In situ atomistic insight into the growth mechanisms of single layer 2D transition metal carbides

Developing strategies for atomic-scale controlled synthesis of new two-dimensional (2D) functional materials will directly impact their applications. Here, using in situ aberration-corrected scanning transmission electron microscopy, we obtain direct insight into the homoepitaxial Frank–van der Merwe atomic layer growth mechanism of TiC single adlayers synthesized on surfaces of Ti3C2 MXene substrates with the substrate being the source material. Activated by thermal exposure and electron-beam irradiation, hexagonal TiC single adlayers form on defunctionalized surfaces of Ti3C2 MXene at temperatures above 500 °C, generating new 2D materials Ti4C3 and Ti5C4. The growth mechanism for a single TiC adlayer and the energies that govern atom migration and diffusion are elucidated by comprehensive density functional theory and force-bias Monte Carlo/molecular dynamics simulations. This work could lead to the development of bottom-up synthesis methods using substrates terminated with similar hexagonal-metal surfaces, for controllable synthesis of larger-scale and higher quality single-layer transition metal carbides.

Supplementary Figure 1 | Electron energy loss spectroscopy elemental mapping from the adlayer areas. Atomic resolution STEM image (left) acquired from a single layer Ti3C2 flake after homoepitaxial growth, and the corresponding C relative composition map obtained from EEL spectrum imaging. Blue areas have low C composition, while yellow and red areas have high C composition. The adlayer areas generally show higher C concentration.

Supplementary Figure 2 | Stacking of h-TiC adlayer on
Ti3C2. a-b, Side view of crystal structure of -Ti4GaC3 (a) and -Ti4GaC3 (b). The structure of Ti4C3 block is the same as we predicted for h-TiC adlayer on Ti3C2. c-d, Side view of structure of Ti5C4 (c) and Ti6C5 (d). The repeating CAB stacking sequence is clear. Light green, Ga; Blue, Ti; gray, C.

Supplementary Figure 3 | Theoretical adsorption energies and capacities for Ti4C3 and
Ti5C4. a, Side and top views of ion adsorption on Ti4C3 nanosheets. b, Theoretical adsorption energies of Ti4C3, Ti5C4, and Ti6C5 for different metal ions: Li, Na, K, Mg, and Al. K + can only form a partial 2/3 layer as observed in Ti2C and Ti3C2. c, Theoretical capacities of Li, Na, K, Mg, and Al ions on Ti4C3, Ti5C4, and Ti6C5.
Supplementary Figure 4 | Migration energy path of Ti and C atoms from the bulk to the Ti3C2 surface. a-c, Calculated migration energy path from body to surface for C atom (a), outer layer Ti atom (b), and middle layer Ti atom (c).
Supplementary Figure 5 | C migration from body to Ti3C2 surface through different pathways. Initial, transition, and final states are shown for different migration pathways. Here "P" denotes pristine Ti3C2, while "TiC" means one Ti and one C atoms have already diffused to Ti3C2 surface and formed TiC dimer. "-S" indicates that after migrating to the Ti3C2 surface the C atom bonds with the TiC dimer, and "-B" means after migrating to the Ti3C2 surface the C atom is not bonded with the TiC dimer. "VTi " denotes Ti vacancy. White, Ti of Ti3C2; gray, C of Ti3C2; red, moving Ti; green, moving C. See Supplementary Fig. 4a for the energy plot.

Supplementary Figure 6 | Different migration pathways for outer layer Ti atoms from body
to Ti3C2 surface. Initial, transition, and final states are shown for different migration pathways. Here "P" denotes pristine Ti3C2 surface, while "C", "TiC", and "CTiC" means originally the Ti3C2 surface has one C adatom, a TiC dimer formed by one C adatom and one Ti adatom, and a CTiC trimer formed by two C adatoms and one Ti adatom, respectively. "-S" indicates that the Ti atom bonds with surface adatoms after migrating to the Ti3C2 surface, and "-B" means the Ti atom is not bonded with surface adatoms after migrating to the Ti3C2 surface. "3VTi" means a vacancy cluster of three Ti vacancies on the surface. White, Ti of Ti3C2; gray, C of Ti3C2; red, moving Ti; green, moving C. See Supplementary Fig. 4b for the energy plot.

Supplementary Figure 7 | Different migration pathways for middle layer Ti atoms from
body to Ti3C2 surface. Initial, transition, and final states are shown for different pathways. Here "V" denotes the pinhole defect of Ti3C2. "1", "2", and "3" indicate the number of Ti vacancy in the outmost Ti layer, and therefore the size of the pinhole. "N" and "F" mean Ti atom diffuses to the first nearest and second nearest adsorption site on Ti3C2 surface, respectively. White, Ti of Ti3C2; gray, C of Ti3C2; red, moving Ti; green, moving C. See Fig. S4c for the energy plot.

Supplementary Figure 8 | Diffusion paths of Ti atom, C atom, TiC dimer, and trimers on
Ti3C2 surface. Initial, transition, and final states for a Ti atom, a C atom, a TiC dimer, a TiCTi trimer, and a CTiC trimer to diffuse on the Ti3C2 surface. White, Ti of Ti3C2; gray, C of Ti3C2; red, moving Ti; green, moving C. The energy barrier of the diffusion paths is shown on the right.

Supplementary Figure 9 | Formation energy of graphene-like C layer versus
MXene-like C layer. a-d, Using density functional theory (DFT), optimized crystal structure along the a axis of an additional MXene-like C layer of (a) 10 C atoms and (b) 25 C atoms, on Ti3C2 substrate. Optimized crystal structure of an additional graphene-like C layer of (c) 36 atoms and (d) 72 atoms. e, Binding energy per C atom for MXene-like C layer and graphene layer as a function of number of C atoms. The binding energy of MXene-like C layer on Ti3C2 surface is 2.65 eV/atom, which is much higher than that of graphene ~ -0.25 eV/atom. This suggests that sequential layer-by-layer growth is unlikely because If C atoms form a layer first, they should prefer the thermodynamically more stable graphene-like morphology. Although Ti atoms can grow on graphene, the theoretical Ti-Ti bond length is 2.46 Å 1 , which is shorter than that of Ti4C3 ~ 3.09 Å. Such lattice mismatch pattern has not been observed experimentally, which therefore excludes the possibility of a growth mode that a carbon layer grows first and the titanium layer grows on top of the carbon layer. L is the length of the Ti4C3 unit cell. In the main text, we discuss the edge structure stability based on the Ti chemical potential difference Ti, where we assume the Ti source is from Ti bulk or Ti3C2. Since we propose that 2D h-TiC should also form by feeding Ti and C atoms in gas sources, we extend our study on the stability of edge structures to a wider chemical potential range as a function of the chemical potential difference between Ti and C,  = (Ti -C)/2, which satisfies Ti + C = TiC. Therefore, the Ti-rich and C-rich condition in the main text is  = 1.502 and  = -0.041, respectively. By increasing the chemical potential of Ti, the Titerminated edge becomes more stable. The Ti-terminated AC is stable between 1.779 and 2.432 eV. After that, Ti-terminated ZZ_C dominates. On the other hand, by decreasing the chemical potential of Ti, the C-terminated edge is more stable. We notice that the formation energy of the edge structure becomes negative when  is below -0.51 eV or above 2.56 eV, suggesting the edge structure is not stable and it will undergo a surface reconstruction. Therefore, to grow 2D h-TiC using bottom-up methods, it is better to maintain the chemical potential in slightly Ti-rich condition. Supplementary Figure 14 | Step-edge energy barriers. Migration energy paths of a Ti atom, a C atom, and a TiC dimer climbing up to the top of a h-TiC adlayer. The energies barriers here are lower than energy barriers for Ti and C atom to move from the body to the surface, while the energy barriers are higher than the diffusion barriers of Ti and C adatoms on the Ti3C2 surface.

Supplementary Figure 15 | Comparison between diffusion barriers predicted from ReaxFF and DFT calculation.
Diffusion barrier of Ti and C adatoms on Ti3C2 surface using DFT (solid line) and ReaxFF (dashed line). The red atoms are Ti adatoms while the green atoms are C adatoms. The agreement between DFT and ReaxFF is excellent. Therefore, simulations requiring large number of atoms were performed using ReaxFF instead of DFT.