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Comparison of the low-Q features in diffraction data for silicate glasses and crystals containing Sr or Ba
Journal of Non-Crystalline Solids 248 (1999) 84±91
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Comparison of the low-Q features in diraction data for silicate glasses and crystals containing Sr or Ba Laurent Cormier a
a,* ,
Philip H. Gaskell b, Sophie Creux
c
Laboratoire Min eralogie-Cristallographie, Universit es Paris 6 and 7 and IPGP and UMR CNRS 7590, 4 place Jussieu, 75252 Paris cedex 05, France b Cavendish Laboratory, University of Cambridge, Madingley Road, Cambridge, CB3 0HE, UK c Saint Gobain Recherche, 39 quai Lucien Lefranc, BP 135, 93303 Aubervilliers cedex, France Received 3 June 1998; received in revised form 30 January 1999
Abstract Neutron scattering data have been obtained for a strontium- and a barium-containing silicate glass and a strontium aluminosilicate glass. These data are compared with previously published anomalous wide-angle X-ray scattering data for the Sr-containing glasses. Features in the diraction data at the smaller scattering vectors, Q, are compared with simulated X-ray and neutron diraction patterns for compositionally similar crystals. Peaks are found at Qs close to the `®rst sharp diraction peaks' of the glasses and have a cation±cation dependence. We suggest that this correspondence shows that the smaller Q features in the glasses have similar structural origins to those in the scattering data for the crystals with the same composition and therefore that the medium-range structures and cation±cation arrangements in the glasses are similar too. Ó 1999 Published by Elsevier Science B.V. All rights reserved. PACS: 61.43.Fs; 61.12.ÿq; 61.10.ÿi; 61.43.Bn
1. Introduction Studies of the structure of oxide glasses have mainly concentrated on alkali or alkaline-earth silicate glasses (see Ref. [1] for a review) but, to our knowledge, few investigations have been undertaken for the heavier elements, such as strontium or barium [2,3]. A wide angle X-ray scattering (AWAXS) study has recently been performed on Sr-containing silicate and aluminosilicate glasses [4,5]. Neutron scattering data can contribute to an understanding of the structure of these glasses, as
* Corresponding author. Tel.: +33-1 44 27 50 65; fax: +33-1 44 27 37 85; e-mail: [email protected]
the Sr-centred partial structure factors are less heavily weighted for neutron than for X-ray diffraction. Consequently, the silicate network becomes more apparent in the neutron data. Furthermore, a comparative study of the neutron and X-ray data can help in understanding features in the structure factors at the small scattering vectors, which are related to the medium range order (MRO) in the glass structure. We have carried out neutron diraction measurements on Sr-containing silicate and aluminosilicate glasses (SrOá0.19Na2 Oá1.9SiO2 , SrOáAl2 O3 á4SiO2 ) and on a barium silicate glass (2Ba2 Oá3SiO2 ). A small amount of Na2 O was added to the strontium silicate glass to avoid crystallization upon cooling. The study presented
0022-3093/99/$ ± see front matter Ó 1999 Published by Elsevier Science B.V. All rights reserved. PII: S 0 0 2 2 - 3 0 9 3 ( 9 9 ) 0 0 1 0 2 - 7
L. Cormier et al. / Journal of Non-Crystalline Solids 248 (1999) 84±91
in this paper concerns the variations in the position and intensity of the features at the smaller Q in the X-ray and neutron diraction data. (Q is the scattering vector and Q |Q| 4p sinh/k, where 2h is the scattering angle and k the wavelength of the probing radiation). These features are related to some kind of MRO but their origin is still unknown [6±9]. The explanations proposed mainly consider either quasi-crystalline organisations or correlations between clusters or voids. It was shown recently that planar structures in models for vitreous SiO2 are associated with the ®rst peak at smaller Q, the so-called ®rst sharp diraction peak (FSDP) [8]. The occurrence of Bragg diraction in a compositionally equivalent crystal at the same position as the FSDP, in many (or most) glasses, leads to a general explanation of this feature: similarity between the MRO in the two phases and, probably, the presence of quasi-lattice planes in glasses similar to those existing in related crystals [8,9]. 2. Neutron diraction data The neutron diraction intensities were measured at the ISIS spallation neutron source (Rutherford Appleton Laboratory, Didcot), using the Liquids and Amorphous Diractometer (LAD), for the three glasses, the empty vanadium can, the instrumental background, and a vanadium rod used for absolute normalisation. The counting time was about 1 day for each sample. The data were corrected and reduced according to the procedures described in Ref. [10]. The unsmoothed structure factors for the two Sr-conÿ1 , taining glasses are shown in Fig. 1. Above 2 A the signal is dominated by the (alumino-)silicate framework. We observe few dierences in the peak positions and intensities except a shift towards smaller Q for the aluminosilicate glass, which is due to the longer Al±O distances compared to the ÿ1 , a peak can be observed at Si±O ones. Below 2 A ÿ1 in scattering of the strontium (Na) 1.99 A ÿ1 in the scattering of silicate glass and at 1.73 A the strontium aluminosilicate glass. The amplitude and width of this feature are greater for the strontium aluminosilicate than for the strontium
85
Fig. 1. Neutron structure factors, S Q, for SrAl2 Si4 O12 , SrNa0:4 Si1:9 O5 and Ba2 Si3 O8 glasses (from top to bottom).
silicate glass. The structure factor, S Q, for the barium glass (Fig. 1, lower curve) is similar to that obtained for the strontium silicate glass, with a ÿ1 . The main dierence is the peak at 1.94 A presence in the barium glass of a well-de®ned ÿ1 ). shoulder at smaller Q (1.1 A 3. Simulation of the low-Q features in the diraction data We have compared the experimental X-ray and neutron diraction data with the calculated diffraction patterns for compositionally equivalent crystals. It is important to note that the sensitivity to the various atomic species is not identical for neutron and X-ray diraction. Dierences between the neutron and X-ray weighting factors for the partial functions (Table 1) lead to important changes in the smaller Q part of the diffraction pattern. In the Sr(Na) silicate glass, a ÿ1 is present in both the total and peak at 2 A dierential X-ray structure factors [4,5] (Figs. 1 and 4) and since the Sr±Sr contribution is larger (Table 1), this peak is likely to have a larger contribution from Sr±Sr correlations. The aluminosilicate glass scattering has a ®rst peak at 1.92 ÿ1 in the X-ray structure factor with a smaller A ÿ1 in the strontium intensity than the peak at 2 A silicate glass. This dierence indicates that the contribution of the Sr atoms is less in the aluminosilicate glass.
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Table 1 X-ray (WX-ray ), dierential (WDX-ray ) and neutron (Wneu ) weighting factors a for the partial structure factors for the strontium silicate ÿ1 and aluminosilicate and the barium silicate glasses. WX-ray and WDX-ray are averaged over the range 0±2 A SrNa0:4 Si1:9 O5
Pairs
WX-ray b
T±T T±O b T±M b;c O±O M±O c M±M c
0.05 0.16 0.19 0.12 0.30 0.18
SrAl2 Si4 O12 WDX-ray
0.24 0.36 0.40
Wneu
WX-ray
0.009 0.067 0.019 0.123 0.071 0.010
0.14 0.34 0.13 0.21 0.16 0.03
Ba2 Si3 O8 WDX-ray
0.38 0.47 0.16
Wneu
Wneu
0.015 0.090 0.009 0.135 0.028 0.001
0.009 0.068 0.015 0.127 0.056 0.006
Wneu 2 ÿ dij ni nj bi bj , WX-ray Q 2 ÿ dij ni nj R fi Q; Efj Q; E=jhf Q; Eij, WDX-ray nSr nj D fSr fj fSr fj =D jhf ij2 , where ni , bi and fi are, respectively, the atomic fraction, the neutron scattering length and the X-ray atomic diusion factor for element i. D is the dierence between two energies, close and far from the Sr K-edge. b T Si, Al. c M Sr (and Na) or Ba. a
There are no crystals corresponding to the composition of the Sr-containing glasses, but it is possible to compare the Sr(Na) silicate glass with a metasilicate crystal, a-SrSiO3 [11]. Ideally, the glass composition would not have included sodium and the Sr content would have been larger. However, preparation of a pure strontium silicate glass, with larger strontium contents and without phaseseparation or crystallisation, proved infeasible. Also it is possible to compare the scattering data for the glass with that of a sodium strontium metasilicate, Na4 SrSi3 O9 . We have made this comparison, and it is revealing, even though the Na concentration is much larger than that of the glass. However, space prevents discussion here and the most important diculty with this comparison: the fact that we compare a glass with a disilicate composition with a metasilicate crystal, is not avoided. The aluminosilicate glass can be compared with the anorthite form of SrOáAl2 O3 á2SiO2 (c-SrAl2 Si2 O8 ) [12]. For the barium silicate glass, we used the crystal with the same composition, 2BaOá3SiO2 (c-Ba2 Si3 O8 ) [13]. We compared the ÿ1 ) experimental data in the low-Q region (Q < 2 A with the diraction data calculated for the crystalline structures, using the CE R I U S 2 package (Biosym, Molecular Simulations, San Diego, California, USA) for crystallites of 30 nm diameter, to broaden the Bragg peaks. It should be noted that there is no intention to support a microcrystallite model for glasses, which is clearly untenable [14].
4. Results 4.1. The strontium aluminosilicate glass In Fig. 2, we present the simulated neutron and X-ray diraction and the corresponding experimental data for the strontium aluminosilicate sample. If we consider the X-ray diraction ®rst (Fig. 2(a)), we observe a (2 2 0) peak at ÿ1 , in agreement with the peak Q 1.93 0.02 A in the total structure factor for the glass at ÿ1 . The planes parallel to (2 2 0) lie 1.92 0.02 A close to both the (Al,Si,O) network and the Sr atoms (Fig. 3), so that both make in-phase contributions and increase the amplitude. This peak is thus the result of scattering from both the Sr atoms and the aluminosilicate network. We also simulated the diraction by the Sr atoms only, i.e. the Sr±Sr correlations, Fig. 2(a). This curve shows ÿ1 from the a Bragg re¯ection at 0.96 0.02 A (0 2 0) planes that contain the Sr atoms (Fig. 3). The small contribution of this peak to the total structure factor is due to out-of-phase contributions from the aluminosilicate network (Si,Al,O). Indeed, Fig. 3 shows that (Si,Al)O4 tetrahedra are located between the (0 2 0) planes and interfere destructively, which thus limit the intensity of this peak in the total X-ray structure factor. The position of the (0 2 0) peak agrees well with the peak ÿ1 in the experimental dierobserved at 1.06 A ential structure factor, DSr (Q) (Fig. 2(a)). The function, DSr (Q), is in fact the sum of all the
L. Cormier et al. / Journal of Non-Crystalline Solids 248 (1999) 84±91
87
Fig. 2. Simulated X-ray (a) and neutron (b) diraction data for (c-SrAlSi2 O8 ), showing the full crystal, a lattice with Sr atoms only (Sr± Sr) and a lattice with Si, Al and O atoms only (Si,Al,O). The upper curves (displaced for clarity) are the experimental data. In (a), Sexp (Q) and DSr (Q) are respectively the AWAXS total and dierential structure factors from Refs. [4,5] (DSr (Q) is the weighted sum of all the Sr-centred partial functions) and in (b) Sexp (Q) denotes the neutron diraction structure factor for the Sr aluminosilicate glass.
Fig. 3. A projection of the crystalline structure of SrAlSi2 O8 (2 unit cells in each direction).
Sr-centred pairs and this may explain the relatively poor agreement between the simulated Sr± Sr contribution and the experimental DSr (Q) data
ÿ1 in DSr (Q) at larger Q (the peak at 2.2 0.02 A includes Sr±O and Sr±(Si,Al) correlations, not just Sr±Sr).
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In the neutron data for the glass, the peak at ÿ1 in the X-ray data is shifted to 1.92 0.02 A 1.73 0.02 Aÿ1 (Fig. 2). This shift would be expected from correlations similar to those resulting in the 2 0 2 re¯ection in the crystal which has a larger intensity for neutron than for X-ray scattering (Fig. 2) and mainly involves the aluminosilicate framework. The Sr±Sr curve indicates that Sr±Sr pairs are not one of the largest contributors to the total neutron structure factor. The anti-phase contributions between the Sr±Sr pairs and the (Si,Al,O) pairs contribute to a decrease in the intensity of the (0 2 0) and 2 0 2 peaks. This result is in agreement with the fact that the Sr-centred weighting factors are small for the neutron data (Table 1). 4.2. The strontium silicate glass The simulated X-ray structure factor for cSrSiO3 (Fig. 4(a)) has two peaks at 1.77 0.02 ÿ1 and 2.15 0.02 A ÿ1 due to the 3 1 A 1 and (3 1 1) re¯ections, respectively. The similarities
between the diraction from the full crystal and from the Sr±Sr pairs only indicate that the X-ray data are dominated by the lattice planes involving Sr (Fig. 5). The peak observed for the glass lies ÿ1 , between the two Bragg peaks at 2.00 0.02 A ÿ1 . These at 1.77 0.02 Aÿ1 and at 2.15 0.02 A re¯ections correspond to lattice planes containing Sr atoms (several parallel to the same axis of projection). It is therefore reasonable to assert that the eect of disorder in the glass will be to merge the dierent peaks into a single broad ÿ1 in peak. The (0 0 2) peak at 1.25 0.02 A the Sr±Sr curve is not in agreement with the small ÿ1 in DSr (Q) but the precipeak at 0.82 0.02 A sion of the smaller Q X-ray data is less than at other Qs. Once again, the disappearance of this peak in the total diraction spectrum can be explained by out-of-phase contributions from the SiO4 tetrahedra which are located between the planes populated by the Sr atoms and thus give antiphase contributions to the scattering amplitude (Fig. 5).
Fig. 4. Simulated X-ray (a) and neutron (b) diraction data for (c-SrSiO3 ), showing the full crystal, a lattice with Sr atoms only (Sr±Sr) and a lattice with Si and O atoms only (Si,O). The upper curves (displaced for clarity) are the experimental data. In (a) Sexp (Q) and DSr (Q) are, respectively the AWAXS total and dierential structure factors from Refs. [4,5] and in (b) Sexp (Q) denotes the neutron diraction structure factor for the Sr silicate glass.
L. Cormier et al. / Journal of Non-Crystalline Solids 248 (1999) 84±91
89
Fig. 5. A projection of the crystalline structure of SrSiO3 (2 unit cells in each direction).
The simulated neutron data (Fig. 4(b)) have a ÿ1 (due to the (0 2 1), (3 1 0) and peak at 1.87 A 3 1 2 re¯ections), compared to the experimental ÿ1 in the data for the glass. This peak peak at 2 A has a tail at smaller Q compared to the peak in the neutron data for the aluminosilicate glass. The interpretation is not obvious but there are several ÿ1 in smaller features near the (1 1 0) line at 1.04 A the crystal which may relate to the tail in the scattering of the sample. However, there may be dangers in trying to push comparisons between crystals and glasses too far. 4.3. The barium silicate glass In Fig. 6(a), we present the simulation of the Xray structure factor for the c-Ba2 Si3 O8 . Unfortunately, there are no experimental X-ray data for a glass of this composition. The peak at ÿ1 in the crystal, Fig. 6(a), contains a 1.70 0.02 A Ba±Ba contribution, associated with a (2 1 0) re¯ection. This result indicates that the Ba±Ba pairs dominate the X-ray diraction, as the Sr±Sr correlations do in the strontium silicate glass. In the simulated neutron diraction data for cBa2 Si3 O8 , Fig. 6(b), a ®rst peak at 1.69 0.02 ÿ1 , corresponding to the 1 1 2 planes, is obA served. Agreement with the data for the glass,
ÿ1 , is by no means perfect. The major 1.94 0.02 A contribution to this peak for the crystal comes from the silicate network and therefore this discrepancy may indicate topological dierences in the organisation of SiO4 tetrahedra between the glass and the crystal. In the glass, a shoulder is ÿ1 , close to the crystalline observed at 1.1 0.1 A ÿ1 . If we consider (1 0 2) re¯ection at 1.07 0.05 A the diraction from the Ba±Ba pairs only (Ba±Ba in Fig. 6(b)) and from the silicate network only ((Si,O) in Fig. 6(b)), we note the presence of this feature in both curves. The reduced intensity in the total diraction curve indicates that these contributions scatter with (partial) opposition of phase for the (1 0 2) re¯ection. 5. Discussion The approach advocated here (in contrast to those developed for chalcogenide glasses) does not suppose any layer-like structure. For example, the anorthite structure (c-SrAl2 Si2 O8 ) can be described by a three-dimensional network of interconnected SiO4 and AlO4 tethahedra and it is the presence of lattice planes that gives rise to diraction. Comparisons between the diracted intensity data at low Q for the glasses and similar crystals are in
90
L. Cormier et al. / Journal of Non-Crystalline Solids 248 (1999) 84±91
Fig. 6. Simulated X-ray (a) and neutron (b) diraction data for (c-Ba2 Si3 O8 ), showing the full crystal, a lattice with Ba atoms only (Ba± Ba) and a lattice with Si and O atoms only (Si,O). In (b) the upper curve, Sexp (Q), is the experimental neutron diraction structure factor for the Ba silicate glass (displaced for clarity).
semi-quantitative agreement with both AWAXS and neutron data. We suggest that this result is reminiscent in the glass of quasi-lattice planes (distorted, imperfect and not necessarily `planar') [8,9]. The X-ray and neutron diraction patterns calculated for c-SrAl2 Si2 O8 are in agreement with the data for the strontium aluminosilicate glass. They indicate that the role of Sr is not very important in the smaller Q feature, which is due to ÿ1 the aluminosilicate network. The peak at 1.06 A in DSr (Q) is well-reproduced by the simulations. We suggest that the fact that this peak is dependent on the Sr±Sr correlations is because the distribution of Sr in the glass resembles that in the crystal. The simulations for SrSiO3 show that the crystal and the glass have neutron and X-ray features at similar Q, although dierences remain that probably result from topological disorder in the ÿ1 for the crystal glass (two peaks around 2 A instead of one for the glass). The smaller Q peaks in both the glass and the crystal are attributed
mainly to the Sr±Sr pairs. It is thus likely that the ÿ1 in this glass comes from a similar peak at 2 A organisation of the strontium atoms in the glass and the crystal. For the barium silicate glass, the position of the ÿ1 is not well reproduced, experimental peak at 2 A which indicates that topological dierences exist between the crystal and the glass. This topology could be related to the existence of a variety of barium silicate crystals that dier by the topology of the silicate network [13,15]. However, the ÿ1 is simulated in the crystal by shoulder near 1.1 A the (1 0 2) Bragg re¯ection that corresponds to lattice planes mainly populated by Ba atoms. X-ray diraction data should give more information on the structure of this glass and particularly, on the Ba±Ba atomic pairs to which this technique is more sensitive. Although a microcrystallite model is not implied, some important similarities between glasses and compositionally equivalent crystals seem to exist at the medium range scale. The idea that glass structure can be related to that of a crystal with
L. Cormier et al. / Journal of Non-Crystalline Solids 248 (1999) 84±91
similar composition is supported by the observation that distorted (but topologically identical) models of cristoballite can give an excellent ®t to the FSDP for a-SiO2 [16]. Moreover, neutron diffraction of isotopically substituted ions has also shown the presence in glasses of ordered cationic domains, similar to those existing in compositonally equivalent crystals [17]. For glasses containing heavy elements, the X-ray diraction amplitude of the heavy element dominates the Xray low-Q scattering, while the balance between the in-phase and out-of-phase contributions is important for the neutron data. The similarity between the position of the simulated and experimental ®rst peaks and the cation dependence of these peaks illustrate that the cation±cation arrangement in the glass is close to that of related crystalline phases. 6. Conclusions A comparison between AWAXS and neutron data reveals important changes in features in the structure factor at low Q. Simulations for small crystallites reproduce the position and (qualitatively) the intensity of these patterns. This reproduction indicates that the presence in glasses of quasi-lattice planes, similar to those observed in compositionally equivalent crystals, may be responsible for these features. The cation arrangement and the constructive/destructive interferences
91
between the Sr±Sr (Ba±Ba) pairs and the (alumino-) silicate network are important factors in explaining the low-Q region (the presence of one or more peaks, or of shoulders). These factors indicate similarities, at the medium range scale, between the structure of glasses and related crystals.
References [1] P.H. Gaskell, Materials Science and Technology, vol. 9, VCH, Weinheim, 1991, p. 175. [2] C. Brosset, Phys. Chem. Glasses 4 (1963) 99. [3] C.D. Hanson, T. Egami, J. Non-Cryst. Solids 87 (1986) 171. [4] S. Creux, B. Bouchet-Fabre, P.H. Gaskell, J. Non-Cryst. Solids 192&193 (1995) 360. [5] S. Creux, PhD thesis, Universite Paris 6, 1996. [6] D.L. Price, S.C. Moss, R. Reijers, M.-L. Saboungi, S. Susman, J. Phys. C 21 (1988) L1069. [7] S.R. Elliott, J. Phys.: Condens. Matter 4 (1992) 7661. [8] P.H. Gaskell, D.J. Wallis, Phys. Rev. Lett. 76 (1996) 66. [9] P.H. Gaskell, in: A.C. Wright, S.A. Feller, A.C. Hannon (Eds.), Borate Glasses, Crystals and Melts, Society of Glass Technology, Sheeld, 1997, p. 71. [10] A.K. Soper, W.S. Howells, A.C. Hannon, Rutherford Appleton Laboratory Report RAL-89 046, 1989. [11] K.-I. Machida, G.-Y. Adchi, J. Shiokawa, M. Shimada, M. Koizumi, Acta Crystallogr. B 38 (1982) 386. [12] G. Chiari, M. Calleri, E. Bruno, Am. Miner. 60 (1975) 111. [13] K.-F. Hesse, L. Liebau, Z. Kristallogr. 153 (1980) 3. [14] A.C. Wright, J. Non-Cryst. Solids 106 (1988) 1. [15] M. Czank, P.R. Buseck, Z. Kristallogr. 153 (1980) 19. [16] A. Le Bail, J. Non-Cryst. Solids 183 (1995) 39. [17] P.H. Gaskell, M.C. Eckersley, A.C. Barnes, P. Chieux, Nature 375 (1991) 350.
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Comparison of the low-Q features in diraction data for silicate glasses and crystals containing Sr or Ba Laurent Cormier a
a,* ,
Philip H. Gaskell b, Sophie Creux
c
Laboratoire Min eralogie-Cristallographie, Universit es Paris 6 and 7 and IPGP and UMR CNRS 7590, 4 place Jussieu, 75252 Paris cedex 05, France b Cavendish Laboratory, University of Cambridge, Madingley Road, Cambridge, CB3 0HE, UK c Saint Gobain Recherche, 39 quai Lucien Lefranc, BP 135, 93303 Aubervilliers cedex, France Received 3 June 1998; received in revised form 30 January 1999
Abstract Neutron scattering data have been obtained for a strontium- and a barium-containing silicate glass and a strontium aluminosilicate glass. These data are compared with previously published anomalous wide-angle X-ray scattering data for the Sr-containing glasses. Features in the diraction data at the smaller scattering vectors, Q, are compared with simulated X-ray and neutron diraction patterns for compositionally similar crystals. Peaks are found at Qs close to the `®rst sharp diraction peaks' of the glasses and have a cation±cation dependence. We suggest that this correspondence shows that the smaller Q features in the glasses have similar structural origins to those in the scattering data for the crystals with the same composition and therefore that the medium-range structures and cation±cation arrangements in the glasses are similar too. Ó 1999 Published by Elsevier Science B.V. All rights reserved. PACS: 61.43.Fs; 61.12.ÿq; 61.10.ÿi; 61.43.Bn
1. Introduction Studies of the structure of oxide glasses have mainly concentrated on alkali or alkaline-earth silicate glasses (see Ref. [1] for a review) but, to our knowledge, few investigations have been undertaken for the heavier elements, such as strontium or barium [2,3]. A wide angle X-ray scattering (AWAXS) study has recently been performed on Sr-containing silicate and aluminosilicate glasses [4,5]. Neutron scattering data can contribute to an understanding of the structure of these glasses, as
* Corresponding author. Tel.: +33-1 44 27 50 65; fax: +33-1 44 27 37 85; e-mail: [email protected]
the Sr-centred partial structure factors are less heavily weighted for neutron than for X-ray diffraction. Consequently, the silicate network becomes more apparent in the neutron data. Furthermore, a comparative study of the neutron and X-ray data can help in understanding features in the structure factors at the small scattering vectors, which are related to the medium range order (MRO) in the glass structure. We have carried out neutron diraction measurements on Sr-containing silicate and aluminosilicate glasses (SrOá0.19Na2 Oá1.9SiO2 , SrOáAl2 O3 á4SiO2 ) and on a barium silicate glass (2Ba2 Oá3SiO2 ). A small amount of Na2 O was added to the strontium silicate glass to avoid crystallization upon cooling. The study presented
0022-3093/99/$ ± see front matter Ó 1999 Published by Elsevier Science B.V. All rights reserved. PII: S 0 0 2 2 - 3 0 9 3 ( 9 9 ) 0 0 1 0 2 - 7
L. Cormier et al. / Journal of Non-Crystalline Solids 248 (1999) 84±91
in this paper concerns the variations in the position and intensity of the features at the smaller Q in the X-ray and neutron diraction data. (Q is the scattering vector and Q |Q| 4p sinh/k, where 2h is the scattering angle and k the wavelength of the probing radiation). These features are related to some kind of MRO but their origin is still unknown [6±9]. The explanations proposed mainly consider either quasi-crystalline organisations or correlations between clusters or voids. It was shown recently that planar structures in models for vitreous SiO2 are associated with the ®rst peak at smaller Q, the so-called ®rst sharp diraction peak (FSDP) [8]. The occurrence of Bragg diraction in a compositionally equivalent crystal at the same position as the FSDP, in many (or most) glasses, leads to a general explanation of this feature: similarity between the MRO in the two phases and, probably, the presence of quasi-lattice planes in glasses similar to those existing in related crystals [8,9]. 2. Neutron diraction data The neutron diraction intensities were measured at the ISIS spallation neutron source (Rutherford Appleton Laboratory, Didcot), using the Liquids and Amorphous Diractometer (LAD), for the three glasses, the empty vanadium can, the instrumental background, and a vanadium rod used for absolute normalisation. The counting time was about 1 day for each sample. The data were corrected and reduced according to the procedures described in Ref. [10]. The unsmoothed structure factors for the two Sr-conÿ1 , taining glasses are shown in Fig. 1. Above 2 A the signal is dominated by the (alumino-)silicate framework. We observe few dierences in the peak positions and intensities except a shift towards smaller Q for the aluminosilicate glass, which is due to the longer Al±O distances compared to the ÿ1 , a peak can be observed at Si±O ones. Below 2 A ÿ1 in scattering of the strontium (Na) 1.99 A ÿ1 in the scattering of silicate glass and at 1.73 A the strontium aluminosilicate glass. The amplitude and width of this feature are greater for the strontium aluminosilicate than for the strontium
85
Fig. 1. Neutron structure factors, S Q, for SrAl2 Si4 O12 , SrNa0:4 Si1:9 O5 and Ba2 Si3 O8 glasses (from top to bottom).
silicate glass. The structure factor, S Q, for the barium glass (Fig. 1, lower curve) is similar to that obtained for the strontium silicate glass, with a ÿ1 . The main dierence is the peak at 1.94 A presence in the barium glass of a well-de®ned ÿ1 ). shoulder at smaller Q (1.1 A 3. Simulation of the low-Q features in the diraction data We have compared the experimental X-ray and neutron diraction data with the calculated diffraction patterns for compositionally equivalent crystals. It is important to note that the sensitivity to the various atomic species is not identical for neutron and X-ray diraction. Dierences between the neutron and X-ray weighting factors for the partial functions (Table 1) lead to important changes in the smaller Q part of the diffraction pattern. In the Sr(Na) silicate glass, a ÿ1 is present in both the total and peak at 2 A dierential X-ray structure factors [4,5] (Figs. 1 and 4) and since the Sr±Sr contribution is larger (Table 1), this peak is likely to have a larger contribution from Sr±Sr correlations. The aluminosilicate glass scattering has a ®rst peak at 1.92 ÿ1 in the X-ray structure factor with a smaller A ÿ1 in the strontium intensity than the peak at 2 A silicate glass. This dierence indicates that the contribution of the Sr atoms is less in the aluminosilicate glass.
86
L. Cormier et al. / Journal of Non-Crystalline Solids 248 (1999) 84±91
Table 1 X-ray (WX-ray ), dierential (WDX-ray ) and neutron (Wneu ) weighting factors a for the partial structure factors for the strontium silicate ÿ1 and aluminosilicate and the barium silicate glasses. WX-ray and WDX-ray are averaged over the range 0±2 A SrNa0:4 Si1:9 O5
Pairs
WX-ray b
T±T T±O b T±M b;c O±O M±O c M±M c
0.05 0.16 0.19 0.12 0.30 0.18
SrAl2 Si4 O12 WDX-ray
0.24 0.36 0.40
Wneu
WX-ray
0.009 0.067 0.019 0.123 0.071 0.010
0.14 0.34 0.13 0.21 0.16 0.03
Ba2 Si3 O8 WDX-ray
0.38 0.47 0.16
Wneu
Wneu
0.015 0.090 0.009 0.135 0.028 0.001
0.009 0.068 0.015 0.127 0.056 0.006
Wneu 2 ÿ dij ni nj bi bj , WX-ray Q 2 ÿ dij ni nj R fi Q; Efj Q; E=jhf Q; Eij, WDX-ray nSr nj D fSr fj fSr fj =D jhf ij2 , where ni , bi and fi are, respectively, the atomic fraction, the neutron scattering length and the X-ray atomic diusion factor for element i. D is the dierence between two energies, close and far from the Sr K-edge. b T Si, Al. c M Sr (and Na) or Ba. a
There are no crystals corresponding to the composition of the Sr-containing glasses, but it is possible to compare the Sr(Na) silicate glass with a metasilicate crystal, a-SrSiO3 [11]. Ideally, the glass composition would not have included sodium and the Sr content would have been larger. However, preparation of a pure strontium silicate glass, with larger strontium contents and without phaseseparation or crystallisation, proved infeasible. Also it is possible to compare the scattering data for the glass with that of a sodium strontium metasilicate, Na4 SrSi3 O9 . We have made this comparison, and it is revealing, even though the Na concentration is much larger than that of the glass. However, space prevents discussion here and the most important diculty with this comparison: the fact that we compare a glass with a disilicate composition with a metasilicate crystal, is not avoided. The aluminosilicate glass can be compared with the anorthite form of SrOáAl2 O3 á2SiO2 (c-SrAl2 Si2 O8 ) [12]. For the barium silicate glass, we used the crystal with the same composition, 2BaOá3SiO2 (c-Ba2 Si3 O8 ) [13]. We compared the ÿ1 ) experimental data in the low-Q region (Q < 2 A with the diraction data calculated for the crystalline structures, using the CE R I U S 2 package (Biosym, Molecular Simulations, San Diego, California, USA) for crystallites of 30 nm diameter, to broaden the Bragg peaks. It should be noted that there is no intention to support a microcrystallite model for glasses, which is clearly untenable [14].
4. Results 4.1. The strontium aluminosilicate glass In Fig. 2, we present the simulated neutron and X-ray diraction and the corresponding experimental data for the strontium aluminosilicate sample. If we consider the X-ray diraction ®rst (Fig. 2(a)), we observe a (2 2 0) peak at ÿ1 , in agreement with the peak Q 1.93 0.02 A in the total structure factor for the glass at ÿ1 . The planes parallel to (2 2 0) lie 1.92 0.02 A close to both the (Al,Si,O) network and the Sr atoms (Fig. 3), so that both make in-phase contributions and increase the amplitude. This peak is thus the result of scattering from both the Sr atoms and the aluminosilicate network. We also simulated the diraction by the Sr atoms only, i.e. the Sr±Sr correlations, Fig. 2(a). This curve shows ÿ1 from the a Bragg re¯ection at 0.96 0.02 A (0 2 0) planes that contain the Sr atoms (Fig. 3). The small contribution of this peak to the total structure factor is due to out-of-phase contributions from the aluminosilicate network (Si,Al,O). Indeed, Fig. 3 shows that (Si,Al)O4 tetrahedra are located between the (0 2 0) planes and interfere destructively, which thus limit the intensity of this peak in the total X-ray structure factor. The position of the (0 2 0) peak agrees well with the peak ÿ1 in the experimental dierobserved at 1.06 A ential structure factor, DSr (Q) (Fig. 2(a)). The function, DSr (Q), is in fact the sum of all the
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Fig. 2. Simulated X-ray (a) and neutron (b) diraction data for (c-SrAlSi2 O8 ), showing the full crystal, a lattice with Sr atoms only (Sr± Sr) and a lattice with Si, Al and O atoms only (Si,Al,O). The upper curves (displaced for clarity) are the experimental data. In (a), Sexp (Q) and DSr (Q) are respectively the AWAXS total and dierential structure factors from Refs. [4,5] (DSr (Q) is the weighted sum of all the Sr-centred partial functions) and in (b) Sexp (Q) denotes the neutron diraction structure factor for the Sr aluminosilicate glass.
Fig. 3. A projection of the crystalline structure of SrAlSi2 O8 (2 unit cells in each direction).
Sr-centred pairs and this may explain the relatively poor agreement between the simulated Sr± Sr contribution and the experimental DSr (Q) data
ÿ1 in DSr (Q) at larger Q (the peak at 2.2 0.02 A includes Sr±O and Sr±(Si,Al) correlations, not just Sr±Sr).
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In the neutron data for the glass, the peak at ÿ1 in the X-ray data is shifted to 1.92 0.02 A 1.73 0.02 Aÿ1 (Fig. 2). This shift would be expected from correlations similar to those resulting in the 2 0 2 re¯ection in the crystal which has a larger intensity for neutron than for X-ray scattering (Fig. 2) and mainly involves the aluminosilicate framework. The Sr±Sr curve indicates that Sr±Sr pairs are not one of the largest contributors to the total neutron structure factor. The anti-phase contributions between the Sr±Sr pairs and the (Si,Al,O) pairs contribute to a decrease in the intensity of the (0 2 0) and 2 0 2 peaks. This result is in agreement with the fact that the Sr-centred weighting factors are small for the neutron data (Table 1). 4.2. The strontium silicate glass The simulated X-ray structure factor for cSrSiO3 (Fig. 4(a)) has two peaks at 1.77 0.02 ÿ1 and 2.15 0.02 A ÿ1 due to the 3 1 A 1 and (3 1 1) re¯ections, respectively. The similarities
between the diraction from the full crystal and from the Sr±Sr pairs only indicate that the X-ray data are dominated by the lattice planes involving Sr (Fig. 5). The peak observed for the glass lies ÿ1 , between the two Bragg peaks at 2.00 0.02 A ÿ1 . These at 1.77 0.02 Aÿ1 and at 2.15 0.02 A re¯ections correspond to lattice planes containing Sr atoms (several parallel to the same axis of projection). It is therefore reasonable to assert that the eect of disorder in the glass will be to merge the dierent peaks into a single broad ÿ1 in peak. The (0 0 2) peak at 1.25 0.02 A the Sr±Sr curve is not in agreement with the small ÿ1 in DSr (Q) but the precipeak at 0.82 0.02 A sion of the smaller Q X-ray data is less than at other Qs. Once again, the disappearance of this peak in the total diraction spectrum can be explained by out-of-phase contributions from the SiO4 tetrahedra which are located between the planes populated by the Sr atoms and thus give antiphase contributions to the scattering amplitude (Fig. 5).
Fig. 4. Simulated X-ray (a) and neutron (b) diraction data for (c-SrSiO3 ), showing the full crystal, a lattice with Sr atoms only (Sr±Sr) and a lattice with Si and O atoms only (Si,O). The upper curves (displaced for clarity) are the experimental data. In (a) Sexp (Q) and DSr (Q) are, respectively the AWAXS total and dierential structure factors from Refs. [4,5] and in (b) Sexp (Q) denotes the neutron diraction structure factor for the Sr silicate glass.
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Fig. 5. A projection of the crystalline structure of SrSiO3 (2 unit cells in each direction).
The simulated neutron data (Fig. 4(b)) have a ÿ1 (due to the (0 2 1), (3 1 0) and peak at 1.87 A 3 1 2 re¯ections), compared to the experimental ÿ1 in the data for the glass. This peak peak at 2 A has a tail at smaller Q compared to the peak in the neutron data for the aluminosilicate glass. The interpretation is not obvious but there are several ÿ1 in smaller features near the (1 1 0) line at 1.04 A the crystal which may relate to the tail in the scattering of the sample. However, there may be dangers in trying to push comparisons between crystals and glasses too far. 4.3. The barium silicate glass In Fig. 6(a), we present the simulation of the Xray structure factor for the c-Ba2 Si3 O8 . Unfortunately, there are no experimental X-ray data for a glass of this composition. The peak at ÿ1 in the crystal, Fig. 6(a), contains a 1.70 0.02 A Ba±Ba contribution, associated with a (2 1 0) re¯ection. This result indicates that the Ba±Ba pairs dominate the X-ray diraction, as the Sr±Sr correlations do in the strontium silicate glass. In the simulated neutron diraction data for cBa2 Si3 O8 , Fig. 6(b), a ®rst peak at 1.69 0.02 ÿ1 , corresponding to the 1 1 2 planes, is obA served. Agreement with the data for the glass,
ÿ1 , is by no means perfect. The major 1.94 0.02 A contribution to this peak for the crystal comes from the silicate network and therefore this discrepancy may indicate topological dierences in the organisation of SiO4 tetrahedra between the glass and the crystal. In the glass, a shoulder is ÿ1 , close to the crystalline observed at 1.1 0.1 A ÿ1 . If we consider (1 0 2) re¯ection at 1.07 0.05 A the diraction from the Ba±Ba pairs only (Ba±Ba in Fig. 6(b)) and from the silicate network only ((Si,O) in Fig. 6(b)), we note the presence of this feature in both curves. The reduced intensity in the total diraction curve indicates that these contributions scatter with (partial) opposition of phase for the (1 0 2) re¯ection. 5. Discussion The approach advocated here (in contrast to those developed for chalcogenide glasses) does not suppose any layer-like structure. For example, the anorthite structure (c-SrAl2 Si2 O8 ) can be described by a three-dimensional network of interconnected SiO4 and AlO4 tethahedra and it is the presence of lattice planes that gives rise to diraction. Comparisons between the diracted intensity data at low Q for the glasses and similar crystals are in
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Fig. 6. Simulated X-ray (a) and neutron (b) diraction data for (c-Ba2 Si3 O8 ), showing the full crystal, a lattice with Ba atoms only (Ba± Ba) and a lattice with Si and O atoms only (Si,O). In (b) the upper curve, Sexp (Q), is the experimental neutron diraction structure factor for the Ba silicate glass (displaced for clarity).
semi-quantitative agreement with both AWAXS and neutron data. We suggest that this result is reminiscent in the glass of quasi-lattice planes (distorted, imperfect and not necessarily `planar') [8,9]. The X-ray and neutron diraction patterns calculated for c-SrAl2 Si2 O8 are in agreement with the data for the strontium aluminosilicate glass. They indicate that the role of Sr is not very important in the smaller Q feature, which is due to ÿ1 the aluminosilicate network. The peak at 1.06 A in DSr (Q) is well-reproduced by the simulations. We suggest that the fact that this peak is dependent on the Sr±Sr correlations is because the distribution of Sr in the glass resembles that in the crystal. The simulations for SrSiO3 show that the crystal and the glass have neutron and X-ray features at similar Q, although dierences remain that probably result from topological disorder in the ÿ1 for the crystal glass (two peaks around 2 A instead of one for the glass). The smaller Q peaks in both the glass and the crystal are attributed
mainly to the Sr±Sr pairs. It is thus likely that the ÿ1 in this glass comes from a similar peak at 2 A organisation of the strontium atoms in the glass and the crystal. For the barium silicate glass, the position of the ÿ1 is not well reproduced, experimental peak at 2 A which indicates that topological dierences exist between the crystal and the glass. This topology could be related to the existence of a variety of barium silicate crystals that dier by the topology of the silicate network [13,15]. However, the ÿ1 is simulated in the crystal by shoulder near 1.1 A the (1 0 2) Bragg re¯ection that corresponds to lattice planes mainly populated by Ba atoms. X-ray diraction data should give more information on the structure of this glass and particularly, on the Ba±Ba atomic pairs to which this technique is more sensitive. Although a microcrystallite model is not implied, some important similarities between glasses and compositionally equivalent crystals seem to exist at the medium range scale. The idea that glass structure can be related to that of a crystal with
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similar composition is supported by the observation that distorted (but topologically identical) models of cristoballite can give an excellent ®t to the FSDP for a-SiO2 [16]. Moreover, neutron diffraction of isotopically substituted ions has also shown the presence in glasses of ordered cationic domains, similar to those existing in compositonally equivalent crystals [17]. For glasses containing heavy elements, the X-ray diraction amplitude of the heavy element dominates the Xray low-Q scattering, while the balance between the in-phase and out-of-phase contributions is important for the neutron data. The similarity between the position of the simulated and experimental ®rst peaks and the cation dependence of these peaks illustrate that the cation±cation arrangement in the glass is close to that of related crystalline phases. 6. Conclusions A comparison between AWAXS and neutron data reveals important changes in features in the structure factor at low Q. Simulations for small crystallites reproduce the position and (qualitatively) the intensity of these patterns. This reproduction indicates that the presence in glasses of quasi-lattice planes, similar to those observed in compositionally equivalent crystals, may be responsible for these features. The cation arrangement and the constructive/destructive interferences
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between the Sr±Sr (Ba±Ba) pairs and the (alumino-) silicate network are important factors in explaining the low-Q region (the presence of one or more peaks, or of shoulders). These factors indicate similarities, at the medium range scale, between the structure of glasses and related crystals.
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