Fig. 2: Reciprocal lattice of 1T-TaS₂ and diffraction geometry.

a, Visualization of the 1T-TaS₂ specimen located within the objective lens of the UTEM. The optical excitation drives a transformation of the layered CDW lattice between two incommensurate CDW phases (grey and red spheres), probed by a nanometre-sized electron beam of variable tilt (double arrow). b, Ewald construction visualizing the diffraction geometry. The intensity scattered into individual first-order CDW spots is governed by proximity to the Laue condition, that is, where the Ewald sphere (green) intersects the CDW reciprocal lattice rods (red). Accessing the FOLZ requires an electron beam tilted slightly away from the [001] zone axis. The low curvature of the Ewald sphere for 120 keV electron energy results in a dense sampling of the rod shape. c, Reciprocal lattice of the NC phase (open grey) and IC phase (open red) of 1T-TaS₂ (first-order spots only). Due to the CDW stacking periodicity, the CDW spots are located in the FOLZ (l = 3n ± 1 in equation (1)) of the CDW lattice, while the related host lattice reflections (solid grey) lie in the ZOLZ. d, Temporally averaged experimental diffractogram. The high electron beam coherence leads to a clear separation of NC and IC spots. The coloured overlay indicates the local height k_z of the Ewald sphere above the ZOLZ in units of b₃*. While first-order spots of both phases are the dominant feature in the FOLZ and contain information on the stacking periodicity, the low-intensity second-order NC spots appearing between bright host reflections in the ZOLZ are a sensitive measure of the CDW amplitude.