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RAMAN STUDIES OF STRUCTURAL DEFECTS IN VITREOUS SiO2
284
RAMAN STUDIES OF STRUCTURAL DEFECTS IN VITREOUS SiO,
F. L. Galeener, J. C. Mikkelsen, Jr., and N. M. Johnson Xerox Palo Alto Research Center, Palo Alto, CA 94304 ABSTRACT This paper discusses the two sharp lines which are seen at 495 cm"1 and 606 cm" in the Raman spectrum of pure fused silica. We conclude that the 495 cm"1 line is probably a longitudinal optical mode of the network, although defect origin is not entirely ruled out. More importantly, we conclude that the 606 cm"1 is due to a large concentration of non-bridging oxygen defects. We show how the strength of the 606 cm"1 line varies with the water concentration and the thermal history of bulk samples of Suprasil fused silica. INTRODUCTION Figure 1 shows the polarized Raman spectra of high purity fused silica as a function of water concentration (OH). These spectra, measured on samples as-received from the manufacturer, are discussed in detail by Galeener and Geils (1). In most respects, they are similar to the spectra reported by Stolen and Walrafen (2). The important features for the present discussion are as follows. At high frequencies, there is the 3700 cm"1 O-H stretch mode [Fig. 1(c)] which we use to monitor OH concentrations down to the level of 2 ppm by weight. At intermediate frequencies [Fig. K b ) ] the main observation is the absence of any structure other than that due to second order vibrations of the Si02 network, discussed elsewhere by Galeener and Lucovsky (3). In particular, there is the absence of Si-H stretch modes, which Hartwig (4) has shown to occur at 2285 cm"1 in deliberately hydrogenated silica. At lower frequencies [Fig. 1(a)] the features of interest are the 975 cm"1 Si-OH stretch mode induced in high water content material, the 606 cm"1 line whose intensity is reduced in the high water content as-received material, and the 495 cm"1 line whose intensity is unchanged. These latter two lines are the focus of attention in this paper; all other features in Fig. 1 which are not mentioned here have been identified elsewhere (5) as transverse optical (TO) or longitudinal optical (LO) modes of the ideal (perfect) network. THERMAL STUDIES Figure 2 shows the variation in strength of the 495 cm"1 and 606 cm"1 lines with thermal treatment of the sample. The line strength is measured by the area between the defect line and a baseline drawn with a French curve (assuming that the 495 cm"1 line has a total width at its baseline of 40 cm"1 while the 606 cm"1 line has a total width of 100 c m " 1 ) . The samples were of two types, those of low water content (solid lines) and those of high water content (dotted lines). All samples were about 3 m m x 6 m m x l 2 m m and Raman spectra were obtained from the interior of these materials. Water content was not affected by the heat treatments, as determined by measuring the area of the 3700 cnT 1 line before and after each treatment. There were
285 no changes in the frequency range 1500 cm"1 to 3000 cm"1 indicating that neither Si-H bonds nor molecular water were created. Beginning with a new set of samples, treatments (A) through (G) were carried out in the order [ l] through [ 7]. Study of the left half of Fig. 2 reveals that the area under the 495 cm"1 line varies erratically about an average value of -18. For example, in the sequence [ 3] through [ 7] the area for the low water content sample is alternately above then below the area for the high water content material. This simply reflects the difficulty in determining the base line for a peak that rides on the steep slope of the main Raman line (whose position varies by a few wavenumbers with thermal treatment). By placing spectra over one another we conclude that the area under the 495 cm"1 line is constant within 5%.
THERMAL STUDIES OF VITREOUS SILICA ■ SUPRASIL-WI • SUPRASIL-1 THERMAL TREATMENT
i__
(0H)<2ppm (OH»-1200ppm
495 c m ' 1 R A M A N LINE AREA 0
10
6 0 6 c m -1 R A M A N L I N E
►
AREA 20
3
10
— 20
30
AS RECEIVEO
AIR QUENCHED FROM 1500 C WATER QUENCH FROM 1500 C ANNEALE0: 1230 C 35 MIN. ANNEALED: 1100C 15 HRS.
2000
2500
WAVENUMBER, W, c m " 1
Ί—rRAMAN SPECTRA
-i—i—|—r
NEW SAMPLES: ANNEALED AT 1190 C-16 HRS. WATER QUENCH
I I I I / i
/HV 3500
ANNEALED: 910 C 60 HRS.
OH < 5 PPM - O H - 180 ΡΡΛ O H - 1200 PP , 4000
WAVENUMBER, W. c m - 1
Fig. 1. The OH dependence of the polarized Raman spectra of as-received Suprasil. The sharp lines at 495 cm"1 and 606 cm"1 in (a) are the features of special interest in this paper.
Fig. 2. The strengths of the 495 cm"1 and 606 cm"1 Raman lines after different thermal treatments (A) through (H). Note the time sequence of steps, [ l] through [ 7]. The variations in the 495 cm"1 line are erratic and small, while the 606 cm"1 line strength varies strongly and systematically.
286 The right half of Fig. 2 reveals clear changes in the strength of the 606 cm"1 line. The line strength in high water content material is always less than (or equal to) that for low water content material. Material quenched from high temperatures has a larger 606 cm*1 line than material quenched from low temperatures. Figures 2(f) and 2(h) suggest that after sufficiently long periods at a given temperature >_1100°C, the strength of the 606 cm*1 line is independent of the water concentration. This contradicts the most obvious interpretation of Fig. 2(a), namely that the 606 cm"1 defect concentration is lower in high water content samples. Our hypothesis for resolving this is to assume that equilibrium is reached far more quickly in high water content samples, but that the equilibrium concentration is not very dependent on water content. This is consistent with the fact that high water content material has significantly lower viscosity (6). Thus, we suppose that watercontaining and water-free as-received material have different 606 cm"l line strength either because they have been annealed at different temperatures, or, if annealed at the same temperature, because the low water content material was not annealed long enough for the defect concentration to achieve equilibrium value. Another possibility is that there is, in fact, a real difference in the equilibrium 606 cm"1 defect concentrations in watercontaining and water-free samples that have been annealed at temperatures below 1100 C. More data is being obtained, with careful attention to the role of annealing time and quenching speed, and the results will be discussed more extensively elsewhere. DISCUSSION Stolen, Krause, and Kurkjian (7) first suggested that the 606 cm"1 line might be due to a defect, when they observed that this line increased at least fivefold after the sample had been irradiated with ~10 2 ° fast neutrons/cm2. Their data showed essentially no change in the area of the 495 cm"1 line with irradiation, although this line did shift to slightly higher frequency, as did the 606 cm"1 line and the main Raman peak. These results were corroborated in an extensive study of neutron effects by Bates, Hendricks, and Schaffer (8). The latter authors reported a seven-fold increase in the 606 cm"1 line for an exposure of 2 x 1 0 2 0 neutrons/cm2, as well as a possible slight increase in the strength of the 495 cm"1 line. They conclude that both of these lines are due to defects that are intrinsic in vitreous (v-)Si02, and that both may be associated with the defect formed when a Si-0 bond is left broken, i.e., associated with a "non-bridging oxygen defect" (NBOD) of the form ESi + 0"-SiH. As Bates, et al. (8) point out, their results do not rule out the possibility that the lines are due to other kinds of structural defects. Indeed, from theoretical studies, Laughlin and coworkers (9) have suggested that the 606 cm"1 line is due to a "wrong bond" defect of the form =si-Si=, which we refer to as the Si-Si bond defect. The neutron bombardment studies thus clearly establish the 606 cm"1 line as having defect origin. On the other hand, we believe that the very small observed changes in the 495 cm"1 line demonstrate that it cannot be associated with precisely the same defect that gives rise to the rapidly increasing 606 cm"1 line. Were this so, both lines would rise by the same percentage. Moreover, the small reported changes in strength of the 495 cm"1 line may be due to the difficulty of measuring its strength, or they may be due to changes in matrix elements brought about by the compaction of the network under neutron irradiation. If the 495 cm"1 is a defect, the defect concentration is very little affected by neutron bombardment; nor is it affected by water content or thermal treatment, as we have shown. At the present, we
287 think it more likely that the 495 cm"1 line is an LO mode of the basic network, as argued in Ref. 5. Accordingly, we focus the rest of our attention on the 606 cm"1 line. A set of as-received samples of Suprasil 1 and Suprasil W-l were exposed to 30 Mrad of X-rays from a 60 kV DC machine. This induced the expected UV absorption and strong spin resonance signals, but caused no detectable change in the Raman spectra. Thus, X-irradiation does not induce the 606 cm"1 defect, but it may activate associated electronic states. It can be demonstrated that the 606 cm"1 line is not due to Si-Si bonds or 0-0 bonds, by appeal to measurements made on v-Ge02- Galeener and Geils (1) reported a line at 520 cm"1 in the Raman spectrum of v-Ge02 which they believed was analogous to the 606 cm"1 line in v-SiOo. This has been confirmed by making measurements on v-Ge02 irradiated by 10 2 * neutrons/cm2 which show a large increase in the strength of the 520 cm"1 line. Raman measurements were also made on non-phase-separated v-Ge02 that was 10% Ge-rich. The defect line at 520 cm"1 was unaffected. This proves that the 520 cm"1 line in normally stoichiometric material is not due to a small concentration of Ge-Ge bonds, which would increase greatly in the Ge-rich material, nor is it due to a small concentration of 0-0 bonds which would most probably go to zero in the Ge-rich material. It then follows that the 606 cm"1 defect in V-S1O2 is not a wrong bond defect of the Si-Si or 0-0 type. Having eliminated wrong bond defects, we next consider the most likely broken bond defects, which are the isolated dangling silicon bond HSi , the isolated dangling oxygen bond "O-Sin, or their spatial juxtaposition, the previously defined NBOD. Also, in this category are the missing oxygen (Ξβί ΞίΞ) and the missing silicon defects, both of which might be formed under neutron bombardment. Since the NBOD is locally neutral, it will have lower energy associated with its existence than will the other four (charged) defects. Thus, we expect the NBOD to be the most numerous defect. Also, since the 606 cm"1 defect line is the only one observed, it is reasonable to ascribe this line to the existence of NBOD's. We believe this identification is consistent with all experimental observations to date, including thermal history and neutron bombardment. The question now arises whether the 606 cm"1 line is due to the NBOD as an inseparable whole, or whether it can be assigned to only one part of the defect, either the dangling oxygen, or the silicon with the dangling bond. We eliminate the isolated dangling oxygen by appeal to the OH-dependence data in Fig. 1(a). First, we make the reasonable assumption that the addition of a hydrogen to a dangling oxygen, forming the OH unit, will result in very little change in the frequency or Raman activity of defect vibrational modes previously involving the dangling oxygen, but now involving the dangling OH unit. Since the 975 cm"1 line was non-existent before introduction of 1200 ppm OH, the concentration of isolated dangling oxygen units in the water-free material must be very small. Furthermore, if the 606 cm"1 line were due to the dangling oxygen half of the NBOD, then this line should have increased dramatically with the introduction of danglinq OH units. Instead, it decreased slightly, and after annealing at 1100 C or 1190°C showed the same strength as in the water-free material. Moreover, its concentration can be increased by quenching the glass from a higher temperature, without any concurrent change in the 975 cm"1 line.
288 Although we presently feel that the 606 cm"1 line is most likely the signature of silicon atoms with one dangling bond, we are not yet able to eliminate the possibility that it represents a mode of the NBOD as a whole. We are working further in an effort to answer this question. REFERENCES (1)
F. L. Galeener and R. H. Geils (1977), The Polarized Raman Spectra of OH in Vitreous S1O2 and Ge0 2 , The Structure of Non-Crystalline Materials, ed. P. H. Gaskell, Taylor and Francis, London, 223.
(2)
R. H. Stolen and G. E. Walrafen, Water and Its Relation to Broken Bond Defects in Fused Silica, J. Chem. Phys. 64, 2623 (1976).
(3)
F. L. Galeener and G. Lucovsky (1976), Second Order Vibrational Spectra of Vitreous Silica, Light Scattering in Solids, ed. M. Balkanski, R. C. C. Leite and S. P. S. Porto, Flammarion, Paris, 641.
(4)
C M . Hartwig, The Radiation-Induced Formation of Hydrogen and Deuterium Compounds in Silica and Observed by Raman Scattering, J. Chem. Phys. 66, 227 (1977).
(5)
F. L. Galeener and G. Lucovsky, Longitudinal Optical Vibrations in Glasses: Ge0 2 and Si0 2 , Phys. Rev. Lett. 37, 1474 (1976).
(6)
See R. H. Doremus (1973) Glass Science, Wiley, New York, 105.
(7)
R. H. Stolen, J. T. Krause, and D. R. Kurkjian, Raman Scattering and Far Infra-Red Absorption in Neutron Compacted Silica, Disc. Faraday Soc. 50, 103 (1970).
(8)
J. B. Bates, R. W. Hendricks, and L. B. Shaffer, Neutron Irradiation Effects and Structure of Noncrystalline Si0 2 , J. Chem. Phys. 61, 4163 (1974).
(9)
R. B. Laughlin, J. D. Joannopoulous, C A. Murray, K. J. Hartnett, and T. J. Greytak, Intrinsic Surface Phonons in Porous Glass, Phys. Rev. Lett. 40, 461 (1978).
RAMAN STUDIES OF STRUCTURAL DEFECTS IN VITREOUS SiO,
F. L. Galeener, J. C. Mikkelsen, Jr., and N. M. Johnson Xerox Palo Alto Research Center, Palo Alto, CA 94304 ABSTRACT This paper discusses the two sharp lines which are seen at 495 cm"1 and 606 cm" in the Raman spectrum of pure fused silica. We conclude that the 495 cm"1 line is probably a longitudinal optical mode of the network, although defect origin is not entirely ruled out. More importantly, we conclude that the 606 cm"1 is due to a large concentration of non-bridging oxygen defects. We show how the strength of the 606 cm"1 line varies with the water concentration and the thermal history of bulk samples of Suprasil fused silica. INTRODUCTION Figure 1 shows the polarized Raman spectra of high purity fused silica as a function of water concentration (OH). These spectra, measured on samples as-received from the manufacturer, are discussed in detail by Galeener and Geils (1). In most respects, they are similar to the spectra reported by Stolen and Walrafen (2). The important features for the present discussion are as follows. At high frequencies, there is the 3700 cm"1 O-H stretch mode [Fig. 1(c)] which we use to monitor OH concentrations down to the level of 2 ppm by weight. At intermediate frequencies [Fig. K b ) ] the main observation is the absence of any structure other than that due to second order vibrations of the Si02 network, discussed elsewhere by Galeener and Lucovsky (3). In particular, there is the absence of Si-H stretch modes, which Hartwig (4) has shown to occur at 2285 cm"1 in deliberately hydrogenated silica. At lower frequencies [Fig. 1(a)] the features of interest are the 975 cm"1 Si-OH stretch mode induced in high water content material, the 606 cm"1 line whose intensity is reduced in the high water content as-received material, and the 495 cm"1 line whose intensity is unchanged. These latter two lines are the focus of attention in this paper; all other features in Fig. 1 which are not mentioned here have been identified elsewhere (5) as transverse optical (TO) or longitudinal optical (LO) modes of the ideal (perfect) network. THERMAL STUDIES Figure 2 shows the variation in strength of the 495 cm"1 and 606 cm"1 lines with thermal treatment of the sample. The line strength is measured by the area between the defect line and a baseline drawn with a French curve (assuming that the 495 cm"1 line has a total width at its baseline of 40 cm"1 while the 606 cm"1 line has a total width of 100 c m " 1 ) . The samples were of two types, those of low water content (solid lines) and those of high water content (dotted lines). All samples were about 3 m m x 6 m m x l 2 m m and Raman spectra were obtained from the interior of these materials. Water content was not affected by the heat treatments, as determined by measuring the area of the 3700 cnT 1 line before and after each treatment. There were
285 no changes in the frequency range 1500 cm"1 to 3000 cm"1 indicating that neither Si-H bonds nor molecular water were created. Beginning with a new set of samples, treatments (A) through (G) were carried out in the order [ l] through [ 7]. Study of the left half of Fig. 2 reveals that the area under the 495 cm"1 line varies erratically about an average value of -18. For example, in the sequence [ 3] through [ 7] the area for the low water content sample is alternately above then below the area for the high water content material. This simply reflects the difficulty in determining the base line for a peak that rides on the steep slope of the main Raman line (whose position varies by a few wavenumbers with thermal treatment). By placing spectra over one another we conclude that the area under the 495 cm"1 line is constant within 5%.
THERMAL STUDIES OF VITREOUS SILICA ■ SUPRASIL-WI • SUPRASIL-1 THERMAL TREATMENT
i__
(0H)<2ppm (OH»-1200ppm
495 c m ' 1 R A M A N LINE AREA 0
10
6 0 6 c m -1 R A M A N L I N E
►
AREA 20
3
10
— 20
30
AS RECEIVEO
AIR QUENCHED FROM 1500 C WATER QUENCH FROM 1500 C ANNEALE0: 1230 C 35 MIN. ANNEALED: 1100C 15 HRS.
2000
2500
WAVENUMBER, W, c m " 1
Ί—rRAMAN SPECTRA
-i—i—|—r
NEW SAMPLES: ANNEALED AT 1190 C-16 HRS. WATER QUENCH
I I I I / i
/HV 3500
ANNEALED: 910 C 60 HRS.
OH < 5 PPM - O H - 180 ΡΡΛ O H - 1200 PP , 4000
WAVENUMBER, W. c m - 1
Fig. 1. The OH dependence of the polarized Raman spectra of as-received Suprasil. The sharp lines at 495 cm"1 and 606 cm"1 in (a) are the features of special interest in this paper.
Fig. 2. The strengths of the 495 cm"1 and 606 cm"1 Raman lines after different thermal treatments (A) through (H). Note the time sequence of steps, [ l] through [ 7]. The variations in the 495 cm"1 line are erratic and small, while the 606 cm"1 line strength varies strongly and systematically.
286 The right half of Fig. 2 reveals clear changes in the strength of the 606 cm"1 line. The line strength in high water content material is always less than (or equal to) that for low water content material. Material quenched from high temperatures has a larger 606 cm*1 line than material quenched from low temperatures. Figures 2(f) and 2(h) suggest that after sufficiently long periods at a given temperature >_1100°C, the strength of the 606 cm*1 line is independent of the water concentration. This contradicts the most obvious interpretation of Fig. 2(a), namely that the 606 cm"1 defect concentration is lower in high water content samples. Our hypothesis for resolving this is to assume that equilibrium is reached far more quickly in high water content samples, but that the equilibrium concentration is not very dependent on water content. This is consistent with the fact that high water content material has significantly lower viscosity (6). Thus, we suppose that watercontaining and water-free as-received material have different 606 cm"l line strength either because they have been annealed at different temperatures, or, if annealed at the same temperature, because the low water content material was not annealed long enough for the defect concentration to achieve equilibrium value. Another possibility is that there is, in fact, a real difference in the equilibrium 606 cm"1 defect concentrations in watercontaining and water-free samples that have been annealed at temperatures below 1100 C. More data is being obtained, with careful attention to the role of annealing time and quenching speed, and the results will be discussed more extensively elsewhere. DISCUSSION Stolen, Krause, and Kurkjian (7) first suggested that the 606 cm"1 line might be due to a defect, when they observed that this line increased at least fivefold after the sample had been irradiated with ~10 2 ° fast neutrons/cm2. Their data showed essentially no change in the area of the 495 cm"1 line with irradiation, although this line did shift to slightly higher frequency, as did the 606 cm"1 line and the main Raman peak. These results were corroborated in an extensive study of neutron effects by Bates, Hendricks, and Schaffer (8). The latter authors reported a seven-fold increase in the 606 cm"1 line for an exposure of 2 x 1 0 2 0 neutrons/cm2, as well as a possible slight increase in the strength of the 495 cm"1 line. They conclude that both of these lines are due to defects that are intrinsic in vitreous (v-)Si02, and that both may be associated with the defect formed when a Si-0 bond is left broken, i.e., associated with a "non-bridging oxygen defect" (NBOD) of the form ESi + 0"-SiH. As Bates, et al. (8) point out, their results do not rule out the possibility that the lines are due to other kinds of structural defects. Indeed, from theoretical studies, Laughlin and coworkers (9) have suggested that the 606 cm"1 line is due to a "wrong bond" defect of the form =si-Si=, which we refer to as the Si-Si bond defect. The neutron bombardment studies thus clearly establish the 606 cm"1 line as having defect origin. On the other hand, we believe that the very small observed changes in the 495 cm"1 line demonstrate that it cannot be associated with precisely the same defect that gives rise to the rapidly increasing 606 cm"1 line. Were this so, both lines would rise by the same percentage. Moreover, the small reported changes in strength of the 495 cm"1 line may be due to the difficulty of measuring its strength, or they may be due to changes in matrix elements brought about by the compaction of the network under neutron irradiation. If the 495 cm"1 is a defect, the defect concentration is very little affected by neutron bombardment; nor is it affected by water content or thermal treatment, as we have shown. At the present, we
287 think it more likely that the 495 cm"1 line is an LO mode of the basic network, as argued in Ref. 5. Accordingly, we focus the rest of our attention on the 606 cm"1 line. A set of as-received samples of Suprasil 1 and Suprasil W-l were exposed to 30 Mrad of X-rays from a 60 kV DC machine. This induced the expected UV absorption and strong spin resonance signals, but caused no detectable change in the Raman spectra. Thus, X-irradiation does not induce the 606 cm"1 defect, but it may activate associated electronic states. It can be demonstrated that the 606 cm"1 line is not due to Si-Si bonds or 0-0 bonds, by appeal to measurements made on v-Ge02- Galeener and Geils (1) reported a line at 520 cm"1 in the Raman spectrum of v-Ge02 which they believed was analogous to the 606 cm"1 line in v-SiOo. This has been confirmed by making measurements on v-Ge02 irradiated by 10 2 * neutrons/cm2 which show a large increase in the strength of the 520 cm"1 line. Raman measurements were also made on non-phase-separated v-Ge02 that was 10% Ge-rich. The defect line at 520 cm"1 was unaffected. This proves that the 520 cm"1 line in normally stoichiometric material is not due to a small concentration of Ge-Ge bonds, which would increase greatly in the Ge-rich material, nor is it due to a small concentration of 0-0 bonds which would most probably go to zero in the Ge-rich material. It then follows that the 606 cm"1 defect in V-S1O2 is not a wrong bond defect of the Si-Si or 0-0 type. Having eliminated wrong bond defects, we next consider the most likely broken bond defects, which are the isolated dangling silicon bond HSi , the isolated dangling oxygen bond "O-Sin, or their spatial juxtaposition, the previously defined NBOD. Also, in this category are the missing oxygen (Ξβί ΞίΞ) and the missing silicon defects, both of which might be formed under neutron bombardment. Since the NBOD is locally neutral, it will have lower energy associated with its existence than will the other four (charged) defects. Thus, we expect the NBOD to be the most numerous defect. Also, since the 606 cm"1 defect line is the only one observed, it is reasonable to ascribe this line to the existence of NBOD's. We believe this identification is consistent with all experimental observations to date, including thermal history and neutron bombardment. The question now arises whether the 606 cm"1 line is due to the NBOD as an inseparable whole, or whether it can be assigned to only one part of the defect, either the dangling oxygen, or the silicon with the dangling bond. We eliminate the isolated dangling oxygen by appeal to the OH-dependence data in Fig. 1(a). First, we make the reasonable assumption that the addition of a hydrogen to a dangling oxygen, forming the OH unit, will result in very little change in the frequency or Raman activity of defect vibrational modes previously involving the dangling oxygen, but now involving the dangling OH unit. Since the 975 cm"1 line was non-existent before introduction of 1200 ppm OH, the concentration of isolated dangling oxygen units in the water-free material must be very small. Furthermore, if the 606 cm"1 line were due to the dangling oxygen half of the NBOD, then this line should have increased dramatically with the introduction of danglinq OH units. Instead, it decreased slightly, and after annealing at 1100 C or 1190°C showed the same strength as in the water-free material. Moreover, its concentration can be increased by quenching the glass from a higher temperature, without any concurrent change in the 975 cm"1 line.
288 Although we presently feel that the 606 cm"1 line is most likely the signature of silicon atoms with one dangling bond, we are not yet able to eliminate the possibility that it represents a mode of the NBOD as a whole. We are working further in an effort to answer this question. REFERENCES (1)
F. L. Galeener and R. H. Geils (1977), The Polarized Raman Spectra of OH in Vitreous S1O2 and Ge0 2 , The Structure of Non-Crystalline Materials, ed. P. H. Gaskell, Taylor and Francis, London, 223.
(2)
R. H. Stolen and G. E. Walrafen, Water and Its Relation to Broken Bond Defects in Fused Silica, J. Chem. Phys. 64, 2623 (1976).
(3)
F. L. Galeener and G. Lucovsky (1976), Second Order Vibrational Spectra of Vitreous Silica, Light Scattering in Solids, ed. M. Balkanski, R. C. C. Leite and S. P. S. Porto, Flammarion, Paris, 641.
(4)
C M . Hartwig, The Radiation-Induced Formation of Hydrogen and Deuterium Compounds in Silica and Observed by Raman Scattering, J. Chem. Phys. 66, 227 (1977).
(5)
F. L. Galeener and G. Lucovsky, Longitudinal Optical Vibrations in Glasses: Ge0 2 and Si0 2 , Phys. Rev. Lett. 37, 1474 (1976).
(6)
See R. H. Doremus (1973) Glass Science, Wiley, New York, 105.
(7)
R. H. Stolen, J. T. Krause, and D. R. Kurkjian, Raman Scattering and Far Infra-Red Absorption in Neutron Compacted Silica, Disc. Faraday Soc. 50, 103 (1970).
(8)
J. B. Bates, R. W. Hendricks, and L. B. Shaffer, Neutron Irradiation Effects and Structure of Noncrystalline Si0 2 , J. Chem. Phys. 61, 4163 (1974).
(9)
R. B. Laughlin, J. D. Joannopoulous, C A. Murray, K. J. Hartnett, and T. J. Greytak, Intrinsic Surface Phonons in Porous Glass, Phys. Rev. Lett. 40, 461 (1978).