A Ginzburg-Landau theory of intrinsic dislocation-loop formation in diamond with machine-learned atomistic simulations

Defects limit the performance of diamond in electronics and quantum technologies, yet how they nucleate from migrating point defects is rarely described as a phase transition. Here we show that dislocation-loop formation in diamond is a \emph{first-order phase transition}. We build a Ginzburg-Landau theory of it whose order parameter – the loop area – and coefficients are fixed directly from quantum-mechanically accurate machine-learned atomistic simulations. From simulations at nanometre and nanosecond scales, we find that carbon self-interstitials aggregate, by diffusion-recombination and lattice exchange, into line-defect motifs that seed a prismatic $\frac{1}{2}⟨110⟩$ dislocation loop and two platelet-like planar defects. We also characterize the dynamics of the transition with Kramers’ rate theory. The transition is strongly first-order, driven overwhelmingly ($\approx 98\mathrm{\%}$) by bond-energy reorganisation rather than elastic relief. Because these defects form \emph{intrinsically} – from carbon interstitials alone, without nitrogen – our results offer a nitrogen-free pathway complementary to the nitrogen-mediated routes long debated for type-Ia diamond, and a transferable framework for irradiation-induced loops.