PHYSICAL REVIEW B 84, 155128 (2011) Role of iron in the incorporation of uranium in ferric garnet matrices Zs. R´ ak, * R. C. Ewing, and U. Becker Department of Geological Sciences, University of Michigan, Ann Arbor, Michigan 48109, USA (Received 30 June 2011; published 18 October 2011) 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. DOI: 10.1103/PhysRevB.84.155128 PACS number(s): 71.15.Mb, 71.20.Ps, 71.55.Ht I. INTRODUCTION A continuing concern with the potential expansion in nuclear power generation is the safe disposal and isolation of both the spent fuel from nuclear reactors and the high-level wastes (HLW) generated mainly by reprocessing the spent nuclear fuel. In order to dispose of highly-radioactive or long- lived radionuclides (half-life: 239 Pu = 24,100 years, 237 Np = 2.1 million years), there has been an increased interest in designing and developing specific materials for actinide incorporation, which would allow the radioactivity to decay while the materials retain their integrity for hundreds of thousands of years. 1–3 A recently investigated structure is garnet. 4 Numerous studies have been completed on a wide range of compositions with the garnet structure, specifically on its capacity to incorporate actinides, 5,6 radiation resistance, 7–11 and stability in aqueous solutions. 5,9,12 Garnet, A 3 B 2 X 3 O 12 (Ia3d, Z = 8), is a common mineral in nature with a wide variety of compositions because it has three cation sites: A site (8-coordinated, dodecahedral), B site (6-coordinated, octahedral), and X site (4-coordinated, tetrahe- dral). Most natural garnets are silicates, with Si 4+ occupying the tetrahedral site (X site). In spite of the compositional diversity, the actinide content in natural garnet is very low (usually less than 0.1 %). Nevertheless, it has been found that synthetic ferrites with garnet structure in which the Si 4+ ions (at the X site) are replaced by Fe 3+ , have a high capacity to incorporate actinides (e.g., up to 30 wt% of U). 5,6 This suggests that the garnet structure is a good candidate for the incorporation of uranium and, possibly, other actinides, such as Pu and Np. The explanation for the increased actinide capacity has been that the structural polyhedra together with unit cell size increase when the small Si atom is replaced by the larger Fe. As a result, the large actinide elements can easily be accommodated in the structure. 13 In addition to this rather simplistic explanation, we find that the coupling between the partially filled f and d shells of the actinides and Fe, respectively, play a crucial role in the incorporation mechanism of actinides into the garnet structure. We have described the electronic structure of Ca 3 (Ti, Zr, Hf, Sn) 2 (Fe 2 Si)O 12 garnet systems and calculated the energies required to incorporate uranium at the A and B sites of the structure. 14 The motivation for additional investiga- tions was stimulated by the recent discovery of a natural uranian-garnet, elbrusite-(Zr), with a U content as high as 27 wt%. 15 The chemical formula of the end member of elbrusite-(Zr) is Ca 3 (U 6+ Zr)(Fe 3+ 2 Fe 2+ )O 12 , and it has been described to form a complex solid solution with kimzeyite (Ca 3 Zr 2 Fe 3+ 2 SiO 12 ), schorlomite (Ca 3 Ti 2 Fe 3+ 2 SiO 12 ), and to- turite (Ca 3 Sn 2 Fe 3+ 2 SiO 12 ). We note that the low silicon concentration (0.6–1.1 wt%) and the high Fe content of this newly discovered uranian garnet is similar to that of synthetic, actinide-bearing ferrigarnets. In this paper, we further explore the energetics of the Ca 3 (Ti, Zr, Hf, Sn) 2 (Fe 2 Si)O 12 system by investigating the electronic structure of the U-containing garnet. In order to obtain a fundamental understanding of the incorporation mechanism and the stability of U inside the garnet structure, we have analyzed the details of the electronic interactions between the partially filled U fshell and the neighboring Fe d shells. In order to clarify the role of Fe, the U incorporation energies (E inc ) have been recalculated for several different ionic configurations for which the number of Fe atoms in the vicinity of U is varied. The incorporation of U at the A site of the garnet structure can be regarded in two, slightly different ways. In the first case, from the viewpoint of semiconductor physics, since the neutral U (5f 3 6d 1 7s 2 ) atom has more electrons outside a closed shell than the neutral Ca atom (4s 2 ), it can be regarded as a donor impurity, which provides extra electrons to the system. When U substitutes a Ca atom, two of the valence electrons of the U atom will form bonds with its neighbors (the same way the two electrons of Ca did), while the remaining valence 155128-1 1098-0121/2011/84(15)/155128(10) ©2011 American Physical Society