Numerical simulation of the formation volume of point defect clusters in bcc Fe

The formation volumes of vacancy and self-interstitial atom (SIA) clusters in bcc Fe were evaluated using 0 K molecular statics (MS) calculations combined with the elastic-dipole formalism. Cluster sizes ranged from isolated point defects to NV=12209 and NI=10621. The stress of each defect-containing cell was corrected by subtracting the residual stress of a perfect crystal of the same size. Finite-size convergence tests were performed to assess the adequacy of the simulation cells. Vacancy-cluster formation volumes were positive and approached the conventional geometric relation VfV=NVΩ0 with increasing size. In contrast, SIA-cluster formation volumes were much smaller and became slightly negative in the large 1/2111 dislocation-loop regime. For the largest vacancy and SIA clusters, the normalized formation volumes VfV/NVΩ0 and VfI/NIΩ0 were 0.9946 and −0.00673, respectively. Thus, the conventional normalized large-size limits of 1 and 0 were recovered to within approximately 1%, while pronounced atomic-scale relaxation effects remained for small clusters. Based on the relaxed morphologies of large clusters and established continuum size dependences, physics-constrained size relations for the formation volume were constructed. The functional forms were constrained by these size dependences, and the numerical coefficients were determined from the MS data. These relations provide compact expressions for vacancy- and SIA-cluster formation volumes in bulk bcc Fe at 0 K for use in rate-theory and cluster-dynamics models.