Periodic DFT Study of the Structure, Raman Spectrum and Mechanical Properties of Schoepite Mineral Francisco Colmeneroa*, Joaquín Cobosb and Vicente Timóna aInstituto de Estructura de la Materia (IEM-CSIC). C/ Serrano, 113. 28006 – Madrid, Spain. bCentro de Investigaciones Energéticas, Medioambientales y Tecnológicas (CIEMAT). Avda/ Complutense, 40. 28040 – Madrid, Spain. Orcid Francisco Colmenero: https://orcid.org/0000-0003-3418-0735 Orcid Joaquín Cobos: https://orcid.org/0000-0003-0285-7617 Orcid Vicente Timón: https://orcid.org/0000-0002-7460-7572 *E-mail: [email protected] 1 ABSTRACT The structure and Raman spectrum of schoepite mineral, [(UO2)8O2(OH)12] · 12 H2O, was studied by means of theoretical calculations. The computations were carried out by using Density Functional Theory with plane waves and pseudopotentials. A norm-conserving pseudopotential specific for the uranium atom developed in a previous work was employed. Since it was not possible to locate hydrogen atoms directly from X-ray diffraction data by structure refinement in the previous experimental studies, all the positions of the hydrogen atoms in the full unit cell were determined theoretically. The structural results, including the lattice parameters, bond lengths, bond angles and X-ray powder pattern were found in good agreement with their experimental counterparts. However, the calculations performed using the unit cell designed by Ostanin and Zeller in 2007, involving half of the atoms of the full unit cell, leads to significant errors in the computed X-ray powder pattern. Furthermore, Ostanin and Zeller’s unit cell contains hydronium ions, + H3O , that are incompatible with the experimental information. Therefore, while the use of this schoepite model may be a very useful approximation requiring a much smaller amount of computational effort, the full unit cell should be used to study this mineral accurately. The Raman spectrum was also computed by means of density functional perturbation theory and compared with the experimental spectrum. The results were also in agreement with the experimental data. A normal mode analysis of the theoretical spectra was performed to assign the main bands of the Raman spectrum. This assignment improved significantly the current empirical assignment of the bands of the Raman spectrum of schoepite mineral. In addition, the equation of state and elastic properties of this mineral were determined. The crystal structure of schoepite was found to be stable mechanically and dynamically. Schoepite can be described as a brittle material exhibiting small anisotropy and large compressibility in the direction perpendicular to the layers, which characterize its structure. The calculated bulk modulus, B, was ~ 35 GPa. 2 KEYWORDS Spent nuclear fuel, Schoepite, DFT, X-ray diffraction, Raman Spectroscopy, Mechanical Properties. I. INTRODUCTION Hydrated uranyl oxyhydroxide mineral schoepite is a fundamental component of the paragenetic sequence of secondary phases that results from the weathering of uraninite ore deposits.1-6 The study of the paragenesis and structure of uranyl oxide hydrates is extraordinarily important, because they not only occur as products of the secondary alteration of uraninite under oxidizing conditions, but are also prominent phases appearing from the UO2 alteration of the spent nuclear fuel (SNF).7-17 Therefore, the study of these minerals is indispensable for understanding the long- term performance of a geological repository for nuclear waste. The knowledge of their structures may be also crucial to evaluate the possible incorporation of fission products and transuranic elements into their crystal structures,18-21 thus reducing their release and environmental impact. 22 Schoepite was originally described by Walker in 1923. Its formula was reported in 1932 by 23 24-25 Schoep as 3UO3 · 7H2O, subsequently as 4UO3 · 9H2O and, finally, as UO3 · 2H2O by Christ and Clark26 in 1960. The chemical composition and structure of schoepite have been a matter of discussion over time.3-4,27-33,20 The structure solution of schoepite29-30 leads to the structural formula of schoepite [(UO2)8O2(OH)12] · 12H2O, corresponding to the composition UO3 · 24 2.25H2O, in agreement with the original one determined by Billiet and de Jong from density and unit-cell measurements. X-ray diffraction studies of synthetic UO3 hydrates indicate only one schoepite phase. However, infrared spectroscopy and thermogravimetric analysis suggest the existence of a second mineral 3 phase,33 named metaschoepite. This related mineral species has a lower water content than 26,32 schoepite. The composition commonly reported for metaschoepite is UO3 · 2H2O ([(UO2)8O2(OH)12] · 10H2O), and was determined by thermogravimetric analysis (TGA) on both natural and synthetic material.34-36 A third related phase, paraschoepite, has remained less well 25 characterized. Paraschoepite, UO3 · 1.9H2O, has not been synthesized, not much being known about its structure. Further dehydration of metaschoepite leads to different phases reported as 37-38 38 dehydrated schoepite, UO2O0.25−x(OH)1.25+2x, or the related mineral paulscherrerite. These 39 dehydrated schoepite phases are related to the α uranyl hydroxide, α − UO2(OH)2. The distinction between schoepite, metaschoepite, and dehydrated schoepite is still an open issue, because the conversion between the three closely related phases in natural and laboratory settings is easy to occur, the samples being usually present as a mixture. The chemistry of the hydrated oxides of uranium(VI) is extremely complex and approximately 20 phases have been described in the literature.20-21,40-54 All the structures of these materials are composed of polyhedral sheets with composition (UO2)xOy(OH)z, consisting of uranyl groups linked by oxide and hydroxide ions. For the higher oxide hydrates, water molecules may be incorporated inside the interlayer space between the sheets.29-32 The structures of many of these materials have been described in detail by Finch and coworkers.29-31 The inter-relationships between these phases have been also studied.31-32 In particular, the structure of schoepite was investigated in different studies leading to the full structure solution from a naturally occurring sample by Finch et al.29 in 1996. The structure of metaschoepite was precisely determined from a synthetic sample by Weller et al.32 in 2000. However, it was not possible to locate H atoms directly from X-ray diffraction data by structure refinement and difference-Fourier maps for such highly absorbing materials as the uranium oxy- 4 hydroxy-hydrate minerals. This is unfortunate because the H bonding must be the mechanism whereby the sheets of the structural unit are linked. Furthermore, the similar physical and crystallographic properties of schoepite and metaschoepite26,55 suggest that these structures are distinguished primarily by differences in their arrangements of the interlayer H-bonding. Despite these problems, an idea of the H atom positions and interlayer H-bonding in schoepite may be obtained from the locations of the O atoms of the H2O groups and from the stereochemical 29 characteristics of H2O groups and their associated networks of H bonds. The resulting scheme of H bonds in schoepite structure, described in detail by Finch et al.,29 is nearly that predicted by our calculations. The same is not true for the structure calculated by Ostanin and Zeller in 200756 using Molecular Dynamics (MD) from the half unit cell. Furthermore, this structure shows the presence + of hydronium ions, H3O , which are not consistent with the proposed interlayer structure of Finch and coworkers.29 Therefore, although the use of this schoepite model may be a very useful approximation requiring a much smaller amount of computational effort, the full unit cell should be used to study this mineral accurately. This should be taken into account if theoretical calculations are performed using this model since only semiquantitative results can be expected. For example, first-principles GIPAW (Gauge Including Projector-Augmented Wave) chemical shift calculations were carried by Alam et al.57 out using Ostanin and Zeller unit cells of schoepite and metaschoepite. The theoretical calculations of schoepite are very computationally demanding, not only due to the large size of the corresponding unit cell (344 atoms are involved), but also to the high level of theory required to describe correctly uranium atom containing systems.58-59 There is a very small number of works about the theoretical vibrational spectra of uranium containing solids in the literature since only recently a norm conserving pseudopotential60 for uranium atom appropriate 5 for this purpose was developed,61-62 which has been used extensively for the research of the structural, mechanical, thermodynamic and spectroscopic properties of other uranyl containing materials.61-69 The hydrogen atom positions in the structure of schoepite were not determined by experimental X-ray diffraction techniques. In this paper, we performed a complete structural characterization of schoepite by theoretical solid-state methods, which allowed us to obtain a full unit cell structure in agreement with that obtained experimentally. Besides, although the Raman spectrum of this mineral has been recorded experimentally,70-72,49 a precise assignment of the main bands in the spectra is lacking, since they have been characterized incompletely by using empirical arguments. The theoretical Raman spectrum