  We have studied the body-centered cubic (bcc), face-centered cubic (fcc) and
hexagonal close-packed (hcp) phases of Fe alloyed with 25 at. % of Ni at
Earth's core conditions using an ab initio local density approximation +
dynamical mean-field theory (LDA+DMFT) approach. The alloys have been modeled
by ordered crystal structures based on the bcc, fcc, and hcp unit cells with
minimum possible cell size allowing for the proper composition. Our
calculations demonstrate that the strength of electronic correlations on the Fe
3d shell is highly sensitive to the phase and local environment. In the bcc
phase the 3d electrons at the Fe site with Fe only nearest neighbors remain
rather strongly correlated even at extreme pressure-temperature conditions,
with the local and uniform magnetic susceptibility exhibiting a
Curie-Weiss-like temperature evolution and the quasi-particle lifetime {\Gamma}
featuring a non-Fermi-liquid temperature dependence. In contrast, for the
corresponding Fe site in the hcp phase we predict a weakly-correlated
Fermi-liquid state with a temperature-independent local susceptibility and a
quadratic temperature dependence of {\Gamma}. The iron sites with nickel atoms
in the local environment exhibit behavior in the range between those two
extreme cases, with the strength of correlations gradually increasing along the
hcp-fcc-bcc sequence. Further, the inter-site magnetic interactions in the bcc
and hcp phases are also strongly affected by the presence of Ni nearest
neighbors. The sensitivity to the local environment is related to modifications
of the Fe partial density of states due to mixing with Ni 3d-states.
