Modeling of multicomponent glasses: a review

Modeling of multicomponent glasses: a review

Current Opinion in Solid State and Materials Science 5 (2001) 451–454 Modeling of multicomponent glasses: a review J.-M. Delaye* ´ ˆ ` Cedex, France ...

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Current Opinion in Solid State and Materials Science 5 (2001) 451–454

Modeling of multicomponent glasses: a review J.-M. Delaye* ´ ˆ ` Cedex, France Atomique ( CEA /DEN /DIEC /SESC /LCLT), Valrho–Marcoule , BP 171, 30207 Bagnols-sur-Ceze Commissariat a` l’ Energie

Abstract The major recent advances in the modeling of multicomponent glasses concern both the techniques (new angular potentials around different equilibrium angles, more efficient treatment of the Ewald’s sum, coupling between molecular dynamics and reverse Monte Carlo to adjust pair potentials) and the knowledge of the glassy structures (evidences for a medium range order, studies of the interactions between the former and modifier networks).  2001 Elsevier Science Ltd. All rights reserved. Keywords: Modeling; Multicomponent glasses; Oxide glasses; Molecular dynamics; Reverse Monte Carlo; Glassy structures

1. Introduction Multicomponent oxide glasses are widely used in industry (optics, electronics, nuclear, construction), and their structures are increasingly investigated using simulation techniques. The first simulation of silica by molecular dynamics dates from 1976, and was followed by calculations of more complex compositions (binary, tertiary, etc.). The constituents of complex oxide glasses include ‘network formers’ (Si, Al, B, Ge, etc.) whose ionic-covalent bonds with oxygen atoms constitute the glass structure, ‘network modifiers’ (alkali and alkaline-earth metals) that attach themselves to the structure via nonbridging oxygen atoms or are situated near groups with a positive charge deficit, and ‘intermediate’ elements that may behave either as formers or modifiers. Molecular dynamics is currently the most widely used method for simulating relatively large structures. Multicomponent glasses contain bonds with different degrees of covalence that raise problems, notably in selecting ionic charges (see Methodology: recent advances). A description of the glass structure, whether simple or complex, must include several scales characteristic of short, medium and long-range orders. Each cation is surrounded locally by a ring of first-neighbor oxygen atoms characterized by a coordination number and a mean

*Tel.: 133-4-6679-1794; fax: 133-4-6679-6620. E-mail address: [email protected] (J.-M. Delaye).

radius. Glass also appears to present a medium-range order ˚ in the arrangement of zones enriched in (above about 5 A) network formers or modifiers (see Principal results).

2. Methodology: recent advances Relatively large cells are required to study the glass structure directly by simulation. Only molecular dynamics and the reverse Monte Carlo method are suitable for this purpose. The advantage of molecular dynamics is that it is based on a physical description of atomic interactions. The potentials used are classically based on ionic charges, which are almost always assigned constant point values; the Coulomb interactions are supplemented by repulsive terms accounting for the repulsion of the electron clouds as they merge. This simple form of interaction potentials often results in the creation of an excessive number of structural defects that are generally corrected using three-body terms. By favoring certain local angles, the three-body terms improve the construction of the frequently tetrahedral local environments of the network formers. They were first used for silica, and were subsequently generalized to multicomponent glasses. Recent work has proposed more accurate formulas for the angular terms by favoring several angles depending on the element coordination numbers [1]. These potentials were capable of reproducing the structure of Na 2 O?GeO 2 glass. A model in which the ionic charges can be modu-

1359-0286 / 01 / $ – see front matter  2001 Elsevier Science Ltd. All rights reserved. PII: S1359-0286( 01 )00028-6

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J.-M. Delaye / Current Opinion in Solid State and Materials Science 5 (2001) 451–454

lated according to the neighboring atom positions was also developed to simulate alkali silicate glasses. For each pair interaction, an elementary charge transfer is defined according to a formula taking into account the interatomic distance. The effective charge of an ion is thus defined by its coordination number and its first-neighbor distances (E. Guilbert, J. Kieffer, private communication). Other approached have also been proposed to modulate the charges according to the local environment [2,3]. Coulomb interactions are long-range phenomena and cannot strictly be disregarded regardless of the distance. The Ewald formalism uses the artificial periodicity created by the use of periodic conditions to propose an efficient mathematical treatment. The Ewald sum component in reciprocal space is sometimes disregarded by evoking long-range masking of the electron clouds. More recent mathematical developments have improved the speed of Ewald sum calculations. One method (mesh Ewald summation) consists in defining a mesh of fixed points on which the Ewald sum is calculated. The ion forces are then extrapolated from the ion position on the mesh, considerably enhancing the performance for large systems [4]. Another approach is to truncate the summation beyond a specified cutoff radius, while neutralizing the charge inside the truncated sphere [5]. In the reverse Monte Carlo (RMC) method, the atom positions must be adjusted experimentally [6]: the atom positions are gradually fitted to reproduce an experimental parameter value representative of the overall structure (typically a structure factor). The atoms are randomly displaced (complying with local environmental constraints if necessary), and a displacement is accepted according to a probability depending on whether or not the simulation is improved. A structure model is thus proposed to account for the experimental data, but with no guarantee that this is the only solution. The constraints generally imposed on RMC calculations ensure that the fabricated structure is physically realistic. A method has recently been developed in which molecular dynamics and the reverse Monte Carlo technique are coupled to simplify the process of fitting the interaction potentials and atomic structure to the experimental structure factors [7]. Existing interaction potentials are used to fabricate an initial glass structure; the structure factor is calculated for the simulation cell and compared with the experimental structure factor. A reverse Monte Carlo step is then used to correct the initial atomic structure. The fact that the structure is already relatively similar to the experimental one significantly accelerates the RMC calculation step. Comparing the structure simulated by molecular dynamics with the structure improved by RMC for two sets of pair distribution functions then allows the interatomic potentials to be tested one by one and individually readjusted. Analyzing the structure refined by RMC yields a model capable of accounting for the experimental results.

3. Principal results The state of the art emerges from a large number of studies of specific glass compositions leading to an overall representation of the network organization. Some of the most significant results obtained with complex oxide glass structures are reviewed here. The local organization of the polymerized network of oxide glass has been known for a relatively long time in simple glasses. The same characteristics of the environments around the major network formers (Si, B, Al) are often found in more complex glasses. Si is systematically found in a tetrahedral environment; B is either 3- or 4-coordinated, while Al remains 4-coordinated when the Al 2 O 3 concentration is low enough to allow it to be completely incorporated in the silicate network. The medium-scale organization is still unclear, although increasing evidence suggests a heterogeneous organization. Gaskell [8] calculated the structure factor for an SiO 2 atomic model, showing that the first narrow peak could be explained by the presence of ordered groups with a characteristic length of about 1 nm. Cormier [9] coupled a reverse Monte Carlo method with X-ray diffraction in K 2 O?TiO 2 ?2SiO 2 glass, revealing the presence of heterogeneous zones enriched in 5-coordinated Ti and locally compensated by K. Ni groups have also been observed in borate glasses [10]. These results confirm recent Raman diffraction experiments [11] on sodium silicate glasses, which indirectly imply the existence of ordered zones with characteristic sizes of between 1 and 2 nm. Molecular dynamics simulations in a binary alkali silicate glass [12] revealed the existence of zones enriched in network formers and other zones enriched in network modifiers, again in the 1–2-nm size range; the alkalienriched zones were also enriched in nonbridging oxygen atoms. Adding Al 2 O 3 to these glasses contributed to a reduction in the number of nonbridging oxygen atoms, because some of the alkali metal atoms were mobilized as charge compensators around the AlO 4 groups [12,13]. The separation between the two types of zones in the network becomes less distinct. The organization of the network modifiers has not been precisely described, although many authors refer to the existence of modifier chains. These conclusions arise from visible observations of the structure and, to the best of our knowledge, the mono dimensional nature of the zones containing network modifiers has never been demonstrated. A mixture of alkali metals has little or no effect on their medium-range environment, but does result in a significant slowdown in their diffusion known as the mixed alkali effect [12]: i.e., it is more difficult for an alkali metal to diffuse toward a site occupied by a different alkali species. A recent review [14] showed that normalizing the

J.-M. Delaye / Current Opinion in Solid State and Materials Science 5 (2001) 451–454

Fig. 1. Cation–cation radial distribution function normalized with respect to the first peak position in four glass compositions: CaSiO 2 , K 2 O?TiO 2 ? 2SiO 2 , 2CaO?NiO?3SiO 2 , Li 2 O?2SiO 2 .

cation–cation radial distribution functions with respect to the position of the first peak for various intermediate elements (Ca, Ti, Ni, Li) in silicate glasses (Fig. 1) ] consistently produces curves with peaks at R and Œ3R, and ] a minimum at Œ2R. Surprisingly, the same characteristic distances are found in the radial distribution functions calculated for an arrangement of packed hard spheres. The groups of cations with their first-neighbor oxygen rings organize themselves and reproduce some of the characteristics of packed hard spheres. This observation highlights the difficulty of discriminating, within the natural order observed in glass, between the effects corresponding to a homogeneous environment and those arising from a heterogeneous distribution together with an energy minimization process. In an attempt to define a homogeneous glass reference structure, we recently calculated the percentages of different types of F1–O–F2 triplets (where F1 and F2 are network formers) using a probabilistic approach [7]. A triplet was considered as a pair of two F–O bonds. In this approach, the number of F1–O–F2 triplets is related to the probability of drawing an F1–O pair and an F2–O pair from the set of possible F–O pairs. By comparison with structures simulated by molecular dynamics, a homogeneous reference structure can be used to reveal exclusion phenomena among compensated charge elements (4coordinated B and Al), as well as the effect of the alkali and alkaline-earth metals on these phenomena. A series of studies coupling molecular dynamics with experimental (NMR, EXAFS, Raman) techniques has recently been undertaken. Analyses of the atomic structures have provided a possible explanation for some

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experimental phenomena, such as the modification of the Al–O–Si angles or the reduction in the Na–O distances in series of aluminosilicate glasses [15,16]. Increasing the concentration of network modifiers enhances their effect on the network of formers, modifying the angles of the Al–O–Si triplets. Coupling molecular dynamics with EXAFS revealed different environments around Fe 21 ions in silicate glasses [17,18]; the EXAFS spectrum can be explained by the presence of Fe 21 simultaneously in 4and 5-coordinated environments. This type of coupling also confirmed the coordination number 6 of Zr in a borosilicate glass [19]. Ab initio methods have been developed to provide an increasingly fine correlation with experimental results [20– 23]. Although the domain of coupling between the atomic structure and macroscopic properties remains largely unexplored, macroscopic models are available to relate the density to the concentrations of the various groups in the glass. These models are outside the scope of atomistic simulation, but could easily be used with input data provided by molecular dynamic calculations [24–26].

4. Conclusions The structure of complex glasses is a vast issue, considering the very wide range of glass compositions now in use. This review of the principal results obtained to date is limited to work on a specific type of glass, and we can only regret the lack (to the best of our knowledge) of generic studies of complex oxide glass structures comparable for instance to the Lennard–Jones models for metallic glasses. Such an approach would allow a broader generalization of the results concerning not only the structure but also the dynamic mechanisms. Significantly improved simulation methods can be expected in the coming years, not only for representing interactions with allowance for charge transfers and for generalizing ab initio approaches, but also for increasing the complexity of the compositions and the size of the simulation cells [27]. The latter improvement will lead to major advances in our knowledge of glass at medium scale. Although ab initio calculations currently remain limited to small clusters, electron density analysis can be expected to lead to the development of a charge transfer algorithm for molecular dynamics. They will also no doubt contribute significantly to our understanding of experimental spectra. Finally, most simulations currently attempt to describe the glass structure and the effects of the glass composition on the structure, while the relations between the structure and the dynamic, elastic or mechanical properties remain relatively unexplored.

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Acknowledgements The author is grateful to the LMCP (Laboratoire de ´ Mineralogie et Cristallographie: Paris VI) for providing their very interesting last results and to D. Ghaleb for the critical reading of this paper.

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