- Email: [email protected]
Structural changes between soda-lime silicate glass and melt
Journal of Non-Crystalline Solids 357 (2011) 926–931
Contents lists available at ScienceDirect
Journal of Non-Crystalline Solids j o u r n a l h o m e p a g e : w w w. e l s ev i e r. c o m / l o c a t e / j n o n c r y s o l
Structural changes between soda-lime silicate glass and melt Laurent Cormier a,⁎, Georges Calas a, Brigitte Beuneu b a
Institut de Minéralogie et de Physique des Milieux Condensés, CNRS UMR 7590, Université Pierre et Marie Curie–Paris 6, Université Denis Diderot–Paris 7, IPGP, 4 place Jussieu, 75005 Paris, France b Laboratoire Léon Brillouin, C.E. Saclay, 91191 Gif-sur-Yvette, France
a r t i c l e
i n f o
Article history: Received 6 July 2010 Received in revised form 14 October 2010 Available online 23 November 2010 Keywords: Structure; Silicate; Neutron scattering
a b s t r a c t Neutron diffraction has been used to study the structure of a glass and melt of composition 75SiO2-15Na2O10CaO. RMC modeling of the neutron and X-ray diffraction data for the glass allowed the determination of the Na and Ca environment. The structure has been investigated at 300K, just below the glass transition at 823 K and in the melt at 1273 K. The short range order does not present important modifications with temperature while significant reorganization appears at the medium range order. These latter changes can be associated with the Si and O pairs and indicate the relaxation of the silicate network. This indicates that the glass formation involved structural rearrangement during cooling. © 2010 Elsevier B.V. All rights reserved.
1. Introduction Soda-lime silica glass, easily synthesized as a homogeneous glass, is probably the technologically most important oxide glass, with a wide range of applications, including structural flat glass, packaging, insulating materials, novel electric devices or bioactive materials. Key properties include high stability against crystallization, high viscosity at the liquidus temperature permitting glass forming, high potential for fiber drawing and compositional control of index of refraction and coefficient of thermal expansion [1]. Many of these physical properties, such as viscosity, electrical conductivity and thermal expansion, are intimately related to the structure of the glass/melt systems, depending on the working temperature. Despite their industrial importance, the detailed structure of sodalime silica glass has been poorly investigated. The pioneering X-ray diffraction work performed by Warren and Biscoe depicted the structure as a continuous random silicate network [2,3], formed by rigid corner-sharing SiO4 tetrahedra. Alkali and alkaline-earth elements are filling the holes in this random network, surrounded by about 6 and 7 oxygens for Na and Ca atoms, respectively. These cations act as network modifiers, reducing the degree of connectivity in the network by replacing bridging oxygens (BOs) by Non-Bridging Oxygens (NBOs). The present understanding of the structure of alkali and alkaline-earth silicate glasses does not correspond anymore to a homogeneous distribution of these cations within the silicate network. Experimental evidence by X-ray absorption spectroscopy [4,5] or neutron diffraction [6,7] indicate the existence of silica-rich and alkali/alkaline-earth-rich regions. Recent 17O NMR experiments
⁎ Corresponding author. Tel.: + 33 1 44 27 52 39. E-mail address: [email protected] (L. Cormier). 0022-3093/$ – see front matter © 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.jnoncrysol.2010.10.014
on soda-lime silicate glasses have shown a non-random distribution of Ca and Na, with the prevalence of Na–Ca pairs [8]. 29Si NMR suggests that Ca2+ cations are preferentially bonding to NBOs [9]. Conversely, Molecular Dynamics (MD) simulations indicate random Ca–Na pairing [10]. Cation–cation interactions, cation–terahedral network interactions and cation coordination numbers are important structural parameters that could impact strongly transport properties. For instance, a “mixed alkali–alkaline earth anomaly” [11] affects the ionic mobility: the mobility of Ca2+ ions is enhanced by the presence of Na+ ions. A similar local environment of Na and Ca ions has been determined for 3xCaO-3(1 − x)Na2O-4SiO2 glasses using neutron diffraction and Reverse Monte Carlo modeling [12], with the presence of two cation–oxygen contributions at 2.25 and 2.65 Å indicating that Ca/Na sites are interchangeable, which enhances cation mobilities. It is expected that the structure of glasses and melts differs because the configurational entropy above the liquid temperatures is usually twice or three times as great as the entropy frozen in at the glass transition [13]. Cation environment, medium range distribution or silicate network organization can be temperature dependent. Such structural modifications upon temperatures will impact ion mobility and thermomechanical properties [14] and are particularly important for shaping and molding of glasses. However, by contrast to borate and borosilicate glass systems, in which the coordination change of B at high temperature modifies the role of cations [15,16], temperaturedriven structural changes in silicate glass/melt systems are mostly subtle: the structural disordering of cations sites at high temperature is not affected by the glass transition, as changes in the silicate network occur only above the glass transition and affect mainly the medium range order (MRO) [17,18]. This paper describes the structure of a soda-lime silicate glass and its corresponding melt using neutron and X-ray diffraction and
L. Cormier et al. / Journal of Non-Crystalline Solids 357 (2011) 926–931
Reverse Monte Carlo modeling. High temperature neutron diffraction data show the significant evolution of the structure above the glass transition temperature up to the liquid state. The composition, close to that of a window glass, allows to infer some conclusions for revealing significant changes with temperatures. 2. Experiments 2.1. Sample preparation A glass of composition 75SiO2-15Na2O-10CaO was synthesized by mixing dried starting materials (SiO2, Na2CO3 and CaCO3). After a slow heating to decompose the carbonates at 850 °C overnight, the mixture was melted in a 90Pt/10Rh crucible at 1200 °C for 2 h. The glass was obtained by rapidly immersing the bottom of the crucible into water. The sample was then ground and remelted twice in the same conditions to ensure a good homogeneity. The final glass appears bubble-free, uncolored and transparent. The composition was checked using electron microprobe microanalyser (CAMECA SX50) at the Camparis Centre (Université Pierre et Marie Curie, France) with an accuracy of ±0.3 mol%. The actual composition of the glass is 73.36 SiO2 ∙ 14.86 Na2O ∙ 11.78 CaO. The room temperature density was obtained in toluene using the Archimedes principle, giving a value of 2.484 ± 0.005 g cm−3. Theoretical melt density at 1000 °C has been calculated using a recent model [19], leading to a value of 2.380 g cm−3. The glass transition is taken at Tg= 835 K according to [20]. 2.2. Neutron diffraction Neutron diffraction experiments have been carried out on the 7 C2 diffractometer at the Orphée reactor of the Laboratoire Léon Brillouin (Saclay, France), using hot neutrons of wavelength 0.729 Å. Approximately 6.5 g of glass powders were loaded into a cylindrical vanadium cell of 11 mm in diameter, at the center of a cylindrical vanadium furnace. Measurements were performed from room temperature up to 1273 K. As detailed in [16,17], data correction includes the scattering from the empty can in the furnace at 300 K and 1273 K, from the empty furnace at 300 K, together with a background correction. The data reduction yields the total structure factor, FN(Q), which is the scattering term of the total neutron cross section (the notations are those used in [21]). The correlation function, DN(r), is obtained by Fourier transformation of FN(Q): ∞
N D ðr Þ = 2 ∫ Q F ðQ ÞM ðQ Þ sinðQr ÞdQ π 0
927
function, D X(r), have been previously explicated [24]. The Fourier transform is calculated using an exponential function, exp(−αQ2) with α = 0.005, as the modification function. 2.4. Reverse Monte Carlo modeling A structural model has been built using the Reverse Monte Carlo (RMC) technique [25] by combining neutron and X-ray diffraction data and coordination constraints. Starting configurations were obtained using MD simulation (DL_POLY code) to provide more reliable models than those obtained by standard RMC modeling [26,27]. MD calculations were performed on a box of 4640 atoms, using the interaction potentials from [28]. The liquid was equilibrated at high temperature (3000 K) and then cooled down to 300 K with a cooling rate of 9 ∙ 1012 K s−1. The initial glass configuration corresponds to a microcanonical (NVE) ensemble obtained at 300 K and the initial melt configuration corresponds to an isothermal-isobaric (NPT) ensemble obtained at 923 K. During the RMC modeling, all Si atoms were constrained to be coordinated to four O atoms. The closest approach distances used for these simulations are 1.8 Å for Si–O, 2.1 Å for Na–O and Ca–O, 2.6 for Si–Na, Si–Ca, Na–Na, Na–Ca, and Ca–Ca and 2.8 Å for Si–Si. The RMC technique has been previously described [29] and consists in minimizing the squared difference between experimental and calculated structure factors by moving the atoms randomly. This ultimately gives atomic models in quantitative agreement with experimental data. In the present study, both neutron and X-ray diffraction data were used to constrain the RMC fitting of the glass while only neutron diffraction data were available for the RMC fitting of the melt. 3. Results 3.1. Total structure factors The total structure factors at room and high temperatures are shown in Fig. 1. The high-Q range (Q N 5 Å−1), which describes the short range order, is similar for all temperatures. The low-Q region,
ð1Þ
where M(Q) is a modification function to limit the truncation effects. A Lorch function was chosen as the modification function [22]. The DN(r) function is defined as a sum of the partial pair distribution functions (PPDFs), gij(r), corresponding to the correlations between atoms i and j: h i N D ðr Þ = 4πrρ0 ∑ ci cj bi bj gij ðr Þ−1 i; j
ð2Þ
with ρ0 the number density, ci and bi the atomic concentration and the bound coherent scattering length for species i. 2.3. X-ray diffraction X-ray diffraction measurements were carried out using a diffractometer (PANalytical X'Pert PRO) operating with a MoKα radiation (λ = 0.7093 Å). Data were measured in the angular range 2 b 2θ b 148° (Q range of 0.3 b Q b 17 Å−1), then corrected for polarization and absorption, Compton scattering and normalized using the Krogh– Moe–Norman method to obtain the weighted structure factor F X(Q) [23]. The X-ray structure factor, F X(Q), and the X-ray correlation
Fig. 1. Total structure factors of the soda-lime silicate glass obtained at different temperatures up to the liquid state. Insert: comparison between the room temperature structure factors of the pristine glass (300 K) and the sample recovered after the cooling in the vanadium can (300 K d).
928
L. Cormier et al. / Journal of Non-Crystalline Solids 357 (2011) 926–931
related to medium range correlation (4–20 Å), is mainly characterized by a sharp peak Qp near 1.72 ± 0.02 Å−1, involving preferred arrangements between silicate units and/or alkali ions. The dampening of the oscillations at high temperature is due to both static and thermal disorder. Even if its origin is still debated [30,31], the low-Q peak can be undoubtedly assigned to the MRO: Q p is associated with density fluctuations over a repeat distance D = 2π / Q p with an uncertainty on D given by σ(D) = 2πσ (Q p) / Q2p, where σ(Q p) is the uncertainty on the position of the first peak [32]. Contrary to other features in the FN(Q) function, Q p peak remains almost unchanged in position and intensity in the glassy state up to 823 K, while in the liquid state it is shifted to 1.65 ± 0.02 Å−1, its intensity is reduced and its width broadened. The characteristic repeat distance increases from D = 3.65 ± 0.08 Å to 3.81 ± 0.08 Å between the glass and liquid state. The insert in Fig. 1 compares the structure factors before and after the melting. This shows that the glass structure is perfectly recovered after the heat treatment of the sample in the vanadium can and that any V contamination is negligible.
shifted in two contributions at 7.1 and 7.5 Å. The structural origin of these modifications must be discussed through RMC modeling.
3.3. RMC models
The DN(r) correlation functions at room and high temperatures are shown in Fig. 2. The position of the first peak, corresponding to the intra-tetrahedral Si–O distances, remains unchanged between 300 K and 823 K at 1.629 ± 0.005 Å and then increases up to 1.635 ± 0.005 Å at 1273 K. The peak corresponding mainly to the O–O pair is continuously shifting from 2.65 to 2.67 Å with temperature. There are some subtle but important changes beyond this peak. Difference functions between the DN(r) functions at 823 K and 300 K and between 1273 K and 823 K can be calculated and show some changes beyond the O–O peak (Fig. 2, lower curves). With increasing temperature we observe a decrease of intensity around 3.6 Å and an increase of intensity around 3.05 Å. The peak at 4.1 Å is slightly affected by temperature; the peak at 4.9 Å decreases in intensity and is shifted to high-r values; the intensity of the peak at 6.3 Å surprisingly increases in temperature with a slight shift to high-r values; the peak at 7.3 Å has a reduced intensity and seems to be
RMC modeling was performed using neutron diffraction data and the comparison between the experimental structure factors and those calculated from the RMC models is plotted in Fig. 3, showing that a good fit is obtained. X-ray diffraction data, only available at room temperature, were added to the RMC procedure for the glass. Fig. 4 shows the partial structure factors Sij(Q) and PPDFs, gij(r), calculated from the RMC structural models, which are mainly weighted by the partials associated with the silicate network. In particular, the Na–Na, Na–Ca and Ca–Ca correlations have a small weighting factor and additional structural information is highly desirable to get a more accurate description of the cation distribution. X-ray diffraction slightly improve the Ca-centered pairs as Ca is more weighted by X-rays than the other glass components. The total structure factors are dominated mainly by the Si–O and O–O pairs. The small variations at low-Q values explain the shift of the first Qp peak observed in the total structure factors FN(Q) with temperature. The first peak in SO–O(Q) is shifted by −0.12 Å−1 but its intensity is not changed at high temperature, which explain a shift in position. The first peak in SSi–O(Q) is shifted by −0.09 Å−1 and its intensity decreases upon temperature, which mainly explains the change in intensity. It can be noted that the Si–Si pair is unchanged in position and intensity. The gij(r) functions show few changes with temperature. We observed a decrease in intensity and a broadening of the first peak in gSi–O(r). Given the variation in the Si–O bond length, a local coefficient of thermal expansion (CTE) of (6±1)×10−6 K−1 is obtained. An interesting trend can be derived by comparison with local CTE values from the literature. This can be compared to the value obtained from neutron total scattering measurements of SiO2 polymorphs, (2.2±0.4)×10−6 K−1 [33] or to the value determined for the potassium disilicate glass, (9±1)×10−6 K−1 [17]. This trend indicates that local CTE tends to increase with the size of the modifying cation.
Fig. 2. Total correlation functions of the soda-lime silicate glass and melt, obtained by Fourier Transform of the total structure factors multiplied by the Lorch modification function, on the Q range 0.5–15.4 Å−1. The two lower curves represent the difference functions between DN(r) functions at 823 K and 300 K and between DN(r) functions at 1273 K and 823 K.
Fig. 3. Comparison between the experimental structure factors and those calculated from the RMC models. The RMC models at room temperature have been obtained by fitting simultaneously the structure factors obtained by neutron and X-ray diffraction, while only neutron diffraction data are available at 823 K and 1273 K.
3.2. Total correlation functions
L. Cormier et al. / Journal of Non-Crystalline Solids 357 (2011) 926–931
929
Fig. 5. From top to bottom, changes in the region 3–10 Å with temperature in the correlation functions for the O–O, Si–O and Si–Si partial pair distribution functions and for the experimental total neutron correlation functions, for the glass (in blue) and the melt (in red). The percentages indicate the relative contribution of each pair in the neutron data.
second contribution discernible at 2.61–2.65 Å. This is in agreement with a previous investigation of soda-lime silicate glasses with lower SiO2 content, in which Na–O and Ca–O correlations were similar with two contributions at 2.25 Å and 2.65 Å [12]. The coordination number for modifier elements is difficult to determine considering an ill-defined first coordination shell [34]. With a cut-off distance of 3.2 Å, the coordination number is 4.9 and 6.0 for Na and Ca, respectively. The Na–O and Ca–O distances tend to become broader and are shifted by −0.1 Å with increasing temperatures. The running coordination number for Na–O and Ca–O are shown in Fig. 6 for the glass and the melt. This shows that the coordination number of these two elements remain unchanged with increasing temperatures.
Fig. 4. (a) Partial structure factors Sij(Q) for the glass (in blue) and the melt (in red). (b) Partial pair distribution functions gij(r) for the glass (in blue) and the melt (in red). The percentages indicate the relative contribution of each pairs in the neutron data.
The peak at 2.67 Å in gO–O(r) is broadened in the melt, which contributes to the increased contribution around 3 Å on the experimental DN(r) functions. Other modifications of the silicate framework are indicated by the shift of the Si–Si peak from 3.12 to 3.19 Å. Several changes at MRO concern the pairs associated with the silicate network (Si–O, O–O and Si–Si) with some decrease in intensity in the liquid state only for some distances, which are indicated by arrows in Fig. 5. These variations correspond well with those in the experimental DN(r) correlation functions. However, the changes around 6.4 Å and 7.2 Å in the experimental data are not explained by these models. This suggests that they are not due to modifications of the silicate framework and may be due to cationrelated changes. The Na–O and Ca–O pairs present a first peak at 2.25 Å and 2.35 Å, respectively, in the glass. These peaks extend to large-r values with a
Fig. 6. Running coordination numbers for Na and Ca as a function of temperature, obtained from the RMC models.
930
L. Cormier et al. / Journal of Non-Crystalline Solids 357 (2011) 926–931
4. Discussion 4.1. Glass structure Neutron diffraction data allow the generation of structural models using RMC modeling. In these models, all silicon atoms are four-fold coordinated (initial constraints) and SiO4 tetrahedra form a cornersharing network, with partial depolymerization associated with the presence of Ca and Na atoms. Na and Ca environments are distorted with two (Na,Ca)–O contributions at 2.25 and 2.65 Å. This agrees with previous studies [12,35,36]. The coordination number around Na is slightly lower than that of Ca. However, the two sites are similar and Ca can easily substitute at Na sites. This is in accordance with a medium range structure almost unchanged by the substitution of Na by Ca [10,12]. It has also been shown that Ca has a greater propensity for coordination by NBO than Na [10,37]. Na and Ca local environments have been determined experimentally and by MD simulations for compositions close to that investigated in this study (Table 1) and an overall good agreement is found for these results. The modifier–modifier PPDFs are weakly weighted but all of them show a first broad contribution between 3 and 4 Å (Fig. 4b). This is a smaller separation than required by a homogeneous distribution and it is usually interpreted using the modified random network model with preferential regions concentrated with modifiers and NBOs [5]. A nonrandom distribution of Ca and Na is also consistent with 17O and 23Na NMR data [8] and configurational entropy variations, which do not follow an ideal mixing term [38]. This non-random distribution differs from the cation random distribution observed in other mixed cation glasses, such as in Ca–Mg silicate glasses [39,40]. The Ca–Na PPDF exhibits a distinct contribution between 3 and 4 Å. This indicates an extensive mixing between Ca and Na atoms. Similarly, NMR data concluded that the Ca–Na distribution around NBOs shows neither complete preference for Na–Ca pairs nor significant clustering into Ca- and Na-rich regions [8]. However, our RMC models are slightly different to the NMR interpretation for a preferential Na–Ca pairing. Indeed, if we consider the number of nearest neighbor around Na or Ca, we observe that around Na atoms there are more Na atoms (84%) than expected from a random distribution (75%). Similarly around Ca atoms, there are more Ca atoms (32%) than expected from a random distribution (25%). Thus, based on the RMC modeling of the diffraction data, there is a slight tendency to have atoms of same type close to each other. Though Ca has a lower mobility than Na, the mobility of Ca2+ ions is enhanced when replaced by Na+ ions which have a positive coupling effects on the movements of divalent cations [11]. The transport of mobile modifier ions in silicate glasses can be considered as a hopping process, based on the existence of well-defined ionic sites [41]. As the local environment of Na and Ca is similar, it was
suggested that the lack of mismatch sites for Ca and Na could improve the diffusion of Ca2+ ions which can easily use empty Na+ sites [12]. The pathways for diffusion appear also from the non-homogeneous distribution of the Ca-Na cations within the silicate network. Below the glass transition temperature, ion mobility takes place in a fixed environment provided by the network structure. At higher temperature, the relaxation of the network increases the topological disorder and opens up the structure. This leads to the formation of more available cation sites, which facilitates ionic diffusion. 4.2. Modification with increasing temperature Neutron total diffraction provides an average, or static, structural picture of the system, corresponding to the sum of a very large number of snap-shots. This method allows the investigation of the structural changes resulting from the thermodynamic reequilibration of the system with temperature variations. The shift in position of the Qp peak can be mainly attributed to the O–O and Si–O pairs. This indicates a relaxation of the silicate network. Other structural modifications can be seen in the total correlation functions. Clearly the changes in Fig. 2 do not correspond to a disordering of the structure due only to thermal effects. The increase of the intensity of some contributions (e.g. at 6.3 Å) indicate some important modification of the structure with temperature, that should be associated with structural relaxation of the silicate network. The RMC models can at least partly reproduce this modification of the silicate network between the glass and the liquid. As shown in Fig. 5, some features in the gSi–O(r) and gO–O(r) functions disappear at specific distances corresponding to the main changes in the total DN(r) correlation functions. The main consequence of the introduction of modifying oxides is to create NBOs and to depolymerize the network leading to the formation of various Qn species, where Qn is a SiO4 tetrahedron containing n BOs. The number of NBO and BO is determined from the RMC models and reported in Table 2 for the glass and melt. The fractions of NBO and BO do not change with temperature and show no major deviation from the values expected based on stoichiometric considerations. The Qn species distributions calculated from the RMC models are compared with previous findings from experiments or simulations on Table 2. The variations with temperature are small and discrepancies can be observed with experiments, which can be due to a difference in composition or to a difference inherited from the MD simulations used as the starting configuration in the present RMC modeling. It should be noted that these Qn species are poorly constrained by the total neutron and X-ray structure factors and thus only slightly modified compared to the initial MD simulations. The substitution of Ca by Na in silicate glasses increases the configurational entropy, which suggests an increase of the disorder and/or a change in the glass network polymerization [38]. Raman data indicate the increase of Q2 species with increasing CaO content.
Table 1 Distances and coordination numbers for Na–O and Ca–O pairs determined by various modelling and simulation investigations in soda–lime silicate glasses. Compositions
Pairs
Distance
CN
3xCaO-3(1 − x)Na2O-4SiO2
Na–O
2.25 2.65 2.25 2.65 2,31 2.28
1.7 ± 0.3 4.2 ± 0.8 1.8 ± 0.4 5.0 + 1.0 5.6 + 0.2 (rc = 3.16 Å) 6.2 ± 0.3 (rc = 3.16 Å) 5.2 (rc = 3.1 Å) 5.8 (rc = 3.03 Å) 5.6 (rc = 3.1 Å) 5.7 (rc = 3.1 Å) 5.4 (rc = 3.1 Å) 5.9 (rc = 3.1 Å) 4.95 (rc = 3.2 Å) 6.0 (rc = 3.2 Å)
Ca–O 11.2CaO-15.3Na2O-73.5SiO2 10CaO-15Na2O-75SiO2 15CaO-10Na2O-75SiO2 15CaO-10Na2O-75SiO2 10CaO-15Na2O-75SiO2
Na–O Ca–O Na–O Ca–O Na–O Ca–O Na–O Ca–O Na–O Ca–O
2.35 2.30 2.35 2.37 2.25 2.35
Method
Ref.
5.9
Neutron + RMC
[12]
6.8
Neutron + RMC
[12]
MD MD MD MD MD MD MD
[44] [44] [10,45,46] [10,45,46] [37] [37] [47]
ab initio ab initio
ab initio ab initio
Neutron+RMC Neutron+RMC
Present work Present work
L. Cormier et al. / Journal of Non-Crystalline Solids 357 (2011) 926–931
931
Table 2 Comparison for various modelling and simulation investigations of the number of bridging (BO) and non–bridging (NBO) oxygens and of the Qn distribution (with n the number of BO in a SiO4 tetrahedra) in soda–lime silicate glasses. Compositions 11.2CaO-15.3Na2O-73.5SiO2 10CaO-15Na2O-75SiO2 15CaO-10Na2O-75SiO2 9.1CaO-22.7Na2O-68.2SiO2 10CaO-15Na2O-75SiO2 glass 10CaO-15Na2O-75SiO2 melt 10CaO-15Na2O-75SiO2
BO
NBO
Q0
Q1
Q2
Q3
Q4
Method
Ref.
7±4 10.9
57 ± 10 46.2
36 ± 4 42.7
2 10.17 10.0
86 41.75 41.9
12 46.7 47.2
MD ab initio MD MD ab initio NMR Neutron+RMC Neutron+RMC Random model
[44] [10,45,46] [37] [9] Present work Present work
71.0
29.0
0
0 0.2
64.0 71.5 71.5 71.3
36.0 28.5 28.5 28.7
0 0 0
0 1.4 0.9
It is often considered that diffraction data show little change with temperature and that the “glass simply inherits the liquid structure and its lack of long range order” [42]. Our diffraction data indicate that the structure of glasses and liquids show significant differences and that the modifications appear already close to the glass transition temperature. This is direct evidence that the structure is affected during the cooling of the liquid and that structural organization can now be taken into account in the glass transition process. Recently, it was shown a direct connection between structural ordering and the dynamic heterogeneities that accompany the kinetics slowing down responsible for the steep increase in the viscosity as approaching the glass transition [43]. The determination of these structural changes is still difficult to establish for multicomponent silicate glasses as changes mainly affect MRO, a range of distances that is yet experimentally challenging to measure in glasses. A better understanding of glass/liquid modifications will be of paramount importance to establish a relationship between the structure and the dynamics in the supercooled region. Fortunately, the development of high temperature devices should increase the number and accuracy of structural experiments and improve our knowledge of structural modifications operating upon temperature. 5. Conclusions The structure of a soda-lime silicate has been investigated in the glassy and liquid state using neutron diffraction, X-ray diffraction and reverse Monte Carlo modeling. Our results give a coordination number close to 6 for Ca atoms and close to 5 for Na atoms, with little variations with temperature. The correlation functions between the glass and the liquid show significant modifications at the medium range scale (3–7 Å) that cannot only be attributed to thermal disordering. The RMC models indicate that these modifications are mainly associated with structural relaxation of the silicate network. This implies that the structure undergoes strong modifications during the cooling and the formation of the glass. Acknowledgements The authors are grateful to the staff of the 7 C2 at LLB for their technical assistance. This work was supported by the French national research agency (ANR) under the program MatetPro2008. References [1] B.G. Bagley, E.M. Vogel, W.G. French, G.A. Pasteur, J.N. Gan, J. Tauc, J. Non-Cryst. Solids 22 (1976) 423.
[2] B.E. Warren, J. Biscoe, J. Am. Ceram. Soc. 21 (1938) 259. [3] W.H. Zachariasen, J. Am. Ceram. Soc. 54 (1932) 3841. [4] G.N. Greaves, A. Fontaine, P. Lagarde, D. Raoux, S.J. Gurman, Local structure of silicate glasses, Nature 293 (1981) 611. [5] G.N. Greaves, Philos. Mag. B 60 (1989) 793. [6] L. Cormier, G. Calas, P.H. Gaskell, Chem. Geol. 174 (2001) 349. [7] P.H. Gaskell, M.C. Eckersley, A.C. Barnes, P. Chieux, Nature 350 (1991) 675. [8] S.K. Lee, J.F. Stebbins, J. Phys. Chem. B 107 (2003) 3141. [9] A.R. Jones, R. Winter, G.N. Greaves, I.H. Smith, J. Non-Cryst. Solids 293-295 (2001) 87. [10] A.N. Cormack, J. Du, J. Non-Cryst. Solids 293–295 (2001) 283. [11] B. Roling, M.D. Ingram, Solid State Ion 105 (1998) 47. [12] C. Karlsson, Zanghellini, J. Swenson, B. Roling, D.T. Bowron, L. Börjesson, Phys. Rev. B 72 (2005) 064206e. [13] P. Richet, Y. Bottinga, Rev. Geophys. 24 (1986) 1. [14] T. Rouxel, J.-C. Sangleboeuf, J. Non-Cryst. Solids 271 (2000) 224. [15] O. Majérus, L. Cormier, G. Calas, B. Beuneu, Phys. Rev. B 67 (2003) 024210. [16] O. Majérus, L. Cormier, G. Calas, B. Beuneu, J. Phys. Chem. B 107 (2003) 13044. [17] O. Majérus, L. Cormier, G. Calas, B. Beuneu, Chem. Geol. 213 (2004) 89. [18] H.E. Fischer, A.C. Barnes, P.S. Salmon, Rep. Prog. Phys. 69 (2006) 233. [19] A. Fluegel, D.A. Earl, A.K. Varshneya, T.R. Seward, Phys. Chem. Glasses Eur. J. Glass Sci. Technol. B 49 (2008) 245. [20] C. Bernard, V. Keryvin, J.C. Sangleboeuf, T. Rouxel, Mech. Mater. 42 (2010) 196. [21] D.A. Keen, J. Appl. Crystallogr. 34 (2001) 172. [22] E. Lorch, J. Phys. C Solid State Phys. 2 (1969) 229. [23] F. Marumo, M. Okuno, in: I. Sunagawa (Ed.), Materials science of the Earth's interior, Terra Scientific, Tokyo, 1984. [24] M. Guignard, L. Cormier, V. Montouillout, N. Menguy, D. Massiot, A.C. Hannon, J. Phys. Condens. Matter 21 (2009) 375107. [25] R.L. McGreevy, J. Phys. Condens. Matter 13 (2001) R877. [26] L. Cormier, D. Ghaleb, J.-M. Delaye, G. Calas, Phys. Rev. B 61 (2000) 14495. [27] M. Guignard, L. Cormier, Chem. Geol. 256 (2008) 111. [28] B. Guillot, N. Sator, Geochim. Cosmochim. Acta 71 (2007) 1249. [29] R.L. McGreevy, P. Zetterström, J. Non–Cryst. Solids 293–295 (2001) 297. [30] P.H. Gaskell, D.J. Wallis, Phys. Rev. Lett. 76 (1996) 66. [31] D.L. Price, S.C. Moss, R. Reijers, M.-L. Saboungi, S. Susman, J. Phys. C Solid State Phys. 21 (1988) L1069. [32] N. Zotov, H. Keppler, A.C. Hannon, A.K. Soper, J. Non-Cryst. Solids 202 (1996) 153. [33] M.G. Tucker, M.T. Dove, D.A. Keen, J. Phys. Condens. Matter 12 (2000) L425. [34] L. Cormier, D.R. Neuville, Chem. Geol. 213 (2004) 103. [35] N. Zotov, H. Keppler, Phys. Chem. Miner. 25 (1998) 259. [36] U. Hoppe, D. Stachel, D. Beyer, Phys. Scr. T57 (1995) 122. [37] A. Tilocca, N.H. de Leeuw, J. Mater. Chem. 16 (2006) 1950. [38] D.R. Neuville, Chem. Geol. 229 (2006) 28. [39] J.R. Allwardt, J.F. Stebbins, Am. Miner. 89 (2004) 777. [40] L. Cormier, G. Calas, G.J. Cuello, J. Non-Cryst. Solids 356 (2010) 2327. [41] G.N. Greaves, K.L. Ngai, Phys. Rev. B 52 (1995) 6358. [42] J.C. Dyre, Rev. Mod. Phys. 78 (2006) 953. [43] H. Tanaka, T. Kawasaki, H. Shintani and K. Watanabe, Nat. Mater. 9 324. [44] J. Machacek, S. Charvatova, O. Gedeon, M. Liska, in: M. Liska, D. Galusek, R. Klement, V. Petruskova (Eds.), Glass - the Challenge for the 21st Century, Trans Tech Publications Ltd, Stafa-Zurich, 2008. [45] X. Yuan, A.N. Cormack, Mater. Res. Soc. Symp. Proc. 455 (1996) 241. [46] X. Yuan, A.N. Cormack, Ceram. Trans. 82 (1997) 281. [47] A. Pedone, M. Malavasi, C. Menziani, U. Segre, A.N. Cormack, J. Phys. Chem. 112 (2008) 11034.
Contents lists available at ScienceDirect
Journal of Non-Crystalline Solids j o u r n a l h o m e p a g e : w w w. e l s ev i e r. c o m / l o c a t e / j n o n c r y s o l
Structural changes between soda-lime silicate glass and melt Laurent Cormier a,⁎, Georges Calas a, Brigitte Beuneu b a
Institut de Minéralogie et de Physique des Milieux Condensés, CNRS UMR 7590, Université Pierre et Marie Curie–Paris 6, Université Denis Diderot–Paris 7, IPGP, 4 place Jussieu, 75005 Paris, France b Laboratoire Léon Brillouin, C.E. Saclay, 91191 Gif-sur-Yvette, France
a r t i c l e
i n f o
Article history: Received 6 July 2010 Received in revised form 14 October 2010 Available online 23 November 2010 Keywords: Structure; Silicate; Neutron scattering
a b s t r a c t Neutron diffraction has been used to study the structure of a glass and melt of composition 75SiO2-15Na2O10CaO. RMC modeling of the neutron and X-ray diffraction data for the glass allowed the determination of the Na and Ca environment. The structure has been investigated at 300K, just below the glass transition at 823 K and in the melt at 1273 K. The short range order does not present important modifications with temperature while significant reorganization appears at the medium range order. These latter changes can be associated with the Si and O pairs and indicate the relaxation of the silicate network. This indicates that the glass formation involved structural rearrangement during cooling. © 2010 Elsevier B.V. All rights reserved.
1. Introduction Soda-lime silica glass, easily synthesized as a homogeneous glass, is probably the technologically most important oxide glass, with a wide range of applications, including structural flat glass, packaging, insulating materials, novel electric devices or bioactive materials. Key properties include high stability against crystallization, high viscosity at the liquidus temperature permitting glass forming, high potential for fiber drawing and compositional control of index of refraction and coefficient of thermal expansion [1]. Many of these physical properties, such as viscosity, electrical conductivity and thermal expansion, are intimately related to the structure of the glass/melt systems, depending on the working temperature. Despite their industrial importance, the detailed structure of sodalime silica glass has been poorly investigated. The pioneering X-ray diffraction work performed by Warren and Biscoe depicted the structure as a continuous random silicate network [2,3], formed by rigid corner-sharing SiO4 tetrahedra. Alkali and alkaline-earth elements are filling the holes in this random network, surrounded by about 6 and 7 oxygens for Na and Ca atoms, respectively. These cations act as network modifiers, reducing the degree of connectivity in the network by replacing bridging oxygens (BOs) by Non-Bridging Oxygens (NBOs). The present understanding of the structure of alkali and alkaline-earth silicate glasses does not correspond anymore to a homogeneous distribution of these cations within the silicate network. Experimental evidence by X-ray absorption spectroscopy [4,5] or neutron diffraction [6,7] indicate the existence of silica-rich and alkali/alkaline-earth-rich regions. Recent 17O NMR experiments
⁎ Corresponding author. Tel.: + 33 1 44 27 52 39. E-mail address: [email protected] (L. Cormier). 0022-3093/$ – see front matter © 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.jnoncrysol.2010.10.014
on soda-lime silicate glasses have shown a non-random distribution of Ca and Na, with the prevalence of Na–Ca pairs [8]. 29Si NMR suggests that Ca2+ cations are preferentially bonding to NBOs [9]. Conversely, Molecular Dynamics (MD) simulations indicate random Ca–Na pairing [10]. Cation–cation interactions, cation–terahedral network interactions and cation coordination numbers are important structural parameters that could impact strongly transport properties. For instance, a “mixed alkali–alkaline earth anomaly” [11] affects the ionic mobility: the mobility of Ca2+ ions is enhanced by the presence of Na+ ions. A similar local environment of Na and Ca ions has been determined for 3xCaO-3(1 − x)Na2O-4SiO2 glasses using neutron diffraction and Reverse Monte Carlo modeling [12], with the presence of two cation–oxygen contributions at 2.25 and 2.65 Å indicating that Ca/Na sites are interchangeable, which enhances cation mobilities. It is expected that the structure of glasses and melts differs because the configurational entropy above the liquid temperatures is usually twice or three times as great as the entropy frozen in at the glass transition [13]. Cation environment, medium range distribution or silicate network organization can be temperature dependent. Such structural modifications upon temperatures will impact ion mobility and thermomechanical properties [14] and are particularly important for shaping and molding of glasses. However, by contrast to borate and borosilicate glass systems, in which the coordination change of B at high temperature modifies the role of cations [15,16], temperaturedriven structural changes in silicate glass/melt systems are mostly subtle: the structural disordering of cations sites at high temperature is not affected by the glass transition, as changes in the silicate network occur only above the glass transition and affect mainly the medium range order (MRO) [17,18]. This paper describes the structure of a soda-lime silicate glass and its corresponding melt using neutron and X-ray diffraction and
L. Cormier et al. / Journal of Non-Crystalline Solids 357 (2011) 926–931
Reverse Monte Carlo modeling. High temperature neutron diffraction data show the significant evolution of the structure above the glass transition temperature up to the liquid state. The composition, close to that of a window glass, allows to infer some conclusions for revealing significant changes with temperatures. 2. Experiments 2.1. Sample preparation A glass of composition 75SiO2-15Na2O-10CaO was synthesized by mixing dried starting materials (SiO2, Na2CO3 and CaCO3). After a slow heating to decompose the carbonates at 850 °C overnight, the mixture was melted in a 90Pt/10Rh crucible at 1200 °C for 2 h. The glass was obtained by rapidly immersing the bottom of the crucible into water. The sample was then ground and remelted twice in the same conditions to ensure a good homogeneity. The final glass appears bubble-free, uncolored and transparent. The composition was checked using electron microprobe microanalyser (CAMECA SX50) at the Camparis Centre (Université Pierre et Marie Curie, France) with an accuracy of ±0.3 mol%. The actual composition of the glass is 73.36 SiO2 ∙ 14.86 Na2O ∙ 11.78 CaO. The room temperature density was obtained in toluene using the Archimedes principle, giving a value of 2.484 ± 0.005 g cm−3. Theoretical melt density at 1000 °C has been calculated using a recent model [19], leading to a value of 2.380 g cm−3. The glass transition is taken at Tg= 835 K according to [20]. 2.2. Neutron diffraction Neutron diffraction experiments have been carried out on the 7 C2 diffractometer at the Orphée reactor of the Laboratoire Léon Brillouin (Saclay, France), using hot neutrons of wavelength 0.729 Å. Approximately 6.5 g of glass powders were loaded into a cylindrical vanadium cell of 11 mm in diameter, at the center of a cylindrical vanadium furnace. Measurements were performed from room temperature up to 1273 K. As detailed in [16,17], data correction includes the scattering from the empty can in the furnace at 300 K and 1273 K, from the empty furnace at 300 K, together with a background correction. The data reduction yields the total structure factor, FN(Q), which is the scattering term of the total neutron cross section (the notations are those used in [21]). The correlation function, DN(r), is obtained by Fourier transformation of FN(Q): ∞
N D ðr Þ = 2 ∫ Q F ðQ ÞM ðQ Þ sinðQr ÞdQ π 0
927
function, D X(r), have been previously explicated [24]. The Fourier transform is calculated using an exponential function, exp(−αQ2) with α = 0.005, as the modification function. 2.4. Reverse Monte Carlo modeling A structural model has been built using the Reverse Monte Carlo (RMC) technique [25] by combining neutron and X-ray diffraction data and coordination constraints. Starting configurations were obtained using MD simulation (DL_POLY code) to provide more reliable models than those obtained by standard RMC modeling [26,27]. MD calculations were performed on a box of 4640 atoms, using the interaction potentials from [28]. The liquid was equilibrated at high temperature (3000 K) and then cooled down to 300 K with a cooling rate of 9 ∙ 1012 K s−1. The initial glass configuration corresponds to a microcanonical (NVE) ensemble obtained at 300 K and the initial melt configuration corresponds to an isothermal-isobaric (NPT) ensemble obtained at 923 K. During the RMC modeling, all Si atoms were constrained to be coordinated to four O atoms. The closest approach distances used for these simulations are 1.8 Å for Si–O, 2.1 Å for Na–O and Ca–O, 2.6 for Si–Na, Si–Ca, Na–Na, Na–Ca, and Ca–Ca and 2.8 Å for Si–Si. The RMC technique has been previously described [29] and consists in minimizing the squared difference between experimental and calculated structure factors by moving the atoms randomly. This ultimately gives atomic models in quantitative agreement with experimental data. In the present study, both neutron and X-ray diffraction data were used to constrain the RMC fitting of the glass while only neutron diffraction data were available for the RMC fitting of the melt. 3. Results 3.1. Total structure factors The total structure factors at room and high temperatures are shown in Fig. 1. The high-Q range (Q N 5 Å−1), which describes the short range order, is similar for all temperatures. The low-Q region,
ð1Þ
where M(Q) is a modification function to limit the truncation effects. A Lorch function was chosen as the modification function [22]. The DN(r) function is defined as a sum of the partial pair distribution functions (PPDFs), gij(r), corresponding to the correlations between atoms i and j: h i N D ðr Þ = 4πrρ0 ∑ ci cj bi bj gij ðr Þ−1 i; j
ð2Þ
with ρ0 the number density, ci and bi the atomic concentration and the bound coherent scattering length for species i. 2.3. X-ray diffraction X-ray diffraction measurements were carried out using a diffractometer (PANalytical X'Pert PRO) operating with a MoKα radiation (λ = 0.7093 Å). Data were measured in the angular range 2 b 2θ b 148° (Q range of 0.3 b Q b 17 Å−1), then corrected for polarization and absorption, Compton scattering and normalized using the Krogh– Moe–Norman method to obtain the weighted structure factor F X(Q) [23]. The X-ray structure factor, F X(Q), and the X-ray correlation
Fig. 1. Total structure factors of the soda-lime silicate glass obtained at different temperatures up to the liquid state. Insert: comparison between the room temperature structure factors of the pristine glass (300 K) and the sample recovered after the cooling in the vanadium can (300 K d).
928
L. Cormier et al. / Journal of Non-Crystalline Solids 357 (2011) 926–931
related to medium range correlation (4–20 Å), is mainly characterized by a sharp peak Qp near 1.72 ± 0.02 Å−1, involving preferred arrangements between silicate units and/or alkali ions. The dampening of the oscillations at high temperature is due to both static and thermal disorder. Even if its origin is still debated [30,31], the low-Q peak can be undoubtedly assigned to the MRO: Q p is associated with density fluctuations over a repeat distance D = 2π / Q p with an uncertainty on D given by σ(D) = 2πσ (Q p) / Q2p, where σ(Q p) is the uncertainty on the position of the first peak [32]. Contrary to other features in the FN(Q) function, Q p peak remains almost unchanged in position and intensity in the glassy state up to 823 K, while in the liquid state it is shifted to 1.65 ± 0.02 Å−1, its intensity is reduced and its width broadened. The characteristic repeat distance increases from D = 3.65 ± 0.08 Å to 3.81 ± 0.08 Å between the glass and liquid state. The insert in Fig. 1 compares the structure factors before and after the melting. This shows that the glass structure is perfectly recovered after the heat treatment of the sample in the vanadium can and that any V contamination is negligible.
shifted in two contributions at 7.1 and 7.5 Å. The structural origin of these modifications must be discussed through RMC modeling.
3.3. RMC models
The DN(r) correlation functions at room and high temperatures are shown in Fig. 2. The position of the first peak, corresponding to the intra-tetrahedral Si–O distances, remains unchanged between 300 K and 823 K at 1.629 ± 0.005 Å and then increases up to 1.635 ± 0.005 Å at 1273 K. The peak corresponding mainly to the O–O pair is continuously shifting from 2.65 to 2.67 Å with temperature. There are some subtle but important changes beyond this peak. Difference functions between the DN(r) functions at 823 K and 300 K and between 1273 K and 823 K can be calculated and show some changes beyond the O–O peak (Fig. 2, lower curves). With increasing temperature we observe a decrease of intensity around 3.6 Å and an increase of intensity around 3.05 Å. The peak at 4.1 Å is slightly affected by temperature; the peak at 4.9 Å decreases in intensity and is shifted to high-r values; the intensity of the peak at 6.3 Å surprisingly increases in temperature with a slight shift to high-r values; the peak at 7.3 Å has a reduced intensity and seems to be
RMC modeling was performed using neutron diffraction data and the comparison between the experimental structure factors and those calculated from the RMC models is plotted in Fig. 3, showing that a good fit is obtained. X-ray diffraction data, only available at room temperature, were added to the RMC procedure for the glass. Fig. 4 shows the partial structure factors Sij(Q) and PPDFs, gij(r), calculated from the RMC structural models, which are mainly weighted by the partials associated with the silicate network. In particular, the Na–Na, Na–Ca and Ca–Ca correlations have a small weighting factor and additional structural information is highly desirable to get a more accurate description of the cation distribution. X-ray diffraction slightly improve the Ca-centered pairs as Ca is more weighted by X-rays than the other glass components. The total structure factors are dominated mainly by the Si–O and O–O pairs. The small variations at low-Q values explain the shift of the first Qp peak observed in the total structure factors FN(Q) with temperature. The first peak in SO–O(Q) is shifted by −0.12 Å−1 but its intensity is not changed at high temperature, which explain a shift in position. The first peak in SSi–O(Q) is shifted by −0.09 Å−1 and its intensity decreases upon temperature, which mainly explains the change in intensity. It can be noted that the Si–Si pair is unchanged in position and intensity. The gij(r) functions show few changes with temperature. We observed a decrease in intensity and a broadening of the first peak in gSi–O(r). Given the variation in the Si–O bond length, a local coefficient of thermal expansion (CTE) of (6±1)×10−6 K−1 is obtained. An interesting trend can be derived by comparison with local CTE values from the literature. This can be compared to the value obtained from neutron total scattering measurements of SiO2 polymorphs, (2.2±0.4)×10−6 K−1 [33] or to the value determined for the potassium disilicate glass, (9±1)×10−6 K−1 [17]. This trend indicates that local CTE tends to increase with the size of the modifying cation.
Fig. 2. Total correlation functions of the soda-lime silicate glass and melt, obtained by Fourier Transform of the total structure factors multiplied by the Lorch modification function, on the Q range 0.5–15.4 Å−1. The two lower curves represent the difference functions between DN(r) functions at 823 K and 300 K and between DN(r) functions at 1273 K and 823 K.
Fig. 3. Comparison between the experimental structure factors and those calculated from the RMC models. The RMC models at room temperature have been obtained by fitting simultaneously the structure factors obtained by neutron and X-ray diffraction, while only neutron diffraction data are available at 823 K and 1273 K.
3.2. Total correlation functions
L. Cormier et al. / Journal of Non-Crystalline Solids 357 (2011) 926–931
929
Fig. 5. From top to bottom, changes in the region 3–10 Å with temperature in the correlation functions for the O–O, Si–O and Si–Si partial pair distribution functions and for the experimental total neutron correlation functions, for the glass (in blue) and the melt (in red). The percentages indicate the relative contribution of each pair in the neutron data.
second contribution discernible at 2.61–2.65 Å. This is in agreement with a previous investigation of soda-lime silicate glasses with lower SiO2 content, in which Na–O and Ca–O correlations were similar with two contributions at 2.25 Å and 2.65 Å [12]. The coordination number for modifier elements is difficult to determine considering an ill-defined first coordination shell [34]. With a cut-off distance of 3.2 Å, the coordination number is 4.9 and 6.0 for Na and Ca, respectively. The Na–O and Ca–O distances tend to become broader and are shifted by −0.1 Å with increasing temperatures. The running coordination number for Na–O and Ca–O are shown in Fig. 6 for the glass and the melt. This shows that the coordination number of these two elements remain unchanged with increasing temperatures.
Fig. 4. (a) Partial structure factors Sij(Q) for the glass (in blue) and the melt (in red). (b) Partial pair distribution functions gij(r) for the glass (in blue) and the melt (in red). The percentages indicate the relative contribution of each pairs in the neutron data.
The peak at 2.67 Å in gO–O(r) is broadened in the melt, which contributes to the increased contribution around 3 Å on the experimental DN(r) functions. Other modifications of the silicate framework are indicated by the shift of the Si–Si peak from 3.12 to 3.19 Å. Several changes at MRO concern the pairs associated with the silicate network (Si–O, O–O and Si–Si) with some decrease in intensity in the liquid state only for some distances, which are indicated by arrows in Fig. 5. These variations correspond well with those in the experimental DN(r) correlation functions. However, the changes around 6.4 Å and 7.2 Å in the experimental data are not explained by these models. This suggests that they are not due to modifications of the silicate framework and may be due to cationrelated changes. The Na–O and Ca–O pairs present a first peak at 2.25 Å and 2.35 Å, respectively, in the glass. These peaks extend to large-r values with a
Fig. 6. Running coordination numbers for Na and Ca as a function of temperature, obtained from the RMC models.
930
L. Cormier et al. / Journal of Non-Crystalline Solids 357 (2011) 926–931
4. Discussion 4.1. Glass structure Neutron diffraction data allow the generation of structural models using RMC modeling. In these models, all silicon atoms are four-fold coordinated (initial constraints) and SiO4 tetrahedra form a cornersharing network, with partial depolymerization associated with the presence of Ca and Na atoms. Na and Ca environments are distorted with two (Na,Ca)–O contributions at 2.25 and 2.65 Å. This agrees with previous studies [12,35,36]. The coordination number around Na is slightly lower than that of Ca. However, the two sites are similar and Ca can easily substitute at Na sites. This is in accordance with a medium range structure almost unchanged by the substitution of Na by Ca [10,12]. It has also been shown that Ca has a greater propensity for coordination by NBO than Na [10,37]. Na and Ca local environments have been determined experimentally and by MD simulations for compositions close to that investigated in this study (Table 1) and an overall good agreement is found for these results. The modifier–modifier PPDFs are weakly weighted but all of them show a first broad contribution between 3 and 4 Å (Fig. 4b). This is a smaller separation than required by a homogeneous distribution and it is usually interpreted using the modified random network model with preferential regions concentrated with modifiers and NBOs [5]. A nonrandom distribution of Ca and Na is also consistent with 17O and 23Na NMR data [8] and configurational entropy variations, which do not follow an ideal mixing term [38]. This non-random distribution differs from the cation random distribution observed in other mixed cation glasses, such as in Ca–Mg silicate glasses [39,40]. The Ca–Na PPDF exhibits a distinct contribution between 3 and 4 Å. This indicates an extensive mixing between Ca and Na atoms. Similarly, NMR data concluded that the Ca–Na distribution around NBOs shows neither complete preference for Na–Ca pairs nor significant clustering into Ca- and Na-rich regions [8]. However, our RMC models are slightly different to the NMR interpretation for a preferential Na–Ca pairing. Indeed, if we consider the number of nearest neighbor around Na or Ca, we observe that around Na atoms there are more Na atoms (84%) than expected from a random distribution (75%). Similarly around Ca atoms, there are more Ca atoms (32%) than expected from a random distribution (25%). Thus, based on the RMC modeling of the diffraction data, there is a slight tendency to have atoms of same type close to each other. Though Ca has a lower mobility than Na, the mobility of Ca2+ ions is enhanced when replaced by Na+ ions which have a positive coupling effects on the movements of divalent cations [11]. The transport of mobile modifier ions in silicate glasses can be considered as a hopping process, based on the existence of well-defined ionic sites [41]. As the local environment of Na and Ca is similar, it was
suggested that the lack of mismatch sites for Ca and Na could improve the diffusion of Ca2+ ions which can easily use empty Na+ sites [12]. The pathways for diffusion appear also from the non-homogeneous distribution of the Ca-Na cations within the silicate network. Below the glass transition temperature, ion mobility takes place in a fixed environment provided by the network structure. At higher temperature, the relaxation of the network increases the topological disorder and opens up the structure. This leads to the formation of more available cation sites, which facilitates ionic diffusion. 4.2. Modification with increasing temperature Neutron total diffraction provides an average, or static, structural picture of the system, corresponding to the sum of a very large number of snap-shots. This method allows the investigation of the structural changes resulting from the thermodynamic reequilibration of the system with temperature variations. The shift in position of the Qp peak can be mainly attributed to the O–O and Si–O pairs. This indicates a relaxation of the silicate network. Other structural modifications can be seen in the total correlation functions. Clearly the changes in Fig. 2 do not correspond to a disordering of the structure due only to thermal effects. The increase of the intensity of some contributions (e.g. at 6.3 Å) indicate some important modification of the structure with temperature, that should be associated with structural relaxation of the silicate network. The RMC models can at least partly reproduce this modification of the silicate network between the glass and the liquid. As shown in Fig. 5, some features in the gSi–O(r) and gO–O(r) functions disappear at specific distances corresponding to the main changes in the total DN(r) correlation functions. The main consequence of the introduction of modifying oxides is to create NBOs and to depolymerize the network leading to the formation of various Qn species, where Qn is a SiO4 tetrahedron containing n BOs. The number of NBO and BO is determined from the RMC models and reported in Table 2 for the glass and melt. The fractions of NBO and BO do not change with temperature and show no major deviation from the values expected based on stoichiometric considerations. The Qn species distributions calculated from the RMC models are compared with previous findings from experiments or simulations on Table 2. The variations with temperature are small and discrepancies can be observed with experiments, which can be due to a difference in composition or to a difference inherited from the MD simulations used as the starting configuration in the present RMC modeling. It should be noted that these Qn species are poorly constrained by the total neutron and X-ray structure factors and thus only slightly modified compared to the initial MD simulations. The substitution of Ca by Na in silicate glasses increases the configurational entropy, which suggests an increase of the disorder and/or a change in the glass network polymerization [38]. Raman data indicate the increase of Q2 species with increasing CaO content.
Table 1 Distances and coordination numbers for Na–O and Ca–O pairs determined by various modelling and simulation investigations in soda–lime silicate glasses. Compositions
Pairs
Distance
CN
3xCaO-3(1 − x)Na2O-4SiO2
Na–O
2.25 2.65 2.25 2.65 2,31 2.28
1.7 ± 0.3 4.2 ± 0.8 1.8 ± 0.4 5.0 + 1.0 5.6 + 0.2 (rc = 3.16 Å) 6.2 ± 0.3 (rc = 3.16 Å) 5.2 (rc = 3.1 Å) 5.8 (rc = 3.03 Å) 5.6 (rc = 3.1 Å) 5.7 (rc = 3.1 Å) 5.4 (rc = 3.1 Å) 5.9 (rc = 3.1 Å) 4.95 (rc = 3.2 Å) 6.0 (rc = 3.2 Å)
Ca–O 11.2CaO-15.3Na2O-73.5SiO2 10CaO-15Na2O-75SiO2 15CaO-10Na2O-75SiO2 15CaO-10Na2O-75SiO2 10CaO-15Na2O-75SiO2
Na–O Ca–O Na–O Ca–O Na–O Ca–O Na–O Ca–O Na–O Ca–O
2.35 2.30 2.35 2.37 2.25 2.35
Method
Ref.
5.9
Neutron + RMC
[12]
6.8
Neutron + RMC
[12]
MD MD MD MD MD MD MD
[44] [44] [10,45,46] [10,45,46] [37] [37] [47]
ab initio ab initio
ab initio ab initio
Neutron+RMC Neutron+RMC
Present work Present work
L. Cormier et al. / Journal of Non-Crystalline Solids 357 (2011) 926–931
931
Table 2 Comparison for various modelling and simulation investigations of the number of bridging (BO) and non–bridging (NBO) oxygens and of the Qn distribution (with n the number of BO in a SiO4 tetrahedra) in soda–lime silicate glasses. Compositions 11.2CaO-15.3Na2O-73.5SiO2 10CaO-15Na2O-75SiO2 15CaO-10Na2O-75SiO2 9.1CaO-22.7Na2O-68.2SiO2 10CaO-15Na2O-75SiO2 glass 10CaO-15Na2O-75SiO2 melt 10CaO-15Na2O-75SiO2
BO
NBO
Q0
Q1
Q2
Q3
Q4
Method
Ref.
7±4 10.9
57 ± 10 46.2
36 ± 4 42.7
2 10.17 10.0
86 41.75 41.9
12 46.7 47.2
MD ab initio MD MD ab initio NMR Neutron+RMC Neutron+RMC Random model
[44] [10,45,46] [37] [9] Present work Present work
71.0
29.0
0
0 0.2
64.0 71.5 71.5 71.3
36.0 28.5 28.5 28.7
0 0 0
0 1.4 0.9
It is often considered that diffraction data show little change with temperature and that the “glass simply inherits the liquid structure and its lack of long range order” [42]. Our diffraction data indicate that the structure of glasses and liquids show significant differences and that the modifications appear already close to the glass transition temperature. This is direct evidence that the structure is affected during the cooling of the liquid and that structural organization can now be taken into account in the glass transition process. Recently, it was shown a direct connection between structural ordering and the dynamic heterogeneities that accompany the kinetics slowing down responsible for the steep increase in the viscosity as approaching the glass transition [43]. The determination of these structural changes is still difficult to establish for multicomponent silicate glasses as changes mainly affect MRO, a range of distances that is yet experimentally challenging to measure in glasses. A better understanding of glass/liquid modifications will be of paramount importance to establish a relationship between the structure and the dynamics in the supercooled region. Fortunately, the development of high temperature devices should increase the number and accuracy of structural experiments and improve our knowledge of structural modifications operating upon temperature. 5. Conclusions The structure of a soda-lime silicate has been investigated in the glassy and liquid state using neutron diffraction, X-ray diffraction and reverse Monte Carlo modeling. Our results give a coordination number close to 6 for Ca atoms and close to 5 for Na atoms, with little variations with temperature. The correlation functions between the glass and the liquid show significant modifications at the medium range scale (3–7 Å) that cannot only be attributed to thermal disordering. The RMC models indicate that these modifications are mainly associated with structural relaxation of the silicate network. This implies that the structure undergoes strong modifications during the cooling and the formation of the glass. Acknowledgements The authors are grateful to the staff of the 7 C2 at LLB for their technical assistance. This work was supported by the French national research agency (ANR) under the program MatetPro2008. References [1] B.G. Bagley, E.M. Vogel, W.G. French, G.A. Pasteur, J.N. Gan, J. Tauc, J. Non-Cryst. Solids 22 (1976) 423.
[2] B.E. Warren, J. Biscoe, J. Am. Ceram. Soc. 21 (1938) 259. [3] W.H. Zachariasen, J. Am. Ceram. Soc. 54 (1932) 3841. [4] G.N. Greaves, A. Fontaine, P. Lagarde, D. Raoux, S.J. Gurman, Local structure of silicate glasses, Nature 293 (1981) 611. [5] G.N. Greaves, Philos. Mag. B 60 (1989) 793. [6] L. Cormier, G. Calas, P.H. Gaskell, Chem. Geol. 174 (2001) 349. [7] P.H. Gaskell, M.C. Eckersley, A.C. Barnes, P. Chieux, Nature 350 (1991) 675. [8] S.K. Lee, J.F. Stebbins, J. Phys. Chem. B 107 (2003) 3141. [9] A.R. Jones, R. Winter, G.N. Greaves, I.H. Smith, J. Non-Cryst. Solids 293-295 (2001) 87. [10] A.N. Cormack, J. Du, J. Non-Cryst. Solids 293–295 (2001) 283. [11] B. Roling, M.D. Ingram, Solid State Ion 105 (1998) 47. [12] C. Karlsson, Zanghellini, J. Swenson, B. Roling, D.T. Bowron, L. Börjesson, Phys. Rev. B 72 (2005) 064206e. [13] P. Richet, Y. Bottinga, Rev. Geophys. 24 (1986) 1. [14] T. Rouxel, J.-C. Sangleboeuf, J. Non-Cryst. Solids 271 (2000) 224. [15] O. Majérus, L. Cormier, G. Calas, B. Beuneu, Phys. Rev. B 67 (2003) 024210. [16] O. Majérus, L. Cormier, G. Calas, B. Beuneu, J. Phys. Chem. B 107 (2003) 13044. [17] O. Majérus, L. Cormier, G. Calas, B. Beuneu, Chem. Geol. 213 (2004) 89. [18] H.E. Fischer, A.C. Barnes, P.S. Salmon, Rep. Prog. Phys. 69 (2006) 233. [19] A. Fluegel, D.A. Earl, A.K. Varshneya, T.R. Seward, Phys. Chem. Glasses Eur. J. Glass Sci. Technol. B 49 (2008) 245. [20] C. Bernard, V. Keryvin, J.C. Sangleboeuf, T. Rouxel, Mech. Mater. 42 (2010) 196. [21] D.A. Keen, J. Appl. Crystallogr. 34 (2001) 172. [22] E. Lorch, J. Phys. C Solid State Phys. 2 (1969) 229. [23] F. Marumo, M. Okuno, in: I. Sunagawa (Ed.), Materials science of the Earth's interior, Terra Scientific, Tokyo, 1984. [24] M. Guignard, L. Cormier, V. Montouillout, N. Menguy, D. Massiot, A.C. Hannon, J. Phys. Condens. Matter 21 (2009) 375107. [25] R.L. McGreevy, J. Phys. Condens. Matter 13 (2001) R877. [26] L. Cormier, D. Ghaleb, J.-M. Delaye, G. Calas, Phys. Rev. B 61 (2000) 14495. [27] M. Guignard, L. Cormier, Chem. Geol. 256 (2008) 111. [28] B. Guillot, N. Sator, Geochim. Cosmochim. Acta 71 (2007) 1249. [29] R.L. McGreevy, P. Zetterström, J. Non–Cryst. Solids 293–295 (2001) 297. [30] P.H. Gaskell, D.J. Wallis, Phys. Rev. Lett. 76 (1996) 66. [31] D.L. Price, S.C. Moss, R. Reijers, M.-L. Saboungi, S. Susman, J. Phys. C Solid State Phys. 21 (1988) L1069. [32] N. Zotov, H. Keppler, A.C. Hannon, A.K. Soper, J. Non-Cryst. Solids 202 (1996) 153. [33] M.G. Tucker, M.T. Dove, D.A. Keen, J. Phys. Condens. Matter 12 (2000) L425. [34] L. Cormier, D.R. Neuville, Chem. Geol. 213 (2004) 103. [35] N. Zotov, H. Keppler, Phys. Chem. Miner. 25 (1998) 259. [36] U. Hoppe, D. Stachel, D. Beyer, Phys. Scr. T57 (1995) 122. [37] A. Tilocca, N.H. de Leeuw, J. Mater. Chem. 16 (2006) 1950. [38] D.R. Neuville, Chem. Geol. 229 (2006) 28. [39] J.R. Allwardt, J.F. Stebbins, Am. Miner. 89 (2004) 777. [40] L. Cormier, G. Calas, G.J. Cuello, J. Non-Cryst. Solids 356 (2010) 2327. [41] G.N. Greaves, K.L. Ngai, Phys. Rev. B 52 (1995) 6358. [42] J.C. Dyre, Rev. Mod. Phys. 78 (2006) 953. [43] H. Tanaka, T. Kawasaki, H. Shintani and K. Watanabe, Nat. Mater. 9 324. [44] J. Machacek, S. Charvatova, O. Gedeon, M. Liska, in: M. Liska, D. Galusek, R. Klement, V. Petruskova (Eds.), Glass - the Challenge for the 21st Century, Trans Tech Publications Ltd, Stafa-Zurich, 2008. [45] X. Yuan, A.N. Cormack, Mater. Res. Soc. Symp. Proc. 455 (1996) 241. [46] X. Yuan, A.N. Cormack, Ceram. Trans. 82 (1997) 281. [47] A. Pedone, M. Malavasi, C. Menziani, U. Segre, A.N. Cormack, J. Phys. Chem. 112 (2008) 11034.