In situ homoepitaxial growth

The homoepitaxial growth process is experimentally investigated using a Nion UltraSTEM 100 microscope at a vacuum of roughly 10−9 Torr combined with a Protochips Fusion in situ heating system (see Methods). Monolayer Ti 3 C 2 2D material is prepared from annealing monolayer Ti 3 C 2 T x flakes inside the microscope at above 500 °C (Fig. 1a). Ti 3 C 2 T x is the chemical exfoliation product from the selective etching of “Al” out of the MAX phase Ti 3 AlC 2 4,26,27, and T x denotes functional groups such as –F, –OH and –O. The crystal structure of Ti 3 C 2 T x can be regarded as a Ti–C–Ti–C–Ti quintuple layered-structured Ti 3 C 2 core terminated by T x on two surfaces (Fig. 1b). When projected along the c axis, the three Ti layers labeled as CAB form a hexagonal pattern of three different sites (Fig. 1b), which is also displayed in the corresponding STEM image acquired at room temperature (Fig. 1c). The bright dots with similar intensity in STEM images represent projected Ti atoms from the three different layers, while the C atoms cannot be detected due to their overlap with heavier Ti atoms along the c axis28. The dark contrast (indicated by white dotted circles) results from Ti vacancies on the bottom and top surfaces from the etching process27,29. At room temperature, due to the surface stabilization by functional groups and the much lower thermal energy, the Ti 3 C 2 T x flakes are stable under e- beam irradiation (Supplementary Movie 1).

Fig. 1 Homoepitaxial growth of MXene. a Schematic of the homoepitaxial growth process to form single layer h-TiC on a monolayer Ti 3 C 2 substrate through electron-beam irradiation and heating. Ti atoms from different layers are plotted using different shades of blue. b Crystal structure of monolayer Ti 3 C 2 T x viewed from [100] and [001] zone axes. c Atomic resolution STEM image acquired from monolayer Ti 3 C 2 T x along the [001] zone axis at room temperature. Areas of Ti vacancies are indicated by white dotted circles. Inset shows comparison between atomic resolution STEM image and projected crystal structure of Ti 3 C 2 T x . d A STEM image acquired after heating and electron-beam irradiating monolayer Ti 3 C 2 flakes inside the microscope at 500 °C. The black areas are pores, while areas framed by green, blue, and black dashed lines are the substrate (Ti 3 C 2 ), nanoscale areas of single h-TiC adlayer on one surface (Ti 4 C 3 ), and nanoscale areas of single h-TiC adlayers on both surfaces (Ti 5 C 4 ), respectively. e A STEM image acquired after heating MXene flakes inside the microscope at 1000 °C. f EEL spectra before and after e-beam irradiation at 500 °C for the C-K edge at 284 eV, Ti-L 2,3 edge at 456 eV, and O-K edge at 532 eV. g Perspective view of eight different stacking configurations (I-VIII) of h-TiC adlayer on a Ti 3 C 2 substrate. The relative total energy (eV) to the ground state (I) is shown for each structure. h Experimental (EXP) and simulated (SIM) STEM images of Ti 4 C 3 and Ti 5 C 4 , and the corresponding crystal structures projected along [001] and [100] zone axes. The scale bars in c–e are 2 nm, while the scale bars in h are 0.5 nm Full size image

At 500 °C, monolayer Ti 3 C 2 flakes are formed following the removal of T x from Ti 3 C 2 T x MXene, as evidenced by the disappearance of T x -associated oxygen K edge in the electron energy loss spectrum (EELS) acquired after heating and beam irradiation (Fig. 1f). Additionally, Ti 3 C 2 flakes undergo significant morphology changes after electron-beam irradiation and heating for about 20 min (see Fig. 1d and Supplementary Movie 2). The most prominent features are: (1) dark-contrast faceted pores with edges aligned along {100} planes, and (2) bright-contrast triangular islands framed by black and blue dashed triangles that suggest a growth process of an additional atomic layer at least consisting Ti atoms. As revealed by EELS elemental mapping, the adlayer areas have higher relative C concentration than Ti 3 C 2 (Supplementary Fig. 1). The EELS result thus favors a hexagonal TiC adlayer structure rather than pure Ti adlayer structure. Moreover, DFT suggests pure Ti adatoms tend to form 3D clusters with lower formation energy than 2D Ti adlayer when C atoms are absent.

To solve the crystal structure of the triangular islands, we first consider the stable crystal structure of a single h-TiC adlayer on a Ti 3 C 2 substrate (Fig. 1g). Eight models are constructed based on (1) different Ti stacking sequences, CABC (I, IV, VI) or CABA (II, III, V) or CABB (VII, VIII); (2) with C occupying octahedral interstitial sites (I, II) or tetrahedral interstitial sites (III–VIII) or surface tetrahedral sites (V–VIII) (Fig. 1g). DFT total energy calculation predicts the CABC stacking of Ti layers with C atoms at octahedral interstitial sites (configuration I) to be the ground state of an h-TiC adlayer on Ti 3 C 2 . When more h-TiC adlayers are grown, DFT predicts BCABC and ABCABC stacking for two and three h-TiC adlayers on Ti 3 C 2 , respectively (Supplementary Fig. 2). In general, the local crystal structure of nanoscale as-grown areas is modified to Ti n+3 C n+2 if n layers of h-TiC adlayers grow on the Ti 3 C 2 substrate.

Theoretical STEM images simulated using DFT-optimized crystal structure of Ti n+3 C n+2 exhibit unique patterns that can readily be used to unambiguously identify the number of h-TiC adlayers solely from the experimental STEM images (Fig. 1h). All the triangular areas in Fig. 1e are identified as one h-TiC adlayer with a local structure of Ti 4 C 3 (one Ti site is brighter than the other two) or two h-TiC adlayers with a local structure of Ti 5 C 4 (two Ti sites are brighter than the third). Considering that both the top and bottom h-Ti surfaces of a suspended Ti 3 C 2 flake can function as substrates, the growth is mostly limited to one h-TiC adlayer on each h-Ti surface, while Ti 5 C 4 areas result from overlapping of single h-TiC adlayers grown on both surfaces. The islands are generally several nanometers and their size is likely limited by the available source of Ti and C atoms. Future growth of large area TMCs will need external metal and carbon sources beyond the substrate material.

Heating at 1000 °C significantly accelerates the homoepitaxial growth process. With the electron beam blanked, the sample was kept at 1000 °C for several seconds and then cooled down to room temperature. Solely activated by thermal energy, h-TiC adlayers rapidly grow on both h-Ti surfaces of monolayer Ti 3 C 2 flakes, forming network of Ti 5 C 4 and Ti 4 C 3 regions (Fig. 1e) that are much larger than those formed at 500 °C. The h-TiC adlayers exhibit irregular shapes, possibly due to the non-equilibrium nature of fast diffusion and growth at the elevated temperature. Growth of mostly single h-TiC adlayers on Ti 3 C 2 , strongly suggests an island type FM growth mode that prefers 2D layer formation. Moreover, the homoepitaxial growth here leads to the formation of a mixture of new MXenes Ti 4 C 3 , Ti 5 C 4 , which are predicted to possess excellent energy storage properties (Supplementary Fig. 3)30, but have never been synthesized using conventional top-down exfoliation methods. To elucidate the growth mechanism, we employ time-dependent STEM imaging and DFT.

Growth mechanisms and kinetics

Activated by electron-beam irradiation and/or thermal exposure, Ti and C atoms in monolayer Ti 3 C 2 flakes migrate onto the h-Ti surface, providing Ti and C adatoms as the source material for growth, thereby leaving pores in the substrate. This is the first step of homoepitaxial growth. At 500 °C, individual STEM image frames (Fig. 2a–i) are acquired at different times to show pore evolution from a three-Ti-vacancy (3-V Ti ) cluster as indicated by dashed white circles in Fig. 2a. The 3-V Ti cluster is likely formed by the removal of three adjacent Ti atoms from one of the surface layers during chemical etching27. The Ti vacancy cluster grows as Ti atoms migrate onto the surface (Fig. 2b, c). The remaining Ti atoms in the center rearrange to adopt the minimum energy state and eventually there are only enough Ti atoms to form a single Ti layer in the center (Fig. 2d). From Fig. 2d–f, the central Ti atom (indicated by the green circle) finally diffuses away. The Ti single layer area immediately collapses, and then a vacuum pore continues to expand as shown from Fig. 2g–i.

Fig. 2 Dynamic growth process as revealed by atomic resolution STEM imaging. a–i Pore expansion captured by a series of time-lapsed STEM images acquired from a monolayer Ti 3 C 2 area following electron-beam irradiation and heating at 500 °C. The initial 3-V Ti cluster is indicated by three white dotted circles. The last Ti atom that migrates to the surface before pore formation is indicated by the green dotted circle. j–m Time-lapsed STEM images showing the dynamic expansion of island growth of h-TiC adlayers (Ti 4 C 3 : blue dotted lines, Ti 5 C 4 : black dotted lines) on Ti 3 C 2 substrate at 500 °C. White arrows in l and m indicate overlap of h-TiC adlayers on bottom and up surfaces to form Ti 5 C 4 . Cyan dashed lines in l and m indicate the projected grain boundary where the two adlayers first encounter in k. The scale bars are 2 nm Full size image

The energy barriers associated with migration of C and Ti atoms onto the h-Ti surfaces are investigated using DFT (Fig. 3a–e). In defect-free Ti 3 C 2 , the energy barriers for a C atom (green path from “I” to “F” in Fig. 3a) or a Ti atom (red path from “I” to “F” in Fig. 3c) in the surface layers to move onto the surface are 2.91 eV and 5.32 eV, respectively. Both energy barriers are quite high, especially for the Ti atom migration that requires breaking of strong Ti–C bonds and overcoming repulsive force from other Ti cations. The migration barrier, however, is reduced by the presence of defects. Similar to the experimental condition in Fig. 2a, when a 3-V Ti cluster (white balls in Fig. 3b, d) is present, the green C atom at position “I” in Fig. 3b is only bonded to three Ti atoms in the middle layer instead of 6 Ti atoms for defect-free Ti 3 C 2 . Consequently, a migrating C atom only needs to break 3 Ti–C bonds and the migration barrier is reduced to 0.97 eV (path 3-V Ti , Fig. 3b). Although a 3-V Ti cluster does not help migration of Ti atoms (Fig. 3d), the migration barrier of a Ti atom near a C vacancy (V C ) is reduced to 2.56 eV (path V C in Fig. 3e) because it possesses one fewer Ti–C bond. Other possible migration paths for surface Ti and C atoms at various defective environments show comparable migration energy barriers (Supplementary Figs. 4–6). For Ti atoms in the middle layer, the migration barrier is 6 eV, which can be lowered when all the surrounding Ti and C atoms are moved away (Fig. 2d, Supplementary Fig. 7). In that case, the Ti atom at the middle layer first diffuses to one of the two outer layers, and then migrates to the surface with a barrier of 2.99 eV. The DFT results agree well with experiment, where the migration starts from the defective surface layers, followed by the middle layer. DFT also indicates that C atoms move to the surface first, followed by Ti atoms. The maximum energy transferred to a Ti atom from 100 kV electron beam is 5 eV based on Eq. (1) in Ref. 31 and is sufficient to activate the migration process.

Fig. 3 Migration and diffusion barriers for Ti and C atoms. a–e Carbon atom migration pathways for a perfect crystal (“P”, a), and with help of 3-V Ti cluster (“3V Ti ”, b); and titanium atom migration pathways for a perfect crystal (“P”, c), with help of 3-V Ti cluster (“3V Ti ”, d), and with help of a single C vacancy (“V C ”, e). “I” and “F” denote the initial and final positions of the migration paths. Cyan, Ti; gold, C; red, diffusing Ti atom; green, diffusing C atom; white, Ti vacancy site; blue, C vacancy site. f Diffusion pathways of Ti adatom, C adatom, and TiC dimer on the Ti 3 C 2 surface. The migration or diffusion energy barrier for each case in a–f is labeled in eV. g, h Calculated energy along the migration paths for C (g) and Ti (h) from Ti 3 C 2 body to Ti 3 C 2 surface. i Energy along the diffusion paths on the Ti 3 C 2 surface for a Ti adatom, a C adatom, and a TiC dimer Full size image

The second step in the growth process is island formation of h-TiC adlayer on h-Ti surface, which occurs by the self-assembly of C and Ti adatoms that have already migrated onto the surface. The diffusion barrier of a Ti and a C adatom on the bare surface of Ti 3 C 2 is 0.10 and 1.04 eV, respectively (Fig. 3f, i), which suggests that Ti atoms are more mobile on the surface as compared to C atoms. When a Ti atom diffuses within proximity of a C atom, it is energetically more favorable for them to bond into a TiC dimer than for them to remain separate. With a diffusion barrier (0.72 eV) lower than a C atom or a Ti–C–Ti trimer (1.24 eV, see Supplementary Fig. 8 for diffusion path and energy for dimers and trimers), the TiC dimer should be a common molecule moving on the surface. When several TiC dimers cluster together and become immobile because of increased diffusion barriers, they could serve as a nucleation site for bonding of additional TiC dimers, resulting in island formation and expansion. A growth mechanism, assuming that a layer of C atoms grows on the substrate first followed by a layer of Ti atoms, is unlikely considering the very high formation energy of such MXene-like C layers (2.65 eV/atom, see Supplementary Fig. 9 for more details).

An example of island growth is shown in Fig. 2j–m (see Supplementary Movie 2 for more details). Two pores of dark contrast continuously expand from Fig. 2j–m and serve as the Ti and C sources that sustain the growth process. The two islands of single h-TiC adlayer framed by blue dotted lines are initially separated (Fig. 2j), and they continue to grow strictly limited to lateral expansion to meet and overlap as shown in Fig. 2k–m, respectively. The two adlayers are most likely formed on the top and bottom surfaces, respectively, because their triangular outlines show opposite orientations, which is to be expected assuming the adlayers grow following “CABC” stacking sequence and have the same edge structure (see Supplementary Fig. 10 for more details). This is further confirmed by the fact that when the two h-TiC adlayers starts to overlap in STEM images to form local Ti 5 C 4 structure (marked by white arrows in Fig. 2l), the growth is not interrupted, and both grains grow past the initial grain boundary line as indicated by cyan dashed lines. Therefore, previously observed Ti 5 C 4 regions should mostly result from overlapping of single h-TiC adlayers growing on both h-Ti surfaces. It is also possible that the Ti 5 C 4 region could result from two adlayers growing on one surface. The Ti 5 C 4 region framed by the black dashed lines (Fig. 2j–m) has edges parallel to the edges of the outer Ti 4 C 3 area framed by blue dashed lines, suggesting that the two adlayers might be on the same surface. As Ti 6 C 5 areas are rarely observed and Ti 7 C 6 were never observed, growth of two adlayers on one surface happens less frequently than growth of a single adlayer on each surface.

When interacting with Ti 3 C 2 substrate, the 2D h-TiC adlayer has the lowest formation energy compared to different configurations of cubic TiC nanoparticles (NPs) (Fig. 4a), despite cubic TiC being the most stable titanium carbide structure. The total energy mainly depends on the strong covalent bonds between C atoms in the adlayer and Ti atoms in the surface. The 2D h-TiC has the largest interaction area with the h-Ti surface, the largest number of Ti–C bonds, and therefore the lowest total energy of 0.44 eV/TiC (Fig. 4a). Although a planar TiC has similar contact area as a 2D h-TiC layer, the severe mismatch between hexagonal Ti 3 C 2 and tetragonal TiC lattice leads to higher formation energy (0.96 eV/TiC). In contrast, low interacting areas between various cuboid TiC NPs and Ti 3 C 2 substrate lead to high formation energies (1.11 and 1.54 eV/TiC for two different cuboid shapes in Fig. 4a). More configurations and the formation energies can be found in Supplementary Table 1 and Fig. 11. The h-Ti surfaces of monolayer Ti 3 C 2 thus serve as an ideal substrate that ensures that growth of a h-TiC single layer is energetically favorable, hinting that with a careful selection of the substrate, bottom-up synthesis of TMCs may become a reality by the mechanisms shown by STEM.

Fig. 4 Edges and equilibrium shapes of 2D h-TiC adlayer on Ti 3 C 2 surface. a Side view (left) and top view (right) of optimized crystal structure and formation energy of an h-TiC adlayer, two different cuboid shapes (cuboid 1 and cuboid 3 ), and planar TiC, all composed of 16 atoms, on Ti 3 C 2 surface. b Structural models of the edge structure of h-TiC adlayer on Ti 3 C 2 , including standard armchair (AC), Ti- and C-oriented zigzag (ZZ-Ti and ZZ-C) edges, and cases when they are terminated with Ti or C atoms. The Ti and C atoms in the h-TiC adlayer are red and green respectively. c Calculated edge energies of h-TiC on Ti 3 C 2 as a function of Ti chemical potential difference, Δμ Ti . d An experimental STEM image and simulated model showing the triangular island and the ZZ-C edge crystal structure model. e–g The equilibrium shape of h-TiC on Ti 3 C 2 at varying Δμ Ti : −1.54 eV (e), −0.50 eV (f), and 0 eV (g). The colored outlines represent different types of edge structure Full size image

Edge structure and equilibrium shape

The edge structure of 2D materials critically determines the probability of atom attachment/detachment to/from the edges which impacts growth of 2D materials and tailors the final shape of 2D materials32,33,34,35. STEM images indicate that h-TiC adlayers are mostly terminated with zigzag (ZZ) edges (see Figs. 1c–d, 2j–m, 4d). To help understand the arrangement of C atoms that are indeterminate in the STEM images, we performed DFT calculations for seven hypothetical edges including four ZZ type edges (ZZ-Ti, ZZ-C, ZZ-Ti + C, and ZZ-C + Ti), and three armchair (AC) type edges (AC, AC + Ti, AC + C) (Fig. 4b). The formation energies (γ) of different edges depend on Ti chemical potential difference (Δμ Ti , defined as μ Ti - μ Ti_bulk ), as plotted in Fig. 4c (see Supplementary Figs. 12 and 13 for a broader Δμ Ti range). Near the Ti-rich condition (−0.11 < Δμ Ti < 0 eV), ZZ-Ti is the most stable edge structure, while ZZ-C becomes the most stable edge structure in a wide range of −1.50 < Δμ Ti < −0.11 eV. In both cases, ZZ-type edges are the most stable, in agreement with experimental observation.

Using a Wulff construction based on edge formation energies, the thermodynamic equilibrium shape of 2D h-TiC adlayer on Ti 3 C 2 are visualized for Δμ Ti = −1.54 eV (Fig. 4e), −0.50 eV (Fig. 4f), and 0 eV (Fig. 4g). Generally, edges with lower formation energy are retained during the growth32,33,36. Under C-rich conditions (Δμ Ti = −1.54 eV), h-TiC adlayer adopts the shape of a perfect triangle terminated by ZZ-C edges. At Δμ Ti = −0.5 eV, ZZ-Ti edges start to emerge at the triangle vertices. Under Ti-rich conditions (Δμ Ti = 0), the equilibrium shape turns into a dodecagon consisting of ZZ-C, ZZ-Ti, and AC edges that have similar formation energies. Compared with the experimentally observed adlayers that are typically triangular, it is concluded that experimental growth conditions are C-rich, and the edges are most likely ZZ-C. In Fig. 4d, an experimental triangular adlayer from 500 °C heating shows excellent agreement with the ZZ-C terminated structure model. At 1000 °C (Fig. 1e), h-TiC adlayers exhibit more diverse shapes because (1) thermodynamic equilibrium states cannot be reached within the short evolution time, and (2) merging of fast-growing islands obscures the original shapes.

With the knowledge of the h-TiC adlayer edge structure, we can now calculate the step-edge barrier for adatoms on Ti 3 C 2 surface to climb up onto h-TiC adlayer through aZZ-C edge. The step-edge barriers for a Ti adatom, a C adatom, and a TiC dimer are 2.23, 1.36, and 2.56 eV, respectively (Supplementary Fig. 14), which are comparable to Ti and C migration energy from the body onto the Ti 3 C 2 surface (Fig. 3g, h), but much higher than the diffusion barriers of adatoms on the Ti 3 C 2 surface (Fig. 3i). Energetically, the adatoms prefer diffusing on the h-Ti surface until attaching on a h-TiC adlayer, to climbing up onto a h-TiC adlayer. The vertical growth of h-TiC adlayer would only occur after the Ti 3 C 2 surface is fully covered by the first h-TiC adlayer, which is difficult to achieve experimentally. In rare cases (see the brightest region in Fig. 1e, and black dashed triangle in Fig. 2j–m), localized growth of multiple h-TiC adlayer is possible when TiC dimers cannot diffuse out.

ReaxFF simulations of homoepitaxial growth

The dynamic growth process is simulated using the reactive force field (ReaxFF) method, which provides atomistic level details as well as a realistic representation of chemistry37,38,39, at a larger length scale than DFT. A ReaxFF force field that was developed for Ti 3 C 2 MXene structures40 is employed here, and is shown to correctly predict energy barrier for Ti and C adatoms diffusion on Ti 3 C 2 substrate (Supplementary Fig. 15). In the simulations, two initial pores were introduced by deleting Ti and C atoms and placing them randomly at the surface a monolayer Ti 3 C 2 flake consisting of around 10,000 atoms and a size of 112 by 129 Ǻ. Also, a small seed cluster of Ti and C adatoms was created near the pores. Clustering of surface adatoms into crystalline triangular islands (indicated by white dashed lines in Fig. 5d) is observed by using hybrid force-bias Monte Carlo (fbMC) and MD simulation at 1500 K. Figure 5a–d focuses on the island growth dynamics, showing the formation of a triangular shaped h-TiC adlayer from scattered Ti and C atoms, which is analog to the growth process of MBE. It should be noted here that because of time-scale limitation of these simulations, we chose higher temperatures than experiment to accelerate the dynamics of the system during a short time scale. For simulating pore expansion, temperature was set to 2500 K to overcome higher energy barriers of Ti and C diffusion to the surface. As shown in Fig. 5e–h, the initial pores expand during the simulation and the atoms migrate to the MXene surface. As revealed in ReaxFF simulation, diffusion of Ti and C adatoms leads to the nucleation of the local h-TiC island, which then expand as more Ti and C atoms are attached to the edges, similar to the lateral growth of islands in Fig. 2j–m.

Fig. 5 ReaxFF Molecular dynamic simulation showing the structural evolution in MXene. a–d Island growth observed for an initial configuration with a Ti–C seed after different time periods of ReaxFF force-bias Monte Carlo/molecular dynamics (fbMC/MD) simulation at 1500 K. e–h Pore expansion observed for initial configuration with two pores and Ti–C seed after different time of fbMC/MD simulation at 2500 K. The scale bars are 1 nm. (adatom Ti: red, Ti: cyan, C: gold, adatom C: yellow) Full size image