Extended Data Fig. 4: c lattice constant-dependent (0 0 0 l) XRD peak intensity.
a, Side view of the unit cells of Ti3C2 MXene with z coordinates of Ti atoms indicated. b, Relationship between the intensity ratio for (0 0 0 2)/(0 0 0 l) XRD peaks and the c lattice constant. When the c lattice constant varies, the ratio of the peak intensities for the (0 0 0 2) reflection to those of the (0 0 0 l) peaks can change by several orders of magnitude. To quantify these changes, the theoretical peak intensities for each Bragg reflection were calculated using the equation: \({I}_{{hkl}}={({\sum }_{j}^{N}{f}_{j}\cos {\varphi }_{j})}^{2}+{({\sum }_{j}^{N}{f}_{j}{isin}{\varphi }_{j})}^{2}\), where I is the relative integrated intensity, f is the atomic form factor, and φn \(=2\pi (\)hxn \(+k\)yn \(+l\)zn\()\). Here, the equation was simplified by ignoring light atoms with small atomic numbers Z, including N (Z = 7), C (Z = 6), and H (Z = 1), considering their sufficiently lower f ~ Z2 compared to Ti (Z = 22). The imaginary part \({\sum }_{j}^{N}{f}_{j}i\sin {\varphi }_{j}\) is eliminated when a collection of atoms has a center of symmetry41. For (0 0 0 l) lamella peaks, \({\varphi }_{n}=2l\pi {* z}_{n}\). As a result, this equation can be further simplified to \({I}_{{hkl}}={({\sum }_{j}^{N}{f}_{j}\cos (2l\pi {* z}_{n}))}^{2}\). The value of d was found from STEM images to be around 2.4 Å. The correlations between the calculated (0 0 0 2)/(0 0 0 l) peak intensity ratio and the c-lattice constant are shown in Extended Data Fig. 3b. This qualitative analysis helps to understand the non-monotonic variation of peak intensity ratios with c lattice constants among h-MXenes. For example, it explains why the difference between the intensities of (0 0 0 2) and (0 0 0 4) peaks gradually decreases when the c lattice constant increases for alkylimido-terminated Ti3C2 MXenes. It also explains why the (0 0 0 6) peak of Ti3C2(oca)2/3 becomes less intense when the c lattice parameter decreases from 52.93 Å to 49.45 Å in Fig. 5d.
