ELECTRONIC STRUCTURE OF Pu 3+ AND Pu 4+ IMPURITY CENTERS IN ZIRCON INTRODUCTION

Journal of Structural Chemistry. Vol. 51, No. 1, pp. 1-8, 2010 Original Russian Text Copyright 2010 by M. V. Ryzhkov, A. L. Ivanovskii, A. V. Porotnikov, Yu. V. Shchapova, and S. L. Votyakov ELECTRONIC STRUCTURE OF Pu 3+ AND Pu 4+ IMPURITY CENTERS IN ZIRCON M. V. Ryzhkov, 1 A. L. Ivanovskii, 1 A. V. Porotnikov, 2 Yu. V. Shchapova, 2 and S. L. Votyakov 2 UDC 539.2.01:541.57 Using a fully relativistic DV cluster method, we study the electronic structure of a large fragment of the crystal lattice of zircon ZrSiO 4 with a plutonium dopant atom replacing a Zr 4+ zirconium atom. Three possible states of the impurity center are considered: Pu 4+ (isovalent substitution), Pu 3+ (non-isovalent substitution), and Pu 3+ with an oxygen vacancy in the nearest environment that provides charge compensation. Relaxation of the ZrSiO 4 crystal lattice near a defect is simulated using a semi-empirical method of atomic pair potentials (GULP program). An analysis of overlap populations and effective charges on atoms shows that the chemical bonding of plutonium with a matrix is covalent, while isovalent substitution yields a more stable system than a Pu 3+ impurity. In the presence of vacancies the structure of chemical bonding is intermediate with respect to substitutions Pu 4+ Zr 4+ and Pu 3+ Zr 4+. Keywords: cluster calculation, relativistic effects, chemical bond of a Pu impurity with the ZrSiO 4 matrix. INTRODUCTION High isomorphic capacity of ZrSiO 4 zircon mineral relative to rare earth and radioactive elements determines its promising use as a material for nuclear waste disposal [1], in particular, isotopes of reactor-grade and weapons-grade plutonium ( 238 Pu, 239 Pu, 240 Pu, 241 Pu, 242 Pu). Long-term safe storage of Pu, isomorphically substituting for the Zr dodecahedral site in the zircon structure, depends on the radiative thermal stability of the structure of synthetic ceramics based on ZrSiO 4 [2] subjected to radiation damage (metamictization) because of -decay of Pu isotopes and their daughter nuclei (for instance, 235 U in the case of 239 Pu). Due to a high activity of zircon containing Pu, experimental studies of the features of its local structure and chemical bond are scarce [3-6]. During the synthesis under reductive conditions plutonium is known to enter into the structure of zircon in the Pu 3+ charge state; annealing in air transforms it into the Pu 4+ state [4]. By analogy with a uranium impurity in zircon, whose charge state can take the values of U 4+ and U 5+ depending on the degree of metamictness of samples [7], it is possible to suppose that in zircon plutonium can be in different valence states. Variations in the charge state of a dopant cation should result in relaxation of the structure of its nearest environment, changes in characteristics of the chemical bonding with the matrix, and appearance of structural strain. A detailed information on the atomic and electronic structure of impurity defects can be obtained by computer modeling methods. Previously in [8], the formation energies for point Pu 3+ and Pu 4+ defects were calculated with different ways of charge compensation; it is shown that the lowest formation energies E characterize: (1) Pu 4+ Zr 4+ (E = 0.26 ev/pu), isolated Pu 4+ substitution for one Zr 4+ ; (2) 2Pu 3+ + V O 2Zr 4+ (1.02 ev/pu), substitution of two neighboring Zr 4+ by two Pu 3+ with compensation by a V O oxygen ion vacancy; and (3) 1 Institute of Solid State Chemistry, Ural Division, Russian Academy of Sciences, Ekaterinburg; ryz@ihim.uran.ru. 2 Institute of Geology and Geochemistry, Ural Division, Russian Academy of Sciences, Ekaterinburg. Translated from Zhurnal Strukturnoi Khimii, Vol. 51, No. 1, pp. 7-14, January-February, 2010. Original article submitted March 5, 2009. 0022-4766/10/5101-0001 2010 Springer Science+Business Media, Inc. 1

Pu 3+ + V O Zr 4+ (4.5 ev/pu), an isolated Pu 3+ substitution for one Zr 4+ with compensation by a V O oxygen vacancy. By means of semi-empirical structural simulation, the characteristics of structural relaxation of Pu 3+ short range order have previously been determined [9], and the case of its local charge compensation by a dopant cation P 5+ Si 4+ in the neighboring tetrahedral site was considered. An analysis of the structure of Pu 3+ short range order with charge compensation by an oxygen vacancy has not previously been performed; non-empirical calculations of the features of chemical bonding of impurity plutonium in the zircon matrix have either not been made. These calculations should be carried out within relativistic calculation methods that allow for spin-orbital interaction; such an approach we have used to study the electronic structure of impurity uranium in zircon [10]. The purpose of this work is the quantum chemical simulation of the electronic structure of the ZrSiO 4 crystal lattice fragment with a plutonium atom substituting for zirconium; an analysis of the effect of the dopant charge state (Pu 4+ and Pu 3+ ) on the degree of structural relaxation of the site, the electron energy spectrum, the charge density distribution and Pu O, Zr O, and O Si chemical bonds, and also a study of the effect of a vacancy in the nearest environment of impurity serving as charge compensation in heterovalent substitution Pu 3+ Zr 4+. OBJECTS AND CALCULATION PROCEDURES In the work, we used an original program implementing the relativistic discrete variation method (RDV) [11, 12] based on the solution of the Dirac-Slater equation for four component wave functions transforming according to the irreducible representations of double groups (in the present calculations, the point groups of clusters are S 4 and C s ). In order to obtain symmetrization coefficients we applied an original program implementing the method of projection operators [11] and a matrix of the irreducible representations of double groups obtained in the work [13]. An extended basis set of numerical atomic four component orbitals (AOs) produced by solving the one-electron problem for isolated neutral atoms included also the virtual states of the Zr5p 1/2,5p 3/2 and Pu7p 1/2,7p 3/2 type. Numerical Diophantine integration in the calculation of matrix elements was performed over the set of 298,000 points distributed in the cluster space. In the work, we used the exchangecorrelation potential [14], and the effective charges on atoms were calculated by integrating the charge density in the spatial domains between the minimum electron density points [15]. In order to determine the relaxation of the short range order structure of the mineral when a plutonium impurity enters it, we used a semi-empirical method of atomic pair potentials implemented in the GULP program [16]. Point defects were modeled within the Mott-Littleton approach of embedded spheres; the internal region directly adjacent to a defect participates in the energy minimization procedure, whereas the external region is considered as a polarized dielectric continuum. When simple zircon point defects were modeled, the internal sphere contained 130 atoms; when pair substitution defects were modeled, its dimensions were enlarged to 600 atoms. Parameters of calculation potentials for Si and O ions were taken from the library [17], and for Zr and Pu from [18]. Atomic shifts found by this approach for several dopant coordination spheres, obtained by a comparison of calculated positions of atoms in ideal zircon and plutonium doped zircon, were then added to their experimental coordinates in ideal ZrSiO 4, Cluster models. In order to study the electronic structure of Pu in ZrSiO 4 we selected a 213-atomic fragment of PuZr 22 Si 30 O 160 with a center on the plutonium atom replacing zirconium. The point symmetry of such a cluster is S 4, however, when charge compensation by an oxygen vacancy was modeled, the PuZr 22 Si 30 O 159 cluster symmetry was lowered to s. In order to take into account the effect of the crystal environment, we employed the extended cluster procedure described in detail in [19]. In this procedure, the fragment in question consists of the main (central) part (or the core of the cluster), which is the object of study, and the outer part (or the shell) that usually includes the atoms of several coordination spheres surrounding the core (with the necessary condition that each of peripheral Zr and Si atoms has a complete number of the nearest ligands). During the self-consistency procedure, the electron density and the potential of centers in the shell were replaced by the corresponding values obtained for crystallographically equivalent atoms of the cluster core. Moreover, 2

TABLE 1. Values of Interatomic Distances in MO 8 Dodecahedra (M = Zr, Pu) According to the GULP Calculation and Experimental [20] Data Bond Experiment ZrSiO 4 Calculation ZrSiO 4 Calculation Pu 4+ Zr 4+ Calculation Pu 3+ Zr 4+ Calculation Calculation (Pu 3+ +V O1 ) Zr 4+ (Pu 3+ +V O2 ) Zr 4+ M O 1 2.27 2.30 2.45 2.50 2.39 M O 1 2.27 2.30 2.45 2.50 2.42 2.42 M O 1 2.27 2.30 2.45 2.50 2.44 2.42 M O 1 2.27 2.30 2.45 2.50 2.44 2.42 M O 2 2.13 2.10 2.15 2.30 2.22 M O 2 2.13 2.10 2.15 2.30 2.22 2.25 M O 2 2.13 2.10 2.15 2.30 2.25 2.26 M O 2 2.13 2.10 2.15 2.30 2.31 2.22 in order to take into account the long range component of the potential of the crystal environment, the extended cluster was embedded in a pseudopotential of the outer crystal lattice including 10,144 atoms with Coulomb and exchange-correlation potentials obtained for the corresponding equivalent atoms in the main part of the cluster. In the present work, as previously in studies on U impurity [10], the main part of the cluster in question involved: the central PuO 8 group (hereinafter, these ligands will be referred to as O 1, O 2 ); two silicon atoms (Si 1 ) the nearest neighbors of 1, 4Zr, and 4Si of the next coordination sphere (Zr 2, Si 2 ); 36 oxygen ions that belong to six crystallographic types and form the nearest environment of Zr 2 and Si 2 (O 3, O 4, O 5, O 6, O 7, 8 ). The other atoms formed the cluster shell, and in the self-consistency process their electron densities and potentials remained unchanged, the same as they were obtained for an ideal crystal of ZrSiO 4 [10]. Simulation of the structure of an ideal zirconium crystal by the GULP method predicts the values of 2.10 Å and 2.30 Å for interatomic Zr O distances and 1.63 Å for Si O, which is consistent with the experimental data of 2.13 Å for Zr O 1, 2.26 Å for Zr O 2, and 1.62 Å for Si O [20] within the limits of 0.6-1.4%. Table 1 contains interatomic distances in the nearest environment of the impurity center in the considered structural models. According to GULP calculations, the relaxation of the nearest environment of Pu dopant atom has the following characteristics. 1. Isolated isovalent substitution Pu 4+ Zr 4+. In plutonium substitution for the central zirconium atom, the dodecahedron sizes increase, and its shape distorts. As in the case of uranium impurity, an increase in sizes is more pronounced along the z axis as compared to an increase along the x, y axes. The Pu 1 distance increases by 0.15 Å relative to the Zr O distance calculated for a pure zircon crystal, and the Pu 2 distance increases by 0.05 Å. 2. Isolated heterovalent substitution Pu 3+ Zr 4+ without local charge compensation. A calculation of the lattice relaxation for Pu 3+ predicts more substantial distortions of the structure of the nearest environment as compared to a tetravalent impurity. The Pu 1 and Pu 2 distances increase by 0.20 Å relative to the Zr O distance calculated for a pure crystalline zircon, which coincides with the sizes of dodecahedra experimentally found by the EXAFS method in synthetic ZrSiO 4 :Pu samples [21]. Here the calculated Pu Zr and Pu Si distances considerably less change as compared to the initial Zr Zr Zr Si (by 0.01 Å and 0.04 Å respectively), which agrees with the data of [21], where the distances to the atoms of the second coordination sphere were obtained as almost identical with the initial ones. Thus, the Pu 3+ embedding into the zircon structure is accompanied by a strong local distortion of the dodecahedral site, damped at small distances (of about 3.6 Å). Preservation of the local structure around the plutonium impurity at high doses of self-radiation experimentally found in [21] indicates the stability of the considered group in the metamict sample. 3. Heterovalent substitution Pu 3+ Zr 4+ with local charge compensation by an oxygen vacancy. Since in the PuZr 22 Si 30 O 160 cluster the nearest environment of the impurity consists of two groups of inequivalent 1 (more remote) and 2 (less remote) ligands, we considered two models of the vacancy: in 1 and 2 polyhedra respectively. A calculation of the lattice relaxation for V O1 and V O2 predicts more substantial distortions of the cluster structure as compared to simple 3

Fig. 1. Partial densities of states for Pu5f,6p,6d,7s,7p, O 1 2s,2p, O 2 2s,2p, Zr 2 4p,4d,5s,5p, and Si2s,2p,3s,3p in the PuZr 22 Si 30 O 160 cluster (Pu 4+ Zr 3+ ). States of the p, d, and f type are shown by solid lines, states of the s type are shown by dashes. plutonium substitution for zirconium. For V O1, the Pu 2 distance increases by 0.12-0.21 Å and Pu 1 by 0.12-0.14 Å. For V O2, the Pu 2 distance increases by 0.12-0.16 Å and Pu 1 by 0.09-0.12 Å. In the second coordination sphere, the nearest neighbors of the oxygen vacancies, Zr (by 0.2-0.3 Å) and Si (by 0.7-0.8 Å) atoms are most shifted. In the presence of a vacancy, out of all symmetry operations only the reflection plane remains, in which the vacancy is; therefore, the symmetry group of the clusters lowers to C s. Atomic shifts found by the GULP method for several coordination spheres of the impurity, obtained by comparing the calculated positions of atoms in ideal zircon and plutonium doped zircon, were then added to their experimental coordinates in ideal ZrSiO 4. The atomic positions thus obtained were further used in RDV calculations of the electronic structure. RESULTS AND DISCUSSION Fig. 1 presents the partial densities of states for Pu, O 1, O 2, Zr 2, and Si 1 atoms obtained for isovalent substitution Pu 4+ Zr 4+. For the plutonium impurity atom as well as for uranium, the relativistic description is of principal importance. Spin-orbital splitting for Pu6p 1/2 (peak with the energy of 27.5 ev) and Pu6p 3/2 ( 16 ev) levels is 6 times higher than that for 4 zirconium orbitals (peaks with the energies of 26.6 ev and 28.4 ev). Here both Pu6p and U6p states cannot be considered to be core ones because hybridization of Pu6p 3/2 and O2s orbitals is quite noticeable (Fig. 1). For the high-energy 4

Fig. 2. Total densities of states for ideal zircon and plutonium doped zircon with different degrees of oxidation and vacancies in the nearest environment. Pu5f,6d,7s,7p levels the spin-orbital splitting is 1 ev, but relativistic effects determine the energy and spatial characteristics of these states along with the order of bonds between the orbitals of each type with O2p AOs of the nearest neighbors. The Pu5f impurity levels fall into the band gap of ZrSiO 4, but unlike uranium, the gap between the impurity band and the edge of O2p valence states is only 1.2 ev. The number of electrons at these levels depends on the model of Pu substitution for Zr. In the model of isovalent substitution, we assumed that plutonium with all its electrons replaced zirconium also with all its electrons, and then the electron density shifted from the actinide atom to the nearest neighbors in accordance with the highest energy gain. Hence, we obtained that the impurity levels have four electrons occupying the orbitals of 5, 6, 7, and 8 symmetry with a close structure: 84% Pu5f, 8%, and 4% 2 2. The contribution of Pu6d turns out to be of about 1%, i.e. remarkably lower than in the case of uranium. The lowest vacant level of the 6 type (LUMO) has a close composition and the energy higher by 0.3 ev than the last occupied 7 state (HOMO). The number of electrons at the impurity levels can be smaller if plutonium with a larger charge substitutes for Zr 4+ (hypothetically, for example, Pu 5+ ) or larger if it is Pu 3+. In the latter case, one more filled orbital of the 5 type appears, which contains the main contribution of Pu5f AO (90%) and (1%) and (5%) impurity. For simple substitution Pu 3+ Zr 4+, a difference between HOMO and LUMO energies turns out to be smaller than 0.01 ev. In calculations with oxygen vacancies, the 5f impurity levels also contain 5 electrons, but in the O2p valence band the number of orbitals is less by 6. In these calculations, MOs correspond to 3 and 4 irreducible representations of the C s double group. It is found that four deeper impurity states contain 87-90% Pu5f AO, the fifth orbital (HOMO) is 80-82% Pu5f, and in the lower vacant MO the Pu5f AO contribution is only 77-79%. Fig. 2 shows the total densities of states for all four models of plutonium substitution for zirconium; the calculation results for ideal zircon are also given for comparison. Apart from differences in the details of line shapes, it is possible to note relative shifts of main bands. As noted above, in the case of Pu 4+, the split between O2p and Pu5f states is 1.2 ev; for Pu 3+ this gap considerably increases to 2.2 ev; for V O1 the split of these bands decreases 5

TABLE 2. Overlap Populations of Zr 1, U, Pu, Zr 2, Si 1, Si 2, and O 1, O 2 AOs Obtained in RDV Calculations of ZrZr 22 Si 30 O 160, UZr 22 Si 30 O 160, PuZr 22 Si 30 O 160, and PuZr 22 Si 30 O 159 Clusters (per Each Pair of Interacting Atoms, 10 3 e) System AO 4d Zr 1 5s 5p U, Pu 5f 6d 7s 7p Zr 2 4d 5s 5p 3s Si 1 3p 3s Si 2 3p ZrSiO 4 U 4+ Zr 4+ Pu 4+ Zr 4+ Pu 3+ Zr 4+ (Pu 3+ +V O1 ) Zr 4+ (Pu 3+ +V O2 ) Zr 4+ 144 54 12 208 55 58 49 153 50 23 79 202 44 20 37 130 50 22 100 221 47 16 23 128 46 19 43 175 54 16 49 145 51 18 62 197 53 22 38 154 55 24 54 191 54 15 208 64 72 134 47 5 196 60 73 142 51 6 250 66 72 114 46 10 283 64 64 138 64 18 211 58 65 160 49 15 206 60 66 165 61 10 214 394 2 1 220 402 1 1 203 386 1 2 207 390 2 1 221 441 2 2 221 399 1 1 1 5 212 392 2 6 211 381 3 8 203 375 2 5 207 393 1 5 214 380 1 6 215 383 to 1.1 ev; and for a vacancy in the 2 environment it again reaches 2.1 ev. Still, in all cases, the value is remarkably lower than that for the uranium impurity (3.7 ev) [10]. The impurity charge state is mainly manifested in an increase in the difference between the energies of Pu5f 5/2 (E F taken as the energy scale zero passes through them) and Pu6p 3/2 states that are deeper by 0.5 ev in all calculations with Pu 3+. Note also that a transformation of the crystal structure in the presence of an impurity affects the position of zirconium orbitals. This can be seen from the transformation of Zr4p 3/2,4p 1/2 Pu6p 1/2 peaks with the energies lower than 25 ev. As in ideal ZrSiO 4, where the Zr O interaction has a covalent character due to hybridization of mainly Zr4d and 2 states, in all states considered for the plutonium dopant atom, considerable covalent mixing of not only Pu6d O2p, but also Pu5f O2p orbitals is observed (Fig. 1). Thus, in the zircon lattice the chemical bonding of plutonium and uranium with oxygen atoms has a covalent nature. A more detailed structure of contributions to the chemical bond of different states is given by overlap populations (n ij ) of Zr, Pu, Si orbitals with the surrounding oxygen atoms. Table 2 lists the n ij values for the external Pu O 1, O 2, Zr 2 O 1, O 2, Si 1 O 1, O 2, and Si 2 O 1, O 2 orbitals. For the sake of comparison, they are divided by the number of bonds of each type, i.e. per each pair of interacting atoms. For all considered types of the center, the number of bonds is four, and for oxygen vacancies the number of bonds with the corresponding ligand is three. For comparison, the results obtained for ideal ZrSiO 4 and uranium impurity are also shown. The distance between the plutonium atom and 1 ligands increases by 0.04 Å, as compared to U O 1, whereas shorter Pu O 2 bonds decrease by 0.06 Å as compared to U O 2. Therefore, the contributions to chemical bonding of Ac6d and Ac5f interactions turns out to be substantially smaller for plutonium than for uranium (Table 2). On the other hand, the Ac6d, 5f -AO overlap populations for the Pu 4+ impurity prove to be higher than for U 4+. The participation of virtual Pu7p-orbitals in chemical bonding, as well as for U7p-AO, turns out to be very sensitive to interatomic distances, whose increase with transition from 2 to 1 changes the character of Pu7p O2p interactions from bonding to antibonding. A similar result was also obtained for virtual Zr 2 5p states (Table 2). The Pu 3+ impurity is bonded to the surrounding ligands substantially weaker than Pu 4+, which is consistent with the experimental fact that annealing of samples converts Pu 3+ to the Pu 4+ state [4]. A comparison between simple substitution Pu 3+ Zr 4+ and substitution with vacancies shows that the latter causes an increase in overlap populations of the impurity center with environment, and in the presence of vacancies the structure of chemical bonding is intermediate between the systems with Pu 4+ and Pu 3+. Thus, the calculations show that the considered vacancies can stabilize the plutonium impurity in zircon. 6

TABLE 3. Effective Charges on the Atoms in ZrSiO 4, U 4+ ZrSiO 4, and Pu ZrSiO 4 in Different Models of Plutonium Substitution for Zirconium (in e units) Compound Q Zr1 Q U, Pu Q O1 Q O2 Q Zr2 Q Si1 Q Si2 ZrSiO 4 2.70 1.26 1.25 2.74 2.30 2.30 U 4+ Zr 4+ 3.07 1.29 1.35 2.74 2.30 2.32 Pu 4+ Zr 4+ 2.67 1.27 1.30 2.75 2.32 2.31 Pu 3+ Zr 4+ 2.37 1.29 1.34 2.76 2.33 2.32 (Pu 3+ +V O1 ) Zr 4+ 2.51 1.30 1.22 (Pu 3+ +V O2 ) Zr 4+ 2.42 1.35 1.30 1.31 *Charges on the atoms nearest to vacancies are marked. 1.34 1.35 1.35 1.31 1.35 2.74 2.79 2.71* 2.74 2.76* 2.74 2.35 1.91* 2.30 2.32 2.30 2.34 2.33 2.29 1.99* 2.30 Table 3 lists the effective charges on atoms (Q ef ) obtained by spatial integration of the electron density inside the regions between the density minimum points. In order to increase the accuracy, Q ef were calculated individually for all atoms of the main part of the cluster, and then they were averaged for crystallographically equivalent centers. The validation criterion for calculations was variation coefficients (mean square deviations divided by the average charge of the ions of the given type). In present calculations they did not exceed 6%. Unlike Mulliken charges and charges in -spheres [15], the charges obtained by this method are the quantitative characteristics of electron density redistribution between the atoms. For calculations with vacancies several values of charges corresponding to all inequivalent atoms in each group are given because of symmetry lowering. From the data of Table 3 it follows that the charge state of plutonium is much closer to that of the substituted zirconium ion than for the uranium impurity. Despite that in the Pu 3+ Zr 4+ model the number of electrons on the impurity 5f states was one more than in the case of Pu 4+ Zr 4+, the charge on the plutonium ion decreased only by 0.3. At the same time, charges on O 1 and O 2 increased; however, this increase was partially due to a shift of the electron density from zirconium and silicon atoms, the nearest neighbors of these ligands. The appearance of vacancies promotes the shift of the electron density from the impurity center to the rest 1 and 2 ligands. However, in the case of V O1, for silicon ions and to a lower extent for zirconium an inverse trend is observed: charges on Si 1 and Si 2 near vacancies are by 0.3-0.4 lower than on the other atoms of this type. Noticeable differences in the effective charges of all atoms from their formal degrees of oxidation indicate the covalent character of the Zr O, Si O, and Pu O interaction in this compound. CONCLUSIONS The calculations that we performed show that plutonium substitution for a zirconium atom in ZrSiO 4 is a probable process because the interaction between the impurity and the oxygen environment has a number of features close to the Zr O interaction in the ideal matrix. It is confirmed that isovalent substitution Pu 4+ Zr 4+ is more stable than Pu 3+ Zr 4+. However, in the latter case, vacancies in the nearest environment of the impurity can produce a positive effect. It is found that in the presence of vacancies the effective charges on the impurity and its bonding with the environment are intermediate relative to simple substitutions Pu 4+ Zr 4+ and Pu 3+ Zr 4+. The obtained results do not give grounds to think that an increase in the number of 5f electrons for plutonium as compared to uranium will substantially change the character of the interaction between the impurity and the matrix. The work was supported by the RAS Program No. 14 (Scientific Bases of Rational Nature Management) and the Interdisciplinary Project of UD RAS (Composition, Structure, and Physics of Radiation Thermal Effects in Phosphate and 7

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