Exfoliation and Cleavage of Crystals from a Universal Potential

Abstract

Exfoliation and cleavage create two-dimensional (2D) materials and surfaces with physical and chemical properties distinct from their bulk parents. The rising class of non-van der Waals (non-vdW) 2D materials derived from non-layered crystals provides a fascinating new platform - greatly expanding the landscape of low-dimensional materials. Current computational models, however, provide limited guidance: existing descriptors are largely tailored to vdW layered systems. Here, we introduce a general framework predicting crystal cleavage and exfoliable 2D subunits directly from bulk structures. At its core is a universal eXfoliation and Cleavage Potential (XCP) enabling large-scale screening of diverse materials at negligible computational cost. Applying this approach, we obtain 37,208 cleavable surfaces and candidate non-vdW 2D materials from which we investigate 2,377 likely exfoliable ones using high-throughput density functional theory. We identify sheets with square and rectangular lattices, semiconducting systems exhibiting an indirect-to-direct band-gap transition upon exfoliation, and first non-vdW 2D metals. Our study thus opens a systematic route to explore and design new 2D materials with unprecedented chemical and structural diversity.

Figures (6)

• Figure 1: Identifying 2D Subunits in Bulk Materials from Bond Energies. Schematic illustration of how 2D sheets can be identified from bulk structures. As an example for the BONDDEL approach, the crystal structure of FeTiO$_3$ (ICSD #43466) (a) is used to compute bond strengths using the XCP model (b). The different Fe-O bonds are labelled by their respective strength. The weakest bonds in the structure are then cut until 2D subunits remain (c), leading to the previously experimentally realized Puthirath_Balan_CoM_2018 non-vdW 2D material ilmenene (d). The HKLSEARCH algorithm is demonstrated for Ca$_3$N$_2$ (ICSD #169727) (e). Using the bond strengths provided by the XCP (f), the planes with lowest energy density (i.e., lowest surface energy) (g) are used to identify the new non-vdW 2D material (001) 2D Ca$_2$N$_3$ (h).
• Figure 2: Surface Energies, Exfoliation, and Cleavage Planes of Silicon. (a) Three-dimensional plot showing the favorability of Si planes in comparison to the maximum energy {100} planes. The quantity $\Delta E (hkl)$ is represented by the radius and color (light = not favored, dark = highly favored). As a guide to the eye, the reciprocal lattice directions (100), (010), and (001), are indicated as arrows. The lowest energy {111} planes relevant for exfoliation and cleavage are marked by orange circles. (b) Wulff shape computed from these surface energies with the same orientation as in panel (a). (c) Crystal structure of Si aligned with the $(111)$ plane normal (= $[111]$ direct lattice direction) pointing upwards. (d) Energy profile of slicing the crystal at different positions. Panels c and d are aligned so that distances and atom positions match along the $(111)$ plane normal direction. The quantity $d$ measures the distance along this direction in while $\delta$ is in units of the spacing of equivalent $(hkl)$ planes.
• Figure 3: Predicted 2D Candidates. (a) Distribution of exfoliability ratios from the HKLSEARCH and BONDDEL approaches. Bars resulting from both methods are stacked. The rightmost bar includes all structures with ratios above $3.75$. The range of investigated potentially exfoliable candidates ($R > 1.5$) is outlined. (b) Pie chart of relative frequencies of different surface-terminations among the identified 2D candidates. The data for the species distribution among compounds in the AFLOW-ICSD is included as inset. (c) Pie chart showing the distribution of bulk parent space groups (by index number) giving rise to 2D sheets. The space group distribution in the AFLOW-ICSD is included as inset. (d) Pie chart showing the distribution of candidates among the five 2D Bravais lattices. (e) Number of 2D candidates containing heavy elements ($72 \leq Z \leq 83$). Each system is counted according to its heaviest constituent element. (f) Distribution of exfoliation energies for the candidates. Relax/static values correspond to computations including/excluding structural relaxation of the obtained 2D sheets. $E_\mathrm{exf} = 140m\eV\per\angstrom^2$ computed for hematene, i.e., 2D (001) Fe$_2$O$_3$Friedrich_NanoLett_2022, is indicated by the green vertical line. The inset highlights the region around the maximum.
• Figure 4: Atomic and Electronic Structure of Selected 2D Candidates. (a,b,c,g,h,j) Top and side views of example non-vdW 2D structures identified by the XCP method including the exfoliation plane, chemical formula, ICSD number, exfoliability ratio according to the HKLSEARCH (H) and BONDDEL (B) approaches, and calculated exfoliation energy. In-plane unit cells are indicated by the black frames. The systems are sorted vertically according to their lattice type, i.e., hexagonal, square, and rectangular. (d,e,f,k,l,m) Corresponding band structures and densities of states (DOSs). The electronic structure data correspond to the material shown in the panel directly above it. For the spin-polarized system in (l), positive DOS corresponds to spin up states while negative values refer to spin down states.
• Figure 5: (Supporting Information) Asymmetry of Nearest Neighbor Radii. Schematic visualization of a hypothetical iron-hydroxide bonding arrangement. Atoms are depicted as circles, nearest neighbor bonds as black lines. The nearest neighbor radius of the oxygen atom (small dashed circle) does not encompass iron, while the iron nearest neighbor radius (large dashed circle) encompasses oxygen.