  Using an ab initio approach, we explore the stability of small vacancy and
vacancy-chromium clusters in dilute body-centred cubic Fe-Cr alloys. To explain
experimental observations described in C.D. Hardie et al., J. Nucl. Mater. 439,
33 (2013) and showing the occurrence of Cr segregation in low-Cr alloys, we
investigate if chromium can form stable bound configurations with vacancies in
alloys with chromium concentration below the low-temperature chromium
solubility limit of 10-11 at. %. We find that a single vacancy can attract up
to four Cr atoms in the most energetically favourable cluster configuration.
The binding energy of a cluster containing a single vacancy and from one to
eight Cr atoms can be well described by a linear function of the number of
chromium atoms in the second, third and fifth nearest neighbour coordination.
The magnetic origin of the binding energy trend is confirmed by a correlation
between the average value of the magnetic moment of a Cr atom and the binding
energy. Similar trends are also found for di-vacancy-Cr clusters, confirming
that they likely also characterise larger systems not yet accessible to ab
initio calculations. The ratio of the binding energy to the number of Cr atoms
increased more than twice in the di-vacancy case in comparison with a single
vacancy case.
