Ripplocations in van der Waals layers.

Dislocations are topological line defects in three-dimensional crystals. Same-sign dislocations repel according to Frank's rule |b1 + b2|(2) > |b1|(2) + |b2|(2). This rule is broken for dislocations in van der Waals (vdW) layers, which possess crystallographic Burgers vector as ordinary dislocations but feature "surface ripples" due to the ease of bending and weak vdW adhesion of the atomic layers. We term these line defects "ripplocations" in accordance to their dual "surface ripple" and "crystallographic dislocation" characters. Unlike conventional ripples on noncrystalline (vacuum, amorphous, or fluid) substrates, ripplocations tend to be very straight, narrow, and crystallographically oriented. The self-energy of surface ripplocations scales sublinearly with |b|, indicating that same-sign ripplocations attract and tend to merge, opposite to conventional dislocations. Using in situ transmission electron microscopy, we directly observed ripplocation generation and motion when few-layer MoS2 films were lithiated or mechanically processed. Being a new subclass of elementary defects, ripplocations are expected to be important in the processing and defect engineering of vdW layers.