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 fluorides (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 calculations 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. 2: Energy volume curves and fit values from Birch EOS in non- ′ spin-polarized (NSP) and spin-polarized (SP) configurations. provides equilibrium parameters E0, V0, B0 and B , respectively, for the energy, the volume, the bulk modulus and its pressure derivative. The obtained values with goodness of magnetization from the present PAW-GGA calculations, fit χ2 magnitudes are displayed in the insets of Fig. 3. The i.e. they do not point to the long-range magnetic order or equilibrium volumes for both compounds UNF (Table 1) 3 −1 the ground state which is searched for and precised in the and UO2 come close to experiment: V(UO2) = 163.73 Å cell next section. or 40.93 Å3 per FU [33].

In fact, UO2, in which uranium is also tetravalent, is The SP volumes are larger than the NSP ones and known to be an insulating antiferromagnet in the ground the corresponding energies are lower. Also ΔEUO2(SP– −1 state [30] provided that the Hubbard U [31] method is used NSP) = −0.23 eV FU whereas ΔEUNF(SP–NSP) = −0.29 eV in further calculations, as is shown for UNF here below. FU−1, meaning that somehow the U–N bond less ionic 728 S. F. Matar: Structures and properties of uranium nitride fluoride than U–O prevails. This can be verified from the trend of Also it is interesting to note the large difference of charge transfer between the two compounds which can be magnitude of the bulk moduli B0 pointing to more com- rationalized from the analysis of charge density resulting pressible UNF than UO2. This is partly due to the larger 3 −1 3 −1 from the calculations within AIM theory based on Bader’s volume of UNF (43.5 Å FU ) versus UO2 (39.95 Å FU ); work [24]. Such an analysis is particularly relevant when it i.e. the larger the volume the more compressible the com- comes to comparing two electronically close compounds pound; but this could also be due to the rather layered such as UNF and UO2 here. The results of computed charge nature of the UNF structure versus tri-dimensional fluo- changes Q between neutral and ionized elements and rite-type UO2. resulting overall ΔQ in the structure are as follows: At this point, it is interesting to show the 2D-like structure from the point of view of EL which is expected to illus- UNF: QU()=+2.29;(QQN) =−1.47;(F) =−0.82;2∆=Q ± .29 trate further the different chemical behaviors of N and F versus U with smaller U–N versus U–F distances observed UO2 : QQ(U)2=+ .48; (O)1=− .24; ∆=Q ±2.48 experimentally and by calculations. The EL with the ELF Charge transfer is as expected from U to N, O, F with based on the kinetic energy [25, 26] is used here. In the different magnitudes: N−1.47, O−1.24, F−0.82 not translating their projections, blue, green and red contours represent zero, formal ionizations but proportional with the electron- free electron like and strong localizations, respectively. egativities χ increasing along N, O and F, i.e. χ(N) = 3.04 Figure 3 shows ELF slices along the (101) plane with a pro- 2+ < χ(N) = 3.44 < χ(F) = 3.98. The overall ΔQ translating the jection over four adjacent cells. The succession of [U2N2] - 2− total ± transfer is smaller for UNF which stresses further like and [F2] -like planes along the tetragonal c axis is the covalent role brought by N through the formation of clearly observed. The isolated fluorine is displayed by the 2+ [U2N2] layers as illustrated below. blue zones of no localization around it.

Fig. 4: Non-spin-polarized (NSP) calculations for UNF (left) and UO2 (right) displaying site-projected DOS (up) and chemical bonding from unit-less integrated COOP iCOOP (bottom). S. F. Matar: Structures and properties of uranium nitride fluoride 729

4 Electronic structure and bonding

All-electron full potential scalar relativistic ASW calculations were then undertaken for assessing the electronic band structure and qualitative analysis chemical bonding.

A comparison between UNF and UO2 was done with spin- degenerate (NSP) calculations in order to examine the role of each chemical constituent in the site PDOS as well as in the chemical bonding. For UNF and UO2, the top panels in Fig. 4 show the NSP site PDOS. The zero energy along the x axis is with respect to the Fermi level EF which crosses the lower energy part of the U(5f) states within the valence band (VB). The main part of U(5f) is centered in the empty conduction band (CB) above EF due to the low filling of 5f states. Nevertheless, the crossing occurs at a relatively high PDOS. This is connected with an instability of the electronic system in such a spin degenerate configuration of both compounds and with the expected onset of magnetic polarization as shown in the next paragraph. Large differences characterize the VB where N(2s) is at −15 eV versus O(2s) at −20 eV; these states show little mixing with uranium itinerant states. Oppositely, the hybridization (mixing) between uranium itinerant states and those of N, O p states is identified, respectively, in the energy windows {−5.5; −3 eV} and {8; −5.4 eV}; this shift of energies is due to the larger electronegativity of O versus N. In agreement 2+ with the observation above on the [U2N2] -like layers sep- 2− arated by [F2] -like layers characterizing the structure of UNF (cf. text and Fig. 3), there is little mixing to be noted between U and F states at −7.5 eV. This aspect should be confirmed from the qualitative analysis of the chemical Fig. 5: Spin-polarized calculations for UNF and UO2 displaying site- projected DOS (up) and chemical bonding (bottom). bonding based on the overlap integral Sij (i and j desig- nate two chemical species) as implemented in the ASW method with the COOP criterion. The comparative bonding strengths (U–N versus U–F as well as U–O) is qualitatively Fig. 5, showing the corresponding PDOS along the two spin estimated with the integrated COOP, iCOOP shown in Fig. 4 channels (↑;↓), the integer value is due to the full polari- (lower panels). In both panels, little bonding can be iden- zation of electrons in ↑ spin PDOS with a gap appearing tified in the VB lower part where where s-like states are in ↓ PDOS and an energy shift between ↑ and ↓ U PDOS dominant; and significant bonding is found above −10 eV signaling the onset of magnetic polarization. The non- with p states. Comparing the areas below the iCOOP shows metal s, p states do not show energy shifts. However, the larger U–N iCOOP versus U–F iCOOP leading to prevailing calculations were conducted with plain GGA calculations

U–N bonding. The U–O bond in UO2 shows closely similar and it is known that for uranium-based compounds, such behavior to U–N albeit with slightly larger iCOOP (note that as UO2, a Hubbard U repulsive parameter is required to be −1 there are 2 FU in UNF and 4 FU in fluorite UO2 with only 1 added [33]. With U = 4.1 eV, the magnetization M = 2 μB FU FU accounted for in the calculations due to the F center- is reproduced with a small gap opening in ↑ spin PDOS, ing). Nevertheless, U–N iCOOP keeps positive bonding as shown in Fig. 6 (top panel). The compound exhibits a behavior above EF, whereas U–O iCOOP drops rapidly to magnetic semi-conductor-like behavior. Yet in view of the negative magnitude within the CB. Again this is due to the antiferromagnetic isoelectronic UO2, further calculations covalent U–N bond versus rather ionic U–O. assuming two magnetic sub-cells, one considered as UP

Subsequent SP calculations lead to an onset of mag- SPINS and the second as DOWN SPINS, lead to ±2 μB per −1 netization in both UNF and UO2 with M = 2 μB FU . From magnetic sub-cell and to larger opening of the band gap 730 S. F. Matar: Structures and properties of uranium nitride fluoride

DFT, this has been quantitatively identified through electronic structure calculations in both non-magnetic spin-degenerate and SP configurations and illustrated by electron localization mapping, charge changes, site- and spin-projected density of states and chemical bonding based on overlap integrals describing the magnitudes of U–O, U–N and U–F bonding. UNF is found relative to be

an insulating antiferromagnet, likewise UO2 in the ground state.

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