First-Principles Study of Barium and Zirconium Stability in Uranium

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First-principles Study of Barium and Zirconium Stability in Uranium Mononitride Nuclear Fuels Yu-Juan Zhang, Jianhui Lan, Tao Bo, Cong-Zhi Wang, Zhifang Chai, and Wei-Qun Shi J. Phys. Chem. C, Just Accepted Manuscript • Publication Date (Web): 12 Jun 2014 Downloaded from http://pubs.acs.org on June 15, 2014

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The Journal of Physical Chemistry

First-principles Study of Barium and Zirconium Stability in Uranium Mononitride Nuclear Fuels Yu-Juan Zhang1, Jian-Hui Lan1, Tao Bo1, Cong-Zhi Wang1, Zhi-Fang Chai1,2*, Wei-Qun Shi1* 1

Key Laboratory of Nuclear Radiation and Nuclear Energy Technology, Institute of

High Energy Physics, Chinese Academy of Sciences, 100049, Beijing (China) 2

School of Radiological & Interdisciplinary Sciences, Soochow University, 215123,

Suzhou (China) *Corresponding author: Tel: +86 (10)88233968; Fax: +86(10)88235294 E-mail: [email protected], [email protected]

ACS Paragon Plus Environment


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ABSTRACT

Barium and zirconium solution behaviors in antiferromagnetic uranium mononitride (UN) have been studied based on first-principles density functional theory. By calculating the incorporation and solution energies in UN, it is found that the most favorable solution sites are U vacancies for both Ba and Zr, and Zr is more soluble than Ba. The volume of Ba-doped system keeps expanding with increasing Ba doping concentration, while that of Zr-doped system changes from swelling to contraction with increasing Zr doping concentration. This phenomenon may result from the difference of these two elements in atom radius and coordination mechanism. Furthermore, the solution energies of metallic and nitride phases of Ba and Zr indicate that both phases of Ba are insoluble in the UN matrix, while the metallic phase Zr is insoluble, and its nitride ZrN is soluble in the UN matrix.

Key Words: density functional theory, incorporation energy, solution energy, uranium mononitride


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I.

INTRODUCTION

As a promising fuel in the generation-IV nuclear reactor, uranium nitride possesses several advantages such as high actinide density, superior thermophysical properties, easy re-processing as a high soluble fuel in nitric acid, and high burn-up, thus attracting much attention recently1-3. Uranium nitride can be also desired as a target material for transmutation of plutonium or minor actinides in nuclear reactors4. Uranium mononitride (UN) with a simple rock-salt structure5 is one of the potentially advanced nuclear fuels because of its good breeding performance and high melting temperature. As a key issue for nuclear fuel evolution, the effect of fission products on the performance of the nuclear fuel during irradiation can’t be ignored. For example, barium, a typical fission product, plays an important role for providing reactor residual heat in nuclear pellets. Actually, barium and zirconium are often considered together, because they always simultaneously appear in many chemical compounds. For example, the stability of Ba and Zr in UO2± x has been studied by density functional theory (DFT)6,7. These works involved the localization and speciation of fission products Ba and Zr in UO2 ± x. To the best of our knowledge, previous theoretical studies about defects in UN mainly focused on the intrinsic defects and some nonmetal radiation defects. For example, oxygen dopant defect and the migration path of N atom in UN crystal8-10, atomic and molecular oxygen adsorption on the UN surface11, oxygen atom incorporation into the UN surface and subsurface vacancies12 have been studied. However, the microscopic behaviors of Ba and Zr in



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UN crystal have been scarcely reported in spite of their great value for safety study of nuclear fuels. Given the difficulty of experimental studies on uranium compounds, theoretical predictions are particularly important. From a basic science point of view, it can be visualized that many physical and chemical properties of uranium compounds are closely related to the quantum process of localization and delocalization due to partially filled uranium 5f electrons13. Many previous theoretical studies on uranium compounds have been carried out with conventional DFT approaches. For example, the behaviors of Kr, He, Xe, Cs and Sr in UO2 were studied by conventional DFT methods14-16, as well as the point defects and He, Xe in UC17. Up to now, theoretical investigations of the point defects and oxygen impurity in bulk UN or on the surface have been done with the conventional DFT8,12,18. However, conventional DFT schemes underestimate the strong on-site Coulomb repulsion of the uranium 5f electrons and consequently fail to capture the correlation-driven localization. For example, applying the conventional DFT methods, the ground state of UN has been predicted to be ferromagnetic, which is in contradiction with the experimentally observed antiferromagnetic ground state19,20. To overcome the conventional DFT failures in calculations of actinide compounds, a number of approximate methods such as hybrid DFT approximation21,22, GW approximation23 and DFT+U approach20,24 have been developed. The hybrid DFT approximation21 combines a fixed portion of exact, nonlocal Hartree-Fock exchange into the exchange correlation functional to correct the self-interaction error of conventional DFT. The GW


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approximation23 can be regarded as a generalization of the Hartree-Fock approximation but with a dynamically screened Coulomb interaction. The DFT+U method24 by including a Hubbard correction to the on-site Coulombic repulsion has been developed and proved to successfully describe the properties of uranium compounds6,17,20,25-27. Gryaznov et al.20 have modeled the strong electron correlation effects in UN employing the DFT+U method. The DFT+U method is known to make electronic optimization algorithms get stuck in metastable states and may lead to improper defect energetics27-29. Up to now, several approaches, such as the Quasi Annealing (QA) approach28, the “U-ramping” technique30, the occupation matrix control (OMC) scheme31 and the controlled symmetry reduction (CSR) method20,27, have been developed to solve the multiple minima problem in DFT+U method. In our work, we applied the QA approach to eliminate the metastable states in the DFT+U calculations. In this work, we have systematically studied the microscopic behaviors of barium and zirconium in antiferromagnetic uranium mononitride using the DFT+U schemes according to Dudarev et al.32,33. The formation energies of the intrinsic point defects were calculated above all. The incorporation and solution energies of Ba and Zr in UN were then predicted and discussed. The influence of Ba and Zr defects at different concentrations on the volume of UN system has been modeled. In addition, we have also analyzed the dissolution process of metallic and nitride phases of Ba and Zr in UN. The obtained results which need further verification by future experimental data provide useful theoretical insights for understanding the evolution behaviors of



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irradiated nuclear fuels and are meaningful for genuine nuclear industry applications. II. COMPUTATIONAL METHODS A. First-principles calculation In this study, we have performed simulations for the behaviors of barium and zirconium in UN using the Vienna ab initio simulation package (VASP) plane-wave pseudopotential code34, which was developed at the Technical University of Vienna35,36. The exchange-correlation functional is described by generalized gradient approximation (GGA) with the parameterization of Perdew-Burke-Ernzerhof37. The N 2s22p3, U 6s26p65f36d17s2, Ba 5s25p66s2 and Zr 4d25s25p0 are treated as valance electrons. In all the calculations, the rock-salt crystal structure of UN and its collinear antiferromagnetic order with the atomic magnetic moments along the [001] direction have been taken into account. To simplify the calculation of defect properties, the spin-orbit coupling effect is ignored in this work. Gryaznov et al.20 reported that the spin-orbit coupling effects on both the band structure and the total density of states (DOS) for UN are insignificant. Sedmidubsky et al.4 also found that the spin-orbit coupling has little effect on the formation and cohesive energies of actinide nitrides. The plane-wave cut-off energy is chosen as 550 eV. The Brillouin-zone integrations are performed using 3×3×3 Monkhorst-Pack38 special k-points in a 2×2×2 supercell with 32 U and 32 N atoms (one conventional unit cell contains 4 U and 4 N atoms) under the periodic boundary conditions. The geometries are optimized until the forces are smaller than 0.02 eV/Å, and the total energy is relaxed until the difference value is smaller than 10-5 eV.


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The strong on-site Coulomb repulsion amongst the localized U 5f electrons is considered within DFT+U schemes. The details of performance have been displayed elsewhere by Gryaznov et al.20, where the Coulomb U is treated as a variable, and the exchange energy is set to be a constant J=0.51 eV herein. For perfect UN, we have calculated the total energy of UN supercell applying GGA+U (U is selected to be from 0 to 5 eV) method in nonmagnetic, ferromagnetic and antiferromagnetic phases. We find that the ferromagnetic phase is the most favorable state with U=0, which is in contrast to the experimentally observed antiferromagnetic ground state19,20. When U is close to 2 eV, the antiferromagnetic state becomes the favorable state, and the lattice parameter of UN is well consistent with the experiments39. To justify the validity of the Hubbrad parameter U of 2 eV for UN, we have also provided the total electronic DOS together with the projected DOS of perfect UN as shown in Fig. 1, which is well consistent with previous results2,20. At the Fermi level, the strong overlap of the U f orbitals mainly contributes to the metallic property of UN phase. The number of U 5f electrons located at the Fermi level is about 2.4, which agrees well with the experimental value 2.2±0.540. Lu et al.39 have also confirmed in detail that U of 2 eV is the optimal value for the Hubbard parameter to describe UN. In addition, we have tested the effect of QA approach. When U=2 eV, we have calculated the total energy of UN (containing 8 atoms in the supercell) to be -82.119 eV without taking into account of QA approach, while being -82.361 eV with QA approach. Thus the ground state calculated with QA approach is the favorable state. In the following calculations, we have set U=2 eV with the QA approach in



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antiferromagnetic phase.

FIG. 1. (Color online) The total and projected DOS of perfect UN crystal. The Fermi energy is set to be zero.

B. Solution energy In order to estimate the localization of the fission product atoms in UN, the of an impurity atom A (A=Ba, Zr) doped in UN can be solution energy E∈ calculated, which includes the incorporation energy E∈ of the dopant and the

formation energy E of the trap as follows41: E∈

E∈ E .

(1)

The incorporation energy of the dopant can be obtained as follows: E∈

E∈ -E -N E ,

(2)

where ∈ and are the total energies of the supercells containing A at site X and a defect site of type X, respectively. N denotes the number of A impurity atoms in the supercell. E is the total energy of an isolated A atom. A negative incorporation energy E∈ indicates that the incorporation of the impurity into the vacancy is


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energetically favorable. The formation energy E of the vacancy is defined as: E E N E -E ,

(3)

where Ehost and Eperfect are the total energies of a host uranium/nitrogen atom and the perfect UN supercell, respectively. The dissolution process of binary compounds (such as binary nitrides AαNβ) in UN can be divided into three steps. The first step is the decomposition of nitride fission product: AαNβ&s' → αAX βNY . The second step is to form the trap sites which are used to incorporate the A and N atoms. The last step is to incorporate the A and N atoms into the trap sites. To analyze the fission product precipitation in UN, the solution energy of AN in UN can be calculated as follows: sol sol sol f

A∈X N∈Y − AN , AN

(4)

f where EAN is the formation energy of binary nitride AN. X and Y are the insertion sol sites for A and N atom, respectively. A positive AN reveals that the binary nitride is

insoluble in UN. III. RESULTS AND DISCUSSION A. Stability of point defects Uranium mononitride (space group Fm3/m, No. 225) has antiferromagnetic order at low temperature (the Néel temperature at 53 K19). Taking into account the antiferromagnetic order, the lattice parameters for the ground state of UN are obtained: a=b=4.959 Å, c=4.846 Å, which is close to the obtained theoretical value (a=b=4.960 Å, c=4.852 Å)42 and the experimental value (4.886 Å)8. The crystal structure of UN



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undergoes tetragonal distortions when considering the antiferromagnetic order, which is consistent with previous experimental observations (|c/a-1|=6.5×10-4)43. The magnetic moment of uranium in perfect UN is calculated to be 1.619 µ B, mainly coming from the f electrons of uranium, which agrees well with the theoretical calculation of Gryaznov et al.20. Three types of point defects including Uva, Nva and UNbiv are discussed in Table I, where Uva, Nva and UNbiv denote U vacancy defect, N atomic vacancy defect and U-N binary defect, respectively. Due to the equivalency of the U atoms with spin up and spin down magnetic orders in a face-centered cubic sublattice, the formation energies for U vacancies with different magnetic orders are essentially identical. Therefore, the U vacancies considered here are selected randomly. The formation energy of N vacancy is 7.231 eV, which is somewhat larger than that of U vacancy (6.246 eV). However, by using GGA approach, the formation energy of N vacancy (9.1 eV) is slightly smaller than that of U vacancy (9.4 eV)8. The volume changes as the presence of point defects in UN are also shown in Table I. Different from volume contraction observed by traditional GGA methods8, the volume of system is swelling to some extent based on our calculation by using GGA+U approximation. Lan et al.42 have also reported that the vacancy defects lead to volume expansion which agrees with the swelling of nuclear fuel materials in the process of irradiation. From Table I, it can also be seen that considering the magnetic order, the UN supercell exhibits magnetic moments after the formation of U vacancy, N vacancy or U-N binary vacancy. TABLE I. Lattice constants, volume changes relative to perfect UN crystal, formation energies


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and total magnetic moments of four types of point defects. UN

Uva

Nva

UNbiv

∆V/V (%)

0

3.22

2.80

2.60

Ef (eV)

-3.172

6.246

7.231

6.827

Mag.( µ B)

0

3.530

-1.859

1.013

B. Stability of Ba and Zr dopants

FIG. 2. (Color online)The perspective map of the 2×2×2 supercell with one fission product atom located at preexisting U site SU (a), N site SN (b), and interstitial site I (c). The green, gray and red balls denote uranium, nitrogen and dopant atoms, respectively.

In this section, we mainly focus on several intrinsic defects including uranium vacancy, nitrogen vacancy and interstitial doped defect to study fission product dopants in UN. The perspective maps of the 2×2×2 supercell with one fission product atom located at preexisting U site SU (a), N site SN (b), and interstitial site I (c) are shown in Fig. 2. The incorporation energy inc which is defined as formula (2) in Section II, is dependent on the atomic radius size of dopant atoms and their coordination ability with the nearest-neighboring nitrogen atoms. The incorporation energies E inc of Ba defects in UN are displayed in Table II. We can see that the



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lowest incorporation energy corresponds to uranium vacancy, which means that uranium vacancy is the most favorable solution site for barium among the defects discussed here. Brillant et al.6 attributed the incorporation of barium in uranium dioxide mainly to chemical bond formation. Since U vacancy has the greatest number of O atoms in the nearest-neighboring shell, it is the most favorable site for barium in UO2. TABLE II. Incorporation energies Einc, displacement of the nearest-neighboring atoms of barium and zirconium ∆d(NN), Bader charge of A (A=Ba, Zr) Q(A) in a 2×2×2 supercell of UN for different configurations. A=Ba

A=Zr

Einc

∆d(NN)

Q(A)

Einc

∆d(NN)

Q(A)

(eV)

(Å)

(|e|)

(eV)

(Å)

(|e|)

SAU

-2.241

+0.293

+1.017

-10.088

+0.053

+2.656

SAN

5.362

+0.335

-0.202

-1.394

+0.228

+1.140

IA

5.745

+0.462

+0.684

-1.284

+0.087

+2.560

Type

Due to the presence of dopant defects in UN, the atomic displacement ∆d of the nearest-neighboring shell referring to the atomic distance in optimized perfect UN has been observed. The atomic displacements of the nearest-neighboring shell for Ba doped in UN are shown in Table II. Positive values indicate the interatomic distances increase. For three types of Ba doped UN, the atomic displacement of the first shell is ranging from 0.293 to 0.462 Å, which can mainly be attributed to the large atomic radius of Ba. The change of the separation between the next-nearest-neighboring shell


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and the nearest-neighboring shell to the central Ba atom is small (

First-Principles Study of Barium and Zirconium Stability in Uranium

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