GoKawiilSample preparation and 4D-STEM
A high-purity (99.999%), undoped, commercially available Si single crystal (Crystal Base Co., Ltd.) was mechanically crushed in a mortar and the resulting fragments dispersed onto a molybdenum TEM grid with a carbon support film and the grid was immediately transferred into the microscope to avoid surface oxidation. To remove hydrocarbon contamination, the TEM grid was annealed overnight at 300 °C under high-vacuum conditions using an in situ TEM heating holder (JEOL, Ltd.) inside the microscope and subsequently cooled to room temperature before observation. STEM observations were performed using a JEM ARM300CF (JEOL, Ltd.) equipped with a cold field emission gun and a JEOL DELTA corrector, operated at an accelerating voltage of 300 kV. The probe-forming aperture semi-angle was set to 9.1 mrad and the probe current was estimated to be approximately 9.1 pA. This convergence semi-angle was chosen so that the probe size matches the Si [110] dumbbell spacing; for substantially larger or smaller probes, the double-slit condition is not satisfied and the characteristic interference fringes do not appear (Supplementary Note 9). 4D-STEM datasets were acquired using a pixelated detector (ARINA37, DECTRIS Ltd.) with 192 × 192 pixels to record the full CBED pattern at each probe position. The scan sampling interval was set to 12 pm for all 4D-STEM measurements.
To realize the atomic-scale double-slit geometry, the crystal was precisely oriented to the [110] zone axis using Kikuchi lines and position-averaged convergent beam electron diffraction (PACBED). The electron-probe position at the centre of the Si [110] dumbbell was determined a posteriori with 12-pm precision from the acquired 4D-STEM dataset using a two-step numerical procedure. We note that the high-angle interference fringes used for correlation extraction are inherently robust against small probe positioning offsets, as the fringe visibility is governed by the intercolumn optical-path difference rather than the absolute probe position, and any residual positional uncertainty is already subsumed within the finite effective source size accounted for in the simulations (Supplementary Note 3). First, initial atomic column positions were estimated from the reconstructed annular dark-field images using 2D Gaussian peak fitting (Extended Data Fig. 8a). Then, to overcome precision limits imposed by scan noise and sample drift, we refined the dumbbell centre positions by exploiting the crystallographic symmetry of the CBED patterns38. Using the twofold rotational symmetry (C 2 ) of the Si [110] projection, we calculated a symmetry score S(r) at each probe position r, defined as 1 minus the normalized MSE between the CBED intensity and its 180°-rotated counterpart:
$$S({\bf{r}})=1-\frac{\sum _{{\bf{k}}}{|I({\bf{k}};{\bf{r}})-{\hat{R}}_{180}I({\bf{k}};{\bf{r}})|}^{2}}{\sum _{{\bf{k}}}{|I({\bf{k}};{\bf{r}})|}^{2}},$$
in which S(r) = 1 (S ∈ [−1, 1]) corresponds to exact twofold rotational symmetry. As shown in Extended Data Fig. 8b, this score exhibits sharp local maxima at high-symmetry points. We identified the refined dumbbell centres by locating these maxima in the vicinity of the coarse estimates. To achieve high signal-to-noise ratios while minimizing the impact of sample drift at each temperature, we acquired several 4D-STEM datasets (typically 10–15 scans within the same tens of nanometres field of view) under identical experimental conditions. For each temperature, equivalent CBED patterns corresponding to the refined dumbbell centres identified across these datasets were extracted and averaged to produce the high signal-to-noise ratio experimental patterns used for quantitative visibility analysis.
In situ heating experiments
Temperature-dependent observations were conducted using the same in situ TEM heating holder. The sample was sequentially heated to 300 K (room temperature), 500 K and 900 K, with sufficient time allowed at each temperature set point to ensure thermal equilibrium before image acquisition. STEM images and 4D-STEM datasets were recorded at each temperature under identical optical conditions to enable quantitative comparison of temperature-dependent changes.
Scattering simulations
CBED patterns were simulated using the multislice method implemented in the abTEM39 code. The microscope parameters were set to match the experimental conditions: an accelerating voltage of 300 kV and a probe-forming aperture semi-angle of 9.1 mrad. The electron probe was positioned at the centre of the Si [110] dumbbell. To account for the finite source size and effective probe instability, we mix adjacent diffraction patterns using Gaussian weights with a FWHM of 0.8 Å as a function of the distance between the probe positions at which the patterns were simulated. No aberrations (defocus, spherical or chromatic) were applied, as the effect of typical residual aberrations was found to be negligible (Supplementary Note 3). The sample thickness for each temperature dataset was determined by maximizing the cross-correlation coefficient between experimental and simulated PACBED patterns40 (Extended Data Fig. 9). We confirmed by simulation that whether the left or the right atomic column terminates last at the exit surface makes no notable difference to the resulting patterns (Supplementary Note 10). The estimated thicknesses were 12.7 nm at 300 K, 10.8 nm at 500 K and 10.4 nm at 900 K. For all simulations, thermal diffuse scattering was calculated by averaging over 1,000 frozen-phonon configurations. In the full correlated model, phonon vibrations in all directions are included. Note that atomic displacements parallel to the beam have a negligible first-order effect on the projected potential and hence on the CBED intensities, so the lateral displacements are the dominant factors governing fringe visibility (Supplementary Note 11).
Phonon-displacement models
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