Role of iron in the incorporation of uranium in ferric garnet matrices

Abstract

The structural relaxations and electronic structure of U-containing Ca${}_{3}$(Ti,Zr,Hf,Sn)${}_{2}$(Fe${}_{2}$Si)O${}_{12}$ garnet systems have been investigated using ab initio methods within density functional theory (DFT) in the generalized gradient approximation with a Hubbard correction $U$ (GGA + $U$). The calculations provide a fundamental understanding of the role of Fe in the incorporation and stability of U in the garnet structure. The atomic relaxations around U are controlled by a delicate balance between the Coulomb interactions among the ions and the size effect of the large U atom. The relaxation pattern indicates that when U occupies the $A$ site, a charge transfer occurs from U to its nearest-neighbor (NN) Fe atom. This is further verified by the detailed analysis of the electronic band structures and charge density distribution. The double exchange coupling of the U $f$ and the NN Fe $d$ shells via the transfer of electrons lowers the energy of the system when the spins of the $f$ and $d$ shells are antiparallel. The incorporation energy of U at the $A$ site (substituting Ca) increases dramatically with the decrease in the number of Fe atoms in the neighboring tetrahedral sites. The presence of Fe is crucial, since it accommodates the extra valence electrons introduced by U and the electron transfer allows the lowering of the total energy of the structure. Comparing the incorporation energies at the $A$ and $B$ site (octahedral site), U clearly prefers the A site, provided that there are sufficient Fe atoms in its vicinity to facilitate the charge transfer.