Fig. 4: Crystallographic volume and topological defects.

Top left, region of sample in which crystallographic volume defects and topological defects were observed, consisting of an open surface and two closed-surface nanovoids, indicated with white isosurfaces. Coloured slabs indicate the height of the layers shown by a–e. a–e, The evolution of the c-axis orientation through the thickness of the sample, with the creation and annihilation of topological defects. Streamlines represent the in-plane components of the orientation and are coloured according to their x component. They are overlaid on the electron density so that the location of volume defects is also visible (white regions). a, A single trefoil defect (T1 in orange) is present near the open surface. Moving up through the thickness, the trefoil defect T1 shifts to be centred on a nanovoid (b), while maintaining its topology, and then it moves out of the nanovoid to the other side (c). d, A pair of dislocations with opposite topological charge (comet C in blue and trefoil T2 in green) are created at the open surface. e, The opposite charge pair consisting of the trefoil defect T1 and comet defect C annihilates and a single trefoil defect T2 remains. Bottom, higher magnifications of slices d and e showing experimental renderings of comet and trefoil topological defects (left) with model representations (right). Scale bars, 120 nm.