Exfoliation-induced increase in van der Waals gap in two-dimensional layered crystals

This work demonstrates that mechanical exfoliation induces measurable distortions in the van der Waals (vdW) gap of layered crystals, while the annealing process can reduce this distortion. Using X-ray diffraction (XRD), lattice parameters were compared in bulk and mechanically exfoliated flakes of selected transition metal dichalcogenides and monochalcogenides. The results reveal a systematic expansion of the lattice parameter along the [00.1] direction (perpendicular to the vdW layers) in the exfoliated samples, corresponding to residual strain values from 0.037% for GeS to 0.39% for ZrS2. This suggests that exfoliation introduces residual structural strain into the crystal lattice. In contrast, optical measurements indicate that these lattice modifications have only a minor effect on the electronic band structure, as the energies of optical transitions do not change significantly. This observation is consistent with density functional theory (DFT) calculations, which show that although the lattice expands predominantly along the [00.1] direction compared to [10.0], the corresponding changes in band gap are small. The results highlight that residual strain is a consequence of mechanical exfoliation and likely a universal feature of two-dimensional layered materials. Ab initio calculations confirm that the vdW gap in mechanically exfoliated multilayer flakes is enlarged by 0.04-0.19% compared with bulk crystals. This observation is important for accurate modelling of heterostructures composed of mechanically exfoliated van der Waals crystals.