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Molecular dynamics study of the structure and dynamic behavior at the surface of a silicate glass
Journal of Non-Crystalline Solids 315 (2003) 187–196 www.elsevier.com/locate/jnoncrysol
Molecular dynamics study of the structure and dynamic behavior at the surface of a silicate glass A. Abbas a, J.-M. Delaye
b,* ,
D. Ghaleb b, G. Calas
c
a
D epartement des Mat eriaux pour le Nucl eaire, CEA/DEN/DMN/SRMP, Commissariat a lÕEnergie Atomique, Direction de lÕEnergie Nucl eaire, Service de Recherche de M etallurgie Physique, BP 17171, 30207 Bagnols-sur-Ceze, France b CEA/DEN/DIEC/SESC/LCLT: Commissariat a lÕEnergie Atomique, Direction de lÕEnergie Nucl eaire, D epartement dÕIng enierie et dÕEtude des Confinements, Service dÕEtude des Syst emes de Confinement, Laboratoire dÕEtudes du Comportement a Long Terme, BP 17171, 30207 Bagnols-sur-Ceze, France c Laboratoire de Min eralogie-Cristallographie, URA CNRS 09, Universit es Paris 6 et 7 et IPGP, 75252 Paris, France Received 3 September 2001
Abstract Molecular dynamics calculations of a complex SiO2 þ B2 O3 þ Al2 O3 þ ZrO2 þ Na2 O þ CaO glass with surfaces revealed the formation of outer layers having different structural properties than the bulk glass. Alkali cations tend to migrate toward the surface, lowering the coordination number of the trivalent elements in the subsurface layer. The outer layer is also enriched in oxygen. Depolymerization leads to the formation of slightly larger rings on average. Atom mobility is enhanced in the lower density layers, as shown by the application of an external electric field and during simulated displacement cascades. Although these results are consistent with previously published findings, it is difficult to assess the actual scope of these surface effects (estimated by molecular dynamics to extend to a depth of ) because this approach does not take into account the effects of long-range diffusion or of the interface with about 10 A the surrounding environment. Ó 2003 Elsevier Science B.V. All rights reserved. PACS: 61.43.B; 68.35; 61.43.F
1. Introduction The structure at the surface of an oxide glass differs from that of the bulk glass, and depends on the fabrication conditions [1,2]. The different behavior of the glass matrix constituent elements at the interface between the glass and the external
*
Corresponding author. Tel.: +33-4 66 79 17 94; fax: 33-4 66 79 66 20. E-mail address: [email protected] (J.-M. Delaye).
medium leads to the formation of a surface layer with a structure that differs from that of the bulk glass. The characteristics of this layer depend on a large number of factors, including the interdiffusion coefficients between the glass elements and the environmental elements, and the possibility of secondary phase precipitation on the surface, depending on the elements available. The nature of the interface is also affected by external perturbations. The application of an electric field, for example [3], induces structural modifications due to differences in the mobility of
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A. Abbas et al. / Journal of Non-Crystalline Solids 315 (2003) 187–196
the elements subjected to the field. Sodium depletion or enrichment of the outer layer may modify the degree of glass polymerization due to correlations between the presence of Na and the stabilization of XO4 groups, where X is a trivalent cation. Atom migration phenomena leading to surface structural modifications have been observed under irradiation [4–6]. Crack simulations have also shown that the surfaces created in the process are structurally different from the bulk glass [7,8]. The sudden rupture of the chemical bonds at the glass surface forces a local reorganization of the atoms. Concentration profile measurements at the surface of glass specimens fractured in a vacuum show that the surface is enriched in alkali cations [9]. Atomistic simulations of glass surfaces are not new. Studies of pure silica and aluminosilicate glass by molecular dynamics [10–12] have revealed modifications in the network organization. Threecoordinated silicon atoms appear in pure silica, as confirmed experimentally by analysis of thin films [13]. When alkali metals are present, they are found in higher quantities at the surface (except for Li [11]). The enrichment is limited if a fraction of the alkali cations is mobilized as charge compensators for groups such as AlO4 [14]. We propose here a study by molecular dynamics of the surfaces of 6-oxide glass compositions containing the major elements of the French nuclear glass, and an investigation of the dynamic behavior of the atoms during displacement cascades.
2. Methodology 2.1. Simulated compositions The simulated compositions were 6-oxide glasses including the major components of the French nuclear glass. The molar composition was the following: 53.3% SiO2 þ 14:05% B2 O3 þ 11:3% Na2 O þ 1:6% ZrO2 þ 3:4% Al2 O3 þ 5:0% CaO. 2.2. Interatomic potentials Born–Mayer–Huggins interatomic potentials were used. A pair of atoms i–j separated by a
distance rij is associated with an interaction energy verifying the following relation: ! rij zi zj /2 ðrij Þ ¼ Aij exp : ð1Þ þ qij rij This is the classic form in which potentials are used to model simple or complex oxide glasses. The Coulomb interaction is associated with an exponential repulsion representing the interaction between the ion electron clouds. Only the real-space portion of the Ewald sum is taken into account for the Coulomb interactions [15]. Some ionic and covalent bonds in the glass are poorly represented by these pure Coulomb terms. We corrected this problem by using three-body terms as defined by Stillinger et al. [16] to simulate pure silica: ci ci /3 ðrij ; rik ; hjik Þ ¼ ki exp þ rij rci rik rci 2 ð2Þ cos hjik cos h0 : When applied to atom triplets (j,i,k) in which atom i is centrally located, the interaction energy is minimized when the triplet angle is equal to h0 , implying that a constraint is applied to the triplet angle to shift it toward h0 . Constraints were applied to the O–Si–O, Si–O–Si, O–B–O and O–Al– O angles. The O–B–O angle term was added to fit the boron coordination number with the values determined by Dell et al. [17]. The tetrahedral angle systematically applied to all the O–B–O triplets led to deformation of the BO3 triangles with angles closer to 116° than to 120°. The three-body terms are necessary to limit the number of structural defects in the simulated glass, and three-coordinated oxygen atoms in particular. The adjustable parameter values are indicated in Tables 1 and 2. 2.3. Computational procedure for the glass model preparation Two types of glasses were simulated: with and without surfaces. A ÔsurfacelessÕ glass was first fabricated from a random configuration, and the initial density was adjusted to fit an empirical model developed from a set of simple glass compositions [18].
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Table 1 except for the O–O pairs (qO–O ¼ 0:35 A ) Parameters: Aij (108 erg), qij ¼ 0:29 A Si O B Na Zr Al Ca
Si
O
B
Na
Zr
Al
Ca
0.14034 – –
0.26368 0.059165 –
0.056624 0.12767 0.020308
0.14476 0.23432 0.062898 0.14136
0.42923 0.80648 0.17318 0.44274 1.31128
0.15323 0.27639 0.063198 0.15562 0.46866 0.16656
0.64095 1.1011 0.27092 0.63932 1.9603 0.69315 2.8675
Table 2 Three-body term parameters k (erg) O–Si–O Si–O–Si O–B–O O–Al–O
9
0:2 10 0:1 1010 0:15 107 0:24 109
) c (A
h0 (deg)
) rci (A
2.6 2.0 2.27 2.6
109.47 160.0 109.47 109.47
3.0 2.6 2.1 3.0
A liquid was prepared for 5 picoseconds (ps), and the temperature was corrected to 4000 K by readjusting the atom velocities whenever it exceeded 6000 K. The liquid was then quenched from 4000 to 1400 K at a rate of 1015 K s1 , followed by quenching from 1400 K to room temperature at 4 1014 K s1 . The quenched structure was relaxed for 4.6 ps, and the cell volume was then adjusted by calculation in an NPH (N: atom number, P: pressure, H: enthalpy) thermodynamic system [19]. This was followed by another relaxation in the microcanonical set by adjusting the simulation cell volume to the previously determined equilibrium volume. The equilibrated surfaceless glass constituted the starting point for simulating a glass with surfaces. The surface was prepared by eliminating the periodic conditions on a simulated bulk glass; this is roughly equivalent to fracturing a glass monolith in a vacuum. Fig. 1 shows the cell temperature variation over time after removal of the periodic conditions. No temperature controls were applied for the first 5 ps, during which the temperature rose by some 1000 K and stabilized at about 1300 K. The glass was then annealed at 4000 K to accelerate diffusion, quenched in two steps to room temperature as for the initial surfaceless glass,
Fig. 1. Temperature profile during surface preparation.
and allowed to stabilize for 5 ps at room temperature. Mirror conditions were applied when fabricating the surface to prevent any ejection of atoms during relaxation. Artificial walls were placed 8 A above the surfaces. Whenever an atom reached these barriers, its velocity perpendicular to the surface was reversed to reinject it into the cell. Relatively few rebounds (less than 0.5% of the atoms involved) occurred on the artificial walls throughout the surface preparation phase. The existence of Coulomb interactions theoretically requires complex mathematical processing
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to take long-range interactions into account in cells of finite size. This method, known as the Ewald sum, becomes very penalizing in the case of a surface [20]. In order to accelerate the calculations, we limited the interactions to short-range interactions in real space with a relatively high . The Coulomb interactions cutoff radius of 12.9 A in Eq. (1) were replaced by the term qi qj erfcðarij Þ= rij , in which the a parameter was assigned a value of 0:139 108 cm1 . We verified that the Ewald sum in reciprocal space did not affect the short- and medium-range structure of the surfaceless glass. Table 3 compares the coordination numbers and Fig. 2 the ring size distributions in the surfaceless glasses fabricated with and without complete Ewald summation: the differences are minor, and have very little effect on the short- and medium-range orders. The densities were also very similar, with 2.3746 g/cm3 for the complete Ewald sum calculation and 2.3635 g/cm3 for the partial Ewald sum calculation, i.e. a difference of about 0.5%.
3. Results 3.1. Structural comparison of glasses with and without surfaces
Complete 4.00 3.72 3.80 5.64 7.08 6.73 Ewald sum Partial Ewald 4.00 3.71 3.83 5.48 7.06 6.67 sum for Si, 2.2 A for B, 2.4 A for Al, 3.0 A for Zr, Cutoff radii: 2.1 A for Na, 3.4 A for Ca. 3.4 A
Fig. 3 shows the concentration profiles of the ionic species versus the depth in the cell. Only three elements are shown here for greater clarity, but the other cations exhibited the same behavior as Si. The extremes in Fig. 3 correspond to the two surfaces, and the zero coordinate to the point farthest from the surfaces. The atomic density near the surface was observed to diminish as O and Na atoms were ejected toward the surface when the periodic conditions were relaxed. The profiles then returned to their equilibrium values after about . 5A Fig. 4 shows the atom displacement distribution along the three axes between the time the periodic conditions were relaxed and the end of the surfaced glass preparation process. The displacements on the Z axis were greater than on the X- and Yaxes, clearly revealing the freedom allowed in the system during relaxation of the periodic conditions along the Z axis. The network-modifying and charge-compensating roles of sodium atoms were discriminated using a definition recently employed to account for the composition effects observed by NMR. A sodium atom is considered to be a charge compensator when the distance to the nearest non; for each bridging oxygen atom exceeds 3.4 A non-bridging oxygen, the nearest Na atom is identified and designated as a modifier.
Fig. 2. Ring size distributions in structures prepared with the complete (black) or partial (gray) Ewald sum method. The y axis indicates the number of rings.
Fig. 3. Si, O and Na concentration profiles in structures with surfaces (the extremes correspond to the two surfaces). The y axis indicates the number of atoms.
Table 3 Structure coordination numbers calculating using complete or partial Ewald sums Si
B
Al
Zr
Na
Ca
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). The y axis indicates Fig. 4. Displacement distributions on the X, Y and Z axes during the surface formation (distribution step: 0.01 A the number of displacements.
The Na concentration profiles for the charge compensators and network modifiers (Fig. 5) clearly shows a higher concentration of modifiers over a few angstroms near the surface. The surface depletion of charge-compensating Na is also clearly visible to a depth of about ten angstroms. The boron atom coordination profiles are shown for three- and four-coordinated boron in Fig. 6. Comparing this figure with Fig. 5 shows that the depletion of charge-compensating sodium is logically correlated with the lower mean boron coordination number. The depletion layers extend in both cases. to a depth of about 10 A We examined the ring distribution in the glasses with and without surfaces. We did not attempt to determine all the rings in the glass structures. Instead, in order to reveal the fineness of the structural mesh, we identified the smallest ring containing each oxygen atom together with only network formers (Si, B or Al). This definition has already been used to analyze the structural effects
Fig. 5. Network modifying (solid lines) and charge compensating (broken line) Na concentration profiles. The y axis indicates the number of atoms.
Fig. 6. Boron coordination profiles. The y axis indicates the number of atoms.
of displacement cascades initiated in complex glasses [21]. The next step was to define the ring position. We chose to calculate the center-of-gravity position of the atoms (oxygen and cations) forming the ring; the Z coordinate of the center of gravity was considered to be the ring depth. The ring size profiles (Fig. 7) can thus be calculated versus the depth in structures with and without surfaces. Two features appear in the graphs for the five- and seven-atom rings. The number of five-atom rings diminishes near the surface, while the number of seven-atom rings increases near the surface (a similar increase, but of lower magnitude, is visible for the eight-atom rings). The surfaceless glass already reveals heterogeneities in the distributions, particularly for the sixand seven-atom rings, showing the existence of regions with larger or smaller rings. The notion of ring-size regions was previously reported by Van Br€ utzel [22]. Nevertheless, when surfaces are added in the simulation, larger rings are observed
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Fig. 7. Ring size profiles (from size 5–8) in glass without surfaces (upper row) and with surfaces (lower row).
to occur near them. This phenomenon may be considered in parallel with the depolymerization that is also observed near the surfaces. The smaller number of oxygen-former bonds results in an increase in the mean ring size.
face. We therefore performed a second annealing operation at the same temperature (4000 K) but of longer duration (20 ps). The concentration profiles for the resulting new structure (Fig. 9) show no additional shrinkage between the surface O and Na layers and the interior Si layer.
3.2. Effect of annealing 3.3. Displacement cascades The glass specimens were prepared in very short time periods compared with laboratory scale. The observed effects could extend to greater depths if the glass preparation time––particularly the duration of the liquid phase––were extended. We therefore annealed the glass for an additional 5 ps at 4000 K before quenching. We then analyzed the structural changes after annealing. The concentration profiles for Si, O and Na in the annealed glass (Fig. 8) show no enhancement of the Na or O enrichment at the sur-
The structural differences between the surface and bulk glass resulted in different behavior of the species affected by displacement cascades. A displacement cascade was initiated by accelerating a particle either parallel to the surface, or from the exterior into the simulation cell. The projectile then initiated a cascade of atom displacements. Results of displacement cascades have been published in previous articles [23].
Fig. 8. Si, O and Na concentration profiles in glass with surfaces after annealing (refer to text for details). The y axis indicates the number of atoms.
Fig. 9. Si, O and Na concentration profiles in glass with surfaces after a second annealing for 20 ps (refer to text for details). The y axis indicates the number of atoms.
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Fig. 10. Displacement cascade morphologies in bulk glass (left) and near a surface (right): 1 keV cascades in a 41472-atom glass, with a are plotted. On the right heavy ion accelerated parallel to the surface (images taken after 3 ps). Only atoms displaced by more than 1 A figure, the surfaces correspond to the upper and lower plans.
Fig. 10 shows the morphology of one such cascade initiated in a surfaceless structure and in a structure with a surface. The difference in the distribution of atom displacements is clearly visible: when a surface exists, the number of surface displacements is higher, forming a sort of atom displacement cone between the surface and the core of the cascade. We concluded that atom displacements occur more readily near the surface, as a result of the lower atomic density observed above.
Fig. 11. Electric field variations over time (E is in dyn/charge unit).
3.4. Effect of an electric field In order to confirm this point, we applied an external electric field to the simulation cells with and without surfaces, and then observed the atom displacement concentrations versus their position with respect to the surface. Field EðtÞ was applied according to the increasing and decreasing intensity ramps in Fig. 11. The maximum field intensity corresponded to the effect of a 1 coulomb charge from each ion. situated at a distance of 0.141 A The glass relaxation lasted for 9000 time steps (1 step ¼ 1015 s). Field E was always exerted at right angles to the surfaces. Intermediate configurations were stored every 1500 time steps to study the atom displacement distributions over time. Fig. 12 shows the absolute values of the displacements for three types of atoms (Si, O and Na) thick, parallel to the averaged over layers 2 A surfaces. The atom displacements are shown after 3, 6 ps, and after cancellation of the electric field. After the first 3 ps step, O and Na displacements
were greater near the surfaces. The O and Si displacements were of similar amplitude, suggesting a correlation between the displacements of these two species. The concept of collective displacements of network formers and oxygen atoms was previously discussed in studies of a simulated glass subjected to random atom displacements at the center of the cell. The Na displacements were significantly longer, and show the greater mobility of these atoms within the oxygen lattice. The 6 and 9 ps images confirm the greater amplitude of the O and Na displacements near the surfaces; this was not true of the Si atoms, however, for which the displacements were no longer near the surface than in the bulk glass. These results confirm the greater mobility of . atoms near the surfaces, on a depth of about 10 A This order of magnitude is consistent with the depth of the previously observed effects (ring size, B coordination profiles, charge compensator and modifier profiles, etc.).
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layer parallel Fig. 12. Mean atom displacements (in A ) per 2 A to the surfaces.
The potential energy of the structure was practically unchanged at the end of the calculation: temporarily applying an electric field did not store any additional potential energy in the structure.
4. Discussion Although these results concern complex glasses comprising network formers and modifiers, they are consistent with simulations of simpler glass surfaces reported by other authors. Molecular dynamics (MD) simulations of vitreous silica [24] have shown that stabilization of the surface is accompanied by the formation of an oxygen-rich outer layer. The progression of the oxygen atoms with respect to silicon is comparable to the be-
havior observed here. MD simulations of a K2 – 3SiO2 glass [9] also revealed the formation of an outer layer containing oxygen and alkali metals, with silicon remaining below the surface. In both cases, the O and Si concentrations to a depth of were observed to be lower than the bulk about 4 A equilibrium concentrations. This is the same order of magnitude we observed in more complex glasses. After eliminating the periodic conditions along one axis, the surface structures stabilized very quickly as already noted by Garofalini. The thickness of the disturbed zone is practically unaffected by an additional high-temperature annealing step, suggesting that the modified structure to a depth of a few atom layers is the result of a reorganization of the local groups rather than of long-range diffusion. The rapidity with which the surface layer forms was also suggested by laboratory scale leaching experiments conducted by Richter et al. [25]. The sodium concentration profiles measured at various times during leaching constantly showed an alkalienriched zone followed by an alkali-depleted zone. Ion exchanges with solution are not sufficient to smooth the alkali concentration profile. The thickness of the alkali-rich zone in these experiments was about an order of magnitude greater than observed in the simulations. The two surface zones enriched and depleted in sodium could indeed form very quickly, but longer-range alkali cation diffusion phenomena along concentration gradients could then increase the actual thickness of these zones. Such longer-range diffusion phenomena are beyond the scope of molecular dynamics simulations limited to a few tens of picoseconds. The migration of elements in the outer layer is accompanied by structural modifications including lower average coordination numbers and larger mean ring sizes. The formation of three-coordinated Si was clearly observed in a study of a pure silica surface (and was confirmed by XPS experiments) [26]. The formation of SiO3 groups was also confirmed by electron diffraction analysis on thin ) films of pure SiO2 [13]. As the film (4–80 A thickness increased, the authors observed an increase in the Si–O and O–O distances together with an increase in the mean Si coordination number, which returned to the tetrahedral coordination
A. Abbas et al. / Journal of Non-Crystalline Solids 315 (2003) 187–196
found in the bulk specimens. These observations can be explained by assuming that SiO3 groups continue to exist near the surface, but that the relative weight of these groups in the mean Si coordination number diminishes as the film thickness increases and eventually becomes difficult to detect in the thickest specimens. This is suggested by the results of the MD studies. For the six-oxide composition studied here, the structural modifications mainly affected the trivalent formers, whose coordination number decreased near the surface. The strong cohesive energy of the SiO4 groups (previously noted during studies of displacement cascades in complex glasses [21]) makes them less ÔvulnerableÕ than BO4 or AlO4 groups, which more easily give up an oxygen atom. The migration of alkali cations toward the outer layer also favors transitions between X3þ O4 and X3þ O3 groups, because they no longer behave as charge compensators but almost exclusively as modifiers bonded to a non-bridging oxygen. On the whole, the glass polymerization diminishes in the subsurface layer, resulting in the formation of slightly larger rings. The surface structural modification affects the dynamic behavior of the atoms. Both in an electric field and during displacement cascades, the surface has a special role. Atom displacements are not only of larger magnitude, but also tend to be concentrated near the surface during displacement cascades. It is logical to consider these observations in the light of the differences in the ring sizes: the increasing average size creates larger voids and favors atom displacements near the surface. Alkali cation diffusion over longer ranges has also been reported in the literature [27]. Nevertheless, it is important not to lose sight of the fact that the observed phenomena arise from the minimization of the energy of the structure following a perturbation induced by releasing the periodic conditions along one axis. The situation is more complex in reality, as the relaxation phenomenon is compounded by chemical and diffusion effects that also modify the final structure. Although the actual impact of the surface structure on processes such as glass reactivity or
195
leaching is difficult to assess on the sole basis of surface calculations in a vacuum, the presence of a higher concentration of structural defects should enhance the reactivity, and the existence of a less dense subsurface layer should promote interdiffusion with the aqueous species, at least initially.
5. Conclusion Molecular dynamics calculations of a complex SiO2 þ B2 O3 þ Al2 O3 þ ZrO2 þ Na2 O þ CaO glass with surfaces revealed the formation of outer layers having different structural properties than the bulk glass. Alkali cations tend to migrate toward the surface, lowering the coordination number of the trivalent elements in the subsurface layer. The outer layer is also enriched in oxygen. Depolymerization leads to the formation of slightly larger rings on average. Atom mobility is enhanced in the lower density layers, as shown by the application of an external electric field and during simulated displacement cascades. Although these results are consistent with previously published findings, it is difficult to assess the actual scope of these surface effects (estimated by molecular dynamics to extend to a depth of ) because this approach does not take about 10 A into account the effects of long-range diffusion or of the interface with the surrounding environment.
References [1] C. Pantano, Ceram. Bull. 60 (1981) 1154. [2] H. Bach, J. Non-Cryst. Solids 209 (1997) 1. [3] P. Regnier, Y. Serruys, A. Zemskoff, Phys. Chem. Glasses 27 (1986) 185. [4] G. Battaglin, G.W. Arnold, G. Mattei, P. Mazzoldi, J.-C. Dran, J. Appl. Phys. 85 (1999) 8040. [5] A. Miotello, G. Clinque, P. Mazzoldi, C.G. Pantano, Phys. Rev. B 43 (1991) 3831. [6] G. Gedeon, K. Jurek, V. Hulinsky, J. Non-Cryst. Solids 246 (1999) 1. [7] J.H. Simmons, T.P. Swiler, R. Ochsa, J. Non-Cryst. Solids 134 (1991) 179. [8] T. Swiler, J. Simmons, A. Wright, J. Non-Cryst. Solids 182 (1995) 68. [9] S.H. Garofalini, J. Am. Ceram. Soc. 67 (1984) 133.
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[10] B.P. Feuston, S.H. Garofalini, J. Chem. Phys. 91 (1989) 564. [11] S.H. Garofalini, S.M. Levine, J. Am. Ceram. Soc. 68 (1985) 376. [12] E.B. Webb, S.H. Garofalini, J. Non-Cryst. Solids 226 (1998) 47. [13] K. Miura, T. Ino, M. Tada, H. Ohsaki, Philos. Mag. B 66 (1992) 25. [14] D.M. Zirl, S.H. Garofalini, J. Am. Ceram. Soc. 75 (1992) 2353. [15] S.W. DeLeeuw, J.W. Perram, E.R. Smith, Proc. R. Soc. Lond. A 373 (5) (1980) 27. [16] F.H. Stillinger, T.A. Weber, Phys. Rev. B 31 (1985) 5262. [17] W.J. Dell, P.J. Bray, S.Z. Xiao, J. Non-Cryst. Solids 58 (1983) 1. [18] D. Ghaleb, J.-L. Dussossoy, C. Fillet, F. Pacaud, N. Jacquet-Francillon, in: T. Murakami, R.C. Ewing (Eds.),
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Scientific Basis for Nuclear Waste management XVIII, 353, 1994, p. 107. H.C. Andersen, J. Chem. Phys. 72 (1980) 2384. J. Hautmann, M.L. Klein, Molec. Phys. 75 (1992) 379. J.-M. Delaye, D. Ghaleb, Phys. Rev. B 61 (2000) 14481. L. Van Br€ utzel, PhD thesis, University of Paris VI (1999). A. Abbas, J.-M. Delaye, D. Ghaleb, Y. Serruys, G. Calas, Mater. Res. Soc. Symp. Proc. 608 (2000) 481. M.I. Trioni, A. Bongiorno, L. Colombo, J. Non-Cryst. Solids 220 (1997) 164. T. Richter, G.H. Frischat, G. Borchardt, S. Scherrer, Phys. Chem. Glasses 26 (1985) 208. C.R. Helms, E.H. Poindexter, Rep. Prog. Phys. 57 (1994) 791. D.A. Litton, S.H. Garofalini, J. Non-Cryst. Solids 217 (1997) 250.
Molecular dynamics study of the structure and dynamic behavior at the surface of a silicate glass A. Abbas a, J.-M. Delaye
b,* ,
D. Ghaleb b, G. Calas
c
a
D epartement des Mat eriaux pour le Nucl eaire, CEA/DEN/DMN/SRMP, Commissariat a lÕEnergie Atomique, Direction de lÕEnergie Nucl eaire, Service de Recherche de M etallurgie Physique, BP 17171, 30207 Bagnols-sur-Ceze, France b CEA/DEN/DIEC/SESC/LCLT: Commissariat a lÕEnergie Atomique, Direction de lÕEnergie Nucl eaire, D epartement dÕIng enierie et dÕEtude des Confinements, Service dÕEtude des Syst emes de Confinement, Laboratoire dÕEtudes du Comportement a Long Terme, BP 17171, 30207 Bagnols-sur-Ceze, France c Laboratoire de Min eralogie-Cristallographie, URA CNRS 09, Universit es Paris 6 et 7 et IPGP, 75252 Paris, France Received 3 September 2001
Abstract Molecular dynamics calculations of a complex SiO2 þ B2 O3 þ Al2 O3 þ ZrO2 þ Na2 O þ CaO glass with surfaces revealed the formation of outer layers having different structural properties than the bulk glass. Alkali cations tend to migrate toward the surface, lowering the coordination number of the trivalent elements in the subsurface layer. The outer layer is also enriched in oxygen. Depolymerization leads to the formation of slightly larger rings on average. Atom mobility is enhanced in the lower density layers, as shown by the application of an external electric field and during simulated displacement cascades. Although these results are consistent with previously published findings, it is difficult to assess the actual scope of these surface effects (estimated by molecular dynamics to extend to a depth of ) because this approach does not take into account the effects of long-range diffusion or of the interface with about 10 A the surrounding environment. Ó 2003 Elsevier Science B.V. All rights reserved. PACS: 61.43.B; 68.35; 61.43.F
1. Introduction The structure at the surface of an oxide glass differs from that of the bulk glass, and depends on the fabrication conditions [1,2]. The different behavior of the glass matrix constituent elements at the interface between the glass and the external
*
Corresponding author. Tel.: +33-4 66 79 17 94; fax: 33-4 66 79 66 20. E-mail address: [email protected] (J.-M. Delaye).
medium leads to the formation of a surface layer with a structure that differs from that of the bulk glass. The characteristics of this layer depend on a large number of factors, including the interdiffusion coefficients between the glass elements and the environmental elements, and the possibility of secondary phase precipitation on the surface, depending on the elements available. The nature of the interface is also affected by external perturbations. The application of an electric field, for example [3], induces structural modifications due to differences in the mobility of
0022-3093/03/$ - see front matter Ó 2003 Elsevier Science B.V. All rights reserved. PII: S 0 0 2 2 - 3 0 9 3 ( 0 2 ) 0 1 4 3 2 - 1
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the elements subjected to the field. Sodium depletion or enrichment of the outer layer may modify the degree of glass polymerization due to correlations between the presence of Na and the stabilization of XO4 groups, where X is a trivalent cation. Atom migration phenomena leading to surface structural modifications have been observed under irradiation [4–6]. Crack simulations have also shown that the surfaces created in the process are structurally different from the bulk glass [7,8]. The sudden rupture of the chemical bonds at the glass surface forces a local reorganization of the atoms. Concentration profile measurements at the surface of glass specimens fractured in a vacuum show that the surface is enriched in alkali cations [9]. Atomistic simulations of glass surfaces are not new. Studies of pure silica and aluminosilicate glass by molecular dynamics [10–12] have revealed modifications in the network organization. Threecoordinated silicon atoms appear in pure silica, as confirmed experimentally by analysis of thin films [13]. When alkali metals are present, they are found in higher quantities at the surface (except for Li [11]). The enrichment is limited if a fraction of the alkali cations is mobilized as charge compensators for groups such as AlO4 [14]. We propose here a study by molecular dynamics of the surfaces of 6-oxide glass compositions containing the major elements of the French nuclear glass, and an investigation of the dynamic behavior of the atoms during displacement cascades.
2. Methodology 2.1. Simulated compositions The simulated compositions were 6-oxide glasses including the major components of the French nuclear glass. The molar composition was the following: 53.3% SiO2 þ 14:05% B2 O3 þ 11:3% Na2 O þ 1:6% ZrO2 þ 3:4% Al2 O3 þ 5:0% CaO. 2.2. Interatomic potentials Born–Mayer–Huggins interatomic potentials were used. A pair of atoms i–j separated by a
distance rij is associated with an interaction energy verifying the following relation: ! rij zi zj /2 ðrij Þ ¼ Aij exp : ð1Þ þ qij rij This is the classic form in which potentials are used to model simple or complex oxide glasses. The Coulomb interaction is associated with an exponential repulsion representing the interaction between the ion electron clouds. Only the real-space portion of the Ewald sum is taken into account for the Coulomb interactions [15]. Some ionic and covalent bonds in the glass are poorly represented by these pure Coulomb terms. We corrected this problem by using three-body terms as defined by Stillinger et al. [16] to simulate pure silica: ci ci /3 ðrij ; rik ; hjik Þ ¼ ki exp þ rij rci rik rci 2 ð2Þ cos hjik cos h0 : When applied to atom triplets (j,i,k) in which atom i is centrally located, the interaction energy is minimized when the triplet angle is equal to h0 , implying that a constraint is applied to the triplet angle to shift it toward h0 . Constraints were applied to the O–Si–O, Si–O–Si, O–B–O and O–Al– O angles. The O–B–O angle term was added to fit the boron coordination number with the values determined by Dell et al. [17]. The tetrahedral angle systematically applied to all the O–B–O triplets led to deformation of the BO3 triangles with angles closer to 116° than to 120°. The three-body terms are necessary to limit the number of structural defects in the simulated glass, and three-coordinated oxygen atoms in particular. The adjustable parameter values are indicated in Tables 1 and 2. 2.3. Computational procedure for the glass model preparation Two types of glasses were simulated: with and without surfaces. A ÔsurfacelessÕ glass was first fabricated from a random configuration, and the initial density was adjusted to fit an empirical model developed from a set of simple glass compositions [18].
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Table 1 except for the O–O pairs (qO–O ¼ 0:35 A ) Parameters: Aij (108 erg), qij ¼ 0:29 A Si O B Na Zr Al Ca
Si
O
B
Na
Zr
Al
Ca
0.14034 – –
0.26368 0.059165 –
0.056624 0.12767 0.020308
0.14476 0.23432 0.062898 0.14136
0.42923 0.80648 0.17318 0.44274 1.31128
0.15323 0.27639 0.063198 0.15562 0.46866 0.16656
0.64095 1.1011 0.27092 0.63932 1.9603 0.69315 2.8675
Table 2 Three-body term parameters k (erg) O–Si–O Si–O–Si O–B–O O–Al–O
9
0:2 10 0:1 1010 0:15 107 0:24 109
) c (A
h0 (deg)
) rci (A
2.6 2.0 2.27 2.6
109.47 160.0 109.47 109.47
3.0 2.6 2.1 3.0
A liquid was prepared for 5 picoseconds (ps), and the temperature was corrected to 4000 K by readjusting the atom velocities whenever it exceeded 6000 K. The liquid was then quenched from 4000 to 1400 K at a rate of 1015 K s1 , followed by quenching from 1400 K to room temperature at 4 1014 K s1 . The quenched structure was relaxed for 4.6 ps, and the cell volume was then adjusted by calculation in an NPH (N: atom number, P: pressure, H: enthalpy) thermodynamic system [19]. This was followed by another relaxation in the microcanonical set by adjusting the simulation cell volume to the previously determined equilibrium volume. The equilibrated surfaceless glass constituted the starting point for simulating a glass with surfaces. The surface was prepared by eliminating the periodic conditions on a simulated bulk glass; this is roughly equivalent to fracturing a glass monolith in a vacuum. Fig. 1 shows the cell temperature variation over time after removal of the periodic conditions. No temperature controls were applied for the first 5 ps, during which the temperature rose by some 1000 K and stabilized at about 1300 K. The glass was then annealed at 4000 K to accelerate diffusion, quenched in two steps to room temperature as for the initial surfaceless glass,
Fig. 1. Temperature profile during surface preparation.
and allowed to stabilize for 5 ps at room temperature. Mirror conditions were applied when fabricating the surface to prevent any ejection of atoms during relaxation. Artificial walls were placed 8 A above the surfaces. Whenever an atom reached these barriers, its velocity perpendicular to the surface was reversed to reinject it into the cell. Relatively few rebounds (less than 0.5% of the atoms involved) occurred on the artificial walls throughout the surface preparation phase. The existence of Coulomb interactions theoretically requires complex mathematical processing
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to take long-range interactions into account in cells of finite size. This method, known as the Ewald sum, becomes very penalizing in the case of a surface [20]. In order to accelerate the calculations, we limited the interactions to short-range interactions in real space with a relatively high . The Coulomb interactions cutoff radius of 12.9 A in Eq. (1) were replaced by the term qi qj erfcðarij Þ= rij , in which the a parameter was assigned a value of 0:139 108 cm1 . We verified that the Ewald sum in reciprocal space did not affect the short- and medium-range structure of the surfaceless glass. Table 3 compares the coordination numbers and Fig. 2 the ring size distributions in the surfaceless glasses fabricated with and without complete Ewald summation: the differences are minor, and have very little effect on the short- and medium-range orders. The densities were also very similar, with 2.3746 g/cm3 for the complete Ewald sum calculation and 2.3635 g/cm3 for the partial Ewald sum calculation, i.e. a difference of about 0.5%.
3. Results 3.1. Structural comparison of glasses with and without surfaces
Complete 4.00 3.72 3.80 5.64 7.08 6.73 Ewald sum Partial Ewald 4.00 3.71 3.83 5.48 7.06 6.67 sum for Si, 2.2 A for B, 2.4 A for Al, 3.0 A for Zr, Cutoff radii: 2.1 A for Na, 3.4 A for Ca. 3.4 A
Fig. 3 shows the concentration profiles of the ionic species versus the depth in the cell. Only three elements are shown here for greater clarity, but the other cations exhibited the same behavior as Si. The extremes in Fig. 3 correspond to the two surfaces, and the zero coordinate to the point farthest from the surfaces. The atomic density near the surface was observed to diminish as O and Na atoms were ejected toward the surface when the periodic conditions were relaxed. The profiles then returned to their equilibrium values after about . 5A Fig. 4 shows the atom displacement distribution along the three axes between the time the periodic conditions were relaxed and the end of the surfaced glass preparation process. The displacements on the Z axis were greater than on the X- and Yaxes, clearly revealing the freedom allowed in the system during relaxation of the periodic conditions along the Z axis. The network-modifying and charge-compensating roles of sodium atoms were discriminated using a definition recently employed to account for the composition effects observed by NMR. A sodium atom is considered to be a charge compensator when the distance to the nearest non; for each bridging oxygen atom exceeds 3.4 A non-bridging oxygen, the nearest Na atom is identified and designated as a modifier.
Fig. 2. Ring size distributions in structures prepared with the complete (black) or partial (gray) Ewald sum method. The y axis indicates the number of rings.
Fig. 3. Si, O and Na concentration profiles in structures with surfaces (the extremes correspond to the two surfaces). The y axis indicates the number of atoms.
Table 3 Structure coordination numbers calculating using complete or partial Ewald sums Si
B
Al
Zr
Na
Ca
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). The y axis indicates Fig. 4. Displacement distributions on the X, Y and Z axes during the surface formation (distribution step: 0.01 A the number of displacements.
The Na concentration profiles for the charge compensators and network modifiers (Fig. 5) clearly shows a higher concentration of modifiers over a few angstroms near the surface. The surface depletion of charge-compensating Na is also clearly visible to a depth of about ten angstroms. The boron atom coordination profiles are shown for three- and four-coordinated boron in Fig. 6. Comparing this figure with Fig. 5 shows that the depletion of charge-compensating sodium is logically correlated with the lower mean boron coordination number. The depletion layers extend in both cases. to a depth of about 10 A We examined the ring distribution in the glasses with and without surfaces. We did not attempt to determine all the rings in the glass structures. Instead, in order to reveal the fineness of the structural mesh, we identified the smallest ring containing each oxygen atom together with only network formers (Si, B or Al). This definition has already been used to analyze the structural effects
Fig. 5. Network modifying (solid lines) and charge compensating (broken line) Na concentration profiles. The y axis indicates the number of atoms.
Fig. 6. Boron coordination profiles. The y axis indicates the number of atoms.
of displacement cascades initiated in complex glasses [21]. The next step was to define the ring position. We chose to calculate the center-of-gravity position of the atoms (oxygen and cations) forming the ring; the Z coordinate of the center of gravity was considered to be the ring depth. The ring size profiles (Fig. 7) can thus be calculated versus the depth in structures with and without surfaces. Two features appear in the graphs for the five- and seven-atom rings. The number of five-atom rings diminishes near the surface, while the number of seven-atom rings increases near the surface (a similar increase, but of lower magnitude, is visible for the eight-atom rings). The surfaceless glass already reveals heterogeneities in the distributions, particularly for the sixand seven-atom rings, showing the existence of regions with larger or smaller rings. The notion of ring-size regions was previously reported by Van Br€ utzel [22]. Nevertheless, when surfaces are added in the simulation, larger rings are observed
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Fig. 7. Ring size profiles (from size 5–8) in glass without surfaces (upper row) and with surfaces (lower row).
to occur near them. This phenomenon may be considered in parallel with the depolymerization that is also observed near the surfaces. The smaller number of oxygen-former bonds results in an increase in the mean ring size.
face. We therefore performed a second annealing operation at the same temperature (4000 K) but of longer duration (20 ps). The concentration profiles for the resulting new structure (Fig. 9) show no additional shrinkage between the surface O and Na layers and the interior Si layer.
3.2. Effect of annealing 3.3. Displacement cascades The glass specimens were prepared in very short time periods compared with laboratory scale. The observed effects could extend to greater depths if the glass preparation time––particularly the duration of the liquid phase––were extended. We therefore annealed the glass for an additional 5 ps at 4000 K before quenching. We then analyzed the structural changes after annealing. The concentration profiles for Si, O and Na in the annealed glass (Fig. 8) show no enhancement of the Na or O enrichment at the sur-
The structural differences between the surface and bulk glass resulted in different behavior of the species affected by displacement cascades. A displacement cascade was initiated by accelerating a particle either parallel to the surface, or from the exterior into the simulation cell. The projectile then initiated a cascade of atom displacements. Results of displacement cascades have been published in previous articles [23].
Fig. 8. Si, O and Na concentration profiles in glass with surfaces after annealing (refer to text for details). The y axis indicates the number of atoms.
Fig. 9. Si, O and Na concentration profiles in glass with surfaces after a second annealing for 20 ps (refer to text for details). The y axis indicates the number of atoms.
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Fig. 10. Displacement cascade morphologies in bulk glass (left) and near a surface (right): 1 keV cascades in a 41472-atom glass, with a are plotted. On the right heavy ion accelerated parallel to the surface (images taken after 3 ps). Only atoms displaced by more than 1 A figure, the surfaces correspond to the upper and lower plans.
Fig. 10 shows the morphology of one such cascade initiated in a surfaceless structure and in a structure with a surface. The difference in the distribution of atom displacements is clearly visible: when a surface exists, the number of surface displacements is higher, forming a sort of atom displacement cone between the surface and the core of the cascade. We concluded that atom displacements occur more readily near the surface, as a result of the lower atomic density observed above.
Fig. 11. Electric field variations over time (E is in dyn/charge unit).
3.4. Effect of an electric field In order to confirm this point, we applied an external electric field to the simulation cells with and without surfaces, and then observed the atom displacement concentrations versus their position with respect to the surface. Field EðtÞ was applied according to the increasing and decreasing intensity ramps in Fig. 11. The maximum field intensity corresponded to the effect of a 1 coulomb charge from each ion. situated at a distance of 0.141 A The glass relaxation lasted for 9000 time steps (1 step ¼ 1015 s). Field E was always exerted at right angles to the surfaces. Intermediate configurations were stored every 1500 time steps to study the atom displacement distributions over time. Fig. 12 shows the absolute values of the displacements for three types of atoms (Si, O and Na) thick, parallel to the averaged over layers 2 A surfaces. The atom displacements are shown after 3, 6 ps, and after cancellation of the electric field. After the first 3 ps step, O and Na displacements
were greater near the surfaces. The O and Si displacements were of similar amplitude, suggesting a correlation between the displacements of these two species. The concept of collective displacements of network formers and oxygen atoms was previously discussed in studies of a simulated glass subjected to random atom displacements at the center of the cell. The Na displacements were significantly longer, and show the greater mobility of these atoms within the oxygen lattice. The 6 and 9 ps images confirm the greater amplitude of the O and Na displacements near the surfaces; this was not true of the Si atoms, however, for which the displacements were no longer near the surface than in the bulk glass. These results confirm the greater mobility of . atoms near the surfaces, on a depth of about 10 A This order of magnitude is consistent with the depth of the previously observed effects (ring size, B coordination profiles, charge compensator and modifier profiles, etc.).
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layer parallel Fig. 12. Mean atom displacements (in A ) per 2 A to the surfaces.
The potential energy of the structure was practically unchanged at the end of the calculation: temporarily applying an electric field did not store any additional potential energy in the structure.
4. Discussion Although these results concern complex glasses comprising network formers and modifiers, they are consistent with simulations of simpler glass surfaces reported by other authors. Molecular dynamics (MD) simulations of vitreous silica [24] have shown that stabilization of the surface is accompanied by the formation of an oxygen-rich outer layer. The progression of the oxygen atoms with respect to silicon is comparable to the be-
havior observed here. MD simulations of a K2 – 3SiO2 glass [9] also revealed the formation of an outer layer containing oxygen and alkali metals, with silicon remaining below the surface. In both cases, the O and Si concentrations to a depth of were observed to be lower than the bulk about 4 A equilibrium concentrations. This is the same order of magnitude we observed in more complex glasses. After eliminating the periodic conditions along one axis, the surface structures stabilized very quickly as already noted by Garofalini. The thickness of the disturbed zone is practically unaffected by an additional high-temperature annealing step, suggesting that the modified structure to a depth of a few atom layers is the result of a reorganization of the local groups rather than of long-range diffusion. The rapidity with which the surface layer forms was also suggested by laboratory scale leaching experiments conducted by Richter et al. [25]. The sodium concentration profiles measured at various times during leaching constantly showed an alkalienriched zone followed by an alkali-depleted zone. Ion exchanges with solution are not sufficient to smooth the alkali concentration profile. The thickness of the alkali-rich zone in these experiments was about an order of magnitude greater than observed in the simulations. The two surface zones enriched and depleted in sodium could indeed form very quickly, but longer-range alkali cation diffusion phenomena along concentration gradients could then increase the actual thickness of these zones. Such longer-range diffusion phenomena are beyond the scope of molecular dynamics simulations limited to a few tens of picoseconds. The migration of elements in the outer layer is accompanied by structural modifications including lower average coordination numbers and larger mean ring sizes. The formation of three-coordinated Si was clearly observed in a study of a pure silica surface (and was confirmed by XPS experiments) [26]. The formation of SiO3 groups was also confirmed by electron diffraction analysis on thin ) films of pure SiO2 [13]. As the film (4–80 A thickness increased, the authors observed an increase in the Si–O and O–O distances together with an increase in the mean Si coordination number, which returned to the tetrahedral coordination
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found in the bulk specimens. These observations can be explained by assuming that SiO3 groups continue to exist near the surface, but that the relative weight of these groups in the mean Si coordination number diminishes as the film thickness increases and eventually becomes difficult to detect in the thickest specimens. This is suggested by the results of the MD studies. For the six-oxide composition studied here, the structural modifications mainly affected the trivalent formers, whose coordination number decreased near the surface. The strong cohesive energy of the SiO4 groups (previously noted during studies of displacement cascades in complex glasses [21]) makes them less ÔvulnerableÕ than BO4 or AlO4 groups, which more easily give up an oxygen atom. The migration of alkali cations toward the outer layer also favors transitions between X3þ O4 and X3þ O3 groups, because they no longer behave as charge compensators but almost exclusively as modifiers bonded to a non-bridging oxygen. On the whole, the glass polymerization diminishes in the subsurface layer, resulting in the formation of slightly larger rings. The surface structural modification affects the dynamic behavior of the atoms. Both in an electric field and during displacement cascades, the surface has a special role. Atom displacements are not only of larger magnitude, but also tend to be concentrated near the surface during displacement cascades. It is logical to consider these observations in the light of the differences in the ring sizes: the increasing average size creates larger voids and favors atom displacements near the surface. Alkali cation diffusion over longer ranges has also been reported in the literature [27]. Nevertheless, it is important not to lose sight of the fact that the observed phenomena arise from the minimization of the energy of the structure following a perturbation induced by releasing the periodic conditions along one axis. The situation is more complex in reality, as the relaxation phenomenon is compounded by chemical and diffusion effects that also modify the final structure. Although the actual impact of the surface structure on processes such as glass reactivity or
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leaching is difficult to assess on the sole basis of surface calculations in a vacuum, the presence of a higher concentration of structural defects should enhance the reactivity, and the existence of a less dense subsurface layer should promote interdiffusion with the aqueous species, at least initially.
5. Conclusion Molecular dynamics calculations of a complex SiO2 þ B2 O3 þ Al2 O3 þ ZrO2 þ Na2 O þ CaO glass with surfaces revealed the formation of outer layers having different structural properties than the bulk glass. Alkali cations tend to migrate toward the surface, lowering the coordination number of the trivalent elements in the subsurface layer. The outer layer is also enriched in oxygen. Depolymerization leads to the formation of slightly larger rings on average. Atom mobility is enhanced in the lower density layers, as shown by the application of an external electric field and during simulated displacement cascades. Although these results are consistent with previously published findings, it is difficult to assess the actual scope of these surface effects (estimated by molecular dynamics to extend to a depth of ) because this approach does not take about 10 A into account the effects of long-range diffusion or of the interface with the surrounding environment.
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