Molecular dynamics modeling of irradiation damage in highly coordinated mineral structures

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1 Molecular dynamics modeling of irradiation damage in highly coordinated mineral structures Grechanovsky A.E., Brik A.B. M.P. Semenenko Institute of Geochemistry, Mineralogy and Ore Formation of NAS of Ukraine, 34 Palladina av., Kyiv, Ukraine Abstract. The radiation stability of zirconolite CaZrTi 2 O 7, pyrochlore Gd 2 Zr 2 O 7 and periclase MgO has been studied by computer simulations methods. Computer simulation of zircon ZrSiO 4 also has been performed for comparison with these structures. These calculations were performed in grid- environment using «GEOPARD» virtual organization. The number of Frenkel pairs after propagation of the primary knock-оn atom of thorium with a kinetic energy of 20 kev (analogue of recoil atom arising due to the alpha decay of actinides) has been characterized by molecular dynamics method. Calculation of the effective charge of oxygen atoms has been performed using density functional theory and B3LYP hybrid functional. It is established that the radiation stability of these minerals depends significantly from two main factors: type of structure and the degree of chemical bonds covalency of the structures (or effective charge of oxygen atoms). The results of computer simulations show that structures with high bond iconicity and high coordination number of cations (periclase, pyrochlore) are characterized by high radiation resistance to amorphization. Keywords Radiation resistance of minerals, semiempirical interatomic potential method, grid-calculations, computer simulation, method of molecular dynamics 1 Introduction Over recent decades, in a number of countries there has been traced a tendency to increase the use of electricity generated by nuclear power plants. In particular, according to the International Atomic Energy Agency (IAEA) data, in 2009 the share of electricity generated by nuclear power plants is 75% in France, 49% in Ukraine, 20% in the United States, and 18% in the Russian Federation [1]. On the other hand, the prospects for the development of nuclear power engineering are associated with the effective management of nuclear waste. The development of nuclear power engineering raises a number of problems relating to the disposal of long-lived radioactive waste and plutonium. One of the main problems in this respect is the choice of radiation resistant matrices, which, in contact with long-lived high-level radioactive waste, for a long time will not change their physical and chemical properties. At present, aluminophosphate or borosilicate glasses have been used as matrices for spent fuel. However, high-level radioactive waste can be stored in these matrices for a time of no longer than years. This is the reason that the search for matrices with efficient performance characteristics has been actively continued. It has been found that crystalline ceramic materials are significantly better suited for the utilization of high-level radioactive waste. To date, a number of ceramic materials have been developed for the disposal of high-level radioactive waste and plutonium. Extensive studies have been performed on materials such as zircon ZrSiO 4, pyrochlores Gd 2 Ti 2 O 7 and Gd 2 Zr 2 O 7, monazites (La,Ce,Nd)PO 4, zirconolite CaZrTi 2 O 7, perovskite CaTiO 3, and other complex oxides, as well as rutile TiO 2 and baddeleyite ZrO 2. Many researchers have considered zircon as a promising matrix for the disposal of nuclear fuel and weapon-grade plutonium [2 5]. However, over geological time, the alpha decay of uranium and thorium atoms leads to the damage of the structure of zircon and its transition from the crystalline state to the X-ray amorphous (metamict) state. Each act of alpha decay results in the formation of an alpha particle and a heavy recoil atom [5]. Alpha particles with an energy of MeV, as was noted in [4], displace approximately 100 atoms in the end of the path with a length of μm, whereas heavy recoil atoms with an energy of kev displace several thousand atoms within an interval of 20 nm. A promising replacement of zircon can be minerals with highly coordinated structure. In contrast to zircon, these compounds are characterized by high radiation stability [6]. In this respect, the purpose of the present work was to -156-

2 investigate the relation between the radiation stability of zirconolite CaZrTi 2 O 7, compounds Gd 2 Zr 2 O 7 with the structure of pyrochlore and periclase MgO and characteristics of its crystalline structures using method of molecular dynamics (MD). MD simulation of zircon structure also has been performed for comparison with these structures. 2 Simulation technique The molecular dynamics (MD) method consists in calculating trajectories of the motion of all atoms involved in a system on the basis of Newton s second law. The initial data are taken as the initial coordinates and velocities of all the atoms and the interatomic interaction potentials. In the majority of such model experiments, the atoms are endowed with some effective charges. The magnitude of these charges depends on the degree of covalency of interatomic bonds and can vary from zero (for covalent compounds) to values of formal charges of ions (for ionic crystals). In addition to the Coulomb interactions of all electrostatic charges between themselves, the interatomic interaction potential takes into account the repulsion of electron shells of the atoms and the dipole dipole interaction between the atoms in terms of the short-range interaction potentials of the following form: a) the Buckingham potential 6 V ( r) = A exp( r / ρ ) С r, (1) where r is the distance between two atoms (Å), A is the pre-exponential factor for the term characterizing the repulsion (ev), ρ is the stiffness parameter (Å), and C is the force parameter of the van der Waals interaction (ev Å 6 ); b) the Morse potential V r) = D [ exp( 2α ( r r )) 2exp( α ( r ))], (2) ( 0 r0 where D is the dissociation energy of the bond between the atoms (ev), α is the softness parameter (Å -1 ), r 0 is the standard bond length between the atoms (Å). Parameters specified in (1) and (2) were taken from works [7-11].Optimization of these structures was made using experimental values of unit-cell parameters, atom coordinates, elastic constants, and thermodynamic properties. In the structure of a mineral, we chose a fragment containing approximately million atoms. One of atoms was replaced by a thorium atom. At the preliminary stage of the simulation, the structural fragment was brought into the thermal equilibrium state for 10 ps at the temperature of modeling T mod (300 K) with the use of an NPT ensemble (here, the number of atoms N in the structural fragment, the pressure P on the walls of the fragment, and the temperature T are constant). At small interatomic distances (less than 1 Å), we used the internuclear repulsion potential ZBL, which was introduced to correctly take into account the strong internuclear repulsion [6]. The simulation time step was 0.5 fs. The main stage of the simulation was performed using the microcanonical ensemble NVE (here, the number of atoms N in the structural fragment, the volume of the structure V, and the energy E are constant). At the beginning of this stage, we specified the direction of motion and the velocity of the thorium atom, which corresponded to a particular kinetic energy. This energy was limited by the number of atoms in the fragment (25 50 atoms per electron-volt, depending on the elastic properties of the mineral). Keeping this in mind, energy of 20 kev has been chosen for the structure fragment consisting of million atoms. Limitations of computation capability prevented us from considering a greater structure fragment. As a result of critical consideration of various programs, we dwelt on the DL_POLY program complex [12], elaborated for simulation of structural fragments of minerals, macromolecules, polymers, and ion systems. This program complex gives an opportunity to of radiation mineralogy (investigation of structures due to alpha decay of actinides), study of processes in minerals, study of forming migrations of point defects in these minerals. For the calculation of the effective charge of oxygen atoms in the minerals we have performed quantum-chemical calculations using density functional theory and the B3LYP hybrid functional. We have used the PC GAMESS code [13] for this purpose. For realization of calculations the web-sites of uagrid.org.ua and grid.inpracom.kiev.ua were used. All calculations were executed in the virtual organization «GEOPARD», organized by Glushkov Institute of Cybernetic of NAS of Ukraine, M.P. Semenenko Institute of Geochemistry, Mineralogy and Ore Formation of NAS of Ukraine and S.I. Subbotin Institute of Geophysics of NAS of Ukraine

3 Results and discussion The motion of a primary knock-on atom leads to its collision with other atoms of the system.

$A substantial fraction of displaced atoms returns to their original positions during a period of several picoseconds. Other atoms form a displacement cascade.$ Radiation damage, produced by Th recoil with energy of 20 kev in zircon, zirconolite and pyrochlore at the peak of the formation of defect region and after structure recovery of minerals shows in

Radiation damage, produced by Th recoil with energy of 20 kev in zircon, zirconolite and pyrochlore at the peak of the formation of defect region and after structure recovery of minerals shows in

3 3 Results and discussion The motion of a primary knock-on atom leads to its collision with other atoms of the system. These atoms are displaced from their equilibrium positions, begin to move, and, in turn, displace other atoms. This stage can be referred to as ballistic. This process results in the creation of an amorphous zone surrounded by relatively undistorted regions (point defects). A substantial fraction of displaced atoms returns to their original positions during a period of several picoseconds. Other atoms form a displacement cascade. Radiation damage, produced by Th recoil with energy of 20 kev in zircon, zirconolite and pyrochlore at the peak of the formation of defect region and after structure recovery of minerals shows in Figure. The results of performed MDand DFT simulations are given in Table. The following quantities are indicated in the table: the mineral and its chemical formula, the effective charge of oxygen atoms Q(O), the number of Frenkel pairs at the end of simulation N FP, and the critical temperature of amorphization T c (if T > T c, then a mineral cannot be amorphized), obtained from the ion-beam irradiation experiments with 800 kev-1.5 MeV Kr + ions [6, 14]. Figure. Radiation damage, produced by 20 kev Th recoil in zircon (a), zirconolite (b) and pyrochlore (c) at the peak of the damage (left column) and after structure relaxation (right column)

4 Table. Results of MD- and DFT simulations of studied minerals Mineral and its chemical formula Q(O), e 0 N FP T c, K Zircon ZrSiO Zirconolite CaZrTi 2 O Pyrochlore Gd 2 Zr 2 O Periclase MgO The results of computer simulations show that periclase MgO and chemical compound Gd 2 Zr 2 O 7 with the structure of pyrochlore are characterized by high bond ionicity (high value of oxygen effective charge) and high radiation stability, obtained from MD simulation and from experimental data. Zirconolite structure CaZrTi 2 O 7 shows the intermediate both bond ionicity and critical temperatures of amorphization T c. Zircon structure ZrSiO 4 is characterized by low bond ionicity (the value of oxygen effective charge is equal to e 0 ) and low radiation stability. In simple terms, the relevance of the type of interatomic forces for resistance to amorphization can be discussed as follows. After the displacement of atoms due to propagating heavy ion, the rearrangement of atoms needed to regain coherence with the crystalline lattice involves significant atomic motion. In a covalent structure, the interactions can be thought of as short-range directional constraints, due to the substantial electronic charge being localized between the neighbouring atoms. Therefore cooperative atomic motion is hooked by the electrons between neighbouring atoms, and requires breaking directional covalent bonds with associated energy cost. On the other hand, highly ionic structure can be viewed as a collection of charged ions. The cooperative rolling of spheres which are only electrostatically charged, does not require additional activation energy, giving damaged ionic structure better chances to re-establish coherence with crystalline lattice. 4 Conclusions The mechanisms of radiation-induced damages in zircon ZrSiO 4, zirconolite CaZrTi 2 O 7, pyrochlore Gd 2 Zr 2 O 7 and periclase MgO structures as a result of the alpha decay due to the recoil of the nucleus have been investigated using the molecular dynamics computer simulation. All calculations were performed in grid-environment using «GEOPARD» virtual organization. The results of researches show that the radiation stability of studied minerals caused by two main factors: type of structure and the degree of chemical bonds covalency of the structures (or effective charge of oxygen atoms). It should be noted that the type of structure and the effective charge of oxygen atoms mainly are interconnected. Highly coordinated structures (periclase, pyrochlore) are characterized by large values of both the effective charge of oxygen atoms and the radiation stability. Structures with a small coordination number of cations (zircon) are characterized by small values of both the effective charge of oxygen atoms and the radiation stability. Results of this study can be used for solving fundamental and practice tasks connected with immobilization and disposal of a high-level waste. In particular, these results can be used for the assessment of radiation stability of matrices, proposed for immobilization of the high-level waste. Our computer simulations permit to analyze and predicted matrices reliability under radiation damage. Using computer simulation methods can save timing and money budgets and promotes to choice of the appropriated matrix. 5 Acknowledgments This research was supported by Government scientific and technical program of introduction and application of gridtechniques in , project 38/13 «Application of grid technology for research of the radiation-enhanced processes, phase transformations and isomorphic substitutions in minerals in connection with the applied problems decision»

5 References [1] Nuclear power reactors in the World. Reference data series No. 2. International atomic energy agency. Vienna, P. 77 [2] Ewing R.C. Zircon: A host phase for the disposal of weapons plutonium // J. Mater. Res Vol. 10. P [3] Shpak A.P., Grechanovsky A.E., Lytovchenko A.S., Legkova G.V., Sayenko S.Yu. Influence of temperature and uranium on the radiation stability of zircon // J. Nucl. Mater V N 1-2. P [4] Grechanovsky A.E. Radiation Stability of Natural and Man-Made Mineral Matrices for Long-Term and Environmentally Safe Disposal of High Level Radioactive Waste [in Russian] Kiev: Logos, p. [5] Robinson M.T. Basic physics of radiation damage production // J. Nucl. Mater Vol. 216, N 1. P [6] Trachenko K., Pruneda J.M., Artacho E., Dove M.T. How the nature of the chemical bond governs resistance to amorphization by radiation damage // Phys. Rev. B V. 71. N 18. P [7] Yu J., Devanathan R., Weber W.J. Molecular dynamics simulation of defect production in collision cascades in zircon // J. Mater. Chem V. 19. Issue 23. P [8] Kramer G.J., Farragher N.P., van Beest B.W.H., van Santen R.A. Interatomic force fields for silicas, aluminophosphates, and zeolites: Derivation based on ab initio calculations // Phys. Rev. B V. 43. N 6. P [9] Qun-bo Fan. Molecular dynamics calculation of thermal expansion coefficient of a series of rare-earth zirconates // J. Comp. Mat. Sci Vol. 46. P [10] Veiller L. Molecular dynamics simulation of the α-recoil nucleus displacement cascade in zirconolite // J. Nucl. Mat Vol. 306, Iss. 1. P [11] Shukla P. Thermal transport properties of MgO and Nd 2 Zr 2 O 7 pyrochlore by molecular dynamics simulation // J. Nucl. Mat Vol P. 1 7 [12] Todorov I.T., Smith W. DL_POLY_3: the CCP5 national UK code for molecular-dynamics simulations // Phil. Trans. Royal Soc. A V P [13] Nemukhin A.V. Molecular modelling by using the PC GAMESS program: From diatomic molecules to enzymes // Moscow Univ. Chem. Bull Vol. 45, N 2. P [14] Meldrum A. A comparison of radiation effects in crystalline ABO 4 -type phosphates and silicates // Miner. Mag Vol. 64, N 2. P

The effect of point defects in zircon

aterials for nuclear waste immobilization: The effect of point defects in zircon iguel Pruneda Department of Earth Sciences University of Centre for Ceramic Immobilisation Radiation damage process α-decay