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First-Principles Investigations of the Electronic and Magnetic Structures Z. Naturforsch. 2017; 72(10)b: 725–730 Samir F. Matar* First-principles investigations of the electronic and magnetic structures and the bonding properties of uranium nitride fluoride (UNF) https://doi.org/10.1515/znb-2017-0096 respectively. A small number of tetravalent metal nitride Received May 12, 2017; accepted June 13, 2017 fluorides exist such as transition metal-based TiNF [1] and ZrNF [2] on one hand and heavier actinide equia- Abstract: Based on geometry optimization and magnetic tomic ternaries such as ThNF [3] and UNX (X = halogen) structure investigations within density functional theory, [4, 5] on the other hand. Besides the actinide-based a unique uranium nitride fluoride, isoelectronic with compounds, only the rare-earth ternary CeNCl was UO , is shown to present peculiar differentiated physical 2 evidenced by Ehrlich et al. [6]. Recently, CeNF [7] was properties. These specificities versus the oxide are related proposed with potential experimental synthesis routes to the mixed anionic substructure and the layered-like besides a full account of physical properties based on tetragonal structure characterized by covalent-like [U N ]2+ 2 2 extended theoretical works within well-established motifs interlayered by ionic-like [F ]2− ones and illustrated 2 density functional theory (DFT) [8, 9]. In fact, it has been herein with electron localization function projections. shown in recent decades that this theory with DFT-based Particularly, the ionocovalent chemical picture shows, methods allowed us not only to explain and interpret based on overlap population analyses, stronger U–N experimental results resolved at the atomic chemical bonding versus U–F and d(U–N) < d(U–F) distances. Fur- constituent scale but also to operate it as a predictive ther generalized gradient approximation + U calculations tool to propose new compositions with targeted specific provide the ground state magnetic structure as insulating properties. As an example of largely investigated com- antiferromagnet with ±2 μ magnetization per magnetic B pounds within the BCN pseudo phase diagram, binary sub-cell and ~2 eV band gap. carbon nitrides and ternary boron carbon nitrides were Keywords: bonding; DFT; magnetism; uranium identified theoretically with high hardness close to well- compounds. known ultra-hard diamond and potentially enabled to replace diamond in tooling machinery, industry and forage applications [10–12]. In continuation of our investigations of nitride fluo- rides (cf. [7] and references therein) we focus herein on 1 Introduction the electronic and magnetic properties of uranium nitride fluoride (UNF) isoelectronic with UO [13]. It needs to be From the iso-electronic relationship for valence shell 2 mentioned here that UO is known, and a complete study states: 2O (2s2, 2p4) ≡ N (2s2, 2p3) + F (2s2, 2p5), nitride 2+x on the average structure and local configuration of oxygen fluorides of formulation MIVNF type can be considered excess with pertaining physical effects has recently been as pseudo-oxides and isoelectronic with MIVO (MIV 2 reported [14]. However, such an investigation is out of the stands for a generic tetravalent metal). Compared to scope of present work. homologous oxides, some relevant physical properties UNF is tetragonal and crystallizes in the space group can be expected due to differentiated bonding of M with P4/n [4]. The structure is shown in Fig. 1. In spite of its nitrogen and fluorine qualified as less and more ionic, overall three-dimensional character, it can be consid- 2+ ered along the c axis as successions of [U2N2] -like motifs 2− separated by [F2] -like layers; this is supported by the shorter U–N versus U–F distances: 2.29 Å versus 2.61 Å. *Corresponding author: Samir F. Matar, CNRS, University of Bordeaux, ICMCB, 33600 Pessac, France; and Lebanese German It will be shown that this structural setup has an impor- University (LGU), Sahel-Alma, Jounieh P.O. Box 206, Lebanon, tant influence on the electronic distribution (cf. Fig. 3, e-mail: [email protected] see below). 726 S. F. Matar: Structures and properties of uranium nitride fluoride compounds are examined; it does not constitute a tool for evaluating absolute ionizations. Bader’s analysis is performed using a fast algorithm operating on a charge density grid arising from high-precision VASP calcula- tions and generates the total charge associated with each atom. From the calculations, we also extract information on the electron localization (EL) at atomic sites thanks to the EL function (ELF) [25, 26]. Normalizing the ELF between 0 (zero localization) and 1 (strong localization) – with the value of 1/2 corresponding to a free electron gas behavior – enables analyzing the contour plots following a color code: blue zones for zero localization, red zones for full localization and green zone for ELF = 1/2, corresponding to a free electron gas. Then for a full account of the electronic structure, the Fig. 1: Tetragonal structure of UNF showing [F2]2− planes at 0, 0, 1/2 2+ site-projected density of states (PDOS) and the properties interlayering [U2N2] blocks (also cf. Fig. 3). of chemical bonding based on the overlap matrix (Sij) with the COOP criterion [27] within DFT, we used the scalar relativistic full potential augmented spherical wave (ASW) 2 Computational methodology method [28, 29] with the GGA scheme [18]. The basis set, limited in the ASW method, was chosen to account for the Within DFT we first used the Vienna ab initio simula- outermost shells to represent the valence states for the tion package (VASP) code [15, 16] for geometry optimi- band calculations. The matrix elements were constructed zation, total energy calculations as well as establishing using partial waves up to lmax + 1 = 4 for U and lmax + 1 = 2 the energy-volume equations of state. The projector-aug- for N, O and F. F-2s states at low energy (much lower than mented wave (PAW) method [16, 17] is used with atomic corresponding O and N 2s states) were considered as core potentials built within the generalized gradient approxi- states, i.e. not included in the valence basis set; in the mation (GGA) scheme following Perdew et al. [18]. This limited ASW basis set they were replaced by 3s states. exchange-correlation scheme was preferred to the local Self-consistency was achieved when charge transfers density approximation [19], which is known to be under- and energy changes between two successive cycles were estimating interatomic distances and energy band gaps. such that ΔQ < 10−8 and ΔE < 10−6 eV, respectively. The BZ The conjugate-gradient algorithm [20] is used in this integrations were performed using the linear tetrahedron computational scheme to relax the atoms of the different method within the irreducible tetragonal wedge following crystal setups. The tetrahedron method with Blöchl cor- Blöchl [21]. rections [21] as well as a Methfessel-Paxton [22] scheme was applied for both geometry relaxation and total energy calculations. Brillouin zone (BZ) integrals were approxi- mated using a special k-point sampling of Monkhorst 3 Geometry optimization and and Pack [23]. The optimization of the structural para- energy-dependent results meters was performed until the forces on the atoms were <0.02 eV Å−1 and all stress components <0.003 eV Å−3. The Table 1 shows the starting experimental and calculated calculations were converged at an energy cut-off of 400 eV lattice parameters and zU coordinate for both spin degen- for the plane-wave basis set with respect to the k-point erate (NSP: non-spin-polarized) as well as spin-resolved integration in the BZ with a starting mesh of 6 × 6 × 6 up (SP: spin-polarized) configurations. Better agreement to 12 × 12 × 12 for best convergence and relaxation to zero with experiment is observed with SP calculations. These strains. calculations lead – expectedly – to a magnetization of 4 μB The charge density issued from the self-consistent cal- (Bohr magnetons) per unit cell or 2 μB per formula unit culations can be analyzed using the atoms in molecules (FU) which arises from the presence of two unpaired elec- theory (AIM) approach developed by Bader [24]. Such trons in the U 5f states of tetravalent uranium. Note that an analysis can be useful when trends between similar these calculations merely indicate the trend of developing S. F. Matar: Structures and properties of uranium nitride fluoride 727 Table 1: Experimental [4] and calculated (NSP, SP) structural parameters for UNF. UNF Exp. NSP SP a 3.951 3.86 3.90 c 5.724 5.71 5.72 V 89.35 85.1 87.0 zU 0.2024 0.200 0.205 d(U–F) 2.61 2.59 2.58 d(U–N) 2.29 2.24 2.28 Lattice parameters and distances are in Å (1 Å = 10−10 m). P4/n. Origin 1. N (2a) 0, 0, 0; F (2b) 0, 0, 1/2; U (2c) 0, 1/2, z. Fig. 3: UNF electron localization function slice along the (101) plane with a projection over four adjacent cells showing the succession 2+ 2− of [U2N2] -like blocks and [F2] -like planes. Blue, green and red spheres represent U, N and F atoms, respectively (see the text). The trend to magnetic polarization can be checked as a function of volume by establishing the energy-volume equation of state (EOS) in both NSP and SP configurations. We also verify this for UO2. The NSP and SP E(V) curves are shown in Fig. 2. They all exhibit quadratic behavior with systematically lower SP energy minima. The SP solution is favored for larger volumes, but both NSP and SP curves merge together at small volumes or high pressure. The fit of the curves with a Birch EOS [32] up to the third order: 9 E()VE=+()VVBV[( /)V 2/32−1] 00 8 00 0 9 +−BB(4′ )[VV(/V )12/33− ] 16 000 Fig.
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