  Point defects in body-centred cubic Fe, Cr and concentrated random magnetic
Fe-Cr are investigated using density functional theory and theory of
elasticity. The volume of a substitutional Cr atom in ferromagnetic bcc Fe is
approximately 18\% larger than the volume of a host Fe atom, whereas the volume
of a substitutional Fe atom in antiferromagnetic bcc Cr is 5\% smaller than the
volume of a host Cr atom. Elastic dipole $\boldsymbol{P}$ and relaxation volume
$\boldsymbol{\Omega}$ tensors of vacancies and self-interstitial atom (SIA)
defects exhibit large fluctuations, with vacancies having negative and SIA
large positive relaxation volumes. Dipole tensors of vacancies are nearly
isotropic across the entire alloy composition range, with diagonal elements
$P_{ii}$ decreasing as a function of Cr content. Fe-Fe and Fe-Cr SIA dumbbells
are more anisotropic than Cr-Cr dumbbells. Fluctuations of elastic dipole
tensors of SIA defects are primarily associated with the variable
crystallographic orientations of the dumbbells. Statistical properties of
tensors $\boldsymbol{P}$ and $\boldsymbol{\Omega}$ are analysed using their
principal invariants, suggesting that point defects differ significantly in
alloys containing below and above 10\% at. Cr. The relaxation volume of a
vacancy depends sensitively on whether it occupies a Fe or a Cr lattice site. A
correlation between elastic relaxation volumes and magnetic moments of defects
found in this study suggests that magnetism is a significant factor influencing
elastic fields of defects in Fe-Cr alloys.
