The structure of Y- and La-bearing aluminosilicate glasses and melts: A combined molecular dynamics and diffraction study
Introduction
Rare earth elements (REE) are widely used as geochemical tracers of magmatic processes and thus, their structural incorporation in silicates is of interest for the development of predictive geochemical models. Alkali and alkaline earth bearing (alumino)silicate glasses and melts have been studied extensively, due to their broad range of technological applications and their importance in geoscience. Hence, their structure and properties are relatively well understood (Stebbins et al., 1995, Mysen and Richet, 2005). On the other hand, aluminosilicates containing rare earth elements (REE) are less well studied but have recently attracted considerable interest owing to their remarkable properties and their use in various applications. They exhibit high glass transition temperatures, hardness and refractive indices as well as moderate thermal expansion coefficients (Shelby and Kohli, 1990, Iftekhar et al., 2011). REE-bearing aluminosilicate glasses have been proposed for optical devices (Kohli and Shelby, 1991, Tanabe, 1999). Since rare-earth elements represent analogs for actinides, these glasses have also been studied for applications in nuclear waste storage, and high corrosion resistance in the presence of aqueous fluids was found (Bois et al., 2002).
REE-bearing aluminosilicate glasses have been investigated by a range of experimental techniques, including nuclear magnetic resonance (NMR) (Schaller and Stebbins, 1998, Clayden et al., 1999, Marchi et al., 2005, Florian et al., 2007, Iftekhar et al., 2011, Iftekhar et al., 2009), infrared spectroscopy (Clayden et al., 1999, Marchi et al., 2005) as well as neutron and X-ray diffraction (Wilding et al., 2002, Pozdnyakova et al., 2008). These techniques provide valuable insight into the local atomic structure of glasses such as coordination environments of the probed elements, glass network structures and vibrational properties. Often, the interpretation of experimental data relies on more or less heuristic assumptions about the atomic structure of the probed material. For instance, Iftekhar et al. (2009) fitted a structural model to the measured NMR peak shifts and were able to extract information about the glass network connectivity from 29Si signals alone. Another example is the interpretation of X-ray and neutron diffraction data: a common approach to obtain bond lengths and coordination numbers is to fit Gaussian peaks to the Fourier-transformed structure factor, i.e. to implicitly assume a specific structural model for the quantitative analysis of experimental data (Wilding et al., 2002, Pozdnyakova et al., 2008).
Molecular dynamics (MD) simulations are a particularly powerful and predictive method to generate three-dimensional structural models for disordered systems (Allen and Tildesley, 1987) and therefore yield information which is not directly accessible experimentally. To date, there are only a few classical MD studies on REE-bearing aluminosilicate glasses and melts: Du (2009) investigated low-silica (<40 mol%) yttrium aluminosilicates, and Iftekhar et al. (2012) performed MD simulations of Y- and Lu-bearing glasses, with compositions containing less than 50 mol% SiO2. Haigis et al. (2013) used classical MD simulations to investigate structure of Y in (alumino)silicate melts, with different degree of network polymerization. Recently, Jaworski et al. (2012) and Okhotnikov et al. (2013) published results from classical MD simulations on aluminosilicate glasses also containing La.
The simulation of melts and glasses, however, also poses a fundamental challenge to the MD method: all predictions are dependent on the chosen interaction potentials and their applicability for a given set of conditions has to be tested carefully. Moreover, the MD method allows to simulate the motion of the individual atoms in the system over a certain time, and macroscopic quantities are then obtained by averaging over these atomic trajectories. The statistical results are meaningful only to the extent that the phase space available to the system is sufficiently sampled during the simulation, i.e. that all relevant atomic configurations are visited during the MD run. Even for comparatively dynamic systems such as melts, it can be challenging to ensure that a system has reached equilibrium, especially in chemically complex systems such aluminosilicates. The construction of glass structure models from MD simulations that are comparable to real glasses poses an additional challenge as the glass transition temperature depends on the time scale to freeze the liquid. Depending on the interaction model and available computing resources, the maximum simulation times reach from tens of picoseconds to perhaps hundreds of nanoseconds. To address these issues, we used two complementary simulation approaches.
Ab initio or first-principles MD is based on fundamental laws of nature (quantum mechanics) in the form of density functional theory (DFT) (Hohenberg and Kohn, 1964, Kohn and Sham, 1965) and yields a parameter-free description of arbitrary systems of atoms. Although some approximations have to be made for practical purposes, it provides the most reliable description of atomic interactions currently available and highly predictive in many cases. These qualities, however, come at the expense of high computational cost, which limits simulation times to some tens of picoseconds and system sizes to a few hundred atoms at most. For these reasons, we use ab initio calculations primarily to gain insight into melt structures.
The ab initio simulations are not only expected to provide accurate structural information on melts but also serve as a benchmark for classical MD simulations, which constitute the second approach to modeling melt and glass structures. In the latter case, atomic interactions are described by a classical potential. Classical simulations are much less demanding in terms of computation time, but their accuracy is not warranted and has to be tested carefully. Their computational efficiency allows simulated quenching of the melts to glasses at much lower rates than can be afforded with ab initio techniques (though still much faster than in experiments). The resulting glass structures can then be compared to results from neutron and X-ray diffraction experiments, which were performed in this study to provide a reference for the simulations (see below). The classical MD simulations also allow to study the structural changes between the melt and the glass and to assess the often used assumption that glasses are good structural approximates of melts (and vice versa). The potentials for REE-bearing aluminosilicates used here are an extension of already established and well tested sets of advanced polarizable ion potentials (Jahn and Madden, 2007, Haigis et al., 2013). It is desirable to further develop such accurate and transferable classical potentials, as they are a key to investigate complex geological systems such as mantle melts and solid solutions of mineral phases and the behavior of trace elements therein.
Here, we present the results of a combined MD and neutron/X-ray diffraction study on yttrium- and lanthanum-bearing aluminosilicate melts and glasses, REE2O3-Al2O3-SiO2 (REE = Y, La), with high silica content (76 mol% SiO2). We utilize and compare more refined simulation methods than in cited previous work – new polarizable classical interatomic potentials and ab initio molecular dynamics – and systematically analyze the effects of interaction potential, temperature and quench rate on melt and glass structures. Keeping the molar fraction of SiO2 fixed, the REE/Al ratio was varied between 0.09 and 0.5. We investigated the atomic-scale changes in the structure in response to 1) exchanging Y by La, 2) varying the REE content, i.e. the REE/Al ratio, of the system and 3) increasing the complexity of the classical interaction potential. A particular focus lies on the coordination environment of Y and La, as these are difficult to probe by the otherwise rather powerful NMR technique (Dupree et al., 1989, Schaller and Stebbins, 1998) and diffraction experiments (Leydier, 2010).
Section snippets
First-principles molecular dynamics for melts
We performed first-principles, Car-Parrinello molecular dynamics simulations using the CPMD code (Car and Parrinello, 1985, Marx and Hutter, 2000) of REE-bearing aluminosilicate melts of four different compositions, REEAl11Si19O56 and REE4Al8Si19O56, where REE stands for either Y or La. Each simulation cell contained 174 atoms and was repeated periodically in space. Assuming that densities of the melt and the respective glass are similar, we chose the dimensions of the simulation cells such as
Sample preparation
All glasses were synthesized by mixing commercially available oxides La2O3 (99.9% - Sigma-Aldrich), Y2O3 (99.9% - Sigma-Aldrich), Al2O3 (99.9% - Pechiney) and SiO2 (99.5% - Prolabo). The powders were weighed and mixed together directly except La2O3 which was first annealed in an alumina crucible during 2 h at 1100 °C to remove the anionic impurities (CO, HO −) and H2O, then mixed with the other components and finally, heat-treated a second time. All mixtures were then melted in air at about
Ab initio MD of melts at 3000 K
From the trajectories of the ab initio MD simulations at 3000 K for each composition, the coordination environment of the cations is extracted. Figs. 1 and 2 show the radial distribution functions gXO(r) (X = Y/La, Al, Si, O) for the Y-bearing and the La-bearing melts, respectively. The average coordination number of a cation X is calculated as the average number of oxygen ions around the cation within a cutoff radius rcutXO, which is given by the first minimum of the respective radial
Classical MD of melts at 3000 K
The reliability of the two classical interaction potentials (DIPPIM and QUAIM) can be assessed by comparison of their predictions either to ab initio results or to experimental data. Here, we first check melt structures derived from classical MD at 3000 K against the ones obtained from Car-Parrinello simulations (see Section 4.1). A comparison with diffraction data will be made in Section 4.4. The radial distribution functions for X-O pairs (X = Y/La, Al, Si, O) are plotted along with the DFT
Melt structures: ab initio vs. classical MD
The quality of the structure models for the melts and glasses obtained from classical MD simulations is assessed by comparison to ab initio-derived melt structures and to experimental diffraction data for the glasses. Figs. 1 and 2 demonstrate an overall reasonable agreement between classical and DFT simulations for the partial radial distribution functions in the four investigated melts. In the case of the DIPPIM potential, peaks corresponding to the first coordination shells of oxygen around
Conclusions
The atomic-scale structure of four Y- and La-bearing aluminosilicate glasses and melts with high SiO2 content (76 mol%) was investigated by ab initio and classical MD simulations as well as neutron and X-ray diffraction experiments. By combining information from all four approaches, we described the coordination environments of the cations and found robust evidence for structural trends as a function of composition: coordination numbers of rare earth element (REE) cations are between 7 and 8 and
Acknowledgments
We would like to thank the staff at ID11 (ESRF) and D4C (ILL) for their help during the diffraction experiments. Parts of the simulations were performed at John von Neumann Institute for Supercomputing in the framework of NIC project HPO15. Financial support by the German Research Foundation DFG (project JA 1469/4-1) and by the Helmholtz graduate school GEOSIM are gratefully acknowledged.
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