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Inelastic neutron scattering on sodium aluminosilicate melts: sodium diffusion and intermediate range order
Chemical Geology 213 (2004) 165 – 172 www.elsevier.com/locate/chemgeo
Inelastic neutron scattering on sodium aluminosilicate melts: sodium diffusion and intermediate range order F. Kargl, A. Meyer* Physik Department E13, Technische Universita¨t Mu¨nchen, 85748 Garching, Germany Received 20 December 2003; received in revised form 18 June 2004; accepted 31 August 2004
Abstract The interplay of structure and mass transport in sodium aluminosilicate melts at temperatures up to 1600 K has been investigated with inelastic neutron scattering. We compare results of ion dynamics and elastic structure of ternary 3Na2Od Al2O3d 12SiO2, 3Na2Od Al2O3d 8SiO2, Na2Od Al2O3d 6SiO2 and Na2Od Al2O3d 4SiO2 with recent results of binary Na2Od 3SiO2 and Na2Od 2SiO2. Addition of alumina to the binary silicates leads to a decrease in sodium mobility. The prepeak in the elastic structure factor which appears in binary alkali silicates at 0.9 21 and which is interpreted to reflect a network of Na diffusion channels decreases in intensity with increasing alumina content. We find no indication for a prepeak in the Na2O/ Al2O3 = 1 samples. The addition of alumina is apparently disrupting the channel structure found in sodium silicates. D 2004 Elsevier B.V. All rights reserved. Keywords: Sodium aluminosilicates; Microscopic dynamics; Neutron scattering; Ternary silicates; Melt; In situ
1. Introduction It is a fundamental aim to develop an understanding of the interplay of structure and dynamics on a microscopic level and of its influence on properties of multicomponent silicate melts. However, even in binary alkali silicates it was not fully understood how alkali atoms are built into the Si–O network. For example the origin of the fast sodium ion diffusion as
* Corresponding author. E-mail address: [email protected] (A. Meyer). URL: http://www.e13.physik.tu-muenchen.de. 0009-2541/$ - see front matter D 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.chemgeo.2004.08.040
well as the highly non-linear dependence of the viscosity on modifier concentration do not have unambiguous explanations. A first model for alkali silicates assuming a random distribution of the alkali ions (Zachariasen, 1931; Warren and Biscoe, 1938) and thus leading to a continuous disruption of the Si– O4 tetrahedral network, was not in agreement with the observed properties of mass transport. Therefore, different models on the basis of EXAFS (Greaves, 1985) and simulation studies (Angell et al., 1982) were developed proposing an inhomogeneous distribution of the alkali ions in channel- or cluster-like formations also serving as preferential ion conducting pathways.
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In the last decade molecular dynamics (MD) simulations have become a more and more powerful tool in studying dynamics and structure in oxide melts. The main reasons are an increase in computer power and the development of more realistic potentials. There have been several studies on alkali silicate (Huang and Cormack, 1990; Smith et al., 1995; Oviedo and Sanz, 1998) and mixed alkali (Vessal et al., 1992) glasses. In these simulations, potentials based on the potential developed by Vessal were used. These studies resulted in a heterogeneous distribution of the alkali ions in the silica network and showed that the alkali ions are bound to non-bridging oxygens (NBO). Some studies (e. g. Smith et al., 1995) also investigated dynamical properties. However, diffusion coefficients differ by at least one to two orders of magnitude compared to experimental values (Gupta and King, 1966; Jambon and Carron, 1976; Braedt and Frischat, 1988). Nevertheless, activation energies for alkali ion transport are reported to be in good agreement with experimental values. The simulation studies of Oviedo and Sanz (1998) indicated for Na2O concentrations above ~10 mole % microsegregation of sodium supporting the fast sodium ion diffusion. Recently, molecular dynamics simulations (Horbach et al., 2001; Jund et al., 2001; Horbach et al., 2002; Sunyer et al., 2002) using a modified BKS potential originally developed by van Beest et al. (1990) and inelastic neutron scattering (Meyer et al., 2002, 2004; Kargl et al., unpublished) on binary sodium silicate melts and glasses provided evidence for the existence of sodium diffusion channels. Experimental and simulated structure factors of sodium silicate melts exhibit an emerging prepeak around 0.9 21 (Meyer et al., 2004). This prepeak has its origin in the formation of sodium rich channels in the static structure. The channels serve as preferential ion conducting pathways in a relative immobile Si–O matrix. The sodium diffusion channels persist over a broad Na2O concentration range (at least 20–40 mole %). The presence of this channel network in binary alkali silicates provides an explanation for the highly non-linear dependence of viscosity on alkali concentration. The viscosity drops by several orders of magnitude by adding only a few mole % Na2O to SiO2 (e.g. Poole, 1948; Bockris et al., 1956; Knoche et al., 1994). On further Na2O addition, the viscosity
exhibits a relatively weak decrease. Not only can the existence of sodium channels in the static structure account for this fact, but in addition, the channel structure can also explain the fast Na ion transport that is decoupled by several orders of magnitude from the Si–O network dynamics even at typical melt temperatures. Sodium aluminosilicates have been the subject of investigation for a long time, since several geological and technological relevant compositions like albite and jadeite occur in this system. They also act as base components in most natural magmas. Raman scattering investigations performed on glasses and melts elucidate the speciation of Si and the bond length and binding angles of Al as a function of composition and temperature (Neuville and Mysen, 1996). Most of the Al is found in a tetrahedral configuration, charge balanced by Na ions. In compositions close to the tectosilicate join (Na2O /Al2O3 = 1) and in the peraluminous region (Na2O /Al2O3 b 1) different ideas about the structural role of excess aluminum are presented (see e.g. Toplis et al., 1997a). However, the model of a formation of triclusters based on the statistical approach of Lacy (1963) is favoured by investigating the viscosity-concentration and viscosity-temperature behaviour in these systems (Riebling, 1966; Toplis et al., 1997a). In addition, Na, K, Rb, and Cs tracer diffusion experiments on alkali aluminosilicate melts and glasses have been performed comparing transport properties as a function of alkali size, temperature and composition. Here, the highest diffusivities and lowest activation energies are reported for Na (Jambon and Carron, 1976; Roselieb and Jambon, 1997). Nuclear magnetic resonance studies on sodium aluminosilicate glasses and liquids link local structure and sodium dynamics (Georges and Stebbins, 1996). Those authors concluded that in the peralkaline region (Na2O /Al2O3 N1) sodium transport is mainly governed by sodium atoms connected to NBO’s. In the peraluminous region (Na2O /Al2O3 b 1) however, the sodium atoms associated with aluminum atoms for charge balancing dominate sodium diffusion. More recently, neutron diffraction experiments using isotopic substitution combined with reverse Monte Carlo modelling on silicate glasses revealed a heterogeneous distribution of the Li ions in Li2Od Al2O2d 2SiO2 (Cormier et al., 2001).
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Here, we report on inelastic neutron scattering results on sodium aluminosilicate melts. In situ inelastic neutron scattering experiments provide access to structure on intermediate length scales and microscopic dynamics at times ranging from sub picoseconds to several tens of nanoseconds. We discuss the evolution of mass transport properties and structure found in binary silicates with the addition of alumina.
2. Experimental We synthesized four ternary sodium aluminosilicate glasses from reagent grade (99.999%) SiO2, Na2CO3 and Al2O3 powders. The powder mixtures were melted in air at 1400 8C in a 5% Au/Pt crucible for several hours. Sodium aluminosilicates feature a relatively high viscosity even at 1450 8C (Toplis et al., 1997b). Thus, a mixture of sodium silicate and Al2O3 powders was used as starting materials. In this way the synthesis time was significantly reduced. In order to get bubble free and homogeneous samples, the melts were stirred with a Pt-spindle at 1450 8C for more than 24 h in air. Volatilization of Na was negligible as verified by weight measurements of the CO2 free samples before and after the synthesizing process. For each composition we used 40 g of raw material to reduce the compositional error of the weighed sample in the per mill range. Finally, glasses were obtained by cooling the samples in their Ptcrucibles in air from 1450 8C down to room temperature. In the following NxAySz is used as general abbreviation for xNa2Od yAl2O3d zSiO2. Two samples in the peralkaline region N3AS12 and N3AS8 as well as two samples on the tectosilicate join NAS6 and NAS4 were fused. N3AS12 and NAS6 as well as N3AS8 and NAS4 were chosen on the 75 and 66 mole % iso silica join, respectively. An overview of the samples is given in Fig. 1. Inelastic neutron scattering investigations were performed at the time-of-flight spectrometer IN6 at the Institut Laue-Langevin. For the scattering experiments we used a Pt sample holder with a hollow cylindrical sample geometry (22.5 mm outer diameter, 1.25 mm sample thickness, and 30 mm sample height). With these sample dimensions the sample matches the neutron beam size and multiple scattering
.
Fig. 1. Na2O–Al2O3–SiO2 diagram: sodium aluminosilicates ( ) and sodium silicates (o). The dashed line represents the Na2O/ Al2O3 = 1 join. The pointed double dashed lines represent constant Na2O concentration joins, starting from NS3 and NS4, respectively. We note that N3AS8 and NS3 have the same Na2O content.
is negligible. We investigated each sample at room temperature in the glassy state and in the melt up to 1600 K. We used an incoming neutron wavelength of 5.9 2 providing an instrumental energy resolution of 50 AeV (FWHM). Thus, timescales up to 40 ps were accessible. In addition, this configuration provided an accessible wavenumber range of 0.2 21 V q V 1.75 21 at zero energy transfer. The standard Nb resistor high temperature vacuum furnace of the ILL exhibits a temperature gradient over the whole sample at 1600 K that was less than five degrees and a temperature stability within 1 8. Run durations were 6–12 h per temperature. Normalization to a vanadium standard, correction for self-absorption and container scattering and interpolation to constant wavenumbers q yielded the scattering law S( q,x). It is still convoluted with the instrumental energy resolution, that is given by the room temperature measurements. The density correlation function S( q,t) is obtained by Fourier deconvolution of the scattering law S( q,x).1 The density correlation function correlates the spatial Fourier transform of the particle density,
1 The scattering law and the measured instrumental energy resolution are energy Fourier transformed. For the doconvolution the Fourier transform of the scattering law is divided by the Fourier transform of the resolution function.
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P Y Y Y Y q r ðt Þ ¼ i dðr R i ðt ÞÞ, i.e. the position, R i , of each particle, i, at time t, with its values at time 0: S ðq; t Þ ¼ hq4q ðt Þqq i=hjqq j2 i
ð1Þ
We note that the particle density is directly accessible in molecular dynamics simulations. Beside dynamic information, neutron time-of-flight data also provide structural information. Since inelastic scattering is well separated from the elastic signal, the elastic structure factor S( q,x = 0) is obtained by integrating the scattering law over the instrumental energy resolution function: Z S ðq; x ¼ 0Þ ¼ dx S ðq; xÞ: ð2Þ res:
The elastic structure factor is equal to the static structure factor S( q) multiplied by the Debye-Waller factor f q .2
3. Results We investigated the elastic structure factor of N3AS12, NAS4, N3AS8 and NAS6 at room temperature and at 1600 K in the melt. All structure factors (in the melt and in the glass) contain incoherent as well as coherent scattering contributions. The incoherent contributions result in a flat background in the static structure factor. Si and O exclusively scatter coherently. Scattering on the Al atoms is dominantly coherent with a negligible incoherent contribution. Na features both incoherent as well as coherent scattering. The elastic structure factors exhibit a flat background at small q. Similar to the binary sodium silicates at small wavevectors, incoherent scattering on sodium is the dominant contribution to the signal. The elastic structure factors of the ternary compositions are compared with their binary base compositions NS2 and NS3 at 1600 K taken from Meyer et al. (2002, 2004). In the binary silicate melts the elastic structure factors exhibit a prepeak at f0.9 21 below the first sharp diffraction peak (FSDP) at 1.7 21. The 2
Neglecting in good approximation the wings of the broad quasielastic line in the signal from the incoherent scattering on the diffusing sodium atoms.
FSDP in pure silica represents mean Si–O4 tetrahedra distances (Elliot, 1991). In binary silicates neutron scattering shows that the prepeak at f0.9 21 is emerging with increasing temperature. In the melt is position is constant, but its height is increasing with increasing Na concentration for the studied compositions in the range from NS4 to NS2. MD simulations performed at experimental densities exhibit qualitatively similar behaviour of the prepeak as a function of temperature and Na2O concentration (Meyer et al., 2004). Although the measured and simulated elastic structure factors of the binary sodium silicates in the glass do not display a pronounced prepeak, the channel structure is still present. The simulation shows that only with decreasing density do the positive and negative contributions of the six partial structure factors summed weighted by the neutron scattering length no longer cancel each other at f0.9 21. Therefore, this intermediate range order is in standard neutron (and X-ray) scattering experiments only observable at high temperatures in the equilibrium melt. A comparison of MD simulations performed at experimental densities and our inelastic neutron scattering results on binary silicates shows that the prepeak arises from a formation of sodium rich channels in the static structure (Meyer et al., 2004). Its position represents a characteristic length scale of this channel structure. Typical distances between channels are about 6–8 2. Fig. 2 displays the elastic structure factors of the binary and ternary silicates at 1600 K. With increasing alumina content S( q,x = 0) the first sharp diffraction peak (FSDP) at f1.6 21 is increasing and the height of the prepeak at 0.9 21 is decreasing. In the 66 mole % SiO2 (Fig. 2 left) and 75 mole % SiO2 (Fig. 2 right) containing samples the increase of the prepeak for the Na2O /Al2O3 =3 compositions with temperature is far less pronounced than for the binary sodium silicates. For NAS6 (albite) and NAS4 (jadeite) we have no experimental evidence for a prepeak, neither in the melt nor in the glass. The room temperature spectra of the Na2O/ Al2O3 =3 samples are similar to the S( q,x=0) of the Na2O /Al2O3 = 1 samples below ~1.2 21. With increasing temperature the elastic structure factors should display a decrease in their intensities due to the decreasing Debye-Waller factor. This effect is proportional to exp{q 2hu 2i} and thus, is more pronounced
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Fig. 2. Elastic structure factors of the 66 mole % (left) and 75 mole % (right) SiO2 containing samples at 1600 K. Data were obtained by neutron time-of-flight spectroscopy. The solid lines represent the elastic structure factors for the tectosilicate sample NAS6 at room temperature. For both iso silica joins the prepeak at 0.9 21 is decreasing with increasing Al2O3 content.
at higher q-values. This behaviour becomes evident in the FSDP (see Fig. 2). Neutron backscattering on molten sodium disilicate resulted in mean relaxation times hsi for the structural Si–O network relaxation of about 10 ns at 1600 K (Meyer et al., 2002). A comparison with viscosity data indicates even larger network relaxation times for the other silicate melts discussed here. Therefore, the structural relaxation of the silicate network is too slow to be resolved in our time-of-flight experiment and will reflect itself in a strong elastic contribution to the signal. In contrast, sodium relaxation is on a 10-ps time scale at 1600 K. In neutron time-of-flight spectroscopy this will be visible as a broad quasielastic contribution in S( q,x).
Fig. 3 displays the density correlation functions S( q,t) for NS3, N3AS12, NS2, and N3AS8 at 1600 K and q =0.5 21. At q values below ~0.6 21 the incoherent scattering on Na is the dominant contribution to the signal. Solid lines are fits with F( q,t) (Eq. (3)). The fit function consists of two contributions, a stretched exponential function accounting for the quasielastic scattering contribution and a constant accounting for the elastic scattering: h i F ðq; t Þ ¼ b þ a n ; exp ðt=hsiÞb : ð3Þ hsi denominates the mean relaxation time, b is the stretching exponent, a is the quasielastic amplitude and b is elastic scattering contribution. The density correlation functions S( q, t) are best described by Eq.
Fig. 3. Sodium relaxation in sodium di- and trisilicate melts and in the Na2O /Al2O3 = 3 compositions N3AS8 and N3AS12 as seen by inelastic neutron scattering. Solid lines represent fits to the density correlation functions S( q, t) with Eq. (3) and a stretching exponent b of 0.75.
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(3) with a sample independent stretching exponent bf0.75. A stretching exponent b b1 indicates that Na diffusion is not a simple activated process. The density correlation functions S( q,t) are plotted with a sum of (a+b) as the upper, and b as the lower yscale boundary, respectively. Thus, sodium relaxation times of different samples at the same temperature can be directly compared. The density correlation function of N3AS12 at 0.5 21 (Fig. 3) exhibits a decrease in the relaxation time by a factor of 2.5 as compared to NS3. In albite and jadeite (not plotted), Na-relaxation times are not in the experimentally accessible region of IN6. In albite they are estimated to be an order of magnitude smaller than the Na relaxation times of NS3. In aluminosilicate melts obtained by substituting a quarter and half of the Na2O in NS2 by Al2O3 the dynamical picture is slightly different to the ternary composition based on NS3. The Na-relaxation is decreasing by approximately a factor of two between NS2 and N3AS8 (Fig. 3). However, the increase of Na relaxation times between NS2 (Meyer et al., 2002) and NAS4 (not plotted) is far less pronounced compared to the increase observed between NS3 and NAS6.
4. Discussion Earlier investigations of the binary sodium silicate melts NS2, NS3, and NS4 revealed the existence of a network of sodium diffusion channels in the static structure, experimentally visible in a prepeak at f0.9 21 (Meyer et al., 2004). In the melt at 1600 K, sodium relaxation is on a picosecond timescale. In contrast, relaxation times of the Si–O network are on a nanosecond timescale (Meyer et al., 2002; Kargl et al., unpublished). Thus, the mobility of the sodium atoms is decoupled by about three orders of magnitude from the Si–O relaxation. The channel structure for Na found over a broad Na-concentration range is a key feature in understanding the mass transport in binary silicate melts. Here, we discuss how the partial substitution of the network modifier Na2O in sodium silicates by Al2O3 alters the network of sodium diffusion channels. For sodium aluminosilicates on the Na2O /Al2O3 =3 join, Fig. 2 displays a prepeak emerging with increasing temperature similar to the behaviour in the alkali silicates. However, the increase of the prepeak with temperature is less pronounced than
in binary sodium silicates. In molten NAS6 and NAS4 the elastic structure factors do not show a prepeak. In binary sodium silicates, the mean sodium relaxation times follow a q2 dependence in the low q limit even for q values up to f0.8 21. Therefore in the case of incoherent scattering a self-diffusion coefficient D can be obtained (Boon and Yip, 1991). At 1600 K the sodium self-diffusion coefficient D =1/( q2s q ) is D =3.8F0.3 109 m2 s1 for NS2 and D =2.1F0.3
109 m2 s1 for NS3 (Kargl et al., unpublished). These values agree well with tracer diffusion experiments (Gupta and King, 1966; Braedt and Frischat, 1988). In the aluminosilicates at q values below 0.5 21 the relaxation times exceed the instrumentally accessible time window. Thus, experimental proof of the validity of the q2 dependence is not possible. To estimate the sodium self-diffusion coefficient, we assume that the proportionality of D to 1/(q 2s q ) is also valid for the aluminosilicates at q =0.5 21. Using this relation the following diffusion coefficients for our samples are obtained: D=1.8F0.2 109 m2 s1 (N3AS8) and D=1.0F0.2 109 m2 s1 (N3AS12). At 1600 K the separation of alkali ion relaxation and the network dynamics is even more pronounced in sodium aluminosilicates than in sodium silicates. From the increase in the viscosity, the decrease in the prepeak and the decreasing sodium mobility we conclude that the channel structure present in alkali silicate melts become more and more disrupted with increasing alumina content at a fixed SiO2 concentration. Along the constant Na2O content joins (Fig. 1) relaxation times for Na2O decrease by 20% between NS3 and N3AS8 at 1600 K. In addition, the alumina content is increasing from 0 mole % in NS3 to 8 mole % in N3AS8. Comparing data at constant alumina content, Na relaxation times decrease with increasing Na2O concentration. Along the constant Na/(Na+Al) joins Na-relaxation times are decreasing with decreasing silica concentration. Comparing different joins we observe a non-linear behaviour of relaxation times with increasing alumina content. The latter effect is less pronounced at lower silica content.
5. Conclusion and outlook Investigating sodium aluminosilicates with inelastic neutron neutron scattering has shown itself to be a
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highly versatile method for revealing changes in microscopic dynamics and intermediate range structure with increasing alumina content. The prepeak assigned from MD simulations on binary silicates (Horbach et al., 2002; Meyer et al., 2004) to originate from the formation of sodium rich channels, decreasing in sodium aluminosilicates with increasing alumina content. The mobility of the sodium atoms decreases with increasing Al2 O 3 content. This decrease in the sodium relaxation times is a nonlinear function of SiO2, Na2O and Al2O3 concentration. The decrease in the mobility of the sodium atoms, the increasing viscosity and the decreasing prepeak in the structure factor indicates that the addition of Al2O3 disrupts the sodium channel structure. In ternary aluminosilicates, Na atoms are expected to charge balance Al-tetrahedra (Neuville and Mysen, 1996; Georges and Stebbins, 1996). Therefore, one could think of two types of chemically different surroundings for the Na atoms with a slower relaxation of the Na atoms that charge balance Al. The quasielastic amplitude arising from the fast Na dynamics would then be expected to decrease by more than 25% from NS3 to N3AS12. An inelastic neutron scattering experiment to address this particular question is in preparation. As compared to IN6 the new time-of-flight spectrometer of the new neutron source of the Technical University Munich—the FRM-II— exhibits a better energy resolution and an extended qrange toward small wavenumbers. A combined study using neutron scattering and molecular dynamics has revealed many features of the interplay of structure and microscopic dynamics in binary sodium silicates (Meyer et al., 2004). In the case of sodium aluminosilicates the accuracy of a molecular dynamics model can be assessed by our neutron scattering data. The information obtained by MD simulations will then elucidate the structure and mass transport–property relationship in more detail also in sodium aluminosililcate melts.
Acknowledgements We thank D.B. Dingwell, K.-U. Hess, J. Horbach and W. Kob for stimulating discussions and H.
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Schober for his support during the experiments performed at the Institut Laue Langevin. We thank the ILL for providing the instruments and the possibility to perform our investigations. We acknowledge financial support by the DFG (SP 1055: Bildung, Transport und Differenzierung von Silikatschmelzen) under project number ME 1958/6-1. [RR]
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Inelastic neutron scattering on sodium aluminosilicate melts: sodium diffusion and intermediate range order F. Kargl, A. Meyer* Physik Department E13, Technische Universita¨t Mu¨nchen, 85748 Garching, Germany Received 20 December 2003; received in revised form 18 June 2004; accepted 31 August 2004
Abstract The interplay of structure and mass transport in sodium aluminosilicate melts at temperatures up to 1600 K has been investigated with inelastic neutron scattering. We compare results of ion dynamics and elastic structure of ternary 3Na2Od Al2O3d 12SiO2, 3Na2Od Al2O3d 8SiO2, Na2Od Al2O3d 6SiO2 and Na2Od Al2O3d 4SiO2 with recent results of binary Na2Od 3SiO2 and Na2Od 2SiO2. Addition of alumina to the binary silicates leads to a decrease in sodium mobility. The prepeak in the elastic structure factor which appears in binary alkali silicates at 0.9 21 and which is interpreted to reflect a network of Na diffusion channels decreases in intensity with increasing alumina content. We find no indication for a prepeak in the Na2O/ Al2O3 = 1 samples. The addition of alumina is apparently disrupting the channel structure found in sodium silicates. D 2004 Elsevier B.V. All rights reserved. Keywords: Sodium aluminosilicates; Microscopic dynamics; Neutron scattering; Ternary silicates; Melt; In situ
1. Introduction It is a fundamental aim to develop an understanding of the interplay of structure and dynamics on a microscopic level and of its influence on properties of multicomponent silicate melts. However, even in binary alkali silicates it was not fully understood how alkali atoms are built into the Si–O network. For example the origin of the fast sodium ion diffusion as
* Corresponding author. E-mail address: [email protected] (A. Meyer). URL: http://www.e13.physik.tu-muenchen.de. 0009-2541/$ - see front matter D 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.chemgeo.2004.08.040
well as the highly non-linear dependence of the viscosity on modifier concentration do not have unambiguous explanations. A first model for alkali silicates assuming a random distribution of the alkali ions (Zachariasen, 1931; Warren and Biscoe, 1938) and thus leading to a continuous disruption of the Si– O4 tetrahedral network, was not in agreement with the observed properties of mass transport. Therefore, different models on the basis of EXAFS (Greaves, 1985) and simulation studies (Angell et al., 1982) were developed proposing an inhomogeneous distribution of the alkali ions in channel- or cluster-like formations also serving as preferential ion conducting pathways.
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In the last decade molecular dynamics (MD) simulations have become a more and more powerful tool in studying dynamics and structure in oxide melts. The main reasons are an increase in computer power and the development of more realistic potentials. There have been several studies on alkali silicate (Huang and Cormack, 1990; Smith et al., 1995; Oviedo and Sanz, 1998) and mixed alkali (Vessal et al., 1992) glasses. In these simulations, potentials based on the potential developed by Vessal were used. These studies resulted in a heterogeneous distribution of the alkali ions in the silica network and showed that the alkali ions are bound to non-bridging oxygens (NBO). Some studies (e. g. Smith et al., 1995) also investigated dynamical properties. However, diffusion coefficients differ by at least one to two orders of magnitude compared to experimental values (Gupta and King, 1966; Jambon and Carron, 1976; Braedt and Frischat, 1988). Nevertheless, activation energies for alkali ion transport are reported to be in good agreement with experimental values. The simulation studies of Oviedo and Sanz (1998) indicated for Na2O concentrations above ~10 mole % microsegregation of sodium supporting the fast sodium ion diffusion. Recently, molecular dynamics simulations (Horbach et al., 2001; Jund et al., 2001; Horbach et al., 2002; Sunyer et al., 2002) using a modified BKS potential originally developed by van Beest et al. (1990) and inelastic neutron scattering (Meyer et al., 2002, 2004; Kargl et al., unpublished) on binary sodium silicate melts and glasses provided evidence for the existence of sodium diffusion channels. Experimental and simulated structure factors of sodium silicate melts exhibit an emerging prepeak around 0.9 21 (Meyer et al., 2004). This prepeak has its origin in the formation of sodium rich channels in the static structure. The channels serve as preferential ion conducting pathways in a relative immobile Si–O matrix. The sodium diffusion channels persist over a broad Na2O concentration range (at least 20–40 mole %). The presence of this channel network in binary alkali silicates provides an explanation for the highly non-linear dependence of viscosity on alkali concentration. The viscosity drops by several orders of magnitude by adding only a few mole % Na2O to SiO2 (e.g. Poole, 1948; Bockris et al., 1956; Knoche et al., 1994). On further Na2O addition, the viscosity
exhibits a relatively weak decrease. Not only can the existence of sodium channels in the static structure account for this fact, but in addition, the channel structure can also explain the fast Na ion transport that is decoupled by several orders of magnitude from the Si–O network dynamics even at typical melt temperatures. Sodium aluminosilicates have been the subject of investigation for a long time, since several geological and technological relevant compositions like albite and jadeite occur in this system. They also act as base components in most natural magmas. Raman scattering investigations performed on glasses and melts elucidate the speciation of Si and the bond length and binding angles of Al as a function of composition and temperature (Neuville and Mysen, 1996). Most of the Al is found in a tetrahedral configuration, charge balanced by Na ions. In compositions close to the tectosilicate join (Na2O /Al2O3 = 1) and in the peraluminous region (Na2O /Al2O3 b 1) different ideas about the structural role of excess aluminum are presented (see e.g. Toplis et al., 1997a). However, the model of a formation of triclusters based on the statistical approach of Lacy (1963) is favoured by investigating the viscosity-concentration and viscosity-temperature behaviour in these systems (Riebling, 1966; Toplis et al., 1997a). In addition, Na, K, Rb, and Cs tracer diffusion experiments on alkali aluminosilicate melts and glasses have been performed comparing transport properties as a function of alkali size, temperature and composition. Here, the highest diffusivities and lowest activation energies are reported for Na (Jambon and Carron, 1976; Roselieb and Jambon, 1997). Nuclear magnetic resonance studies on sodium aluminosilicate glasses and liquids link local structure and sodium dynamics (Georges and Stebbins, 1996). Those authors concluded that in the peralkaline region (Na2O /Al2O3 N1) sodium transport is mainly governed by sodium atoms connected to NBO’s. In the peraluminous region (Na2O /Al2O3 b 1) however, the sodium atoms associated with aluminum atoms for charge balancing dominate sodium diffusion. More recently, neutron diffraction experiments using isotopic substitution combined with reverse Monte Carlo modelling on silicate glasses revealed a heterogeneous distribution of the Li ions in Li2Od Al2O2d 2SiO2 (Cormier et al., 2001).
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Here, we report on inelastic neutron scattering results on sodium aluminosilicate melts. In situ inelastic neutron scattering experiments provide access to structure on intermediate length scales and microscopic dynamics at times ranging from sub picoseconds to several tens of nanoseconds. We discuss the evolution of mass transport properties and structure found in binary silicates with the addition of alumina.
2. Experimental We synthesized four ternary sodium aluminosilicate glasses from reagent grade (99.999%) SiO2, Na2CO3 and Al2O3 powders. The powder mixtures were melted in air at 1400 8C in a 5% Au/Pt crucible for several hours. Sodium aluminosilicates feature a relatively high viscosity even at 1450 8C (Toplis et al., 1997b). Thus, a mixture of sodium silicate and Al2O3 powders was used as starting materials. In this way the synthesis time was significantly reduced. In order to get bubble free and homogeneous samples, the melts were stirred with a Pt-spindle at 1450 8C for more than 24 h in air. Volatilization of Na was negligible as verified by weight measurements of the CO2 free samples before and after the synthesizing process. For each composition we used 40 g of raw material to reduce the compositional error of the weighed sample in the per mill range. Finally, glasses were obtained by cooling the samples in their Ptcrucibles in air from 1450 8C down to room temperature. In the following NxAySz is used as general abbreviation for xNa2Od yAl2O3d zSiO2. Two samples in the peralkaline region N3AS12 and N3AS8 as well as two samples on the tectosilicate join NAS6 and NAS4 were fused. N3AS12 and NAS6 as well as N3AS8 and NAS4 were chosen on the 75 and 66 mole % iso silica join, respectively. An overview of the samples is given in Fig. 1. Inelastic neutron scattering investigations were performed at the time-of-flight spectrometer IN6 at the Institut Laue-Langevin. For the scattering experiments we used a Pt sample holder with a hollow cylindrical sample geometry (22.5 mm outer diameter, 1.25 mm sample thickness, and 30 mm sample height). With these sample dimensions the sample matches the neutron beam size and multiple scattering
.
Fig. 1. Na2O–Al2O3–SiO2 diagram: sodium aluminosilicates ( ) and sodium silicates (o). The dashed line represents the Na2O/ Al2O3 = 1 join. The pointed double dashed lines represent constant Na2O concentration joins, starting from NS3 and NS4, respectively. We note that N3AS8 and NS3 have the same Na2O content.
is negligible. We investigated each sample at room temperature in the glassy state and in the melt up to 1600 K. We used an incoming neutron wavelength of 5.9 2 providing an instrumental energy resolution of 50 AeV (FWHM). Thus, timescales up to 40 ps were accessible. In addition, this configuration provided an accessible wavenumber range of 0.2 21 V q V 1.75 21 at zero energy transfer. The standard Nb resistor high temperature vacuum furnace of the ILL exhibits a temperature gradient over the whole sample at 1600 K that was less than five degrees and a temperature stability within 1 8. Run durations were 6–12 h per temperature. Normalization to a vanadium standard, correction for self-absorption and container scattering and interpolation to constant wavenumbers q yielded the scattering law S( q,x). It is still convoluted with the instrumental energy resolution, that is given by the room temperature measurements. The density correlation function S( q,t) is obtained by Fourier deconvolution of the scattering law S( q,x).1 The density correlation function correlates the spatial Fourier transform of the particle density,
1 The scattering law and the measured instrumental energy resolution are energy Fourier transformed. For the doconvolution the Fourier transform of the scattering law is divided by the Fourier transform of the resolution function.
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P Y Y Y Y q r ðt Þ ¼ i dðr R i ðt ÞÞ, i.e. the position, R i , of each particle, i, at time t, with its values at time 0: S ðq; t Þ ¼ hq4q ðt Þqq i=hjqq j2 i
ð1Þ
We note that the particle density is directly accessible in molecular dynamics simulations. Beside dynamic information, neutron time-of-flight data also provide structural information. Since inelastic scattering is well separated from the elastic signal, the elastic structure factor S( q,x = 0) is obtained by integrating the scattering law over the instrumental energy resolution function: Z S ðq; x ¼ 0Þ ¼ dx S ðq; xÞ: ð2Þ res:
The elastic structure factor is equal to the static structure factor S( q) multiplied by the Debye-Waller factor f q .2
3. Results We investigated the elastic structure factor of N3AS12, NAS4, N3AS8 and NAS6 at room temperature and at 1600 K in the melt. All structure factors (in the melt and in the glass) contain incoherent as well as coherent scattering contributions. The incoherent contributions result in a flat background in the static structure factor. Si and O exclusively scatter coherently. Scattering on the Al atoms is dominantly coherent with a negligible incoherent contribution. Na features both incoherent as well as coherent scattering. The elastic structure factors exhibit a flat background at small q. Similar to the binary sodium silicates at small wavevectors, incoherent scattering on sodium is the dominant contribution to the signal. The elastic structure factors of the ternary compositions are compared with their binary base compositions NS2 and NS3 at 1600 K taken from Meyer et al. (2002, 2004). In the binary silicate melts the elastic structure factors exhibit a prepeak at f0.9 21 below the first sharp diffraction peak (FSDP) at 1.7 21. The 2
Neglecting in good approximation the wings of the broad quasielastic line in the signal from the incoherent scattering on the diffusing sodium atoms.
FSDP in pure silica represents mean Si–O4 tetrahedra distances (Elliot, 1991). In binary silicates neutron scattering shows that the prepeak at f0.9 21 is emerging with increasing temperature. In the melt is position is constant, but its height is increasing with increasing Na concentration for the studied compositions in the range from NS4 to NS2. MD simulations performed at experimental densities exhibit qualitatively similar behaviour of the prepeak as a function of temperature and Na2O concentration (Meyer et al., 2004). Although the measured and simulated elastic structure factors of the binary sodium silicates in the glass do not display a pronounced prepeak, the channel structure is still present. The simulation shows that only with decreasing density do the positive and negative contributions of the six partial structure factors summed weighted by the neutron scattering length no longer cancel each other at f0.9 21. Therefore, this intermediate range order is in standard neutron (and X-ray) scattering experiments only observable at high temperatures in the equilibrium melt. A comparison of MD simulations performed at experimental densities and our inelastic neutron scattering results on binary silicates shows that the prepeak arises from a formation of sodium rich channels in the static structure (Meyer et al., 2004). Its position represents a characteristic length scale of this channel structure. Typical distances between channels are about 6–8 2. Fig. 2 displays the elastic structure factors of the binary and ternary silicates at 1600 K. With increasing alumina content S( q,x = 0) the first sharp diffraction peak (FSDP) at f1.6 21 is increasing and the height of the prepeak at 0.9 21 is decreasing. In the 66 mole % SiO2 (Fig. 2 left) and 75 mole % SiO2 (Fig. 2 right) containing samples the increase of the prepeak for the Na2O /Al2O3 =3 compositions with temperature is far less pronounced than for the binary sodium silicates. For NAS6 (albite) and NAS4 (jadeite) we have no experimental evidence for a prepeak, neither in the melt nor in the glass. The room temperature spectra of the Na2O/ Al2O3 =3 samples are similar to the S( q,x=0) of the Na2O /Al2O3 = 1 samples below ~1.2 21. With increasing temperature the elastic structure factors should display a decrease in their intensities due to the decreasing Debye-Waller factor. This effect is proportional to exp{q 2hu 2i} and thus, is more pronounced
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Fig. 2. Elastic structure factors of the 66 mole % (left) and 75 mole % (right) SiO2 containing samples at 1600 K. Data were obtained by neutron time-of-flight spectroscopy. The solid lines represent the elastic structure factors for the tectosilicate sample NAS6 at room temperature. For both iso silica joins the prepeak at 0.9 21 is decreasing with increasing Al2O3 content.
at higher q-values. This behaviour becomes evident in the FSDP (see Fig. 2). Neutron backscattering on molten sodium disilicate resulted in mean relaxation times hsi for the structural Si–O network relaxation of about 10 ns at 1600 K (Meyer et al., 2002). A comparison with viscosity data indicates even larger network relaxation times for the other silicate melts discussed here. Therefore, the structural relaxation of the silicate network is too slow to be resolved in our time-of-flight experiment and will reflect itself in a strong elastic contribution to the signal. In contrast, sodium relaxation is on a 10-ps time scale at 1600 K. In neutron time-of-flight spectroscopy this will be visible as a broad quasielastic contribution in S( q,x).
Fig. 3 displays the density correlation functions S( q,t) for NS3, N3AS12, NS2, and N3AS8 at 1600 K and q =0.5 21. At q values below ~0.6 21 the incoherent scattering on Na is the dominant contribution to the signal. Solid lines are fits with F( q,t) (Eq. (3)). The fit function consists of two contributions, a stretched exponential function accounting for the quasielastic scattering contribution and a constant accounting for the elastic scattering: h i F ðq; t Þ ¼ b þ a n ; exp ðt=hsiÞb : ð3Þ hsi denominates the mean relaxation time, b is the stretching exponent, a is the quasielastic amplitude and b is elastic scattering contribution. The density correlation functions S( q, t) are best described by Eq.
Fig. 3. Sodium relaxation in sodium di- and trisilicate melts and in the Na2O /Al2O3 = 3 compositions N3AS8 and N3AS12 as seen by inelastic neutron scattering. Solid lines represent fits to the density correlation functions S( q, t) with Eq. (3) and a stretching exponent b of 0.75.
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(3) with a sample independent stretching exponent bf0.75. A stretching exponent b b1 indicates that Na diffusion is not a simple activated process. The density correlation functions S( q,t) are plotted with a sum of (a+b) as the upper, and b as the lower yscale boundary, respectively. Thus, sodium relaxation times of different samples at the same temperature can be directly compared. The density correlation function of N3AS12 at 0.5 21 (Fig. 3) exhibits a decrease in the relaxation time by a factor of 2.5 as compared to NS3. In albite and jadeite (not plotted), Na-relaxation times are not in the experimentally accessible region of IN6. In albite they are estimated to be an order of magnitude smaller than the Na relaxation times of NS3. In aluminosilicate melts obtained by substituting a quarter and half of the Na2O in NS2 by Al2O3 the dynamical picture is slightly different to the ternary composition based on NS3. The Na-relaxation is decreasing by approximately a factor of two between NS2 and N3AS8 (Fig. 3). However, the increase of Na relaxation times between NS2 (Meyer et al., 2002) and NAS4 (not plotted) is far less pronounced compared to the increase observed between NS3 and NAS6.
4. Discussion Earlier investigations of the binary sodium silicate melts NS2, NS3, and NS4 revealed the existence of a network of sodium diffusion channels in the static structure, experimentally visible in a prepeak at f0.9 21 (Meyer et al., 2004). In the melt at 1600 K, sodium relaxation is on a picosecond timescale. In contrast, relaxation times of the Si–O network are on a nanosecond timescale (Meyer et al., 2002; Kargl et al., unpublished). Thus, the mobility of the sodium atoms is decoupled by about three orders of magnitude from the Si–O relaxation. The channel structure for Na found over a broad Na-concentration range is a key feature in understanding the mass transport in binary silicate melts. Here, we discuss how the partial substitution of the network modifier Na2O in sodium silicates by Al2O3 alters the network of sodium diffusion channels. For sodium aluminosilicates on the Na2O /Al2O3 =3 join, Fig. 2 displays a prepeak emerging with increasing temperature similar to the behaviour in the alkali silicates. However, the increase of the prepeak with temperature is less pronounced than
in binary sodium silicates. In molten NAS6 and NAS4 the elastic structure factors do not show a prepeak. In binary sodium silicates, the mean sodium relaxation times follow a q2 dependence in the low q limit even for q values up to f0.8 21. Therefore in the case of incoherent scattering a self-diffusion coefficient D can be obtained (Boon and Yip, 1991). At 1600 K the sodium self-diffusion coefficient D =1/( q2s q ) is D =3.8F0.3 109 m2 s1 for NS2 and D =2.1F0.3
109 m2 s1 for NS3 (Kargl et al., unpublished). These values agree well with tracer diffusion experiments (Gupta and King, 1966; Braedt and Frischat, 1988). In the aluminosilicates at q values below 0.5 21 the relaxation times exceed the instrumentally accessible time window. Thus, experimental proof of the validity of the q2 dependence is not possible. To estimate the sodium self-diffusion coefficient, we assume that the proportionality of D to 1/(q 2s q ) is also valid for the aluminosilicates at q =0.5 21. Using this relation the following diffusion coefficients for our samples are obtained: D=1.8F0.2 109 m2 s1 (N3AS8) and D=1.0F0.2 109 m2 s1 (N3AS12). At 1600 K the separation of alkali ion relaxation and the network dynamics is even more pronounced in sodium aluminosilicates than in sodium silicates. From the increase in the viscosity, the decrease in the prepeak and the decreasing sodium mobility we conclude that the channel structure present in alkali silicate melts become more and more disrupted with increasing alumina content at a fixed SiO2 concentration. Along the constant Na2O content joins (Fig. 1) relaxation times for Na2O decrease by 20% between NS3 and N3AS8 at 1600 K. In addition, the alumina content is increasing from 0 mole % in NS3 to 8 mole % in N3AS8. Comparing data at constant alumina content, Na relaxation times decrease with increasing Na2O concentration. Along the constant Na/(Na+Al) joins Na-relaxation times are decreasing with decreasing silica concentration. Comparing different joins we observe a non-linear behaviour of relaxation times with increasing alumina content. The latter effect is less pronounced at lower silica content.
5. Conclusion and outlook Investigating sodium aluminosilicates with inelastic neutron neutron scattering has shown itself to be a
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highly versatile method for revealing changes in microscopic dynamics and intermediate range structure with increasing alumina content. The prepeak assigned from MD simulations on binary silicates (Horbach et al., 2002; Meyer et al., 2004) to originate from the formation of sodium rich channels, decreasing in sodium aluminosilicates with increasing alumina content. The mobility of the sodium atoms decreases with increasing Al2 O 3 content. This decrease in the sodium relaxation times is a nonlinear function of SiO2, Na2O and Al2O3 concentration. The decrease in the mobility of the sodium atoms, the increasing viscosity and the decreasing prepeak in the structure factor indicates that the addition of Al2O3 disrupts the sodium channel structure. In ternary aluminosilicates, Na atoms are expected to charge balance Al-tetrahedra (Neuville and Mysen, 1996; Georges and Stebbins, 1996). Therefore, one could think of two types of chemically different surroundings for the Na atoms with a slower relaxation of the Na atoms that charge balance Al. The quasielastic amplitude arising from the fast Na dynamics would then be expected to decrease by more than 25% from NS3 to N3AS12. An inelastic neutron scattering experiment to address this particular question is in preparation. As compared to IN6 the new time-of-flight spectrometer of the new neutron source of the Technical University Munich—the FRM-II— exhibits a better energy resolution and an extended qrange toward small wavenumbers. A combined study using neutron scattering and molecular dynamics has revealed many features of the interplay of structure and microscopic dynamics in binary sodium silicates (Meyer et al., 2004). In the case of sodium aluminosilicates the accuracy of a molecular dynamics model can be assessed by our neutron scattering data. The information obtained by MD simulations will then elucidate the structure and mass transport–property relationship in more detail also in sodium aluminosililcate melts.
Acknowledgements We thank D.B. Dingwell, K.-U. Hess, J. Horbach and W. Kob for stimulating discussions and H.
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Schober for his support during the experiments performed at the Institut Laue Langevin. We thank the ILL for providing the instruments and the possibility to perform our investigations. We acknowledge financial support by the DFG (SP 1055: Bildung, Transport und Differenzierung von Silikatschmelzen) under project number ME 1958/6-1. [RR]
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