Extended Data Fig. 5: Energetically unfavourable events of interfacial ledge propagation and possible pathways for filling the vacancy column of the interfacial ledge.

a, b, Ledge flow without filling up the Cu-vacancy columns transforms the mismatch dislocation into an isolated edge dislocation in Cu. The mismatch dislocation (blue “T”) is buried by the newly formed Cu and becomes an isolated edge dislocation (red “T”), which will increase its energies due to the required presence of many broken bonds along the isolated dislocation line. By contrast, it is thermodynamically more favourable for the mismatch dislocations to climb to the new interface, by adsorbing extra Cu from the Cu substrate, to release some lattice mismatch strain upon the Cu₂O→Cu interfacial transformation. c, An initially straight ledge stops at a mismatch dislocation core. d, e, A segment of Cu vacancies (marked in red colour) in front of the interfacial ledge is filled up and the segment then resumes its propagation to the next mismatch dislocation core (marked by the blue dashed lines). This is an unfavourable event because it will result in large geometric kinks with their side lengths of seven Cu lattice spacings for each propagation. Such an unsynchronized ledge flow leads to a highly kinked ledge with significantly increased ledge lengths and therefore is energetically unfavourable compared to the propagation of a straight ledge that happens only after all the Cu vacancies in front of the entire interfacial ledge are filled up. f–h, Two possible pathways of filling the vacancies in the interfacial ledge with Cu atoms supplied from the Cu bulk: f, g, randomly occupying the vacant sites, resulting in a high density of atomic kinks in the ledge; g, h, aggregation of Cu atoms into a one-dimensional (1D) segment of Cu, which subsequently grows along the ledge.