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Radionuclide incorporation in negative thermal expansion α-Zr(WO4)2: A density functional theory study
Journal Pre-proofs Research paper Radionuclide incorporation in negative thermal expansion α-Zr(WO4)2: A density functional theory study Eunja Kim, Philippe F. Weck, Jeffery A. Greathouse, Margaret E. Gordon, Charles R. Bryan PII: DOI: Reference:
S0009-2614(20)30087-7 https://doi.org/10.1016/j.cplett.2020.137172 CPLETT 137172
To appear in:
Chemical Physics Letters
Received Date: Revised Date: Accepted Date:
27 November 2019 28 January 2020 29 January 2020
Please cite this article as: E. Kim, P.F. Weck, J.A. Greathouse, M.E. Gordon, C.R. Bryan, Radionuclide incorporation in negative thermal expansion α-Zr(WO4)2: A density functional theory study, Chemical Physics Letters (2020), doi: https://doi.org/10.1016/j.cplett.2020.137172
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Radionuclide incorporation in negative thermal expansion α-Zr(WO4 )2 : A density functional theory study Eunja Kima,∗, Philippe F. Weckb , Jeffery A. Greathouseb , Margaret E. Gordonb , Charles R. Bryanb a Department
of Physics and Astronomy, University of Nevada Las Vegas, 4505 Maryland Parkway, Las Vegas, NV 89154, USA b Sandia National Laboratories, P.O. Box 5800, Albuquerque, NM 87185, USA
Abstract The incorporation of uranium, plutonium and technetium in the negative thermal expansion (NTE) α-Zr(WO4 )2 has been investigated within the framework of density functional theory (DFT). It is found that the vacancy formation energies of the charged vacancies are overall larger than that of its counterpart neutral Frenkel defects and Schottky defects. DFT calculations suggest that U and Pu substitutions for the Zr site are preferred in α-Zr(WO4 )2 . In case of Tc substitution, both Tc(IV) for the Zr site and Tc(VII) for the W site are considered under oxygen-poor and oxygen-rich conditions, while Tc(VII) substitution can be improved significantly by including Y2 O3 (charge compensation). 1. Introduction Over the past few decades, a considerable amount of research has been devoted to the development of host ceramic matrices for the incorporation and long-term immobilization of high-level radioactive waste (HLRW) generated from commercial nuclear reactors and defence operations (1, 2, 3). With the emerging needs for novel wasteforms specifically tailored to handle excess commercial stocks of uranium/plutonium fuels and surplus plutonium from Cold War weapons dismantlement, zirconia-, zircon- and zirconium phosphate-based crystalline ceramics have been suggested as prospective wasteforms (1, 2, 4, 5). Some of these Zr-based materials are stable, naturally occuring minerals, where U and Pu can substitute directly for Zr (1, 5). Owing to their high strength, thermodynamic stability and radiation resistance, a number of zirconium phosphate ceramics, such as Na1−x (Cs1.33 Sr)Zr2 P3 O12 (x = 0.1 − 1.0) or Ca1−2x Zr4 Mo2x P6−2x O24 (x = 0.1 − 0.5) have been recently proposed as potential HLRW host matrices (2). Among Zr-based ceramics, a fascinating subclass of materials in the Zr/W/O and Zr/W/P/O systems feature negative thermal expansion (NTE) (6, 7, 8, 9, 10, 11). Such ceramics that shrink with temperature upon incorporation of heat-generating radionuclides provide an interesting opportunity for the development of novel ∗ Corresponding
author. Email address: [email protected] (Eunja Kim)
Preprint submitted to Chemical Physics Letters
wasteforms that can isolate radionuclides even when radiation-induced metamictization occurs. To the best of our knowledge, NTE ceramics have not been previsouly proposed as possible HLWR wasteforms, although they might significantly slow down the radionuclide release rate to the environment and permit higher radionuclide loads. In this Letter, the incorporation of uranium, plutonium and technetium in a NTE zirconium tungstate, αZr(WO4 )2 ceramic matrix has been investigated within the framework of density functional theory (DFT). This work is a fundamental study of defect formation energies and stabilities. In addition to U and Pu discussed above for incorporation, the long-lived isotope of technetium 99 Tc (t1/2 = 2.13 × 105 years, β− = 294 keV) has been selected, since it is produced in large quantities from the nuclear fuel cycle (up to 6.1 and 5.9% fission yields from the fission of 235 U and 239 Pu) and constitutes an important challenge for nuclear waste storage or disposal and environmental remediation (12). Cubic Zr(WO4 )2 is one of the rare materials featuring isotropic NTE over a broad temperature range including room temperature (7, 8, 10). 2. Computational methods Calculations were conducted using DFT as implemented in the Vienna ab initio simulation package (VASP) (13). The exchange-correlation (XC) energy was obtained using the generalized gradient approximaJanuary 27, 2020
and (iii) V(W6+ ), representing a missing W atom in αZr(WO4 )2 . The latter can be the Frenkel and Schottky defects (see Fig. 1). The Frenkel defect is a vacancyinterstitial pair as shown in Fig. 1 (b)-(c). Fig. 1(b) describes a Frenkel pair of a Zr vacancy (blue) and an interstitial Zr (purple), which is denoted by V(Zr). Fig. 1(c) is a Frenkel defect of a W vacancy (yellow) and an interstitial W (purple), which can be denoted by V(W). Fig. 1(d) is a pair of an oxygen vacancy (silver) and an interstitial oxygen (purple), denoted by V(O).
tion (GGA) with the parameterization of Perdew-BurkeErnzerhof (PBE) (14). This XC functional accurately describes the structure-property relationships for a variety of Zr-based materials (15, 16, 17). In the Kohn-Sham (KS) equations, the interaction between valence electrons and ionic cores was described using the projector augmented wave (PAW) method, with Zr(4s,4p,5s,4d), W(6s,5d), O(2s,2p), U(5d,4 f ), Pu(5d,4 f ), and Tc(4p,5s,4d) electrons treated as valence electrons and the remaining core electrons together with the nuclei represented by PAW pseudopotentials. The blocked Davidson iterative matrix diagonalization scheme was utilized to solve the KS equations, with a plane-wave cutoff energy for the electronic wave-functions set to 500 eV and a total-energy convergence criterion fixed to 1 meV/atom. In inital structure relaxation calculations, the unit-cell characterized by Evans et al. (6) for the cubic Zr(WO4 )2 (space group P21 3, IT No. 198; Z = 4) was used as an initial guess structure. The Monkhorst-Pack k-point scheme (18) was utilized to sample the Brillouin zone with a 5×5×5 k-point mesh. Simultaneous ionic and cell energy-relaxation calculations were carried out, without symmetry constrained applied, until the HellmannFeynman forces acting on atoms were converged within 0.01 eV/Å. The defect formation energy (DFE), E f , was calculated using the following expression (19): E f = P P E(products) − E(reactants).
(a)
(b)
(c)
(d)
3. Results and discussion Lattice parameters of a = 9.241 Å (V = 789.10 Å3 ) and a = 9.310 Å (V = 806.87 Å3 ) were obtained at T = 0 K using PBEsol and PBE, respectively, which reproduce within ∼ 0.6% and ∼ 1.4% the experimental value of 9.1846(7) Å refined by Evans and co-workers (7) at T = 0.3 K. This PBE value is consistent with the result of a = 9.320 Å computed by Gupta et al. (20). With only minute differences between PBEsol and PBE results, both functionals yield lattice parameters in closer agreement with experiment than the value of a = 9.352 Å predicted by Gava et al. (21) using the B3LYP XC functional. Therefore, imperfections in αZr(WO4 )2 were investigated using a standard PBE funcational in this study. Imperfections can be either intrinsic or extrinsic defects, that are introduced in the optimized α-Zr(WO4 )2 structure using GGA/PBE. A. Intrinsic defects: The intrinsic defects comprise charged vacancies and charge neutral vacancies. The former includes (i) V(O2− ), representing a missing oxygen atom, (ii) V(Zr4+ ), representing a missing Zr atom,
Figure 1: Crystal unit cells of (a) pristine α-Zr(WO4 )2 ; Frenkel defects of (b) V(Zr), (c) V(W), and (d) V(O); Schottky defects of (e) V(ZrO2 ) and (f) V(WO3 ). The ZrO6 octahedral and WO4 tetrahedral structural units are in green and grey, respectively. Red spheres represent O atoms. The blue, gold, cyan spheres are missing Zr, W, and O atoms, respectively, while the purple sphere indicates the corresponding interstitial site in Frenkel defects.
The vacancy formation energies were calculated for charged vacancies of V(Zr4+ ) and V(W6+ ) that are 17.07 and 17.10 eV/defect, respectively. There are two different types of oxygen vacancies considered in this case: (i) the unrestrained oxygen atom (O1) that is bonded only to the central W atom and (ii) the other oxygen atoms (O2) that are bridging a W atom and a Zr atom, forming the corner-sharing of polyhedra in α2
Zr(WO4 )2 . Their vacancy formation energies are 4.83 for O1 and 5.48 eV/defect for O2, respectively. In case of the neutral vacancies, the calculated defect formation energies of Frenkel defects are 5.74, 10.66, and 2.222.52 eV/defect for V(Zr), V(W), and V(O), respectively, which are smaller than that of its counterpart charged defects (see Table 1).
fundamental computational study of various defects in the NTE α-Zr(WO4 )2 ceramic material, including doping of hazardous radionuclides (X = U, Pu, and Tc) generated from nuclear fuel cycles (1, 2). The radionuclide atoms were introduced into the lattice in one of the following ways: (i) substitution for Zr and W, referred to as X:S(Zr) and X:S(W), respectively, and (ii) inclusion in the lattice interstitial space, I(X) when X = U, UO2 , Pu, PuO2 , Tc, TcO2 , and Tc2 O7 . The different configurations of the extrinsic defects investigated in this study are depicted in Fig. 2 and Fig. 4. U incorporation: Here, two possible cases of uranium (U) substitution in α-Zr(WO4 )2 have been examined initially. U substituion in Zr, denoted by U:S(Zr), is depicted in Fig. 2(a) while U substitution in W, denoted by U:S(W), is depicted in Fig. 2(b). The calculated U substitution energies are 0.43 and 2.80 eV/U for U:S(Zr) and U:S(W), respectively, implying that U substitution for Zr sites, that is, U:S(Zr), is energetically more favorable to U substitution for W sites, U:S(W). Zr-bearing minerals have been considered as potential actinide wasteforms. Morin et al. reported U LIII-edge XANES and EXAFS data, confirming U-incorporation, up to 8-20%, in zircon (ZrSiO4 ). (28) It is also found that the full substitution of U for Zr is actually favored energetically in α-Zr(WO4 )2 , eventually resulting in U(WO4 )2 (29), as shown in Fig. 3. The U incorporation energy decreases while the unit-cell volume gradually increases with U substitution from 0.25 to 1. In addition Fig. 2(c) and (d) show two possible scenarios of interstitial doping for U, which are denoted by I(U) for U and I(UO2 ) for UO2 , respectively. The defect formation energies of I(U) and I(UO2 ) are 0.90 and 3.80 eV/defect, respectively. This implies that substitutional U doping is preferrable to interstitial U doping in α-Zr(WO4 )2 . Pu incorporation: In case of Pu-doping in αZr(WO4 )2 , the defect formation energies of Pu:S(Zr) and Pu:S(W) are 0.56 and 5.22 eV/Pu, implying that both U and Pu substitutions for the Zr site are preferred. This is in line with Weber et al. (30), reporting that a Zr-bearing ceramic with substantial amounts of Pu substituting for Zr was synthesized (5). It also suggests that Pu-doping may occur through interstitial doping of I(Pu) in α-Zr(WO4 )2 along with substitutional doping of Pu:S(Zr) since the defect formation energy of I(Pu) is 0.49 eV/Pu. Tc incorporation: While U substitution in αZr(WO4 )2 is isovalent for Zr, Tc subsitution in αZr(WO4 )2 can be either isovalent for Zr or altervalent for W. The latter can be facilitated by charge compensation on nearby sites. The calculated defect formation
Table 1: Vacancy formation energies of charged and neutral vacancies. The charged vacancies are V(Zr4+ ), V(W6+ ), and V(O2− ), respectively. The neutral vacancies considered are V(Zr) and V(W) for Frenkel defects as well as V(ZrO2 ) and V(WO3 ) for Schottky defects.
Intrinsic defects Charged defects Frenkel defects Schottky defects
Sites V(Zr4+ ) V(W6+ ) V(O2− ) V(Zr) V(W) V(O) V(ZrO2 ) V(WO3 )
Vacancy formation energy (eV/defect) 17.07 17.10 4.83-5.48 5.74 10.66 2.22-2.52 2.57 3.37
Fig. 1 (e) depicts the Schottky defect of ZrO2 , denoted by V(ZrO2 ), while Fig. 1(f) represents a vacancy of WO3 , denoted by V(WO3 ). The calculated vacancy formation energies are 2.57 eV/defect for V(ZrO2 ) and 3.37 eV/defect for V(WO3 ), respectively. Overall, it is predicted that the formation of the neutral vacancies is more energetically favorable than the conterpart charged vacancies in α-Zr(WO4 )2 . Among the neutral vacancies, Schottky defects are less enegetically expensive to create than the counterpart Frenkel defects. B. Extrinsic defects: Beside these vacancies, a variety of defects are present in materials that can alter materials properties significantly. In fact, the semiconductor industry is based on a small amount of point defects added to the system in order to modify the electrical properties (i.e., n-type or p-type semiconductors). α-Zr(WO4 )2 is a semiconductor with a calculated band gap of 3.44 and 3.45 eV at the PBE and PBEsol levels (22). Due to the unique physical properties including negative thermal expansion (NTE), numerous studies have been carried out to investigate the structure-property relationships in α-Zr(WO4 )2 theoretically (21, 22, 23, 24) and experimentally (6, 7, 8, 25, 26). Recently, classical molecular dynamics (MD) simulations have been carried out to provide a conceptual understanding of the amorphous-crystalline interface in Zr(WO4 )2 (27). However, to the best of our knowledge, no defect study has been reported in this interesting material yet. Therefore, special focus here will be on a 3
(a)
(b) 1.12 1.10
(a)
V/V0
1.08 1.06 1.04 1.02 1.00 0.44
(d)
DFE (eV/U)
(c)
0.43
(b)
0.42 0.41 0.40 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
x in (Zr1-xUx)W2O8
Figure 3: U substitutions for Zr sites, U:S(Zr): (a) volume change (V/V0 ) and (b) defect formation energy (DFE) in terms of U substitutions. The equilibrium volume (V0 ) is 806.87 Å3 /unit-cell using GGA/PBE.
Figure 2: Crystal unit cells of extrinsic defects in α-Zr(WO4 )2 . Substitutional defects: (a) X:S(Zr) and (b) X:S(W); interstitial defects: (c) I(X) and (d) I(XO2 ). Green and grey polyhedra represent ZrO6 octahedral and WO4 tetrahedral structural units, respectively, while slate-blue polyhedron indicates the radionuclide defects (i.e., X = U and Pu). Red spheres are oxygen atoms.
I(TcO2 ), and I(Tc), respectively, for Tc2 O7 , TcO2 , and Tc doping. A possible case that Tc2 O7 dissociates into TcO3 + and TcO4 − is denoted as I(TcO3 + TcO4 ) in this study.
energies are 1.01 eV/Tc for Tc:S(Zr) and 2.28 eV/Tc for Tc:S(W) under the O-poor synthetic condition (i.e., TcO2 ) while they are 2.72 eV/Tc and 1.04 eV/Tc under the O-rich synthetic condition (i.e., Tc2 O7 ). The following reaction is considered for Tc substitution into α-Zr(WO4 )2 with charge compensation using Y2 O3 .
4. Conclusions In summary, DFT calculations to investigate the intrinsic and extrinsic defects in α-Zr(WO4 )2 have been carried out using the standard PBE functional. It is found that charge neutral vacancies are energetically more favorable to form than the charged vacancies. Among the charge neutral vacancies, the defect formation energies of the Schottky defects are smaller than the Frenkel defects. DFT calculations of radionuclide (U, Pu, Tc) substitution at octahedral (Oh ) and tetrahedral sites (T d ) in α-Zr(WO4 )2 indicate that U and Pu substitutions for the Zr site are preferred. It is also found that the full substitution of U for Zr is actually favored energetically in α-Zr(WO4 )2 , eventually resulting in U(WO4 )2 . In case of Tc substitution, both Tc(IV)
2[Zr2 W4 O16 ] + Tc2 O7 + Y2 O3 → 2[(Zr, Y)(W3 , Tc)O16 ] + 2ZrO2 + 2WO3 .
(1)
DFT calculations predict that charge compensation by coupled substitution with Y3+ in the Zr4+ site improves Tc(VII) substititution significantly. According to Equation (1), the substitutional doping of Tc(VII) is energectically favorable by 1.77 eV/Y, when Y2 O3 is introduced. Several scenarios of interstitial Tc doping were examined as shown in Fig. 4 and Table 3. The interstitial impurities under consideration are I(Tc2 O7 ), 4
Table 2: Defect formation energies (DFE) of U and Pu–doping. The substitutional impurities at Zr and W are denoted by U:S(Zr) and U:S(W) for U substitutions, while they are Pu:S(Zr) and Pu:S(W) for Pu substitution, respectively. The interstitial impurities under consideration are I(UO2 ), and I(U) for UO2 and U doping, while they are I(PuO2 ), and I(Pu) for PuO2 and Pu doping, respectively. The equilibrium volume of the pristine α-Zr(WO4 )2 is 806.87 Å3 /unit-cell using GGA/PBE. U-doping Substitutional Interstitial Pu-doping Substitutional Interstitial
Site U:S(Zr) U:S(W) I(UO2 ) I(U)
DFE (eV/U) 0.43 2.80 3.80 0.90
Volume (Å3 /Unit-cell) 822.59 814.43 810.76 814.58
Site Pu:S(Zr) Pu:S(W) I(PuO2 ) I(Pu)
DFE (eV/Pu) 0.56 5.22 4.14 0.49
Volume (Å3 /Unit-cell) 832.45 815.01 812.05 811.92
Table 3: Defect formation energies (DFE) of Tc-doping. The substitutional impurities at Zr and W are denoted by Tc:S(Zr) and Tc:S(W) for Tc substitutions, while the interstitial impurities are I(Tc2 O7 ), I(TcO2 ), and I(Tc), respectively, for Tc2 O7 , TcO2 , and Tc doping. I(TcO3 + TcO4 ) is the interstitial inclusion of TcO3 + and TcO4 − that are the possible dissociation products of Tc2 O7 . Tc-doping Substitutional Interstitial
Site Tc:S(Zr) Tc:S(W) I(TcO2 ) I(Tc) I(Tc2 O7 ) I(TcO3 + TcO4 )
O-poor DFE (eV/Tc) 1.01 2.28 4.07 4.77
O-rich DFE (eV/Tc) 2.72 1.04
(a) I(Tc)
(b) I(TcO2)
(c) I(Tc2O7)
(d) I(TcO3+TcO4)
Figure 4: Crystal unit cells of interstitial Tc defects in α-Zr(WO4 )2 : (a) I(Tc), (c) I(TcO2 ), (c) I(Tc2 O7 ), and (d) I(TcO3 +TcO4 ). Green and grey polyhedra represent ZrO6 octahedral and WO4 tetrahedral structural units, respectively, while blue-tin polyhedron indicates the radionuclide defects (i.e., Tc, TcO2 , Tc2 O7 , TcO3 + , and TcO4 − ). Red and silver spheres are oxygen atoms.
4.00 2.85
for the Zr site and Tc(VII) for the W site are considered under oxygen-poor and oxygen-rich conditions, respectively. Tc(VII) substitution can be promoted by including Y2 O3 (charge compensation).
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Acknowledgments Sandia National Laboratories is a multi-mission laboratory managed and operated by National Technology and Engineering Solutions of Sandia, LLC., a wholly owned subsidiary of Honeywell International, Inc., for the U.S. Department of Energy’s National Nuclear Security Administration under contract DE-NA0003525. This work was supported by Laboratory Directed Research and Development (LDRD) funding from Sandia National Laboratories. This work was performed, in part, at the Center for Integrated Nanotechnologies, an Office of Science User Facility operated for the U.S. Department of Energy (DOE) Office of Science. The 5
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Highlights • DFT calculations of various defects in α-Zr(WO4 )2 were carried out. • The radionuclide (U, Pu, Tc) substitution at octahedral (Oh ) and tetrahedral sites (T d ) in α-Zr(WO4 )2 were investigated using DFT. • U and Pu substitutions for the Zr site were predicted.
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Eunja Kim: Conceptualization, Methodology, Investigation, Formal analysis. Philippe F. Weck: Conceptualization, Methodology, Investigation, Formal analysis. Jeffery A. Greathouse: Writing Review & Editing. Margaret E. Gordon: Writing - Review & Editing. Charles R. Bryan: Writing - Review & Editing.
Graphical abstract
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Highlights • DFT calculations of various defects in α-Zr(WO4 )2 were carried out. • The radionuclide (U, Pu, Tc) substitution at octahedral (Oh ) and tetrahedral sites (T d ) in α-Zr(WO4 )2 were investigated using DFT. • U and Pu substitutions for the Zr site were predicted.
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Declaration of interests ☒ The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. ☐The authors declare the following financial interests/personal relationships which may be considered as potential competing interests:
S0009-2614(20)30087-7 https://doi.org/10.1016/j.cplett.2020.137172 CPLETT 137172
To appear in:
Chemical Physics Letters
Received Date: Revised Date: Accepted Date:
27 November 2019 28 January 2020 29 January 2020
Please cite this article as: E. Kim, P.F. Weck, J.A. Greathouse, M.E. Gordon, C.R. Bryan, Radionuclide incorporation in negative thermal expansion α-Zr(WO4)2: A density functional theory study, Chemical Physics Letters (2020), doi: https://doi.org/10.1016/j.cplett.2020.137172
This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
© 2020 Published by Elsevier B.V.
Radionuclide incorporation in negative thermal expansion α-Zr(WO4 )2 : A density functional theory study Eunja Kima,∗, Philippe F. Weckb , Jeffery A. Greathouseb , Margaret E. Gordonb , Charles R. Bryanb a Department
of Physics and Astronomy, University of Nevada Las Vegas, 4505 Maryland Parkway, Las Vegas, NV 89154, USA b Sandia National Laboratories, P.O. Box 5800, Albuquerque, NM 87185, USA
Abstract The incorporation of uranium, plutonium and technetium in the negative thermal expansion (NTE) α-Zr(WO4 )2 has been investigated within the framework of density functional theory (DFT). It is found that the vacancy formation energies of the charged vacancies are overall larger than that of its counterpart neutral Frenkel defects and Schottky defects. DFT calculations suggest that U and Pu substitutions for the Zr site are preferred in α-Zr(WO4 )2 . In case of Tc substitution, both Tc(IV) for the Zr site and Tc(VII) for the W site are considered under oxygen-poor and oxygen-rich conditions, while Tc(VII) substitution can be improved significantly by including Y2 O3 (charge compensation). 1. Introduction Over the past few decades, a considerable amount of research has been devoted to the development of host ceramic matrices for the incorporation and long-term immobilization of high-level radioactive waste (HLRW) generated from commercial nuclear reactors and defence operations (1, 2, 3). With the emerging needs for novel wasteforms specifically tailored to handle excess commercial stocks of uranium/plutonium fuels and surplus plutonium from Cold War weapons dismantlement, zirconia-, zircon- and zirconium phosphate-based crystalline ceramics have been suggested as prospective wasteforms (1, 2, 4, 5). Some of these Zr-based materials are stable, naturally occuring minerals, where U and Pu can substitute directly for Zr (1, 5). Owing to their high strength, thermodynamic stability and radiation resistance, a number of zirconium phosphate ceramics, such as Na1−x (Cs1.33 Sr)Zr2 P3 O12 (x = 0.1 − 1.0) or Ca1−2x Zr4 Mo2x P6−2x O24 (x = 0.1 − 0.5) have been recently proposed as potential HLRW host matrices (2). Among Zr-based ceramics, a fascinating subclass of materials in the Zr/W/O and Zr/W/P/O systems feature negative thermal expansion (NTE) (6, 7, 8, 9, 10, 11). Such ceramics that shrink with temperature upon incorporation of heat-generating radionuclides provide an interesting opportunity for the development of novel ∗ Corresponding
author. Email address: [email protected] (Eunja Kim)
Preprint submitted to Chemical Physics Letters
wasteforms that can isolate radionuclides even when radiation-induced metamictization occurs. To the best of our knowledge, NTE ceramics have not been previsouly proposed as possible HLWR wasteforms, although they might significantly slow down the radionuclide release rate to the environment and permit higher radionuclide loads. In this Letter, the incorporation of uranium, plutonium and technetium in a NTE zirconium tungstate, αZr(WO4 )2 ceramic matrix has been investigated within the framework of density functional theory (DFT). This work is a fundamental study of defect formation energies and stabilities. In addition to U and Pu discussed above for incorporation, the long-lived isotope of technetium 99 Tc (t1/2 = 2.13 × 105 years, β− = 294 keV) has been selected, since it is produced in large quantities from the nuclear fuel cycle (up to 6.1 and 5.9% fission yields from the fission of 235 U and 239 Pu) and constitutes an important challenge for nuclear waste storage or disposal and environmental remediation (12). Cubic Zr(WO4 )2 is one of the rare materials featuring isotropic NTE over a broad temperature range including room temperature (7, 8, 10). 2. Computational methods Calculations were conducted using DFT as implemented in the Vienna ab initio simulation package (VASP) (13). The exchange-correlation (XC) energy was obtained using the generalized gradient approximaJanuary 27, 2020
and (iii) V(W6+ ), representing a missing W atom in αZr(WO4 )2 . The latter can be the Frenkel and Schottky defects (see Fig. 1). The Frenkel defect is a vacancyinterstitial pair as shown in Fig. 1 (b)-(c). Fig. 1(b) describes a Frenkel pair of a Zr vacancy (blue) and an interstitial Zr (purple), which is denoted by V(Zr). Fig. 1(c) is a Frenkel defect of a W vacancy (yellow) and an interstitial W (purple), which can be denoted by V(W). Fig. 1(d) is a pair of an oxygen vacancy (silver) and an interstitial oxygen (purple), denoted by V(O).
tion (GGA) with the parameterization of Perdew-BurkeErnzerhof (PBE) (14). This XC functional accurately describes the structure-property relationships for a variety of Zr-based materials (15, 16, 17). In the Kohn-Sham (KS) equations, the interaction between valence electrons and ionic cores was described using the projector augmented wave (PAW) method, with Zr(4s,4p,5s,4d), W(6s,5d), O(2s,2p), U(5d,4 f ), Pu(5d,4 f ), and Tc(4p,5s,4d) electrons treated as valence electrons and the remaining core electrons together with the nuclei represented by PAW pseudopotentials. The blocked Davidson iterative matrix diagonalization scheme was utilized to solve the KS equations, with a plane-wave cutoff energy for the electronic wave-functions set to 500 eV and a total-energy convergence criterion fixed to 1 meV/atom. In inital structure relaxation calculations, the unit-cell characterized by Evans et al. (6) for the cubic Zr(WO4 )2 (space group P21 3, IT No. 198; Z = 4) was used as an initial guess structure. The Monkhorst-Pack k-point scheme (18) was utilized to sample the Brillouin zone with a 5×5×5 k-point mesh. Simultaneous ionic and cell energy-relaxation calculations were carried out, without symmetry constrained applied, until the HellmannFeynman forces acting on atoms were converged within 0.01 eV/Å. The defect formation energy (DFE), E f , was calculated using the following expression (19): E f = P P E(products) − E(reactants).
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3. Results and discussion Lattice parameters of a = 9.241 Å (V = 789.10 Å3 ) and a = 9.310 Å (V = 806.87 Å3 ) were obtained at T = 0 K using PBEsol and PBE, respectively, which reproduce within ∼ 0.6% and ∼ 1.4% the experimental value of 9.1846(7) Å refined by Evans and co-workers (7) at T = 0.3 K. This PBE value is consistent with the result of a = 9.320 Å computed by Gupta et al. (20). With only minute differences between PBEsol and PBE results, both functionals yield lattice parameters in closer agreement with experiment than the value of a = 9.352 Å predicted by Gava et al. (21) using the B3LYP XC functional. Therefore, imperfections in αZr(WO4 )2 were investigated using a standard PBE funcational in this study. Imperfections can be either intrinsic or extrinsic defects, that are introduced in the optimized α-Zr(WO4 )2 structure using GGA/PBE. A. Intrinsic defects: The intrinsic defects comprise charged vacancies and charge neutral vacancies. The former includes (i) V(O2− ), representing a missing oxygen atom, (ii) V(Zr4+ ), representing a missing Zr atom,
Figure 1: Crystal unit cells of (a) pristine α-Zr(WO4 )2 ; Frenkel defects of (b) V(Zr), (c) V(W), and (d) V(O); Schottky defects of (e) V(ZrO2 ) and (f) V(WO3 ). The ZrO6 octahedral and WO4 tetrahedral structural units are in green and grey, respectively. Red spheres represent O atoms. The blue, gold, cyan spheres are missing Zr, W, and O atoms, respectively, while the purple sphere indicates the corresponding interstitial site in Frenkel defects.
The vacancy formation energies were calculated for charged vacancies of V(Zr4+ ) and V(W6+ ) that are 17.07 and 17.10 eV/defect, respectively. There are two different types of oxygen vacancies considered in this case: (i) the unrestrained oxygen atom (O1) that is bonded only to the central W atom and (ii) the other oxygen atoms (O2) that are bridging a W atom and a Zr atom, forming the corner-sharing of polyhedra in α2
Zr(WO4 )2 . Their vacancy formation energies are 4.83 for O1 and 5.48 eV/defect for O2, respectively. In case of the neutral vacancies, the calculated defect formation energies of Frenkel defects are 5.74, 10.66, and 2.222.52 eV/defect for V(Zr), V(W), and V(O), respectively, which are smaller than that of its counterpart charged defects (see Table 1).
fundamental computational study of various defects in the NTE α-Zr(WO4 )2 ceramic material, including doping of hazardous radionuclides (X = U, Pu, and Tc) generated from nuclear fuel cycles (1, 2). The radionuclide atoms were introduced into the lattice in one of the following ways: (i) substitution for Zr and W, referred to as X:S(Zr) and X:S(W), respectively, and (ii) inclusion in the lattice interstitial space, I(X) when X = U, UO2 , Pu, PuO2 , Tc, TcO2 , and Tc2 O7 . The different configurations of the extrinsic defects investigated in this study are depicted in Fig. 2 and Fig. 4. U incorporation: Here, two possible cases of uranium (U) substitution in α-Zr(WO4 )2 have been examined initially. U substituion in Zr, denoted by U:S(Zr), is depicted in Fig. 2(a) while U substitution in W, denoted by U:S(W), is depicted in Fig. 2(b). The calculated U substitution energies are 0.43 and 2.80 eV/U for U:S(Zr) and U:S(W), respectively, implying that U substitution for Zr sites, that is, U:S(Zr), is energetically more favorable to U substitution for W sites, U:S(W). Zr-bearing minerals have been considered as potential actinide wasteforms. Morin et al. reported U LIII-edge XANES and EXAFS data, confirming U-incorporation, up to 8-20%, in zircon (ZrSiO4 ). (28) It is also found that the full substitution of U for Zr is actually favored energetically in α-Zr(WO4 )2 , eventually resulting in U(WO4 )2 (29), as shown in Fig. 3. The U incorporation energy decreases while the unit-cell volume gradually increases with U substitution from 0.25 to 1. In addition Fig. 2(c) and (d) show two possible scenarios of interstitial doping for U, which are denoted by I(U) for U and I(UO2 ) for UO2 , respectively. The defect formation energies of I(U) and I(UO2 ) are 0.90 and 3.80 eV/defect, respectively. This implies that substitutional U doping is preferrable to interstitial U doping in α-Zr(WO4 )2 . Pu incorporation: In case of Pu-doping in αZr(WO4 )2 , the defect formation energies of Pu:S(Zr) and Pu:S(W) are 0.56 and 5.22 eV/Pu, implying that both U and Pu substitutions for the Zr site are preferred. This is in line with Weber et al. (30), reporting that a Zr-bearing ceramic with substantial amounts of Pu substituting for Zr was synthesized (5). It also suggests that Pu-doping may occur through interstitial doping of I(Pu) in α-Zr(WO4 )2 along with substitutional doping of Pu:S(Zr) since the defect formation energy of I(Pu) is 0.49 eV/Pu. Tc incorporation: While U substitution in αZr(WO4 )2 is isovalent for Zr, Tc subsitution in αZr(WO4 )2 can be either isovalent for Zr or altervalent for W. The latter can be facilitated by charge compensation on nearby sites. The calculated defect formation
Table 1: Vacancy formation energies of charged and neutral vacancies. The charged vacancies are V(Zr4+ ), V(W6+ ), and V(O2− ), respectively. The neutral vacancies considered are V(Zr) and V(W) for Frenkel defects as well as V(ZrO2 ) and V(WO3 ) for Schottky defects.
Intrinsic defects Charged defects Frenkel defects Schottky defects
Sites V(Zr4+ ) V(W6+ ) V(O2− ) V(Zr) V(W) V(O) V(ZrO2 ) V(WO3 )
Vacancy formation energy (eV/defect) 17.07 17.10 4.83-5.48 5.74 10.66 2.22-2.52 2.57 3.37
Fig. 1 (e) depicts the Schottky defect of ZrO2 , denoted by V(ZrO2 ), while Fig. 1(f) represents a vacancy of WO3 , denoted by V(WO3 ). The calculated vacancy formation energies are 2.57 eV/defect for V(ZrO2 ) and 3.37 eV/defect for V(WO3 ), respectively. Overall, it is predicted that the formation of the neutral vacancies is more energetically favorable than the conterpart charged vacancies in α-Zr(WO4 )2 . Among the neutral vacancies, Schottky defects are less enegetically expensive to create than the counterpart Frenkel defects. B. Extrinsic defects: Beside these vacancies, a variety of defects are present in materials that can alter materials properties significantly. In fact, the semiconductor industry is based on a small amount of point defects added to the system in order to modify the electrical properties (i.e., n-type or p-type semiconductors). α-Zr(WO4 )2 is a semiconductor with a calculated band gap of 3.44 and 3.45 eV at the PBE and PBEsol levels (22). Due to the unique physical properties including negative thermal expansion (NTE), numerous studies have been carried out to investigate the structure-property relationships in α-Zr(WO4 )2 theoretically (21, 22, 23, 24) and experimentally (6, 7, 8, 25, 26). Recently, classical molecular dynamics (MD) simulations have been carried out to provide a conceptual understanding of the amorphous-crystalline interface in Zr(WO4 )2 (27). However, to the best of our knowledge, no defect study has been reported in this interesting material yet. Therefore, special focus here will be on a 3
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x in (Zr1-xUx)W2O8
Figure 3: U substitutions for Zr sites, U:S(Zr): (a) volume change (V/V0 ) and (b) defect formation energy (DFE) in terms of U substitutions. The equilibrium volume (V0 ) is 806.87 Å3 /unit-cell using GGA/PBE.
Figure 2: Crystal unit cells of extrinsic defects in α-Zr(WO4 )2 . Substitutional defects: (a) X:S(Zr) and (b) X:S(W); interstitial defects: (c) I(X) and (d) I(XO2 ). Green and grey polyhedra represent ZrO6 octahedral and WO4 tetrahedral structural units, respectively, while slate-blue polyhedron indicates the radionuclide defects (i.e., X = U and Pu). Red spheres are oxygen atoms.
I(TcO2 ), and I(Tc), respectively, for Tc2 O7 , TcO2 , and Tc doping. A possible case that Tc2 O7 dissociates into TcO3 + and TcO4 − is denoted as I(TcO3 + TcO4 ) in this study.
energies are 1.01 eV/Tc for Tc:S(Zr) and 2.28 eV/Tc for Tc:S(W) under the O-poor synthetic condition (i.e., TcO2 ) while they are 2.72 eV/Tc and 1.04 eV/Tc under the O-rich synthetic condition (i.e., Tc2 O7 ). The following reaction is considered for Tc substitution into α-Zr(WO4 )2 with charge compensation using Y2 O3 .
4. Conclusions In summary, DFT calculations to investigate the intrinsic and extrinsic defects in α-Zr(WO4 )2 have been carried out using the standard PBE functional. It is found that charge neutral vacancies are energetically more favorable to form than the charged vacancies. Among the charge neutral vacancies, the defect formation energies of the Schottky defects are smaller than the Frenkel defects. DFT calculations of radionuclide (U, Pu, Tc) substitution at octahedral (Oh ) and tetrahedral sites (T d ) in α-Zr(WO4 )2 indicate that U and Pu substitutions for the Zr site are preferred. It is also found that the full substitution of U for Zr is actually favored energetically in α-Zr(WO4 )2 , eventually resulting in U(WO4 )2 . In case of Tc substitution, both Tc(IV)
2[Zr2 W4 O16 ] + Tc2 O7 + Y2 O3 → 2[(Zr, Y)(W3 , Tc)O16 ] + 2ZrO2 + 2WO3 .
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DFT calculations predict that charge compensation by coupled substitution with Y3+ in the Zr4+ site improves Tc(VII) substititution significantly. According to Equation (1), the substitutional doping of Tc(VII) is energectically favorable by 1.77 eV/Y, when Y2 O3 is introduced. Several scenarios of interstitial Tc doping were examined as shown in Fig. 4 and Table 3. The interstitial impurities under consideration are I(Tc2 O7 ), 4
Table 2: Defect formation energies (DFE) of U and Pu–doping. The substitutional impurities at Zr and W are denoted by U:S(Zr) and U:S(W) for U substitutions, while they are Pu:S(Zr) and Pu:S(W) for Pu substitution, respectively. The interstitial impurities under consideration are I(UO2 ), and I(U) for UO2 and U doping, while they are I(PuO2 ), and I(Pu) for PuO2 and Pu doping, respectively. The equilibrium volume of the pristine α-Zr(WO4 )2 is 806.87 Å3 /unit-cell using GGA/PBE. U-doping Substitutional Interstitial Pu-doping Substitutional Interstitial
Site U:S(Zr) U:S(W) I(UO2 ) I(U)
DFE (eV/U) 0.43 2.80 3.80 0.90
Volume (Å3 /Unit-cell) 822.59 814.43 810.76 814.58
Site Pu:S(Zr) Pu:S(W) I(PuO2 ) I(Pu)
DFE (eV/Pu) 0.56 5.22 4.14 0.49
Volume (Å3 /Unit-cell) 832.45 815.01 812.05 811.92
Table 3: Defect formation energies (DFE) of Tc-doping. The substitutional impurities at Zr and W are denoted by Tc:S(Zr) and Tc:S(W) for Tc substitutions, while the interstitial impurities are I(Tc2 O7 ), I(TcO2 ), and I(Tc), respectively, for Tc2 O7 , TcO2 , and Tc doping. I(TcO3 + TcO4 ) is the interstitial inclusion of TcO3 + and TcO4 − that are the possible dissociation products of Tc2 O7 . Tc-doping Substitutional Interstitial
Site Tc:S(Zr) Tc:S(W) I(TcO2 ) I(Tc) I(Tc2 O7 ) I(TcO3 + TcO4 )
O-poor DFE (eV/Tc) 1.01 2.28 4.07 4.77
O-rich DFE (eV/Tc) 2.72 1.04
(a) I(Tc)
(b) I(TcO2)
(c) I(Tc2O7)
(d) I(TcO3+TcO4)
Figure 4: Crystal unit cells of interstitial Tc defects in α-Zr(WO4 )2 : (a) I(Tc), (c) I(TcO2 ), (c) I(Tc2 O7 ), and (d) I(TcO3 +TcO4 ). Green and grey polyhedra represent ZrO6 octahedral and WO4 tetrahedral structural units, respectively, while blue-tin polyhedron indicates the radionuclide defects (i.e., Tc, TcO2 , Tc2 O7 , TcO3 + , and TcO4 − ). Red and silver spheres are oxygen atoms.
4.00 2.85
for the Zr site and Tc(VII) for the W site are considered under oxygen-poor and oxygen-rich conditions, respectively. Tc(VII) substitution can be promoted by including Y2 O3 (charge compensation).
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Acknowledgments Sandia National Laboratories is a multi-mission laboratory managed and operated by National Technology and Engineering Solutions of Sandia, LLC., a wholly owned subsidiary of Honeywell International, Inc., for the U.S. Department of Energy’s National Nuclear Security Administration under contract DE-NA0003525. This work was supported by Laboratory Directed Research and Development (LDRD) funding from Sandia National Laboratories. This work was performed, in part, at the Center for Integrated Nanotechnologies, an Office of Science User Facility operated for the U.S. Department of Energy (DOE) Office of Science. The 5
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Highlights • DFT calculations of various defects in α-Zr(WO4 )2 were carried out. • The radionuclide (U, Pu, Tc) substitution at octahedral (Oh ) and tetrahedral sites (T d ) in α-Zr(WO4 )2 were investigated using DFT. • U and Pu substitutions for the Zr site were predicted.
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Eunja Kim: Conceptualization, Methodology, Investigation, Formal analysis. Philippe F. Weck: Conceptualization, Methodology, Investigation, Formal analysis. Jeffery A. Greathouse: Writing Review & Editing. Margaret E. Gordon: Writing - Review & Editing. Charles R. Bryan: Writing - Review & Editing.
Graphical abstract
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Highlights • DFT calculations of various defects in α-Zr(WO4 )2 were carried out. • The radionuclide (U, Pu, Tc) substitution at octahedral (Oh ) and tetrahedral sites (T d ) in α-Zr(WO4 )2 were investigated using DFT. • U and Pu substitutions for the Zr site were predicted.
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Declaration of interests ☒ The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. ☐The authors declare the following financial interests/personal relationships which may be considered as potential competing interests: