A deck of cards in which each card is slightly rotated cannot lie flat: the backs and faces will never align. But if the cards are flexible, they will start to adjust, shifting by fractions of a millimeter to find the perfect match. Something similar happens inside crystals when two thick layers of MoS2 or MoS2 with WS2 are stacked with a twist of 1–2 degrees. Their atomic lattices, like the patterns on cards, strive to align, and to do so, atoms shift, forming regions of perfect stacking.

Until now, such rearrangement was observed only on surfaces or in thin films a couple of atomic layers thick. Hidden interfaces inside thick crystals remained inaccessible: methods that see the surface cannot reach that deep. The authors of the new study used multilayer electron ptychography, a technique that scans the sample with a focused electron beam and reconstructs the structure at different depths from diffraction patterns. It is as if the cards were X-rayed to reveal how each layer inside the deck has shifted.

The experiment showed that at the interface between two MoS2 crystals twisted by 1.23 degrees, extended domains with perfect stacking formed, separated by partial dislocations, which are linear defects where atoms are arranged in a "step" pattern. Away from the interface, the lattice remained almost perfect. Analysis of displacements of more than 40,000 atomic columns revealed that the rearrangement decays with distance: at two layers from the interface, the displacement exceeded 6 picometers, and at four layers it dropped to the noise level. This means the deformation penetrates deep but quickly fades.

Comparison with a theoretical model gave an unexpected result: the actual rearrangement was stronger than predictions based on parameters for thin bilayers. The reason is that the outer layers of a thick crystal suppress bending, forcing the inner layers to compress and stretch more strongly in the plane. This is an important difference from free thin films, which can bend freely.

Now that hidden interfaces have become visible, the path is open to the deliberate design of multilayer materials. Knowing exactly how atoms rearrange upon twisting, one can engineer systems with tailored electronic and mechanical properties. The deck of cards that once seemed randomly shuffled now reveals its order, layer by layer.