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Medium-range order of radiation modified silica glasses studied by spectroscopic and optical methods
286
Journal of Non-Crystalline Solids 123 (1990) 286-290 North-Holland
MEDIUM-RANGE ORDER OF RADIATION MODIFIED SILICA G L A S S E S S T U D I E D BY S P E C T R O S C O P I C AND O P T I C A L M E T H O D S A.V. K O N S T A N T I N O V a, L.V. M A K S I M O V
a, A.R. SILIN b, O.V. Y A N U S H c
a S.L Vavilov State Optical Institute, 199034 Leningrad, USSR b Institute of Solid State Physics, Latvian State University, 226083 Riga, USSR c Leningrad Technological Institute for the Pulp and Paper Industry, 198092 Leningrax~ USSR
Neutron irradiated silica glasses were studied. The increase of density and refractive index with the fluence value were found and Rayleigh and Mandelshtam-Bdllouin scattering, low-frequency Raman scattering and Raman scattering spectra were measured. It was concluded that neutron irradiation of silica glasses led to an alteration of a microinhomogeneous glass structure including correlation regions and 'frozen' density fluctuations.
1. Introduction The influence of particle irradiations with diffeting energies on the solid state structure leads to various alterations in electronic and nuclear subsystems. Consequently, one is compelled to apply experimental techniques characterized by selective sensitivity to structural changes on a given scale. We have investigated the total scattered light spectra of radiation modified silica glasses, Rayleigh and Mandelshtam-Brillouin scattering (RMBS), low-frequency Raman scattering (LFRS) and Raman scattering (RS).
2. Experimental techniques We investigated silica glass samples (type III) irradiated with neutron flux at fluences ( F ) from 1016 to 1020 n cm -2. Raman scattering (RS) and low-frequency Raman scattering (LFRS) spectra were obtained in W and VII polarizations using DFS-24 and Omars-89 spectrometers. The Rayleigh and Mandelshtam-Brillouin scattering (RMBS) spectra in W polarization were detected at a scattering angle 90 ° using a spectrometer including a pressure-scanned F a b r y - P e r r o t interferometer.
The refractive index n was measured using an IRF-23 refractometer with an error of +0.0002; the density p was defined by means of hydrostatic weighing in toluene with the error of + 0.002 g c m - 3.
3. Results and discussion The influence of a neutron flux at fluences F < 1018 n cm -2 does not result in detectable changes of density and refractive index. At F = 1018 to 10 2° n cm -2 the density and the refractive index increase with fluence corresponding to the known data. The quantitative differences are, perhaps, due to the difference in the energetic spectrum of a neutron flux and in temperatures of irradiation [1-4]. The data treatment using the L o r e n t z - L o r e n z formula n2-1 n2+ 2
]'nNa,
(1)
where N is the volume concentration of oscillators, N - p, and a is the polarizability, allows one to conclude that the decrease of polarizability by 0.8% for a neutron flux 102o n cm -2 is a consequence of the growth of the averaged bond ionicity in the SiO 2 network [5]. The ultrasound data
0022-3093/90/$03.50 © 1990 - Elsevier Science Publishers B.V. (North-Holland)
287
A. V. Konstantinov et al. / Radiation modified silica glasses
on the same glass samples are consistent with this assumption. Earlier it was shown that elastic moduli increased with fluence [6]. If interatomic potentials are considered as Mie-Griineisen potentials, U(r)=Ar-b-Br -d, then the calculation of b and d from ultrasound propagation data is an estimation of the bond ionicity change [7]. It is worth noting that bd increases both with the increase of fluence for irradiation of silica glass and with the introduction of alkali ions into SiO 2 [81. The influence of neutron flux on the SiO 2 short-range order appears in RS spectra. It is well-known that fluctuations of the intensities of bands at 495 and 606 cm-1, which are the narrowest and ascribed to 'defect structures', increase with total neutron flux [9]. In fig. 1 RS spectra of irradiated glasses are shown. From the figure it follows that with the growth of integrated flux the band intensities at 495 and 606 cm -1 increase in accordance with the known data [10], the increase beginning at F = 1018 n cm -2. The alterations in RS spectra support the notions about the silica
glass 'defectivity' increasing with integrated neutron flux and do not run counter to the conclusion about the growth of bond ionicity in SiO2 with integrated flux. The shift of RS bonds towards higher frequency (see fig. 2 and ref. [10]) may be evidence of the growth of internal stresses in silica glasses [11]. Passing over from generalized characteristics of glassy SiO 2, reflecting ensemble-averaged changes in nuclear and electron subsystems of nearest neighbours, to characteristics belonging to groupings including several next-nearest neighbours is possible by means of LFRS and RMBS spectroscopy. It is well known that in liquids and glasses there is a low-frequency (Av < 100 cm -1) Raman scattering peak, the existence of which is indicative of medium-range order regions in glass [12]. These are characterized by translation symmetry and interfaces or by gradual loss of translation symmetry which is described by a correlation function of the F ( R ) - e x p ( - R / R c) type, where Rc is the size of the correlation region. R~ can be
]n~ensd.y
'1
?
,,) I
200
I
300
I
400
I
SO0
I
6OO
cm
-t
Fig. 1. RS spectra of unirradiated silica glass (1) and irradiated at the fluenceof F=101°, 1017 (curve 1), 1019 (curve 2) and 10z° (curve 3) n cm-2; VV polarization.
288
A. V. Konstantinoo et al. / Radiation modified silica glasses
l,~h.-%
4
ionicity. The decrease of R c by - 20% at F = 1020 n cm -2 is attributed to local melting of microscopic volumes followed by quenching under pressure [15,16]. It should be emphasized that a microinhomogeneous glass structure is not reduced to the existence of correlation regions. Indeed, regions of - 10 .~ differing in their refractive index by 0.05 hardly can cause Rayleigh scattering the intensity of which is more than two orders of magnitude higher than that of crystalline SiO2 [17,18]. The cause of Rayleigh scattering in single-component glasses is the existence of isobaric density fluctuations 'frozen-in' during cooling of a glassforming liquid (entropy fluctuations) and anisotropy fluctuations, the magnitude of which can reach thousands of Angstroms [19]. It is common knowledge that the contribution of the latter to the Rayleigh scattering intensity for silica glasses does not exceed 3% [20], i.e. Rayleigh scattering can be practically totally defined by entropy fluctuations. RMBS spectroscopy is an effective method for the investigation of fluctuation microinhomogeneities in glasses. The RMBS spectrum includes the Rayleigh scattering component coinciding in frequency with the incident light frequency, p, and doublets at frequencies i, + A~,l and v 5= AJ,t induced by the light wave scattering with adiabatic density fluctuations (pressure fluctuations) propagating in the medium at the velocity of longitudio
L
I
!
I
50
400
150
~0
/la)
cm-4
Fig. 2. Low-frequency Raman scattering spectra of unirradiated silica glass (curve 1) and irradiated with a neutron flux at the 10is (curve 2), 1019 (curve 3), 1020 (curve 4) n cm-2; VH polarization.
defined from the LFRS maximum position measured in the perpendicular (A~,±) polarization [13,14]:
Ro- vt/a~.,
(2)
where ~ is the propagation vdocity of a transverse ultrasound wave. In fig. 2 LFRS spectra of radiation modified silica glasses are presented. In fig. 3 a relationship of the LFRS maximum position (curve 1) and the size of the correlation region (curve 2) on fluence is shown. As shown in the fig. 3 the exposure to a neutron flux leads to a decrease of correlation length, i.e. the loss of translation symmetry at shorter distances due to breaking of Si-O-Si bonds and to the formation of smaller regions of more bond
6O t
55
50
~s t6
18
I
qg
o,8
20
Fig. 3. Relationships of the maximum position in low-frequency Raman scattering spectra (curve 1) and the relative sizes of correlation regions (curve 2) on the fluence F.
289
A. V. Konstantinoo et al. / Radiation modified silica glasses
nal (Mandelshtam-Brillouin scattering) and transverse hypersound waves [2]. The intensity of Mandelshtam-BriUouin scattering components, MBS, is defined by the parameters of a scattering medium and measurement temperatures T [21]: IMBS
nSkT _ __ M '
(3)
where k is the Boltzmann constant, and M = pV2 is the longitudinal elastic modulus. A high resolution RMBS spectrometer resolves the Rayleigh scattering from luminescence, excited by irradiation with wavelength 0.6328 I~m. The intensity of the scattering increases with the increasing integrated flux [13], the result being a decrease of the interference pattern contrast (fig. 4, curve 1). In fig. 4 the relationships of Rayleigh scattering (curve 2) and MBS (curve 3) intensities and Landau-Placzek ratio RL_p=IRaYl/2IMnS (curve 4) on integrated flux are also shown. One can see from the figure that the intensity of MBS is constant. This constantcy can be accounted for by the same character of n and M changes with
l,a,f,.,,. ~L-P f20
-,,.r,._. I
i
2 ~~i~
/
~0 o
,.11 ~ 16
L-V
4. Conclusion
Investigations of the total scattered light spectrum allow us to conclude that a neutron flux leads to changes of the whole hierarchy of silica glass inhomogeneities including structure correlation regions (medium-range order).
References
K I
0
integrated flux. Thus, I MBs can be considered to be an internal reference. The growth of R with integrated flux (fig. 4, curve 4) is associated with structural changes in silica glass, appearing as a result of local melting of microscopic regions and their quenching with the formation of volumes with high refractive index. The increase of volumetric fraction of these microscopic regions and their joining lead to the situation where the scattering microinhomogeneities turn out to be island-like irradiation - unmodified areas corresponding to the downward branch of curves 2 and 4.
~
lg
i
i
20
Fig. 4. The fluence F relationships of the interference pattern contrast in Fabry-Perrot interferometer (curve 1), Rayleigh (curve 2) and Mandelshtam-Brillouin (curve 3) scattering intensities, and the Landan-Placzek ratio (curve 4).
[1] A.R. Silin, L.N. Skuja and A.A. Lapenas, in: Physics and Chemistry of Glass-forming Systems, Vol. 5 (Latvian State University, Riga, 1977) p. 93 (in Russian). [2] J.B. Bates, R.W. Hendricks and L.B. Shaffer, J. Chem. Phys. 61 (1974) 4163. [3] S.M. Brekhovskikh, Yu.N. Viktorova and L.N. Landa, Radiation Effects in Glasses (Energoizdat, Moscow, 1982) (in Russian). [4] V.K. Leko and A.V. Mazurin, Properties of Silica Glass (Nauka, Leningrad, 1985) (in Russian). [5] A.V. Konstantinov, L.V. Maksimov and A.R. Silin, present work. [6] V.N. Bogdanov, L.V. Maksimov, A.R. Silin and O.V. Yanush, in: The Seventh All-Union Conference on Radiation Physics and Chemistry of Non-organic Materials (Zinatne, Riga, 1989) p. 412 (in Russian). [7] S.V. Nemilov, in: A Glassy State, Proc. Fifth All-Union Conference (Nauka, Leningrad, 1971) p. 10 (in Russian). [8] G.O. Karapetyan, V.Ya. Livshitz and D.G. Tennison, Fiz. Khim. Stekla 7 (1981) 188. [9] J.C. Philips, Phys. Rev. B35 (1987) 6409. [10] R.H. Stolen, J.T. Krause and K.R. Kurkijan, Discuss. Faraday Soc. 50 (1970) 103. [11] D.R. Tallant, T.A. Michalske and W.L. Smith, J. NonCryst. Solids 106 (1987) 384.
290
A. K Konstantinov et al. / Radiation modified silica glasses
[12] E. Duval, A. Baukenter and B. Champagnon, Phys. Rev. Lett. 56 (1986) 2052. [13] V.K. Malinovsky and V.N. Novikov, J. Non-Cryst. Solids 85 (1986) 93. [14] V.K. Malinovsky, A.P. Sokolov, Solid State Commun. 57 (1986) 757. [15] G.V. Byurganovskaya, V.V. Vargin, V.K. Leko and N.F. Orlov, Radiation Influence upon Non-Organic Glasses (Nauka, Moscow, 1968) (in Russian). [16] A.R. Silin and A.N. Trukhin. Point Defects and Elementary Excitations in Crystalline and Glassy SiO2 (Zinatne, Riga, 1985).
[17] G.O. Karapetyan and L.V. Maksimov, in: A Glassy State, Proc. Eighth All Union Conference (Nauka, Leningrad, 1988) p. 45 (in Russian). [18] H.M. Daglish, Glass Technol. 11 (1970) 30. [19] J. Schroeder, Treatise on Material Science and Technology, Glass I (New York, 1977) p. 157. [20] N.A. Bokov and N.S. Andreiv, Fiz. Khim. Stelda 7 (1981) 509. [21] I.L. Fabelinsldi, Molecular Scattering of Light (Nanka, Moscow, 1965).
Journal of Non-Crystalline Solids 123 (1990) 286-290 North-Holland
MEDIUM-RANGE ORDER OF RADIATION MODIFIED SILICA G L A S S E S S T U D I E D BY S P E C T R O S C O P I C AND O P T I C A L M E T H O D S A.V. K O N S T A N T I N O V a, L.V. M A K S I M O V
a, A.R. SILIN b, O.V. Y A N U S H c
a S.L Vavilov State Optical Institute, 199034 Leningrad, USSR b Institute of Solid State Physics, Latvian State University, 226083 Riga, USSR c Leningrad Technological Institute for the Pulp and Paper Industry, 198092 Leningrax~ USSR
Neutron irradiated silica glasses were studied. The increase of density and refractive index with the fluence value were found and Rayleigh and Mandelshtam-Bdllouin scattering, low-frequency Raman scattering and Raman scattering spectra were measured. It was concluded that neutron irradiation of silica glasses led to an alteration of a microinhomogeneous glass structure including correlation regions and 'frozen' density fluctuations.
1. Introduction The influence of particle irradiations with diffeting energies on the solid state structure leads to various alterations in electronic and nuclear subsystems. Consequently, one is compelled to apply experimental techniques characterized by selective sensitivity to structural changes on a given scale. We have investigated the total scattered light spectra of radiation modified silica glasses, Rayleigh and Mandelshtam-Brillouin scattering (RMBS), low-frequency Raman scattering (LFRS) and Raman scattering (RS).
2. Experimental techniques We investigated silica glass samples (type III) irradiated with neutron flux at fluences ( F ) from 1016 to 1020 n cm -2. Raman scattering (RS) and low-frequency Raman scattering (LFRS) spectra were obtained in W and VII polarizations using DFS-24 and Omars-89 spectrometers. The Rayleigh and Mandelshtam-Brillouin scattering (RMBS) spectra in W polarization were detected at a scattering angle 90 ° using a spectrometer including a pressure-scanned F a b r y - P e r r o t interferometer.
The refractive index n was measured using an IRF-23 refractometer with an error of +0.0002; the density p was defined by means of hydrostatic weighing in toluene with the error of + 0.002 g c m - 3.
3. Results and discussion The influence of a neutron flux at fluences F < 1018 n cm -2 does not result in detectable changes of density and refractive index. At F = 1018 to 10 2° n cm -2 the density and the refractive index increase with fluence corresponding to the known data. The quantitative differences are, perhaps, due to the difference in the energetic spectrum of a neutron flux and in temperatures of irradiation [1-4]. The data treatment using the L o r e n t z - L o r e n z formula n2-1 n2+ 2
]'nNa,
(1)
where N is the volume concentration of oscillators, N - p, and a is the polarizability, allows one to conclude that the decrease of polarizability by 0.8% for a neutron flux 102o n cm -2 is a consequence of the growth of the averaged bond ionicity in the SiO 2 network [5]. The ultrasound data
0022-3093/90/$03.50 © 1990 - Elsevier Science Publishers B.V. (North-Holland)
287
A. V. Konstantinov et al. / Radiation modified silica glasses
on the same glass samples are consistent with this assumption. Earlier it was shown that elastic moduli increased with fluence [6]. If interatomic potentials are considered as Mie-Griineisen potentials, U(r)=Ar-b-Br -d, then the calculation of b and d from ultrasound propagation data is an estimation of the bond ionicity change [7]. It is worth noting that bd increases both with the increase of fluence for irradiation of silica glass and with the introduction of alkali ions into SiO 2 [81. The influence of neutron flux on the SiO 2 short-range order appears in RS spectra. It is well-known that fluctuations of the intensities of bands at 495 and 606 cm-1, which are the narrowest and ascribed to 'defect structures', increase with total neutron flux [9]. In fig. 1 RS spectra of irradiated glasses are shown. From the figure it follows that with the growth of integrated flux the band intensities at 495 and 606 cm -1 increase in accordance with the known data [10], the increase beginning at F = 1018 n cm -2. The alterations in RS spectra support the notions about the silica
glass 'defectivity' increasing with integrated neutron flux and do not run counter to the conclusion about the growth of bond ionicity in SiO2 with integrated flux. The shift of RS bonds towards higher frequency (see fig. 2 and ref. [10]) may be evidence of the growth of internal stresses in silica glasses [11]. Passing over from generalized characteristics of glassy SiO 2, reflecting ensemble-averaged changes in nuclear and electron subsystems of nearest neighbours, to characteristics belonging to groupings including several next-nearest neighbours is possible by means of LFRS and RMBS spectroscopy. It is well known that in liquids and glasses there is a low-frequency (Av < 100 cm -1) Raman scattering peak, the existence of which is indicative of medium-range order regions in glass [12]. These are characterized by translation symmetry and interfaces or by gradual loss of translation symmetry which is described by a correlation function of the F ( R ) - e x p ( - R / R c) type, where Rc is the size of the correlation region. R~ can be
]n~ensd.y
'1
?
,,) I
200
I
300
I
400
I
SO0
I
6OO
cm
-t
Fig. 1. RS spectra of unirradiated silica glass (1) and irradiated at the fluenceof F=101°, 1017 (curve 1), 1019 (curve 2) and 10z° (curve 3) n cm-2; VV polarization.
288
A. V. Konstantinoo et al. / Radiation modified silica glasses
l,~h.-%
4
ionicity. The decrease of R c by - 20% at F = 1020 n cm -2 is attributed to local melting of microscopic volumes followed by quenching under pressure [15,16]. It should be emphasized that a microinhomogeneous glass structure is not reduced to the existence of correlation regions. Indeed, regions of - 10 .~ differing in their refractive index by 0.05 hardly can cause Rayleigh scattering the intensity of which is more than two orders of magnitude higher than that of crystalline SiO2 [17,18]. The cause of Rayleigh scattering in single-component glasses is the existence of isobaric density fluctuations 'frozen-in' during cooling of a glassforming liquid (entropy fluctuations) and anisotropy fluctuations, the magnitude of which can reach thousands of Angstroms [19]. It is common knowledge that the contribution of the latter to the Rayleigh scattering intensity for silica glasses does not exceed 3% [20], i.e. Rayleigh scattering can be practically totally defined by entropy fluctuations. RMBS spectroscopy is an effective method for the investigation of fluctuation microinhomogeneities in glasses. The RMBS spectrum includes the Rayleigh scattering component coinciding in frequency with the incident light frequency, p, and doublets at frequencies i, + A~,l and v 5= AJ,t induced by the light wave scattering with adiabatic density fluctuations (pressure fluctuations) propagating in the medium at the velocity of longitudio
L
I
!
I
50
400
150
~0
/la)
cm-4
Fig. 2. Low-frequency Raman scattering spectra of unirradiated silica glass (curve 1) and irradiated with a neutron flux at the 10is (curve 2), 1019 (curve 3), 1020 (curve 4) n cm-2; VH polarization.
defined from the LFRS maximum position measured in the perpendicular (A~,±) polarization [13,14]:
Ro- vt/a~.,
(2)
where ~ is the propagation vdocity of a transverse ultrasound wave. In fig. 2 LFRS spectra of radiation modified silica glasses are presented. In fig. 3 a relationship of the LFRS maximum position (curve 1) and the size of the correlation region (curve 2) on fluence is shown. As shown in the fig. 3 the exposure to a neutron flux leads to a decrease of correlation length, i.e. the loss of translation symmetry at shorter distances due to breaking of Si-O-Si bonds and to the formation of smaller regions of more bond
6O t
55
50
~s t6
18
I
qg
o,8
20
Fig. 3. Relationships of the maximum position in low-frequency Raman scattering spectra (curve 1) and the relative sizes of correlation regions (curve 2) on the fluence F.
289
A. V. Konstantinoo et al. / Radiation modified silica glasses
nal (Mandelshtam-Brillouin scattering) and transverse hypersound waves [2]. The intensity of Mandelshtam-BriUouin scattering components, MBS, is defined by the parameters of a scattering medium and measurement temperatures T [21]: IMBS
nSkT _ __ M '
(3)
where k is the Boltzmann constant, and M = pV2 is the longitudinal elastic modulus. A high resolution RMBS spectrometer resolves the Rayleigh scattering from luminescence, excited by irradiation with wavelength 0.6328 I~m. The intensity of the scattering increases with the increasing integrated flux [13], the result being a decrease of the interference pattern contrast (fig. 4, curve 1). In fig. 4 the relationships of Rayleigh scattering (curve 2) and MBS (curve 3) intensities and Landau-Placzek ratio RL_p=IRaYl/2IMnS (curve 4) on integrated flux are also shown. One can see from the figure that the intensity of MBS is constant. This constantcy can be accounted for by the same character of n and M changes with
l,a,f,.,,. ~L-P f20
-,,.r,._. I
i
2 ~~i~
/
~0 o
,.11 ~ 16
L-V
4. Conclusion
Investigations of the total scattered light spectrum allow us to conclude that a neutron flux leads to changes of the whole hierarchy of silica glass inhomogeneities including structure correlation regions (medium-range order).
References
K I
0
integrated flux. Thus, I MBs can be considered to be an internal reference. The growth of R with integrated flux (fig. 4, curve 4) is associated with structural changes in silica glass, appearing as a result of local melting of microscopic regions and their quenching with the formation of volumes with high refractive index. The increase of volumetric fraction of these microscopic regions and their joining lead to the situation where the scattering microinhomogeneities turn out to be island-like irradiation - unmodified areas corresponding to the downward branch of curves 2 and 4.
~
lg
i
i
20
Fig. 4. The fluence F relationships of the interference pattern contrast in Fabry-Perrot interferometer (curve 1), Rayleigh (curve 2) and Mandelshtam-Brillouin (curve 3) scattering intensities, and the Landan-Placzek ratio (curve 4).
[1] A.R. Silin, L.N. Skuja and A.A. Lapenas, in: Physics and Chemistry of Glass-forming Systems, Vol. 5 (Latvian State University, Riga, 1977) p. 93 (in Russian). [2] J.B. Bates, R.W. Hendricks and L.B. Shaffer, J. Chem. Phys. 61 (1974) 4163. [3] S.M. Brekhovskikh, Yu.N. Viktorova and L.N. Landa, Radiation Effects in Glasses (Energoizdat, Moscow, 1982) (in Russian). [4] V.K. Leko and A.V. Mazurin, Properties of Silica Glass (Nauka, Leningrad, 1985) (in Russian). [5] A.V. Konstantinov, L.V. Maksimov and A.R. Silin, present work. [6] V.N. Bogdanov, L.V. Maksimov, A.R. Silin and O.V. Yanush, in: The Seventh All-Union Conference on Radiation Physics and Chemistry of Non-organic Materials (Zinatne, Riga, 1989) p. 412 (in Russian). [7] S.V. Nemilov, in: A Glassy State, Proc. Fifth All-Union Conference (Nauka, Leningrad, 1971) p. 10 (in Russian). [8] G.O. Karapetyan, V.Ya. Livshitz and D.G. Tennison, Fiz. Khim. Stekla 7 (1981) 188. [9] J.C. Philips, Phys. Rev. B35 (1987) 6409. [10] R.H. Stolen, J.T. Krause and K.R. Kurkijan, Discuss. Faraday Soc. 50 (1970) 103. [11] D.R. Tallant, T.A. Michalske and W.L. Smith, J. NonCryst. Solids 106 (1987) 384.
290
A. K Konstantinov et al. / Radiation modified silica glasses
[12] E. Duval, A. Baukenter and B. Champagnon, Phys. Rev. Lett. 56 (1986) 2052. [13] V.K. Malinovsky and V.N. Novikov, J. Non-Cryst. Solids 85 (1986) 93. [14] V.K. Malinovsky, A.P. Sokolov, Solid State Commun. 57 (1986) 757. [15] G.V. Byurganovskaya, V.V. Vargin, V.K. Leko and N.F. Orlov, Radiation Influence upon Non-Organic Glasses (Nauka, Moscow, 1968) (in Russian). [16] A.R. Silin and A.N. Trukhin. Point Defects and Elementary Excitations in Crystalline and Glassy SiO2 (Zinatne, Riga, 1985).
[17] G.O. Karapetyan and L.V. Maksimov, in: A Glassy State, Proc. Eighth All Union Conference (Nauka, Leningrad, 1988) p. 45 (in Russian). [18] H.M. Daglish, Glass Technol. 11 (1970) 30. [19] J. Schroeder, Treatise on Material Science and Technology, Glass I (New York, 1977) p. 157. [20] N.A. Bokov and N.S. Andreiv, Fiz. Khim. Stelda 7 (1981) 509. [21] I.L. Fabelinsldi, Molecular Scattering of Light (Nanka, Moscow, 1965).