. Ring statistics were generated and used to track structural changes between frames (Figs. 2b, 2c). By utilizing the neural network, the pentagon-to-hexagon ratio was evaluated, showing a decrease from 0.23 in Figure 2b to 0.20 in Figure 2c, indicating structural changes in the monolayer toward a more pristine graphene-like configuration.

As the pentagon-to-hexagon ratio might be skewed by the carbon structure at the edges of the holes, the researchers evaluated this value separately for pentagons and hexagons detected at the hole’s edge. In Figure 2b, 2% of the pentagons and hexagons were located at the edge of a hole, with a pentagon-to-hexagon ratio of 0.63, whereas in Figure 2c, 4% of the pentagons and hexagons were at the edge of a hole, with a ratio of 0.42. Excluding these edge polygons would alter the overall ratio by only 2.2% in Figure 2b and 3.5% in Figure 2c, which would not be reflected in the final values as they are rounded to two decimal places.

60 kV Experiments
The hole growth caused by the 80 kV electron beam significantly hampers the ability to study the monolayer. To mitigate knock-on damage while still effectively removing contamination, the experiment was conducted at 60 kV. Initially, the sample was examined at a moderate dose rate, similar to the 80 kV experiments. Under these conditions, hole formation was almost entirely suppressed. Even at high dose rates, holes did not develop readily and only appeared after prolonged exposure (Fig. 3). Another factor contributing to the monolayer’s increased stability is graphene’s ability to self-heal.³⁷ Carbon can fill small holes, as observed under high-dose-rate conditions. By strategically shifting the beam once the onset of damage becomes noticeable—similar to the approach used in the 80 kV experiments—damage could be further minimized, allowing for nearly damage-free imaging at 60 kV.

Under these conditions, it becomes feasible to investigate the monolayer and its response to the electron beam. A high-dose-rate image series was recorded at a frame rate of ~5.5 frames per second, with a dose rate of ~6 × 10⁷ e·nm⁻²·s⁻¹. This setup enables the tracking of grain transformations at atomic resolution and high temporal resolution (Fig. 4). In Figure 4, a neural network-generated overlay for eight frames, selected from a series containing a total of 2,339 frames, is presented. These selected frames highlight key stages of grain boundary dynamics under electron beam exposure. Initially, three distinct grain orientations are clearly separated by a grain boundary and surrounded by contamination (Fig. 4a). As the experiment progresses and contamination is removed, the grain boundary partially encircling the center grain becomes visible. The center grain is smaller than the other two grains (Figs. 4b–4d). Over time, the boundary around the center grain initially closes before breaking again. Subsequently, the center grain is absorbed by the lower grain, leaving behind the upper part of its grain boundary. This process results in an initially winding and elongated grain boundary between the remaining grains (Fig. 4e). As the experiment continues, this boundary significantly straightens (Figs. 4f–4h). The pentagon-to-hexagon ratio decreases from 0.06 in frame 0 to 0.04 in frame 2327. The 60 kV electron beam provides sufficient energy for bond rotations in graphene. This energy is delivered locally, enabling transformations only in the areas directly irradiated by the electron beam. Additionally, by adjusting the beam spread, the dose rate and the size of the irradiated area can be quickly modified. This capability offers a tool to control grain movement by selectively irradiating regions conducive to a specific objective.

40 kV Experiments
In an effort to develop a method for removing contamination without substantially altering the grain structure of the sample, experiments were conducted at half the previously used acceleration voltage, specifically at 40 kV. Observation under a moderate electron dose rate (~10⁶ e·nm⁻²·s⁻¹) at this lower accelerating voltage for ~1 hour indicated only minimal changes in contamination coverage and no hole formation within the sample. However, the maximum dose rate at 40 kV is limited to ~7 × 10⁶ e·nm⁻²·s⁻¹, as exceeding this value would violate radiation safety regulations. This dose rate at 40 kV is approximately three orders of magnitude lower than that at 80 kV. As a result, the effect of the 40 kV beam on the grain structure could not be examined. The researchers speculate that a higher dose rate would enable the removal of contamination even at 40 kV, thereby making the grain boundary structure visible.

Resource: Leist, C., Makurat, M., Jiao, A., Liu, X., Schneider, G. F., & Kaiser, U. (2024). Control of Grain Boundary Formation in Atomically Resolved Nanocrystalline Carbon Monolayers: Dependence on Electron Energy. Microscopy and Microanalysis, 00, 1–9. https://doi.org/10.1093/mam/ozae101