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Small-angle X-ray scattering and Rayleigh scattering studies of the microstructure of some optical glasses
Journal of Non-Crystalline Solids 258 (1999) 198±206
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Small-angle X-ray scattering and Rayleigh scattering studies of the microstructure of some optical glasses F. Geotti Bianchini a, P. Riello b, A. Benedetti b,* b
a Stazione Sperimentale del Vetro, 30141 Murano-Venezia, Italy Dipartimento di Chimica Fisica, Univ. di Venezia, Calle Larga S. Marta 2137, 30123 Venezia, Italy
Received 24 June 1998; received in revised form 30 March 1999
Abstract Several optical glass samples were studied by small-angle X-ray Scattering (SAXS) in order to verify the presence of inhomogeneity in the range (1±100 nm). The results were compared with Rayleigh scattering measurements in order to verify a possible correlation between microstructure and scattering losses. For most glasses investigated, the presence of phase separation was excluded and the Rayleigh scattering intensities were attributed to refractive index ¯uctuations. For glasses ZKN7 and SK11 evidence of phase separation, with size of about 8 nm and less than 2 nm respectively, was obtained using SAXS. The particle size was insensitive to annealing treatments in the case of SK11 and showed a continuous growth with annealing time at 610°C in the case of ZKN7. For these two glasses the overall Rayleigh scattering intensity includes a contribution due to the presence of phase separated particles. Ó 1999 Elsevier Science B.V. All rights reserved.
1. Introduction Rayleigh scattering in optical glasses should be minimized to limit intensity losses. The Rayleigh (elastic) scattering originates at each wavelength in media with ¯uctuations of the refractive index in microscopically small volumes. The equations describing the intensity of scattered light contain the relative refractive index n np =nm (i.e. the ratio between the refractive index of the scattering particle np and of the matrix nm [1]). Theories to describe the Rayleigh scattering vary according to the ratio between particle size and the wavelength of light [1]. The overall light scattering intensity at
* Corresponding author. Tel.: +39-041 257 8544; fax: +39-041 257 8594; e-mail: [email protected]
each wavelength is the sum of all the intensities caused independently by each event. According to M orixbauer and Steinert et al. [2,3] the intensity of Rayleigh scattering in optical glasses varies in a broad range. In principle such scattering can be caused by various glass features with refractive index ¯uctuations including: (a) density and concentration ¯uctuations [4]; (b) metastable phase separation associated with amorphous particles generally in the range 1± 100 nm [5]; (c) technological inhomogeneities (melting remnants caused by refractory and metal (Pt) particles and microbubbles, generally in the micrometer range) [6]. Each of these events is associated with some type of deviation from the ideal (fully random and homogeneous) liquid structure and gives rise to
0022-3093/99/$ - see front matter Ó 1999 Elsevier Science B.V. All rights reserved. PII: S 0 0 2 2 - 3 0 9 3 ( 9 9 ) 0 0 5 4 3 - 8
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Rayleigh scattering whose intensity varies with the size, concentration and refractive index dierence of particles vs. bulk. In the case of optical glasses, events (a) and (c) are well described. Refractive index ¯uctuations are an important source of Rayleigh scattering whose intensity varies greatly with the chemical composition. Scattering losses limit the performance of even the purest optical ®bers [7,8]. Comprehensive studies were published by Maurer [9] and recently by Maksimov [10±12]. Technological inhomogeneities associated with incomplete melting are described by various authors [6,13]. Their presence in commercial optical glass is minimized by suitably adapting the production technology. On the other hand, very little information is available about the possible occurrence of phase separation with the exception of a paper by Winther [14] dated 1962 and Steinert et al. [3] which found for the zinc crown glass ZK7 a dissimmetric indicatrix attributed to phase separation. In order to improve the knowledge about this important issue, small-angle X-ray scattering is used in this study to analyze the presence of inhomogeneities in the range 1±100 nm [5] in several commercial optical glasses. 2. Experimental 2.1. Sample selection A range of optical glasses whose Rayleigh scattering at 546 nm varies from 2 to 150 10ÿ5 cmÿ1 was selected. In Table 1 are reported for each glass the commercial designation, the scattering intensity at 90° measured according to M orixbauer [2] and indications about the chemical composition obtained from Gliemeroth [15]. The samples were selected in order to cover a wide range of Rayleigh scattering levels and of chemical compositions including crown and ¯int glasses. In particular, ZKN7 was selected for its zinc oxide containing formulation (similar to ZK7, which Steinert [3] suggested to be phase separated); F2, BaF13, SK11, SF11 and SF14 for their PbO and BaO content, in the hope to elucidate the role of such oxides in promoting phase separation and Rayleigh scattering.
199
2.2. Small-angle X-ray scattering (SAXS) measurements Samples for small-angle scattering were 10 35 mm platelets prepared by grinding and polishing with cerium oxide. For each source, the thickness was selected in order to optimize the absorption caused by the samples. Ni-®ltered CuKa and Zr®ltered MoKa radiation were used for 0.1 and 0.5 mm thick samples, respectively. The X-ray scattering data were obtained with a Kratky smallangle camera in the Ôquasi-in®nite slitÕ geometry, equipped with an electronic step scanner. A pulse height discriminator and proportional or scintillation counter, depending on the wavelength used, were also employed. The intensities (denominated J(h) for this geometry, where h 4p sin h=k is the modulus of the momentum transfer, h the scattering angle and k is the wavelength employed) were measured by determining the time necessary to accumulate 2 104 counts for each scattering angle. The corrected intensities were obtained by subtracting the instrumental background intensity corrected for sample absorption. 2.3. Description of SAXS data The small-angle intensity scattered by a dilute system of a continuous normalized distribution P(r) of particles with radius r is represented by a monotonically decreasing curve given by Z 1 I h / P rr2 h; r dr; 2
where r2 h; r Dq V 2 S 2 h; r is the dierential scattering cross section of a single particle, V the particle volume, Dq the electronic density dierence between the particle and matrix and S 2 h; r is the particle form factor, that in the case of spherical particles is equal to S h; r 4p
sin hr ÿ hr cos hr 3
hr
:
The small-angle scattering from demixed glasses sometimes shows a strong correlation peak resulting from interparticle interference eects. In such a case, the simple model of uncorrelated particles is no longer adequate to explain the
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Table 1 Trade name, indicative chemical composition [15], refractive index and intensity scattered at 90° at the wavelength of 546 nm [2] of the optical glasses considered R90 105 in cmÿ1 at 546 nm
Glass designation and type
Chemical composition in wt% (Gliemeroth)
Refractive index at 589 nm
BK7 FK3
Boron crown Fluorine crown
1.517 1.464
1.9 2.5
F2 BaF13
Flint Barium ¯int
1.619 1.669
8.4 23
SK11
Dense crown
1.564
29
ZKN7 SF11 SF14
Zinc crown Dense ¯int Dense ¯int
Borosilicate glass Phosphate or borosilicate with high F content Alkali silicate with 39±47% PbO Alkali silicate with BaO + PbO < 40% Aluminoborosilicate with BaO > 15% (Boro)silicate with ZnO > 10% Alkali silicate with PbO > 47% Alkali silicate with PbO > 47%
1.508 1.784 1.762
58 98 154
results. The following more general expression for I(h) has to be considered: Z Z 2 I h / r h; rP r dr q k h; r1 ; r2 r h; r1 r h; r2 P r1 P r2 dr1 dr2 ;
2
where q is the total particle number density, k(h, r1 , r2 ,) is the pair structure function: Z 1 sin hr k h; r1 ; r2 g r; r1 ; r2 ÿ 1 4pr2 dr hr 0 and g(r, r1 , r2 ) known as the radial distribution function, is connected to the probability of ®nding a given con®guration of two particles with radii r1 and r2 , respectively at a distance r. One of the most successful models used to describe systems with an interparticle interference eect is the one in which the interaction between the particles is described by a hard sphere potential [16]. The assumption that the spherical particles with radius ri grow by depleting a surrounding volume of radius Ri ari a P 1:0 and, in this depleted region, there are no other particles equivalent to introducing an interacting hard sphere potential of radius Ri . Dierent solutions are possible for k(h, r1 , r2 ) according to the model used to evaluate g(r, r1 , r2 ). Several authors ®t their data sets with the approach derived from the Percus±Yevick approximation [16,17]. In order to take into account interference eects in our materials we use instead the simpler approximation reported by Guinier
and Fournet [18] and by Mengoni [19] and recently analytically solved by the authors [20]. Following this approach the scattered intensity can be written as Z Z 2 I h A rr h; rP r dr 1=d c h; r1 ; r2 b h; r1 ; r2 k h; r1 ; r2 r h; r1 r h; r2 P r1 P r2 dr1 dr2 ; where A is a scale constant, 3=2 1=d Vf 2p = a3 hVp i; Vf =a3 being the volume fraction of the demixed phase and hVp i the average volume of the particles. The functions c and b are de®ned by p Z 1 2 r eÿ/ r;r1 ;r2 =KT ÿ 1 sin hr dr; hb h; r1 ; r2 p p ÿ1 3 Z dc h; r1 ; r2
1 0
P r3 c h; r1 ; r3
b h; r1 ; r3 b h; r3 ; r2 dr3 :
4
Eqs. (3) and (4) can be solved analytically [20] for a continuous normalized Shultz distribution P(r) of spheres with an interacting hard sphere potential /(r, r1 , r2 ) of radius ar de®ned as P r
1 C z 1
z1 hri
z1
rz exp
ÿ
z1 r hri
F.G. Bianchini et al. / Journal of Non-Crystalline Solids 258 (1999) 198±206
and / r; r1 ; r2
1; 0 6 r 6 ar1 ar2 : 0; r > ar1 ar2
With this approach using Eq. (2) it is theoretically possible to reproduce, by a ®t procedure, an experimental SAS intensity showing a correlation peak with the help of ®ve parameters: hri z > ÿ1 a Vf A
average radius of the distribution; form parameter of the distribution; constant relating the radius of the depleted sphere to that of the particles; total volume fraction of the depleted zone; a scale constant proportional to the number of the demixed particles np and (Dq)2 .
When 1=d 0 Vf 0 the intensity reduces to the low density limit case. All the theoretical intensities have been smeared in order to take into account the experimental set up used. 2.4. Sensitivity of SAXS measurements Small-angle X-ray diraction is due to electron density ¯uctuations with a suitable size within the material. When the glass can be regarded as a system of homogeneous particles embedded in a homogeneous matrix with electron densities respectively equal to q1 and q2 , and relative volume equal to /1 and /2 , the mean square dierence of the electron densities of the phases (in a two-phase 2 2 system) is de®ned as Dq q1 ÿ q2 /1 /2 . qi is 3 expressed in gram electrons P per cm and is given by the formula: qi qm Zi =M where Zi number of electron in the ith atom of the compound under examination, qm (g/cm3 ) is the corresponding mass density of the compound and M is its molecular weight. Multiplying qi by AvogadroÕs number N, the total number of electrons per cm3 is obtained. For example, the electron density of pure bulk vitreous silica with density 2.02 g/cm3 is equal to N 1:099 el/cm3 . As reported by Golubkov et al. [21], the sensitivity of the smallangle equipment makes it possible to detect the
201
presence of microinhomogeneous features from 2 the SAXS curves for samples with Dq > 10ÿ1 3 2 (el/nm ) . If we consider additionally that the size resolution limit of SAXS is about 1±100 nm (with conventional cameras), we can estimate the features of the inhomogeneities that can be detected by this technique. When the system has no heter2 ogeneities and/or their size or Dq is less than the resolution limits reported above, the SAXS signal is given only by a constant uniform intensity. 2.5. Rayleigh scattering measurements The Rayleigh scattering intensity at 546 nm of the as-received glass samples was measured using an equipment similar to that described by M orixbauer [2]. The purpose of the equipment is to measure the intensity of Rayleigh (elastic) scattering in the visible range at an angle of observation of 90° relative to the incident beam, R90 , in order to quantify scattering related intensity losses in optical glasses. The source is a mercury vapour lamp, whose beam is focused on the samples (polished glass blocks about 25 mm 25 mm 18 mm) with the help of an array of lenses. The detector, a Si-photodiode supported by a rotating arm, can be placed in two positions: at 180° to the incident beam, to read the transmitted intensity (attenuated by grey ®lters), then at 90° to read the intensity scattered at 90°. Ratioing the two values eliminates the in¯uence of re¯ection losses due to glass refractive index. To eliminate the in¯uence of spurious illumination, in view of the weak intensity of R90 , the primary beam is modulated with the help of a chopper and the detector signal ampli®ed with a lock-in ampli®er. Monochromatization is achieved by inserting suitable interference ®lters both before and after the sample, to prevent artifacts due to sample luminescence. The overall absolute uncertainty on R90 was estimated to be 19%. The reproducibility, assessed by repeated measurements with sample re-positioning, was between 1% and 2% in the visible range. Additionally, a comparative evaluation of R90 of the heat treated samples was obtained using a procedure suggested by Scott and Rawson [22]. Although not quantitative, it is quite suitable to
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assess dierences when dierent samples are compared. The brightness of the beam of a 2 mW He± Ne laser crossing a polished block of the unknown sample is observed perpendicularly in a dark room and visually compared to the brightness observed on similar blocks of the optical glasses described in Table 1, whose values of R90 at 546 nm are known. To each heat treated sample is attributed a Rayleigh scattering intensity ranging between those of the optical glasses showing the nearest brightness. Considering that for all the optical glasses considered the variation of the scattered intensity with wavelength is similar (a dependence close to kÿ4 with the exception of ZKN7 with a k±4:7 dependence [2,3]), the sequence of intensities was supposed to remain unchanged from 546 to 633 nm. 3. Results The Rayleigh scattering intensity at 90° determined on the as received optical glass samples, R90 , is reported in Table 1. The presence of a large percentage of PbO in samples F2, BaF13, SF11 and SF14 and the corresponding low value of the transmission coecient (eÿlt where l is the linear absorption coecient and t is the sample thickness) did not allow a very accurate analysis of the SAXS curves even for t 0.1 mm. In any case, the constant intensity obtained with both radiation sources indicates that they are homogeneous from the SAXS point of view. A constant J(h) function was obtained also for the samples BK7 and FK3. As an example, the SAXS intensities corresponding to these two latter samples are reported in Fig. 1. For glasses SK11 and ZKN7, SAXS measurements provided more complex results. Figs. 2 and 3 report the experimental intensity of as received samples. In both cases the variation of J(h) vs. h suggests the presence of microstructural features. For these two samples no crystalline phase with crystallite size greater than 1.5 nm (the resolution limit of this technique) could be evidenced by wide angle X-ray scattering measurements, therefore the SAXS intensity can be attributed to phase sepa-
Fig. 1. Experimental SAXS intensity obtained for as-received samples FK3 (solid circles) and BK7 (open circles) using CuKa as a source.
ration phenomena. The SAXS results obtained by a best ®tting procedure of the experimental intensities, plus a background function B C=h3 are given in Table 2. In the same table, in order to give a more readable picture of the system, instead of reporting separately the values of a and Vf , we give the value of the total volume fraction of the demixed phase Vf /a3 . For the ZKN7 glasses, showing a correlation peak, the intensity was ®tted by Eq. (2) and the theoretical model described in Section 2.3. The SK11 SAXS curves that do not show a well-de®ned correlation peak were treated as a dilute system of particles and ®tted by Eq. (1). In order to con®rm the presence of phase separation and to follow its thermal evolution, samples of the two glasses were also heat-treated at dierent temperatures, in the range up to about 100°C above their Tg . ZKN7, with Tg 528°C, showed microstructural changes for treatments between 610°C and 650°C. In particular, the behavior observed after annealing between 6 and 74 h at 610°C was investigated in detail. The annealing program for SK11, with Tg 610°C, was 650°C, 675°C, 700°C and 725°C for 18 h. The results concerning ZKN7 samples and reported in Table 2 show a kinetic growth of the particle sizes and a parallel increase of the light scattering intensity. On the contrary, even prolonged heat
F.G. Bianchini et al. / Journal of Non-Crystalline Solids 258 (1999) 198±206
Fig. 2. Experimental SAXS intensity obtained for an as-received sample of SK11 using CuKa as a source. Continuous line: data ®t. Dashed line: B C=h3 function.
treatments in the range from 40°C up to 115°C above Tg used for glass SK11 were unable to grow the amorphous phase present, since the SAXS as well as the Rayleigh intensities of dierently annealed SK11 samples are identical. Finally, also glass BK7 giving no evidence of phase separation in the as-received state was heat treated for 17 h at 615°C, 650°C and 670°C. Both the SAXS intensities and the Rayleigh intensities of annealed samples were identical to those of asreceived samples. This indicates that heat treatments in the range from 60°C to 110°C above Tg (559°C) do not modify the sub-microinhomogeneous structure of this glass, in particular its refractive index ¯uctuations.
203
Fig. 3. Experimental SAXS intensity obtained for an as-received sample of ZKN7 using CuKa as a source. Continuous line: data ®t. Dashed line: B C=h3 function.
4. Discussion The formation of metastable phase separation is related to the growth of amorphous aggregates in a glassy matrix. The possibility of detecting the presence of amorphous microstructural features embedded in an amorphous matrix was always considered a dicult task [23]. Small-angle scattering is suitable to the investigation of these structures in view of its ability to describe both crystalline and amorphous heterogeneities. Within the limits of SAXS sensitivity (size 1± 100 nm, Dq2 > 10ÿ1 (el/nm3 )2 ), glasses BK7, FK3, F2, BaF13, SF11 and SF14 are homoge-
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Table 2 SAXS analysis results compared with the R90 levels Samples
hri (nm) A Vf /a3 z Relative R90 level a
SK11
ZKN7
As received and heat treated
As received
6 h 610°C
0:9 0:5 ± ± ± SK11a
4:3 0:4 3:1 10ÿ8 0:5 0:13 0:04 27 5 ZKN7a
7:2 0:5 1:9 10ÿ9 0:2 0:17 0:05 20 4 >SF14
23 h 610°C 10:7 0:8 6:3 10ÿ10 0:7 0:29 0:07 16 4 >SF14
74 h 610°C 21:5 1 1:1 10ÿ10 0:1 0:38 0:10 25 6 SF14
As received.
neous. Therefore, their Rayleigh scattering intensity should be attributed to refractive index ¯uctuations, in agreement with the traditional interpretation [9]. For BK7 even prolonged heat treatments above Tg did not aect the R90 or SAXS intensities. In the case of as-received ZKN7 and SK11, SAXS evidence reveals the presence of amorphous particles with size 2hri of 8 and 2 nm, respectively. In both cases the presence of phase separation is most likely, however the kinetics of ripening were quite dierent. For ZKN7 annealing above Tg even for some hours produced 2 coarsening. If we assume Dq constant during the annealing treatment, the decreasing value of A, reported in Table 2, can be related to the disappearance of the smaller particles in the coarsening process as suggested by Lifshitz and Slyozov [24]. Furthermore, the almost constant value of z, the form parameter of the size distribution, indicates that the shape of the particle size distribution curve is not in¯uenced by thermal treatments, but shifts homogeneously towards larger values. For glass SK11 the SAXS and Rayleigh scattering results were absolutely insensitive to heat treatments. For these two glasses the R90 intensity contains additionally a contribution due to phase separation, which becomes predominant for annealed ZKN7 as the particle size and the volume fraction of the demixed phase increase (see Table 2). It is generally believed that the scattering of visible light in optical glasses results from density and concentration ¯uctuations, however, so far little evidence has been published about the size,
nature and composition of such ¯uctuations. Various authors postulated the presence of clusters associated with a non-random distribution of network modi®ers [7,12,25]. The present SAXS results can contribute to this discussion by excluding for glasses BK7, FK3, F2, BaF13, SF11 and SF14 ¯uctuations with size outside the 1±100 nm range and/or mean square dierence of electron densities of the two phases >10ÿ1 (el/nm3 )2 . Similar conclusions are reached if the discussion is generalized to multicomponent glasses, which recently were suggested to have a cluster structure on the nanometer scale. Examples are the modi®ed random network model [26]; the strained mixed cluster model [27]; structural models including channels [28]; the clustered nanosize mixtures [29]. From theoretical calculation Conradt [29] suggests a size of 1±4 nm, Goodman [26] up to 5 nm. According to Nghi^em et al. [30] AFM assisted fractography reveals nanometer scale heterogeneities. In a previous paper by the present authors [31] a ¯at J(h) behavior ± implying lack of inhomogeneities within SAXS resolution ± was found for various commercial soda lime glasses (containers and plate glass) and lead alkali silicate glasses. As concerns the eect of speci®c modi®ers such as PbO on phase separation, the literature does not formulate clear indications. According to Vogel [32], high lead silicate glasses consist of a high SiO2 droplet phase embedded in a high lead matrix, however, the tendency towards immiscibility is suppressed in a suitable region of the ternary K2 O±PbO±SiO2 system. Such statements are insucient to predict the microinhomogeneity of ¯int optical glasses and of the so-called lead crystal
F.G. Bianchini et al. / Journal of Non-Crystalline Solids 258 (1999) 198±206
glasses for tableware and decorative articles, whose chemical composition is relatively complex, as exempli®ed by Table 1 and by a previous SAXS study of the present authors [31]. In the same paper, a commercial sample of lead crystal glass with 26% PbO had a ¯at J(h) behavior similar to those observed here for glasses F2, SF11 and SF14 (containing between 39 and >47 PbO wt%). Its Rayleigh scattering intensity at 633 nm, determined with the procedure described above, was intermediate between those of FK3 and F2. In summary, SAXS evidence does not reveal the presence of any signi®cant microinhomogeneity in lead oxide based optical glasses that could explain the wide range of Rayleigh scattering levels observed (between 8 and 154 10ÿ5 cmÿ1 ). SiO2 -rich droplets are unlikely, since they would be easily detected in view of the electron density dierence. According to some authors [7,12,24] a further possible explanation lies in the formation of clusters that include Pb ions. This might explain the fact that the Rayleigh scattering increases with PbO content, as discussed by Dietzel [25] and Maurer [9]. According to Maksimov [10,12] and Karapetyan et al. [33] the role of PbO is to ÔdecorateÕ ¯uctuational microinhomogeneities in ¯int glasses, causing a corresponding increase of the Rayleigh scattering. The present SAXS results are not incompatible with this model, however the formation of clusters including aggregated Pb atoms is unlikely since their electron density would be suciently dierent from the matrix to cause a detectable SAXS signal. Further signi®cant modi®ers are BaO and ZnO. BaO is present in BaF13 (barium lead alkali silicate) and SK11 (barium aluminoborosilicate), only the latter of which shows inhomogeneous features. ZKN7, described as a zinc aluminoborosilicate, shows phase separation as-received and ripens on annealing. 5. Conclusions SAXS analysis was performed on a range of as received and heat treated commercial optical glasses in order to demonstrate the presence of inhomogeneities in the range 1±100 nm. For
205
glasses BK7 (as received and heat treated), FK3, F2, BaF13, SF11 and SF14 the presence of microstructure could be excluded. From the analysis of the SAXS curves obtained here it can be concluded that the size of the scattering centers is outside the 1±100 nm range and/or the mean square dierence of electronic densities of the two phases is <10ÿ1 (el/nm3 )2 . Therefore, the observed Rayleigh scattering can be attributed to refractive index ¯uctuations. Concerning glass ZKN7, the presence of particles with a size of about 8 nm could be clearly evidenced. The kinetic growth of the particle size after annealing for various times at about 80°C above Tg con®rms the presence of a metastable phase separation. As shown in Table 2, for this glass the overall Rayleigh scattering includes a contribution due to the presence of phase separated particles. For glass SK11, particles with size near the resolution limit of the SAXS measurements (2 nm) were detected. Neither the particle size (less than 2 nm), nor the Rayleigh scattering intensity were in¯uenced by thermal treatments above Tg . Acknowledgements The ®nancial contribution of the Ministry of Industry (MICA, Rome, Italy) and the Italian CNR is acknowledged. We are grateful to Dr F.-T. Lentes (Schott Glass Works, Mainz, Germany) for useful discussions. The authors thank Mr R. Zen (Venice) for preparing 0.1 mm plates and Mrs M. Preo (SSV) and T. Finotto (University) for technical assistance. References [1] I. Fanderlik, Optical Properties of Glass, chap. 4.4, Elsevier, Amsterdam, 1983. [2] R. M orixbauer, diplomarbeit, Fachhochschule Wiesbaden (1987). [3] J. Steinert, W. Rohmann, G. Tittelbach, Silikattechnik 35 (1984) 186. [4] J. Zarzycky, Les Verres et lÕetat Vitreux, chap. 7, Masson, Paris, 1982. [5] E.A. Porai-Koshits, in: D.R. Uhlmann, N.J. Kreidl (Eds.), Glass Science and Technology, vol. 4A, Academic, New York, 1990, p. 1.
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[6] F.-T. Lentes, H.-J. Becker, Fundamentals of the Glass Manufacturing Process 1991, Society of Glass Technology, Hudders®eld, England, 1992, p. 159. [7] M.E. Lines, J. Non-Cryst. Solids 195 (1996) 249. [8] S. Todoroki, S. Sakaguchi, J. Am. Ceram. Soc. 78 (9) (1995) 2566. [9] R.D. Maurer, J. Chem. Phys. 25 (1956) 1206. [10] L.V. Maksimov, Glastechn. Ber. Glass Sci. Technol. 68 (C1) (1995) 51. [11] L.V. Maksimov, Glass Phys. Chem. 22 (3) (1996) 165. [12] L.V. Maksimov, Fundamentals of Glass Science and Technology, Glafo, V axj o Sweden, 1997, p. 247. [13] J.S. Hayden, H.-J. Homan, Schott Inform. 55 (1991) 6. [14] A. Winther, Verres Refract. 16 (1962) no. 5 273.9. [15] G. Gliemeroth, J. Non-Cryst. Solids 47 (1982) 57. [16] J.S. Pedersen, Phys. Rev. B 47 (1993) 657. [17] R. Triolo, E. Caponetti, S. Spooner, Phys. Rev. B 39 (1989) 4588. [18] A. Guinier, G. Fournet, Small Angle Scattering of X-Rays, Wiley, New York, 1955. [19] A. Mengoni, J. Chem. Phys. 87 (1987) 2560. [20] P. Riello, A. Benedetti, J. Chem. Phys. 106 (1997) 8660.
[21] V.V. Golubkov, A.P. Titov, T.N. Vasilevskii, E.A. Porai Koshits, Fiz. Khim. Stekla 3 (1977) 306. [22] B. Scott, H. Rawson, Glass Technol. 14 (5) (1973) 115. [23] O.V. Mazurin, E.A. Porai-Koshits (Eds.), Phase Separation in Glass, North-Holland, Amsterdam, 1984. [24] I.M. Lifshitz, V.V. Slyozov, J. Phys. Chem. Solids 19 (1966) 35. [25] A. Dietzel, Glastech. Ber. 65 (1) (1992) 15. [26] G.N. Greaves, J. Non-Cryst. Solids 71 (1985) 203. [27] C.H.L. Goodman, Phys. Chem. Glasses 26 (1) (1985) 1. [28] Y. Cao, A.N. Cormack, Conference on Glass Problems, Columbus (OH), 1994, Abstracts, p. 53. [29] Conradt, Fundamentals of Glass Science and Technology 1997, Glafo, V axj o Sweden, 1997, p. 15. [30] B. Nghi^em, H. Arribart, F. Creuzet, Fundamental of Glass Science and Technology, Glafo, V axj o Sweden, 1997, p. 33. [31] A. Benedetti, F. Geotti-Bianchini, G. Fagherazzi, P. Riello, G. Albertini, L. De Riu, J. Non-Cryst. Solids 167 (1994) 263. [32] W. Vogel, Chemistry of Glass, American Ceramic Society, Columbus, OH, 1985. [33] G.O. Karapetyan, L.V. Maksimov, O.V. Yanush, Sov. J. Glass Phys. Chem. 18 (6) (1992) 511.
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Small-angle X-ray scattering and Rayleigh scattering studies of the microstructure of some optical glasses F. Geotti Bianchini a, P. Riello b, A. Benedetti b,* b
a Stazione Sperimentale del Vetro, 30141 Murano-Venezia, Italy Dipartimento di Chimica Fisica, Univ. di Venezia, Calle Larga S. Marta 2137, 30123 Venezia, Italy
Received 24 June 1998; received in revised form 30 March 1999
Abstract Several optical glass samples were studied by small-angle X-ray Scattering (SAXS) in order to verify the presence of inhomogeneity in the range (1±100 nm). The results were compared with Rayleigh scattering measurements in order to verify a possible correlation between microstructure and scattering losses. For most glasses investigated, the presence of phase separation was excluded and the Rayleigh scattering intensities were attributed to refractive index ¯uctuations. For glasses ZKN7 and SK11 evidence of phase separation, with size of about 8 nm and less than 2 nm respectively, was obtained using SAXS. The particle size was insensitive to annealing treatments in the case of SK11 and showed a continuous growth with annealing time at 610°C in the case of ZKN7. For these two glasses the overall Rayleigh scattering intensity includes a contribution due to the presence of phase separated particles. Ó 1999 Elsevier Science B.V. All rights reserved.
1. Introduction Rayleigh scattering in optical glasses should be minimized to limit intensity losses. The Rayleigh (elastic) scattering originates at each wavelength in media with ¯uctuations of the refractive index in microscopically small volumes. The equations describing the intensity of scattered light contain the relative refractive index n np =nm (i.e. the ratio between the refractive index of the scattering particle np and of the matrix nm [1]). Theories to describe the Rayleigh scattering vary according to the ratio between particle size and the wavelength of light [1]. The overall light scattering intensity at
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each wavelength is the sum of all the intensities caused independently by each event. According to M orixbauer and Steinert et al. [2,3] the intensity of Rayleigh scattering in optical glasses varies in a broad range. In principle such scattering can be caused by various glass features with refractive index ¯uctuations including: (a) density and concentration ¯uctuations [4]; (b) metastable phase separation associated with amorphous particles generally in the range 1± 100 nm [5]; (c) technological inhomogeneities (melting remnants caused by refractory and metal (Pt) particles and microbubbles, generally in the micrometer range) [6]. Each of these events is associated with some type of deviation from the ideal (fully random and homogeneous) liquid structure and gives rise to
0022-3093/99/$ - see front matter Ó 1999 Elsevier Science B.V. All rights reserved. PII: S 0 0 2 2 - 3 0 9 3 ( 9 9 ) 0 0 5 4 3 - 8
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Rayleigh scattering whose intensity varies with the size, concentration and refractive index dierence of particles vs. bulk. In the case of optical glasses, events (a) and (c) are well described. Refractive index ¯uctuations are an important source of Rayleigh scattering whose intensity varies greatly with the chemical composition. Scattering losses limit the performance of even the purest optical ®bers [7,8]. Comprehensive studies were published by Maurer [9] and recently by Maksimov [10±12]. Technological inhomogeneities associated with incomplete melting are described by various authors [6,13]. Their presence in commercial optical glass is minimized by suitably adapting the production technology. On the other hand, very little information is available about the possible occurrence of phase separation with the exception of a paper by Winther [14] dated 1962 and Steinert et al. [3] which found for the zinc crown glass ZK7 a dissimmetric indicatrix attributed to phase separation. In order to improve the knowledge about this important issue, small-angle X-ray scattering is used in this study to analyze the presence of inhomogeneities in the range 1±100 nm [5] in several commercial optical glasses. 2. Experimental 2.1. Sample selection A range of optical glasses whose Rayleigh scattering at 546 nm varies from 2 to 150 10ÿ5 cmÿ1 was selected. In Table 1 are reported for each glass the commercial designation, the scattering intensity at 90° measured according to M orixbauer [2] and indications about the chemical composition obtained from Gliemeroth [15]. The samples were selected in order to cover a wide range of Rayleigh scattering levels and of chemical compositions including crown and ¯int glasses. In particular, ZKN7 was selected for its zinc oxide containing formulation (similar to ZK7, which Steinert [3] suggested to be phase separated); F2, BaF13, SK11, SF11 and SF14 for their PbO and BaO content, in the hope to elucidate the role of such oxides in promoting phase separation and Rayleigh scattering.
199
2.2. Small-angle X-ray scattering (SAXS) measurements Samples for small-angle scattering were 10 35 mm platelets prepared by grinding and polishing with cerium oxide. For each source, the thickness was selected in order to optimize the absorption caused by the samples. Ni-®ltered CuKa and Zr®ltered MoKa radiation were used for 0.1 and 0.5 mm thick samples, respectively. The X-ray scattering data were obtained with a Kratky smallangle camera in the Ôquasi-in®nite slitÕ geometry, equipped with an electronic step scanner. A pulse height discriminator and proportional or scintillation counter, depending on the wavelength used, were also employed. The intensities (denominated J(h) for this geometry, where h 4p sin h=k is the modulus of the momentum transfer, h the scattering angle and k is the wavelength employed) were measured by determining the time necessary to accumulate 2 104 counts for each scattering angle. The corrected intensities were obtained by subtracting the instrumental background intensity corrected for sample absorption. 2.3. Description of SAXS data The small-angle intensity scattered by a dilute system of a continuous normalized distribution P(r) of particles with radius r is represented by a monotonically decreasing curve given by Z 1 I h / P rr2 h; r dr; 2
where r2 h; r Dq V 2 S 2 h; r is the dierential scattering cross section of a single particle, V the particle volume, Dq the electronic density dierence between the particle and matrix and S 2 h; r is the particle form factor, that in the case of spherical particles is equal to S h; r 4p
sin hr ÿ hr cos hr 3
hr
:
The small-angle scattering from demixed glasses sometimes shows a strong correlation peak resulting from interparticle interference eects. In such a case, the simple model of uncorrelated particles is no longer adequate to explain the
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Table 1 Trade name, indicative chemical composition [15], refractive index and intensity scattered at 90° at the wavelength of 546 nm [2] of the optical glasses considered R90 105 in cmÿ1 at 546 nm
Glass designation and type
Chemical composition in wt% (Gliemeroth)
Refractive index at 589 nm
BK7 FK3
Boron crown Fluorine crown
1.517 1.464
1.9 2.5
F2 BaF13
Flint Barium ¯int
1.619 1.669
8.4 23
SK11
Dense crown
1.564
29
ZKN7 SF11 SF14
Zinc crown Dense ¯int Dense ¯int
Borosilicate glass Phosphate or borosilicate with high F content Alkali silicate with 39±47% PbO Alkali silicate with BaO + PbO < 40% Aluminoborosilicate with BaO > 15% (Boro)silicate with ZnO > 10% Alkali silicate with PbO > 47% Alkali silicate with PbO > 47%
1.508 1.784 1.762
58 98 154
results. The following more general expression for I(h) has to be considered: Z Z 2 I h / r h; rP r dr q k h; r1 ; r2 r h; r1 r h; r2 P r1 P r2 dr1 dr2 ;
2
where q is the total particle number density, k(h, r1 , r2 ,) is the pair structure function: Z 1 sin hr k h; r1 ; r2 g r; r1 ; r2 ÿ 1 4pr2 dr hr 0 and g(r, r1 , r2 ) known as the radial distribution function, is connected to the probability of ®nding a given con®guration of two particles with radii r1 and r2 , respectively at a distance r. One of the most successful models used to describe systems with an interparticle interference eect is the one in which the interaction between the particles is described by a hard sphere potential [16]. The assumption that the spherical particles with radius ri grow by depleting a surrounding volume of radius Ri ari a P 1:0 and, in this depleted region, there are no other particles equivalent to introducing an interacting hard sphere potential of radius Ri . Dierent solutions are possible for k(h, r1 , r2 ) according to the model used to evaluate g(r, r1 , r2 ). Several authors ®t their data sets with the approach derived from the Percus±Yevick approximation [16,17]. In order to take into account interference eects in our materials we use instead the simpler approximation reported by Guinier
and Fournet [18] and by Mengoni [19] and recently analytically solved by the authors [20]. Following this approach the scattered intensity can be written as Z Z 2 I h A rr h; rP r dr 1=d c h; r1 ; r2 b h; r1 ; r2 k h; r1 ; r2 r h; r1 r h; r2 P r1 P r2 dr1 dr2 ; where A is a scale constant, 3=2 1=d Vf 2p = a3 hVp i; Vf =a3 being the volume fraction of the demixed phase and hVp i the average volume of the particles. The functions c and b are de®ned by p Z 1 2 r eÿ/ r;r1 ;r2 =KT ÿ 1 sin hr dr; hb h; r1 ; r2 p p ÿ1 3 Z dc h; r1 ; r2
1 0
P r3 c h; r1 ; r3
b h; r1 ; r3 b h; r3 ; r2 dr3 :
4
Eqs. (3) and (4) can be solved analytically [20] for a continuous normalized Shultz distribution P(r) of spheres with an interacting hard sphere potential /(r, r1 , r2 ) of radius ar de®ned as P r
1 C z 1
z1 hri
z1
rz exp
ÿ
z1 r hri
F.G. Bianchini et al. / Journal of Non-Crystalline Solids 258 (1999) 198±206
and / r; r1 ; r2
1; 0 6 r 6 ar1 ar2 : 0; r > ar1 ar2
With this approach using Eq. (2) it is theoretically possible to reproduce, by a ®t procedure, an experimental SAS intensity showing a correlation peak with the help of ®ve parameters: hri z > ÿ1 a Vf A
average radius of the distribution; form parameter of the distribution; constant relating the radius of the depleted sphere to that of the particles; total volume fraction of the depleted zone; a scale constant proportional to the number of the demixed particles np and (Dq)2 .
When 1=d 0 Vf 0 the intensity reduces to the low density limit case. All the theoretical intensities have been smeared in order to take into account the experimental set up used. 2.4. Sensitivity of SAXS measurements Small-angle X-ray diraction is due to electron density ¯uctuations with a suitable size within the material. When the glass can be regarded as a system of homogeneous particles embedded in a homogeneous matrix with electron densities respectively equal to q1 and q2 , and relative volume equal to /1 and /2 , the mean square dierence of the electron densities of the phases (in a two-phase 2 2 system) is de®ned as Dq q1 ÿ q2 /1 /2 . qi is 3 expressed in gram electrons P per cm and is given by the formula: qi qm Zi =M where Zi number of electron in the ith atom of the compound under examination, qm (g/cm3 ) is the corresponding mass density of the compound and M is its molecular weight. Multiplying qi by AvogadroÕs number N, the total number of electrons per cm3 is obtained. For example, the electron density of pure bulk vitreous silica with density 2.02 g/cm3 is equal to N 1:099 el/cm3 . As reported by Golubkov et al. [21], the sensitivity of the smallangle equipment makes it possible to detect the
201
presence of microinhomogeneous features from 2 the SAXS curves for samples with Dq > 10ÿ1 3 2 (el/nm ) . If we consider additionally that the size resolution limit of SAXS is about 1±100 nm (with conventional cameras), we can estimate the features of the inhomogeneities that can be detected by this technique. When the system has no heter2 ogeneities and/or their size or Dq is less than the resolution limits reported above, the SAXS signal is given only by a constant uniform intensity. 2.5. Rayleigh scattering measurements The Rayleigh scattering intensity at 546 nm of the as-received glass samples was measured using an equipment similar to that described by M orixbauer [2]. The purpose of the equipment is to measure the intensity of Rayleigh (elastic) scattering in the visible range at an angle of observation of 90° relative to the incident beam, R90 , in order to quantify scattering related intensity losses in optical glasses. The source is a mercury vapour lamp, whose beam is focused on the samples (polished glass blocks about 25 mm 25 mm 18 mm) with the help of an array of lenses. The detector, a Si-photodiode supported by a rotating arm, can be placed in two positions: at 180° to the incident beam, to read the transmitted intensity (attenuated by grey ®lters), then at 90° to read the intensity scattered at 90°. Ratioing the two values eliminates the in¯uence of re¯ection losses due to glass refractive index. To eliminate the in¯uence of spurious illumination, in view of the weak intensity of R90 , the primary beam is modulated with the help of a chopper and the detector signal ampli®ed with a lock-in ampli®er. Monochromatization is achieved by inserting suitable interference ®lters both before and after the sample, to prevent artifacts due to sample luminescence. The overall absolute uncertainty on R90 was estimated to be 19%. The reproducibility, assessed by repeated measurements with sample re-positioning, was between 1% and 2% in the visible range. Additionally, a comparative evaluation of R90 of the heat treated samples was obtained using a procedure suggested by Scott and Rawson [22]. Although not quantitative, it is quite suitable to
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assess dierences when dierent samples are compared. The brightness of the beam of a 2 mW He± Ne laser crossing a polished block of the unknown sample is observed perpendicularly in a dark room and visually compared to the brightness observed on similar blocks of the optical glasses described in Table 1, whose values of R90 at 546 nm are known. To each heat treated sample is attributed a Rayleigh scattering intensity ranging between those of the optical glasses showing the nearest brightness. Considering that for all the optical glasses considered the variation of the scattered intensity with wavelength is similar (a dependence close to kÿ4 with the exception of ZKN7 with a k±4:7 dependence [2,3]), the sequence of intensities was supposed to remain unchanged from 546 to 633 nm. 3. Results The Rayleigh scattering intensity at 90° determined on the as received optical glass samples, R90 , is reported in Table 1. The presence of a large percentage of PbO in samples F2, BaF13, SF11 and SF14 and the corresponding low value of the transmission coecient (eÿlt where l is the linear absorption coecient and t is the sample thickness) did not allow a very accurate analysis of the SAXS curves even for t 0.1 mm. In any case, the constant intensity obtained with both radiation sources indicates that they are homogeneous from the SAXS point of view. A constant J(h) function was obtained also for the samples BK7 and FK3. As an example, the SAXS intensities corresponding to these two latter samples are reported in Fig. 1. For glasses SK11 and ZKN7, SAXS measurements provided more complex results. Figs. 2 and 3 report the experimental intensity of as received samples. In both cases the variation of J(h) vs. h suggests the presence of microstructural features. For these two samples no crystalline phase with crystallite size greater than 1.5 nm (the resolution limit of this technique) could be evidenced by wide angle X-ray scattering measurements, therefore the SAXS intensity can be attributed to phase sepa-
Fig. 1. Experimental SAXS intensity obtained for as-received samples FK3 (solid circles) and BK7 (open circles) using CuKa as a source.
ration phenomena. The SAXS results obtained by a best ®tting procedure of the experimental intensities, plus a background function B C=h3 are given in Table 2. In the same table, in order to give a more readable picture of the system, instead of reporting separately the values of a and Vf , we give the value of the total volume fraction of the demixed phase Vf /a3 . For the ZKN7 glasses, showing a correlation peak, the intensity was ®tted by Eq. (2) and the theoretical model described in Section 2.3. The SK11 SAXS curves that do not show a well-de®ned correlation peak were treated as a dilute system of particles and ®tted by Eq. (1). In order to con®rm the presence of phase separation and to follow its thermal evolution, samples of the two glasses were also heat-treated at dierent temperatures, in the range up to about 100°C above their Tg . ZKN7, with Tg 528°C, showed microstructural changes for treatments between 610°C and 650°C. In particular, the behavior observed after annealing between 6 and 74 h at 610°C was investigated in detail. The annealing program for SK11, with Tg 610°C, was 650°C, 675°C, 700°C and 725°C for 18 h. The results concerning ZKN7 samples and reported in Table 2 show a kinetic growth of the particle sizes and a parallel increase of the light scattering intensity. On the contrary, even prolonged heat
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Fig. 2. Experimental SAXS intensity obtained for an as-received sample of SK11 using CuKa as a source. Continuous line: data ®t. Dashed line: B C=h3 function.
treatments in the range from 40°C up to 115°C above Tg used for glass SK11 were unable to grow the amorphous phase present, since the SAXS as well as the Rayleigh intensities of dierently annealed SK11 samples are identical. Finally, also glass BK7 giving no evidence of phase separation in the as-received state was heat treated for 17 h at 615°C, 650°C and 670°C. Both the SAXS intensities and the Rayleigh intensities of annealed samples were identical to those of asreceived samples. This indicates that heat treatments in the range from 60°C to 110°C above Tg (559°C) do not modify the sub-microinhomogeneous structure of this glass, in particular its refractive index ¯uctuations.
203
Fig. 3. Experimental SAXS intensity obtained for an as-received sample of ZKN7 using CuKa as a source. Continuous line: data ®t. Dashed line: B C=h3 function.
4. Discussion The formation of metastable phase separation is related to the growth of amorphous aggregates in a glassy matrix. The possibility of detecting the presence of amorphous microstructural features embedded in an amorphous matrix was always considered a dicult task [23]. Small-angle scattering is suitable to the investigation of these structures in view of its ability to describe both crystalline and amorphous heterogeneities. Within the limits of SAXS sensitivity (size 1± 100 nm, Dq2 > 10ÿ1 (el/nm3 )2 ), glasses BK7, FK3, F2, BaF13, SF11 and SF14 are homoge-
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Table 2 SAXS analysis results compared with the R90 levels Samples
hri (nm) A Vf /a3 z Relative R90 level a
SK11
ZKN7
As received and heat treated
As received
6 h 610°C
0:9 0:5 ± ± ± SK11a
4:3 0:4 3:1 10ÿ8 0:5 0:13 0:04 27 5 ZKN7a
7:2 0:5 1:9 10ÿ9 0:2 0:17 0:05 20 4 >SF14
23 h 610°C 10:7 0:8 6:3 10ÿ10 0:7 0:29 0:07 16 4 >SF14
74 h 610°C 21:5 1 1:1 10ÿ10 0:1 0:38 0:10 25 6 SF14
As received.
neous. Therefore, their Rayleigh scattering intensity should be attributed to refractive index ¯uctuations, in agreement with the traditional interpretation [9]. For BK7 even prolonged heat treatments above Tg did not aect the R90 or SAXS intensities. In the case of as-received ZKN7 and SK11, SAXS evidence reveals the presence of amorphous particles with size 2hri of 8 and 2 nm, respectively. In both cases the presence of phase separation is most likely, however the kinetics of ripening were quite dierent. For ZKN7 annealing above Tg even for some hours produced 2 coarsening. If we assume Dq constant during the annealing treatment, the decreasing value of A, reported in Table 2, can be related to the disappearance of the smaller particles in the coarsening process as suggested by Lifshitz and Slyozov [24]. Furthermore, the almost constant value of z, the form parameter of the size distribution, indicates that the shape of the particle size distribution curve is not in¯uenced by thermal treatments, but shifts homogeneously towards larger values. For glass SK11 the SAXS and Rayleigh scattering results were absolutely insensitive to heat treatments. For these two glasses the R90 intensity contains additionally a contribution due to phase separation, which becomes predominant for annealed ZKN7 as the particle size and the volume fraction of the demixed phase increase (see Table 2). It is generally believed that the scattering of visible light in optical glasses results from density and concentration ¯uctuations, however, so far little evidence has been published about the size,
nature and composition of such ¯uctuations. Various authors postulated the presence of clusters associated with a non-random distribution of network modi®ers [7,12,25]. The present SAXS results can contribute to this discussion by excluding for glasses BK7, FK3, F2, BaF13, SF11 and SF14 ¯uctuations with size outside the 1±100 nm range and/or mean square dierence of electron densities of the two phases >10ÿ1 (el/nm3 )2 . Similar conclusions are reached if the discussion is generalized to multicomponent glasses, which recently were suggested to have a cluster structure on the nanometer scale. Examples are the modi®ed random network model [26]; the strained mixed cluster model [27]; structural models including channels [28]; the clustered nanosize mixtures [29]. From theoretical calculation Conradt [29] suggests a size of 1±4 nm, Goodman [26] up to 5 nm. According to Nghi^em et al. [30] AFM assisted fractography reveals nanometer scale heterogeneities. In a previous paper by the present authors [31] a ¯at J(h) behavior ± implying lack of inhomogeneities within SAXS resolution ± was found for various commercial soda lime glasses (containers and plate glass) and lead alkali silicate glasses. As concerns the eect of speci®c modi®ers such as PbO on phase separation, the literature does not formulate clear indications. According to Vogel [32], high lead silicate glasses consist of a high SiO2 droplet phase embedded in a high lead matrix, however, the tendency towards immiscibility is suppressed in a suitable region of the ternary K2 O±PbO±SiO2 system. Such statements are insucient to predict the microinhomogeneity of ¯int optical glasses and of the so-called lead crystal
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glasses for tableware and decorative articles, whose chemical composition is relatively complex, as exempli®ed by Table 1 and by a previous SAXS study of the present authors [31]. In the same paper, a commercial sample of lead crystal glass with 26% PbO had a ¯at J(h) behavior similar to those observed here for glasses F2, SF11 and SF14 (containing between 39 and >47 PbO wt%). Its Rayleigh scattering intensity at 633 nm, determined with the procedure described above, was intermediate between those of FK3 and F2. In summary, SAXS evidence does not reveal the presence of any signi®cant microinhomogeneity in lead oxide based optical glasses that could explain the wide range of Rayleigh scattering levels observed (between 8 and 154 10ÿ5 cmÿ1 ). SiO2 -rich droplets are unlikely, since they would be easily detected in view of the electron density dierence. According to some authors [7,12,24] a further possible explanation lies in the formation of clusters that include Pb ions. This might explain the fact that the Rayleigh scattering increases with PbO content, as discussed by Dietzel [25] and Maurer [9]. According to Maksimov [10,12] and Karapetyan et al. [33] the role of PbO is to ÔdecorateÕ ¯uctuational microinhomogeneities in ¯int glasses, causing a corresponding increase of the Rayleigh scattering. The present SAXS results are not incompatible with this model, however the formation of clusters including aggregated Pb atoms is unlikely since their electron density would be suciently dierent from the matrix to cause a detectable SAXS signal. Further signi®cant modi®ers are BaO and ZnO. BaO is present in BaF13 (barium lead alkali silicate) and SK11 (barium aluminoborosilicate), only the latter of which shows inhomogeneous features. ZKN7, described as a zinc aluminoborosilicate, shows phase separation as-received and ripens on annealing. 5. Conclusions SAXS analysis was performed on a range of as received and heat treated commercial optical glasses in order to demonstrate the presence of inhomogeneities in the range 1±100 nm. For
205
glasses BK7 (as received and heat treated), FK3, F2, BaF13, SF11 and SF14 the presence of microstructure could be excluded. From the analysis of the SAXS curves obtained here it can be concluded that the size of the scattering centers is outside the 1±100 nm range and/or the mean square dierence of electronic densities of the two phases is <10ÿ1 (el/nm3 )2 . Therefore, the observed Rayleigh scattering can be attributed to refractive index ¯uctuations. Concerning glass ZKN7, the presence of particles with a size of about 8 nm could be clearly evidenced. The kinetic growth of the particle size after annealing for various times at about 80°C above Tg con®rms the presence of a metastable phase separation. As shown in Table 2, for this glass the overall Rayleigh scattering includes a contribution due to the presence of phase separated particles. For glass SK11, particles with size near the resolution limit of the SAXS measurements (2 nm) were detected. Neither the particle size (less than 2 nm), nor the Rayleigh scattering intensity were in¯uenced by thermal treatments above Tg . Acknowledgements The ®nancial contribution of the Ministry of Industry (MICA, Rome, Italy) and the Italian CNR is acknowledged. We are grateful to Dr F.-T. Lentes (Schott Glass Works, Mainz, Germany) for useful discussions. The authors thank Mr R. Zen (Venice) for preparing 0.1 mm plates and Mrs M. Preo (SSV) and T. Finotto (University) for technical assistance. References [1] I. Fanderlik, Optical Properties of Glass, chap. 4.4, Elsevier, Amsterdam, 1983. [2] R. M orixbauer, diplomarbeit, Fachhochschule Wiesbaden (1987). [3] J. Steinert, W. Rohmann, G. Tittelbach, Silikattechnik 35 (1984) 186. [4] J. Zarzycky, Les Verres et lÕetat Vitreux, chap. 7, Masson, Paris, 1982. [5] E.A. Porai-Koshits, in: D.R. Uhlmann, N.J. Kreidl (Eds.), Glass Science and Technology, vol. 4A, Academic, New York, 1990, p. 1.
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