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Structure Of A Calcium Aluminosilicate From M olecular-Dynamics Simulations: Finite Size Effects And Surface Properties.

*P. Ganster, *JM. Delaye, **M. Benoit, **W. Kob *Laboratoire du Comportement à Long Terme, Commissariat à l‘Energie Atomique, BP 171, 30207 Bagnols sur Cèze, France patrick.ganster@ cea.fr - jean-marc.delaye@ cea.fr **Laboratoire des Verres, Université Montpellier II, Place E. Bataillon, 34095 Montpellier, France Magali.Benoit@ ldv.univ-montp2.fr - Walter.Kob@ ldv.univ-montp2.fr

Abstract œ We present results of an investigation of a calcium aluminosilicate (CAS) glass (bulk and surface) by means of classical and ab initio molecular dynamics (MD) simulations. The study of finite size effects and the validation of the potentials used in classical MD are done by using ab initio Car-Parrinello MD and comparing structural characteristics to experimental data. The finite size effects study shows that systems of 100 atoms have a more ordered local structure than systems of 200 to 1600 atoms. For large systems, good agreements with experiments are obtained. We then present the modelling of glass surfaces by two methods: In the first method, the surface is created in the liquid state and quenched to room temperature, and in the second method, the surface is generated in the glass state at 300 K. Depending of the fabrication method, it affects the atomic distribution at the surface and in the bulk, the structural entities concentration and the surface roughness.

I. INTRODUCTION Depending of the Al2O3/CaO ratio, Ca atoms play the role of a network modifier if they create Complex alumino-boro- are non-bridging (NBO) by breaking T-O-T used for the nuclear waste confinement. linkages (T=Si/Al) and/or they play the role of - Numerous studies have been done on simplified charge balancing, by neutralizing (AlO4) nuclear glasses (SiO2 œ Al2O3 œ CaO œ Na2O œ entities. One often observes an excess number of B2O3) in order to understand the leaching NBO compared to what simple stochiometry processes1, 2. In particular, it has been shown that arguments predicts in CAS systems8. The an alteration layer appears between the pristine environment of the Ca atoms is less specific than glass and the solution during water leaching. that of the Si and Al atoms since it is quite This layer is a hydrated silica-like porous gel difficult to attribute a specific coordination of enriched with aluminum and calcium. The long this species experimentally. Nevertheless, in term behavior of the nuclear glass during storage pure CAS glasses, it has been shown by X-ray or is likely to be related to the behavior of the neutron spectroscopy that the distribution of alteration layer during lixiviation. It is therefore oxygens around Ca is independent of the important to study the structure of this calcium composition9, 10 . CAS glasses are also subject to aluminosilicate layer in order to better the Löwenstein rule, i.e. the Al/Al avoidance understand the chemical reactions that take place principle11 which states that Al-O-Al linkages when it is in contact with an aqueous solution. are absent (or rare) in CAS glasses and crystals The use of molecular dynamics simulations is with a low aluminum content. particularly suitable to tackle this type of The first part of this study is dedicated to problems3-5. We report here simulations of a finite size effects because we intend to study the calcium aluminosilicate glass (bulk and surface) obtained glassy structure by means of ab initio of composition (SiO2)0.67 - (Al2O3)0.13 œ (CaO)0.21 MD which, because of limitations in computer which corresponds to the composition of the ressources, can only be applied to very small protective layer6. systems (O(100) atoms). It is therefore important In calcium aluminosilicate glasses, to investigate to what extend the properties of as well as aluminum atoms are network formers small systems are representative of the properties and they have a tetrahedral coordination with of larger ones. The second part presents the atoms7. The tetrahedra are connected by generation of glass surfaces and the study of shared oxygens which are called bridging their structural properties. oxygens (BO) and they form an amorphous network in which Ca atoms are dispersed.

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II. COM PUTATIONAL PROCEDURE are inserted. From the radial distribution functions (RDF) computed for the larger systems 1. Classical and ab initio molecular dynamics (1600 atoms), we can extract the most probable SiO, AlO and CaO interatomic distances which For the classical molecular dynamics are found to be equal to 1.60 Å, 1.76 Å and 2.50 simulations of (SiO2)0.67 - (Al2O3)0.13 œ (CaO)0.21, Å, respectively (Fig. 2, upper panels). The Ca we use 2-body Born-Mayer-Huggins interatomic coordinations range between 4 and 12 oxygen potentials (BMH) and the Stillinger-Weber 3- atoms with a maximum probability at 7-8 which body potentials (SW) modified in order to slightly overestimates the experimental data14. In improve the structure of simplified nuclear the upper panel of Fig. 2, the SiO, AlO and CaO glasses 12, 13. RDFs of two system sizes are compared: the first In ab initio Car-Parrinello MD14, the electronic peaks of these RDFs are all narrower and higher structure, determined within the formalism of in the 100-atoms case than in the 1600-atoms density functional theory, is calculated at each one. This effect is only present in 100-atoms MD step and is used to compute the forces acting systems and disappears in systems larger or on the ions. For each atom, the valence electrons equal to 200 atoms23. are described by plane waves and core electrons by pseudo-potentials. A large computational resource is needed and thus only small systems (100 œ 200 atoms) can be simulated. The details of the electronic structure calculations of the CAS systems can be found in Ref. 15.

2. Glass preparation

To model glasses in bulk condition, we first equilibrate, using classical MD, liquids at 4200 K during 1.8 ns and then quenched them by decreasing their temperature linearly in time with -1 Fig. 1 : Comparison of the experimental (from a rate of 10−¹ K.s to 300 K. In order to study Ref. 7) and calculated neutron structure factor finite size effects, we generated CAS glasses of for a 800-atoms CAS glass of composition 60% 100, 200, 400, 800 and 1600 atoms, all having SiO - 10% AlO - 30% CaO. The scattering the same density of 2.42 g.cm-3. Due to the 2 2 3 lengths were taken to be equal to bSi,O,Al,Ca = computational cost of ab initio MD, we use the 4.149, 5.803, 3.449, 4.700 fm. initial configuration (atomic positions and velocities) of the 100- and 200-atoms glasses Similar finite size effects are found in the SiOSi generated by classical MD as input and SiOAl inter-tetrahedral angular distributions configurations for the ab initio simulations. (not shown) which extend from 110 to 180 degrees and have respectively a maximum at 157 III. BULK STRUCTURE AND FINITE SIZE and 148 degrees in the 1600-atoms case. For the EFFECTS 100-atoms systems, these angular distributions exhibit irregularities that are directly related to 1. Finite size effects the use of 3-body terms in the classical potential16. The ring (i.e., loops of connected We have compared the experimental static tetrahedra) size distributions are comparable to neutron structure factor Sn(q) to a simulated 16 the pure silica ones and the study of the oxygen one (Fig. 1). For this comparison, a slightly coordination allowed to confirm the excess different composition was used ((SiO2)0.60 - number of NBO atoms and the Al/Al avoidance (Al2O3)0.10 œ (CaO)0.30) to coincide with the principle11. Oxygen triclusters (i.e., oxygen experiment. All peaks of the Sn(q) are quite well atoms linked to three network formers, Al or Si) reproduced thus giving evidence that the short are also found in small proportion in the and medium range order are correctly system15. reproduced. In the CAS glass, the Si and Al atoms are found to be surrounded by 4 oxygen atoms and they form a tetrahedral network into which Ca atoms

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The introduction of empty space to create a surface can be done at two different stages of the glass preparation. In the first method (hereafter named —IG“ for —Industrial Glass“), the empty space is introduced in the liquid state and the surface is equilibrated at 4200 K and then quenched to 300 K at 10−¹ K.s-1. It corresponds to the usual fabrication method of industrial glasses. In the second method, the empty space is introduced in the glass state at 300 K (hereafter named —FG“, for —Fracture Glass“) and no temperature constraint is applied. Therefore the temperature of the system reaches 1000 K after Figure 2: First peaks of the SiO, AlO and CaO 0.18 ns due to the surface relaxation. Then the radial distribution functions. Upper graphs: system is quenched to 300 K at 10−¹ K.s-1. This Comparison between 100-atoms and 1600-atoms model method corresponds to a surface CAS systems. Lower graphs: Comparison before fabrication by fracture. and after the ab initio MD relaxation for the 100- atoms systems.

2. Ab initio M D relaxation of the structure

A second validation of the glassy structures generated by classical MD is done by using the configurations obtained from the classical Figure 3 : To generate a surface from a cubic simulations as initial configurations for a CPMD box, empty space is inserted by increasing the simulation (The systems sizes were 100 and 200 box length in the Z direction. atoms, T=300 K, and the length of the trajectory Results was 1 ps). As soon as the CPMD simulation has started, an increase of the temperature up to 500 2. Results K is observed which is due to the structural re- organization in the microcanonical ensemble. At In both cases, and for systems containing 1600 this temperature, the structural modifications are atoms, an expansion of the glasses is observed in only local: the first peaks in the SiO, AlO and the Z direction as soon as the empty space is CaO RDFs become less pronounced and introduced. The expansion is about 4 Å for the resemble the ones obtained for the 1600-atoms IG glass and 1.5 Å for the FG glass. A local system using the classical potential (lower reorganization, more pronounced in the IG glass, graphs in Fig. 2). More generally, all the finite is observed: a surface layer depleted in Ca atoms size effects that were observed on the local and enriched in Al and Si atoms appears (left structure of the 100-atoms systems (RDF first panel in Fig. 4). This reorganization is initiated peaks, angular distributions and Ca environment) during the high temperature phase and is are basically removed during the ab initio conserved during the quench. In the FG glass, dynamics. the Al and Si enrichments of the external layer is lower but the Ca atoms still leave the surface to IV. SURFACE M ODELLING move inside the bulk. The chemical modification very close to the 1. Preparation of the surface surface due to the Ca enrichment induces structural evolutions: a depolymerization of the In order to model the surface of a CAS network (increase of Q2 and Q3 entities, i.e. glass, the length of the cubic simulation box in tetrahedra with 2 and 1 NBO, respectively), an the Z direction is increased by introducing an excess of NBO atoms and tri-coordinated Si empty space. As the periodic boundary atoms are observed. In the right panel of Fig. 4, conditions are conserved, the systems then the oxygen coordination is shown from the correspond to film layers separated by an empty center of the IG glass to the surface: A NBO space (Fig. 3). excess induced by the Ca enrichment clearly appears in the range 7-13 Å. Meanwhile, shorter

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SiO, AlO and CaO interatomic distances, and distributions, roughness). It also shows the smaller SiOSi and SiOAl angles appear at the influence of the atomic distributions on the surface. surface structural properties (O and Si coordinations, interatomic distances etc.) This work constitutes thus a preliminary step for the study of the water/glass interactions which can only be carried out using ab initio simulations. A good knowledge of finite size effects in the bulk and for the surface description is therefore mandatory. The inclusion of water at a surface relaxed by ab initio simulations will be Figure 4 : Left panel: Si, O, Al and Ca the next step of this study. distributions as a function of the distance from the center of the film (located at z=0). Right REFERENCES : panel: Z-dependence of the oxygen coordination 1. S. GIN, Mat. Res. Soc. Symp. Proc., 663, 207 We have also determined the surface roughness (2000). by the following method: using a grid of 8x8 2. F. ANGELI, D. BOSCARINO, S. GIN, G. squares defined in the XY plane, we have DELLA MEA, B. BOIZOT, J.C. PETIT, Phys. computed the height of the atoms for each XY Chem. of glasses, 42, 279 (2001). square. The total roughness is then defined as 3. M. RARIVOMANANTSOA, P. JUND, R. Rt=Rp+Rc where Rp is the maximum height, Rt is JULLIEN, J. Phys. : Cond. Matter, 13, 6707 the lowest point and Ra is the arithmetic average (2001). of the atom heights. From the results presented 4. C. MISCHLER, W. KOB, K. BINDER, in Table 1, one can observe that the roughness of Comp. Phys. Comm., 147, 222 (2002). the IG glass is larger than that of the FG glass 5. E.A. LEED, C.G. PANTANO, J. Non-Cryst. even after the relaxation at high temperature. Solids, 325, 48 (2003). 6. D. REBISCOUL, A.V.D. LEE, F. Table 1 : Roughness characteristics of the RIEUTORD, F. NÉ, O. SPALLA, A. EL- surfaces MANSOURI, P. FRUGIER, A. FRUGIER, A. IG FG glass FG glass AYRAL, S. GIN, J. Nucl. Mat., 326, 9 (2004). glass (before (after 7. Z. WU, C. ROMANO, A. MARCELLI, A. relaxation) relaxation) MOTTANA, G. CIBIN, G. DELLA Ra (Å) 1.34 0.64 0.99 VENTURA, G. GIULI, P. COURTIAL, D. B.

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