Fig. 6: Transition of A15 interstitial clusters into 2D loops.

a Transition barriers of \({I}_{7}^{A15}\) clusters to \(\frac{1}{3}\langle 111\rangle\) Frank loops in Al and Cu. b Transition barriers of \({I}_{7}^{A15}\) clusters to \(\frac{1}{2}\langle 110\rangle\) prismatic loops in Al and Cu. The initial and final states in (a, b) were found using the Activation-Relaxation Technique nouveau (ARTn)³⁷. c Truncated disconnectivity graph between different states of I₈ clusters in fcc Cu, as discovered by TAMMBER^41,66. A15 clusters are detected using distortion scores⁶³; dislocation lines are identified using DXA analysis⁷⁰. A15 clusters are shown with purple atoms, \(\frac{1}{3}\langle 111\rangle\) faulted Frank loop is cyan, \(\frac{1}{2}\langle 110\rangle\) loops are blue, \(\frac{1}{6}\langle 411\rangle\) loop is red, \(\frac{1}{6}\langle 112\rangle\) Shockley dislocations are green. The lowest energy dislocation configurations are built by partial Shockley dislocations that form perfect prismatic loops according to the reaction \(\frac{1}{6}\langle 211\rangle+\frac{1}{6}\langle 12\overline{1}\rangle \to \frac{1}{2}\langle 110\rangle\). d The transition mechanism of the perfect icosahedral A15 cluster to the Frank loop. The atoms are coloured according to the local atomic energies. The corresponding energy barrier is shown with the green curve in subplot (a). The structures are viewed along the 〈111〉 direction.