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Brillouin scattering measurements of attenuation and velocity of hypersounds in SiO2B2O3 glasses
Journal of Non-Crystalline Solids 37 (1980) 349-358 © North-Holland Publishing Company
BRILLOUIN SCATTERING MEASUREMENTS OF ATTENUATION AND
VELOCITY OF HYPERSOUNDS IN SIO2-B203 GLASSES R. JABRA, J. PELOUS * and J. PHALIPPOU Laboratoire de Science des Matdriaux et Laboratoire des Verres du CNRS Universitd des Sciences et Techniques du Languedoc, Place E. Bataillon, 34060 Montpellier Cedex, France
Received 1 August 1979 Revised manuscript received 10 February 1980
Measurements of hypersound wave velocity and attenuation (20-30 GHz) were made at room temperature by Brillouin scattering in SiO2-B203 glasses. The attenuation shows a maximum with composition. An explanation of this maximum is given in relation to the glass structure. It is thought that this maximum may be due to a coupling effect of hypersounds with structural relaxational process involving Si-O-Si and Si-O-B bonds.
1. Introduction The glass-forming systems have been investigated for their dielectric, optical and thermal properties [ 1 - 3 ] . Over the past few years a great deal of work has been done to find out the relationship between their microscopic structure and their elastic properties. The published results concern essentially low frequencies and ultrasonic frequencies range. A wide variety of one-component inorganic glasses, e.g. SiO2, B203, GeO2, and As203, shows a relaxation peak as a function of temperature in the temperature range 5 0 - 3 0 0 K [4]. Two-component oxide glasses SiO2-M20, B 2 0 3 - M 2 0 (M is alkali ion) were also studied to see the effect of the addition of modifying oxide on the structure of the glassy network [5,6]. A number of structural models has been proposed to explain the mechanical properties of glasses [4,7,8]. The elastic properties of some materials were measured by Brillouin scattering [9] for frequencies up to 20 GHz. These measurements were used to test the microscopic models developed for the lower frequency range. In the present work the elastic properties are measured by this technique for the binary SIO2-B203 glasses. The differences of the structure and the properties
* Laboratoixe de Spectrom6trie Rayleigh Briltouin, ERA 460. 349
350
R. Jabra et al. / Hypersounds in Si02 -B203 glasses
between the pure constituents SiO2 and B203 are well known. Therefore it is interesting to study the variation of properties of binary glasses in relation to the proportion of the individual components. 2. Experimental 2.1. Sample preparation
Samples with high silica content were prepared using a method described previously [ 10] which consisted in compacting a dehydrated gel by hot pressing. The gel was obtained by precipitation of a colloidal solution of "Ludox As" *, in which boric anhydride was added as an aqueous solution of ammonium borate. Details of the hot pressing cell and pressing mode have been reported elsewhere [11,10]. Glasses with composition higher than 50 mol% B203 were obtained by melting the gel in platinum crucibles for 4 h at 1300°C. This is advantageous because of their low preparation temperature. Two B203 glasses were prepared by melting H3BO3 (R.P.) in platinum crucibles. The first, containing higher water content, was melted at 900°C for 1 h; for the second glass the melting temperature was increased to 1300°C. Dry oxygen was bubbled throught the melt for 3 h. After annealing treatment the melted glasses were optically polished. The dimensions of the samples were 3 X 3 × 14 mm 3. 2.2. Characterization o f SiO 2-B203 glasses
The physical properties of the glasses SIO2-B203 are summarized in table 1. The density of the samples was measured by Archimedes' method. The refractive index of the glasses containing between 5 and 30 mol% B203 was measured by an Abbe refractometer. The refractive index of the glasses with higher B203 content is available in the literature [12]. The values of refractive indices were obtained by interpolation for 3, = 5245 A, using the values for vitreous silica [13]. The water content of the samples was measured by I.R. spectroscopy from the absorption band at 2.75 ~m by application of the Beer-Lambert relation. The value 70.5 mol 1-1 cm -~ [14] is used for the extinction coefficient. The quantitative evaluation of water content in the B203 sample was made in the same way, using the extinction coefficient for the 2.8-/am peak [15]. Structural information was obtained by I.R. spectroscopy in the 4000-400 cm -x range on samples prepared by pressed KBr pellets [ 10]. 2.3. Brillouin scattering
The Brillouin scattering spectrometer used in this study has been described previously [16]. For the glasses in question, a resolution between 106 and 107 was * Du Pont de Nemours, U.S.A.
R. Jabra et al. /Hypersounds in Si02-B203 glasses
351
Table 1 Physical properties of the SiO2-B203 glasses Composition (mol% B203)
Density (g/cm 3)
Refractive index h = 5145 A
Watercontent (ppm OH)
5 10 15 20 30 50 75 90 100(a) 100(b)
2.182 2.143 2.134 2.110 2.055 1.99 1.905 1.865
1.4604 1.4592 1.4584 1.4582 1.4588 1.4604 1.4612 1.4617
1.844
1.4620
320 9 75 258 620 2155 3408 4496 14.600 930
needed. Therefore, either a double pass plane Fabry-P6rot (thickness 4 mm) or a spherical F a b r y - P 6 r o t (thickness 50 mm) combined with the former was used. The wavelength of the incident light was 5145 A and the scattering angle was 175 °. From the frequency shift (~v) and the linewidth of the Brillouin components ( r ) the hypersound velocity (o) and their attenuation (a), respectively, can be obtained [17]. The frequency of the hypersounds varied from 18.8 GHz for pure B203 to 33.7 GHz for vitreous silica. The velocity and the attenuation were measured with an accuracy of about 1% and 5 - 1 0 % , respectively.
3. Results The frequency shift of the Brillouin line due to longitudinal hypersound at room temperature is shown as a function of composition of the glasses in fig. 1. It can be seen that there is a variation of the slope of the curve for a composition at about 25 mol% B203. The results of the velocity are shown in fig. 2. This curve shows a regular decrease of the hypersound velocities when B203 content increases. Also shown in fig, 2 are the results obtained by other workers [18] for ultrasonic waves. A discrepancy appears between our measurements ( 2 0 - 3 0 GHz) and those made on two glasses in the same system at 20 MHz frequency. This difference seems very likely to be due to an error b y these authors [18] in expressing the glass composition; indeed, the densitities of these glasses lead one to believe that they should contain more B203 than expressed as wt%. The Brillouin linewidth and the attenuation of the hypersounds are shown as a
"el
FREQUENCY SHIFT ~ (GHz)
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8
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~.r~
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'
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, O,
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Fig. 4. Attenuation at hypersonic frequency versus composition in SiO2-B 203 glasses.
Fig. 3. Variation with composition of the Brillouin linewidth in SiO2-B203 glasses.
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.
.
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.
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354
R. Jabra et al. /Hypersounds in Si02-B2 03 glasses
function of the glass composition in figs. 3 and 4, respectively. The attenuation shows a maximum for a composition around 25 mol% B203. Since there is a wide variation of a with the frequency, these results cannot be compared with those obtained by ultrasonic measurements [18]. The water content of the material may greatly influence the attenuation, as is evident from the values obtained for both the B203 glasses.
4. Discussion
In vitreous silica, the hypersound attenuation in the frequency range studied in this work shows a maximum at a temperature around 120 K [19]. Hypersound velocity shows a minimum at a temperature around 80 K and then increases linearly towards room temperature. The height of the peak of attenuation and the slope of the hypersound velocity curve as a function of temperature can be slightly affected by the water content of the material or by the previous thermal history [20]. The measurements obtained for B203 [21 ] exhibit a behaviour qualitatively different from that of vitreous silica. The hypersound's velocity decreased continuously in the temperature range 3 - 3 0 0 K. In the same temperature range the attenuation does not show a peak. These results are also unlike those given by ultrasonic techniques [22]. The silica glass is composed of an arrangement of tetrahedral structural units (SiO4) distributed in such a way that no long-range order exists. On the other hand, in B203 glass, the network is made up of arrangements of planar groups of boroxol units [23]. The silicon and boron ions, which are the only cations in B203-SIO2 glasses, have ionic radii very small compared to that of the oxygen ion. Considering that the oxygen ions essentially make up the volume of the glass, the apparent molar volume of these glasses shows a slight variation with the B203 content; it has also been shown that the structure of these glasses is quite open [10]. Since the modifying ions are absent, it is likely that the boron ion is essentially 3-coordinated. In fact, N.M.R. measurements on the binary glass-forming system GeO2-B203 showed that the boron ion is always 3-coordinated throught the range of composition [24]. Given the structural analogies between SiO2 and GeO2 glasses, it is likely that B203-SiO 2 glasses are composed of planar structural units (BO3) and tetrahedral structural units (SiO4). The rigidity of the glass is due to the energy of the cation-anion bond. It is also related to the individual rigidity of the various structural units from which the spatial network is formed. It seems certain that with the increase of B203 content, the structural groups (BOa) decrease the glass rigidity. The weaker the rigidity, the lower is the hypersound's velocity. This is evident when the B203 content increases. Many models have been proposed in the literature to account for the attenuation of ultrasonic waves in vitreous silica. Anderson and Bommel [7] think that the loss peak observed is due to transverse vibrations of the oxygen ions situated between
R. Jabra et aL / Hypersounds in SiO 2 - B 2 0 3 glasses
355
the two silicon ions with which they are linked. A second interpretation [4] concerns longitidunal vibrations of oxygen ions in the direction of the S i - O - S i bond. Finally, Vukcevich [8] attributed the observed attenuation to a small rotation of the SiO4 groups. On the basis of the acoustic results actually known, it is impossible to conclude which of these three models is the most appropriate. Since the attenuation of the B203-SIO2 glasses at room temperature is well above either that of vitreous silica or that of vitreous B203, the inclusion of B203 in the silica network induces a higher concentration of hypersound absorption centres. All the results obtained by Brillouin scattering [9] on glasses lead to the conclusion that the process responsible for the attenuation in these glasses is not a diffusion process due to the frozen-in fluctuations of the density (possible phase separation, residual microporosity). Obviously, such defects would induce a constant attenuation irrespective of the temperature. Moreover, in the glasses studied, no anomaly in elastic scattering (Rayleigh line) occurs, showing the possibility of the presence of these defects. It can be noted that the synthesis of glasses via gels leads to a better homogeneity than the glasses obtained by the usual melting methods [25,26]. As previously observed, the variation of the attenuation of the hypersonic waves with the composition shows a maximum at around 25 mol% of B203 preceded by a sudden drop around 15 mol% of B203; the same anomaly has been observed for the refractive index [27]. This glass is very interesting because its refractive index is small compared to that of vitreous silica; this property has already been exploited for making optical fibers [27] ; however, to our knowledge, this anomaly is as yet unexplained. It is clear that all the models proposed to account for the attenuation in the glasses are based on the possibility of the oxygen ions taking two stable positions, corresponding to the energy potential wells. The explanation of the attenuation observed should be made on the basis of known structural information with respect to the oxygen ions of the glass. The structure of the binary oxides glasses B203-SIO2 would require three different bonds: S i - O - S i , S i - O - B , and B - O - B . The infrared spectroscopy studies [10] showed the presence of the first two bonds by I.R. absorption bands at 1100, 800, and 460 cm -~ (for S i - O - S i bonds) and at 1380, 910, and 670 cm -~ for S i - O - B bonds). Up to at least 50 mol% B203 no absorption band related to B - O - B was revealed by I.R. spectroscopy. The pure B203 glass does not give rise to a high attenuation of hypersound waves [21]. Na20-B203 glasses do not contain non-bridging oxygens ions up to 33 mol% Na20 [28] because the boron ion changes its coordination. Although these glasses contain a high number of B - O - B bonds, they show a lower ultrasonic absorption than that of B203 glass at room temperature [6]. On the other hand, their' attenuation decreases when the concentration of the modifying ions increases [6]. For the glasses studied here it should be noted that the peak of hypersound absorption is on the silica-rich side. The rise in the attenua-
356
R. Jabra et al. /Hypersounds in SiO2-B 203 glasses
tion, for our range of frequencies, with the concentration of B203 could not be explained by a relaxation process involving the oxygen ions situated between two borons ions. The second assumption is that there is a great influence of S i - O - B bonds on the relaxation mechanism responsible for the attenuation. The coupling effect of the hypersounds and the S i - O - B bonds may be important because of the asymmetry that exists between the S i - O and B - O bonds which have different lengths and also unequal field strengths. Moreover, the probability of occurrence of the S i - O - B bonds with the change of composition of the SiO2-B2Oa glasses has been approximately calculated [29]. This probability shows a maximum at 40 tool% B203. The comparison between the attenuation curve (fig. 4) and that of the probability of the S i - O - B bond shows a slight shift of the maximum towards the silica-rich side; the shapes of the curves are not identical in the region where these parameters (attenuation and probability of S i - O - B bonds) show a decreasing trend. This fact does not exclusively favour the participation of S i - O - B bonds for the attenuation mechanism. There is a third hypothesis which attributes the increase of the hypersounds attenuation to the S i - O - S i bonds. The accommodation of planar structural units BOa and tetrahedral structural units SiO 4 may only occur with a distortion of the S i - O - S i bonds. The addition of B203 to the silica glass increases the structural disorder, as can be confirmed by the decrease of the I.R. band at 800 cm -1, which finally vanishes. This absorption band, strong in crystalline silica, is also present in vitreous silica. It was attributed to the ring structure of SiO4 tetrahedra [30]. It was also related to the "degree" of order in vitreous silica [31]. If the distortion of the S i - O - S i bonds were relatively higher, the activation energy would also be higher. The observed absorption peak in the case of the silica glass would then be shifted to higher temperatures for the SIO2-B203 glasses, which would thus lead to an increase of the attenuation at 300 K. Because of the lack of studies as a function of temperature, no definite conclusion can be reached on this point, although the measurements of ultrasonic absorption made on the two glasses [17] agree with this assumption. If the attenuation is due to the distortion of the S i - O - S i bonds, the probability curves of the bonds in these glasses [29] could explain the shape of the observed attenuation curve. Indeed, at the silica-rich side, where the probability of the S i - O - S i bonds is high, the number of distorted bonds increases with the B203 content and consequently with the probability of S i - O - B bonds. The attenuation should show the same increase as that shown by the S i - O - B bonds probability. This is what is noted experimentally up to 25 mol% B203. After this composition the decrease of the S i - O - S i bonds probability implies a similar decrease of the attenuation (see fig. 4 and [29]). If the hypothesis about the effect of the participation of B - O - B bonds on the attenuation is discounted, it is difficult to know quantitatively the respective influence of S i - O - S i or S i - O - B vibrations on the attenuation process. It is likely that these two bonds both contributed to the
R. Jabra et al. / Hypersounds in SiO 2 - B 2 0 3 glasses
357
hypersonic attenuation; for the low B2Oa content the glass structure favours the relaxation process due to S i - O - S i bonds. However, the decreasing number of these bonds with increasing B203 content implies, up to a certain concentration, the decrease of their participation in the relaxation process in relation to the total attenuation of the glass. The contribution of S i - O - B bonds to the total attenuation is related to their probability of occurrence. The cumulative effect of these two contributions may explain both the shift of the maximum towards the silicarich side and the rapid increase of the attenuation in the same composition range. Following these results the variation of the attenuation of more complex glasses such as alkali borosilicate glasses may be better understood. Comparisons between our glasses and alkali borosilicate glasses can be made in some composition ranges since these glasses do not contain any non-bridging oxygen ions if the ratio M/B is lower than 0.5 (M is an alkali ion). For compositions lower than this one alkali ion is associated with one 4-coordinated boron, as has been confirmed by NMR [32]. The attenuation measurements made on potassium borosilicate glasses [33] give lower values than those for glasses studied in this paper. This can be understood if it is assumed that the modifying cations are situated in the holes of the structure. In this way they impede the vibrations of bridging oxygens which are in their neighbourhood and with which they are coordinated; a smaller number of oxygen ions participate in the attenuation process.
5. Conclusion The elastic properties of the SiO2-B2Oa glasses were studied for frequencies varying between 20 and 30 GHz at room temperature. The velocity of hypersonic waves decreases with increasing B2Oa content. The most noticeable effect is a great increase of the hypersonic attenuation in these glasses when the B203 content is about 25 mol%. This increase was interpreted as being due to a hypersonic coupling effect with the vibration of the oxygen ions of the S i - O - S i and S i - O - B bonds. A cumulative effect of hypersonic absorption of these two kinds of bonds ascertains the position of the attenuation maximum in the composition curve.
References [1] C.R. Kurkjian and G.E. Peterson, in: Recent Advances in Science and Technology of Marials, ed., A. Bishay (Plenum Press N.Y. 1974) 2, 61. [2] P.C. Schultz and H.T. Smyth, in: Amorphous Materials, ed. R.W. Douglas and B. Ellis (Wiley-Interscience, London 1972) p. 453. [3] W. Kern and R.C. Helm, J. Electrochem. Soc. 117 (1970) 568. [4] R.E. Strakna and H.T. Savage, J. Appl. Phys. 35 (1964) 1445. [5] M.H. Manghani and B.K. Singh, Tenth Int. Congress Kyoto 11 (1974) 104. [6] J.T. Krause and C.R. Kurkjian, Amer. Ceram. Soc. Bul. 43 (1964) 649.
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R. Jabra et al. / Hypersounds in S i 0 2 - B 2 0 3 glasses
[7] C.L. Anderson and H.E. Bommel, J. Amer. Ceram. Soc. 38 (1955) 126. [8] M.R. Vukcevich, J. Non-Crystalline Solids 11 (1972) 25. [9] J. Pelous, Thesis, Montpellier (1978). [10l R. Jabra, J. Phalippou and J. Zarzycki, Rev. Chim. Min. 16 (1979) 245. [11] M. Decottignies, J. Phalippou and J. Zarzycki, J. Mater. Sci. 13 (1978) 2605. [12] R. Bruckner and J.F. Navarro, Glastech. Ber. 39 (1966) 283. [13] Handbook of Chemistry and Physics, 44th edition. [14] J.P. Williams, Y.S. Su, W.R. Strezegowski, B.L. Butler, H.L. Hoover and V.O. Altemose, Amer. Ceram. Soc. Bull. 55 (1976) 524. [15] H. Franz, J. Amer. Ceram. Soc. 49 (1966) 473. [161 R. Vacher and J. Pelous, Phys. Rev. B, 14 (1976) 2. [17] R. Vacher and L. Boyer, Phys. Rev. 6 (1972) 639. [18] C.A, Maynell, G.A. Saunders and S. Scholes, J. Non-Crystalline Solids 12 (t973) 271. [191 R. Vacher and J. Pelous, Solid. Stat. Commun. 16 (1975) 279. [20] J.T. Krause, J. Appl. Phys. 42 (1971) 3035. [21] J. Pelous (to be published). [22] J.R. Krause and C.R. Kurkjian, J. Amer. Ceram. Soc. 49 (1966) 134. [23] J. Krogh-Moe, J. Non-Crystalline Solids 1 (1969) 269. [24] J.F. Baugher and P.J. Bray, Phys. Chem. Glasses 13 (1972) 63. [25] W.L. Konijnendijk, M. Van Duuren and H. Groenendijk, Verres Refrac. 27 (1973) 11. [261 M.A. Russak, J. Amer. Ceram. Soc. 61 (1978) 181. [27] S.H. Wemple, D.A. Pinnow, T.C. Rich, R.E. Jaeger, L.G. Van Vitert, J. Appl. Phys. 44 (1973) 5432. [28] P.J. Bray and J.G. O'Keefe, Phys. Chem. Glasses 4 (1963) 37. [291 A.S. Tenny and J. Wong, J. Chem. Phys. 56 (1972) 5516. [30] F. Matossi and H. Bruschke, Phys. 108 (1938) 295. [31] V.A. Florinskaya and R.S. Pechenkina, in: The Structure of Glass (Consultant Bureau, New York, 1958) t. 1, 55. [32] M.E. Milberg, J.G. O'Keefe, R.A. Verhelst and H.O. Hooper, Phys. Chem. Glasses 13 (1972) 79. [33] J. Pelous and R. Vacher, Phys. Chem. Glasses 18 (1977) 36.
BRILLOUIN SCATTERING MEASUREMENTS OF ATTENUATION AND
VELOCITY OF HYPERSOUNDS IN SIO2-B203 GLASSES R. JABRA, J. PELOUS * and J. PHALIPPOU Laboratoire de Science des Matdriaux et Laboratoire des Verres du CNRS Universitd des Sciences et Techniques du Languedoc, Place E. Bataillon, 34060 Montpellier Cedex, France
Received 1 August 1979 Revised manuscript received 10 February 1980
Measurements of hypersound wave velocity and attenuation (20-30 GHz) were made at room temperature by Brillouin scattering in SiO2-B203 glasses. The attenuation shows a maximum with composition. An explanation of this maximum is given in relation to the glass structure. It is thought that this maximum may be due to a coupling effect of hypersounds with structural relaxational process involving Si-O-Si and Si-O-B bonds.
1. Introduction The glass-forming systems have been investigated for their dielectric, optical and thermal properties [ 1 - 3 ] . Over the past few years a great deal of work has been done to find out the relationship between their microscopic structure and their elastic properties. The published results concern essentially low frequencies and ultrasonic frequencies range. A wide variety of one-component inorganic glasses, e.g. SiO2, B203, GeO2, and As203, shows a relaxation peak as a function of temperature in the temperature range 5 0 - 3 0 0 K [4]. Two-component oxide glasses SiO2-M20, B 2 0 3 - M 2 0 (M is alkali ion) were also studied to see the effect of the addition of modifying oxide on the structure of the glassy network [5,6]. A number of structural models has been proposed to explain the mechanical properties of glasses [4,7,8]. The elastic properties of some materials were measured by Brillouin scattering [9] for frequencies up to 20 GHz. These measurements were used to test the microscopic models developed for the lower frequency range. In the present work the elastic properties are measured by this technique for the binary SIO2-B203 glasses. The differences of the structure and the properties
* Laboratoixe de Spectrom6trie Rayleigh Briltouin, ERA 460. 349
350
R. Jabra et al. / Hypersounds in Si02 -B203 glasses
between the pure constituents SiO2 and B203 are well known. Therefore it is interesting to study the variation of properties of binary glasses in relation to the proportion of the individual components. 2. Experimental 2.1. Sample preparation
Samples with high silica content were prepared using a method described previously [ 10] which consisted in compacting a dehydrated gel by hot pressing. The gel was obtained by precipitation of a colloidal solution of "Ludox As" *, in which boric anhydride was added as an aqueous solution of ammonium borate. Details of the hot pressing cell and pressing mode have been reported elsewhere [11,10]. Glasses with composition higher than 50 mol% B203 were obtained by melting the gel in platinum crucibles for 4 h at 1300°C. This is advantageous because of their low preparation temperature. Two B203 glasses were prepared by melting H3BO3 (R.P.) in platinum crucibles. The first, containing higher water content, was melted at 900°C for 1 h; for the second glass the melting temperature was increased to 1300°C. Dry oxygen was bubbled throught the melt for 3 h. After annealing treatment the melted glasses were optically polished. The dimensions of the samples were 3 X 3 × 14 mm 3. 2.2. Characterization o f SiO 2-B203 glasses
The physical properties of the glasses SIO2-B203 are summarized in table 1. The density of the samples was measured by Archimedes' method. The refractive index of the glasses containing between 5 and 30 mol% B203 was measured by an Abbe refractometer. The refractive index of the glasses with higher B203 content is available in the literature [12]. The values of refractive indices were obtained by interpolation for 3, = 5245 A, using the values for vitreous silica [13]. The water content of the samples was measured by I.R. spectroscopy from the absorption band at 2.75 ~m by application of the Beer-Lambert relation. The value 70.5 mol 1-1 cm -~ [14] is used for the extinction coefficient. The quantitative evaluation of water content in the B203 sample was made in the same way, using the extinction coefficient for the 2.8-/am peak [15]. Structural information was obtained by I.R. spectroscopy in the 4000-400 cm -x range on samples prepared by pressed KBr pellets [ 10]. 2.3. Brillouin scattering
The Brillouin scattering spectrometer used in this study has been described previously [16]. For the glasses in question, a resolution between 106 and 107 was * Du Pont de Nemours, U.S.A.
R. Jabra et al. /Hypersounds in Si02-B203 glasses
351
Table 1 Physical properties of the SiO2-B203 glasses Composition (mol% B203)
Density (g/cm 3)
Refractive index h = 5145 A
Watercontent (ppm OH)
5 10 15 20 30 50 75 90 100(a) 100(b)
2.182 2.143 2.134 2.110 2.055 1.99 1.905 1.865
1.4604 1.4592 1.4584 1.4582 1.4588 1.4604 1.4612 1.4617
1.844
1.4620
320 9 75 258 620 2155 3408 4496 14.600 930
needed. Therefore, either a double pass plane Fabry-P6rot (thickness 4 mm) or a spherical F a b r y - P 6 r o t (thickness 50 mm) combined with the former was used. The wavelength of the incident light was 5145 A and the scattering angle was 175 °. From the frequency shift (~v) and the linewidth of the Brillouin components ( r ) the hypersound velocity (o) and their attenuation (a), respectively, can be obtained [17]. The frequency of the hypersounds varied from 18.8 GHz for pure B203 to 33.7 GHz for vitreous silica. The velocity and the attenuation were measured with an accuracy of about 1% and 5 - 1 0 % , respectively.
3. Results The frequency shift of the Brillouin line due to longitudinal hypersound at room temperature is shown as a function of composition of the glasses in fig. 1. It can be seen that there is a variation of the slope of the curve for a composition at about 25 mol% B203. The results of the velocity are shown in fig. 2. This curve shows a regular decrease of the hypersound velocities when B203 content increases. Also shown in fig, 2 are the results obtained by other workers [18] for ultrasonic waves. A discrepancy appears between our measurements ( 2 0 - 3 0 GHz) and those made on two glasses in the same system at 20 MHz frequency. This difference seems very likely to be due to an error b y these authors [18] in expressing the glass composition; indeed, the densitities of these glasses lead one to believe that they should contain more B203 than expressed as wt%. The Brillouin linewidth and the attenuation of the hypersounds are shown as a
"el
FREQUENCY SHIFT ~ (GHz)
b~
<
,<
8
o
o 0 0
~.r~
I
I
VELOCITY
© E 0
~/'(m.s -1 )
R
0
Z 0 r rq
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/
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~ YE
.
.
.
.
+
70
'
'
MOLE % B,
, O,
~oo
+~.i.(<:,) ,+(b)
%
i
~ l
100o0 l
Fig. 4. Attenuation at hypersonic frequency versus composition in SiO2-B 203 glasses.
Fig. 3. Variation with composition of the Brillouin linewidth in SiO2-B203 glasses.
~o{>
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.
.
/ /
.
.
do
.
.
.
.
MOLE % B203
~oo
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354
R. Jabra et al. /Hypersounds in Si02-B2 03 glasses
function of the glass composition in figs. 3 and 4, respectively. The attenuation shows a maximum for a composition around 25 mol% B203. Since there is a wide variation of a with the frequency, these results cannot be compared with those obtained by ultrasonic measurements [18]. The water content of the material may greatly influence the attenuation, as is evident from the values obtained for both the B203 glasses.
4. Discussion
In vitreous silica, the hypersound attenuation in the frequency range studied in this work shows a maximum at a temperature around 120 K [19]. Hypersound velocity shows a minimum at a temperature around 80 K and then increases linearly towards room temperature. The height of the peak of attenuation and the slope of the hypersound velocity curve as a function of temperature can be slightly affected by the water content of the material or by the previous thermal history [20]. The measurements obtained for B203 [21 ] exhibit a behaviour qualitatively different from that of vitreous silica. The hypersound's velocity decreased continuously in the temperature range 3 - 3 0 0 K. In the same temperature range the attenuation does not show a peak. These results are also unlike those given by ultrasonic techniques [22]. The silica glass is composed of an arrangement of tetrahedral structural units (SiO4) distributed in such a way that no long-range order exists. On the other hand, in B203 glass, the network is made up of arrangements of planar groups of boroxol units [23]. The silicon and boron ions, which are the only cations in B203-SIO2 glasses, have ionic radii very small compared to that of the oxygen ion. Considering that the oxygen ions essentially make up the volume of the glass, the apparent molar volume of these glasses shows a slight variation with the B203 content; it has also been shown that the structure of these glasses is quite open [10]. Since the modifying ions are absent, it is likely that the boron ion is essentially 3-coordinated. In fact, N.M.R. measurements on the binary glass-forming system GeO2-B203 showed that the boron ion is always 3-coordinated throught the range of composition [24]. Given the structural analogies between SiO2 and GeO2 glasses, it is likely that B203-SiO 2 glasses are composed of planar structural units (BO3) and tetrahedral structural units (SiO4). The rigidity of the glass is due to the energy of the cation-anion bond. It is also related to the individual rigidity of the various structural units from which the spatial network is formed. It seems certain that with the increase of B203 content, the structural groups (BOa) decrease the glass rigidity. The weaker the rigidity, the lower is the hypersound's velocity. This is evident when the B203 content increases. Many models have been proposed in the literature to account for the attenuation of ultrasonic waves in vitreous silica. Anderson and Bommel [7] think that the loss peak observed is due to transverse vibrations of the oxygen ions situated between
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the two silicon ions with which they are linked. A second interpretation [4] concerns longitidunal vibrations of oxygen ions in the direction of the S i - O - S i bond. Finally, Vukcevich [8] attributed the observed attenuation to a small rotation of the SiO4 groups. On the basis of the acoustic results actually known, it is impossible to conclude which of these three models is the most appropriate. Since the attenuation of the B203-SIO2 glasses at room temperature is well above either that of vitreous silica or that of vitreous B203, the inclusion of B203 in the silica network induces a higher concentration of hypersound absorption centres. All the results obtained by Brillouin scattering [9] on glasses lead to the conclusion that the process responsible for the attenuation in these glasses is not a diffusion process due to the frozen-in fluctuations of the density (possible phase separation, residual microporosity). Obviously, such defects would induce a constant attenuation irrespective of the temperature. Moreover, in the glasses studied, no anomaly in elastic scattering (Rayleigh line) occurs, showing the possibility of the presence of these defects. It can be noted that the synthesis of glasses via gels leads to a better homogeneity than the glasses obtained by the usual melting methods [25,26]. As previously observed, the variation of the attenuation of the hypersonic waves with the composition shows a maximum at around 25 mol% of B203 preceded by a sudden drop around 15 mol% of B203; the same anomaly has been observed for the refractive index [27]. This glass is very interesting because its refractive index is small compared to that of vitreous silica; this property has already been exploited for making optical fibers [27] ; however, to our knowledge, this anomaly is as yet unexplained. It is clear that all the models proposed to account for the attenuation in the glasses are based on the possibility of the oxygen ions taking two stable positions, corresponding to the energy potential wells. The explanation of the attenuation observed should be made on the basis of known structural information with respect to the oxygen ions of the glass. The structure of the binary oxides glasses B203-SIO2 would require three different bonds: S i - O - S i , S i - O - B , and B - O - B . The infrared spectroscopy studies [10] showed the presence of the first two bonds by I.R. absorption bands at 1100, 800, and 460 cm -~ (for S i - O - S i bonds) and at 1380, 910, and 670 cm -~ for S i - O - B bonds). Up to at least 50 mol% B203 no absorption band related to B - O - B was revealed by I.R. spectroscopy. The pure B203 glass does not give rise to a high attenuation of hypersound waves [21]. Na20-B203 glasses do not contain non-bridging oxygens ions up to 33 mol% Na20 [28] because the boron ion changes its coordination. Although these glasses contain a high number of B - O - B bonds, they show a lower ultrasonic absorption than that of B203 glass at room temperature [6]. On the other hand, their' attenuation decreases when the concentration of the modifying ions increases [6]. For the glasses studied here it should be noted that the peak of hypersound absorption is on the silica-rich side. The rise in the attenua-
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tion, for our range of frequencies, with the concentration of B203 could not be explained by a relaxation process involving the oxygen ions situated between two borons ions. The second assumption is that there is a great influence of S i - O - B bonds on the relaxation mechanism responsible for the attenuation. The coupling effect of the hypersounds and the S i - O - B bonds may be important because of the asymmetry that exists between the S i - O and B - O bonds which have different lengths and also unequal field strengths. Moreover, the probability of occurrence of the S i - O - B bonds with the change of composition of the SiO2-B2Oa glasses has been approximately calculated [29]. This probability shows a maximum at 40 tool% B203. The comparison between the attenuation curve (fig. 4) and that of the probability of the S i - O - B bond shows a slight shift of the maximum towards the silica-rich side; the shapes of the curves are not identical in the region where these parameters (attenuation and probability of S i - O - B bonds) show a decreasing trend. This fact does not exclusively favour the participation of S i - O - B bonds for the attenuation mechanism. There is a third hypothesis which attributes the increase of the hypersounds attenuation to the S i - O - S i bonds. The accommodation of planar structural units BOa and tetrahedral structural units SiO 4 may only occur with a distortion of the S i - O - S i bonds. The addition of B203 to the silica glass increases the structural disorder, as can be confirmed by the decrease of the I.R. band at 800 cm -1, which finally vanishes. This absorption band, strong in crystalline silica, is also present in vitreous silica. It was attributed to the ring structure of SiO4 tetrahedra [30]. It was also related to the "degree" of order in vitreous silica [31]. If the distortion of the S i - O - S i bonds were relatively higher, the activation energy would also be higher. The observed absorption peak in the case of the silica glass would then be shifted to higher temperatures for the SIO2-B203 glasses, which would thus lead to an increase of the attenuation at 300 K. Because of the lack of studies as a function of temperature, no definite conclusion can be reached on this point, although the measurements of ultrasonic absorption made on the two glasses [17] agree with this assumption. If the attenuation is due to the distortion of the S i - O - S i bonds, the probability curves of the bonds in these glasses [29] could explain the shape of the observed attenuation curve. Indeed, at the silica-rich side, where the probability of the S i - O - S i bonds is high, the number of distorted bonds increases with the B203 content and consequently with the probability of S i - O - B bonds. The attenuation should show the same increase as that shown by the S i - O - B bonds probability. This is what is noted experimentally up to 25 mol% B203. After this composition the decrease of the S i - O - S i bonds probability implies a similar decrease of the attenuation (see fig. 4 and [29]). If the hypothesis about the effect of the participation of B - O - B bonds on the attenuation is discounted, it is difficult to know quantitatively the respective influence of S i - O - S i or S i - O - B vibrations on the attenuation process. It is likely that these two bonds both contributed to the
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hypersonic attenuation; for the low B2Oa content the glass structure favours the relaxation process due to S i - O - S i bonds. However, the decreasing number of these bonds with increasing B203 content implies, up to a certain concentration, the decrease of their participation in the relaxation process in relation to the total attenuation of the glass. The contribution of S i - O - B bonds to the total attenuation is related to their probability of occurrence. The cumulative effect of these two contributions may explain both the shift of the maximum towards the silicarich side and the rapid increase of the attenuation in the same composition range. Following these results the variation of the attenuation of more complex glasses such as alkali borosilicate glasses may be better understood. Comparisons between our glasses and alkali borosilicate glasses can be made in some composition ranges since these glasses do not contain any non-bridging oxygen ions if the ratio M/B is lower than 0.5 (M is an alkali ion). For compositions lower than this one alkali ion is associated with one 4-coordinated boron, as has been confirmed by NMR [32]. The attenuation measurements made on potassium borosilicate glasses [33] give lower values than those for glasses studied in this paper. This can be understood if it is assumed that the modifying cations are situated in the holes of the structure. In this way they impede the vibrations of bridging oxygens which are in their neighbourhood and with which they are coordinated; a smaller number of oxygen ions participate in the attenuation process.
5. Conclusion The elastic properties of the SiO2-B2Oa glasses were studied for frequencies varying between 20 and 30 GHz at room temperature. The velocity of hypersonic waves decreases with increasing B2Oa content. The most noticeable effect is a great increase of the hypersonic attenuation in these glasses when the B203 content is about 25 mol%. This increase was interpreted as being due to a hypersonic coupling effect with the vibration of the oxygen ions of the S i - O - S i and S i - O - B bonds. A cumulative effect of hypersonic absorption of these two kinds of bonds ascertains the position of the attenuation maximum in the composition curve.
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