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Raman studies of the GeO2 glass preparation history
56
Journal
RAMAN
STUDIES
Solids 94 (1987) 56-61 North-Holland. Amsterdam
OF THE GeO, GLASS PREPARATION
R.H. MAGRUDER,
III
Belmonr
TN 37203,
College,
of Non-Crystalline
Nashville,
HISTORY
USA
S. MORGAN Fisk
Universiry.
Nashville,
D.L. KINSER Vanderbilt Received Revised
University,
TN 37203,
USA
and R.A. WEEKS Nashville,
22 December 1986 manuscript received
TN 37235,
20 April
USA
1987
A series of high purity GeO, glasses with T+‘s from 1960 to 1450°C were prepared and the Raman spectra measured. In the normalized spectras the 977 and 862 cm-’ LO and TO pair as well as the 558 cm- ’ shoulder were seen to decrease with increasing T+. The decreases observed are a consequence of the increase of depolymerization of the equilibrated liquid with increasing T+. As the melt liquid is quenched through Tg, remnants of the liquid structure are preserved to room temperature resulting in a decrease in the degree of polymerization of the glass structure.
1. Introduction A number of investigators have established assignments for Raman bands in amorphous SiO, and GeO, based upon oxygen motion in these materials [l-5]. The correlation of oxygen motions with local structural parameters such as bond angle has allowed the use of Raman techniques to study the effect of variables such as pressure [4,6], thermal history [7-91 and irradiation [5] upon these arrangements. Galeener [7] and McMillan [9] have sought to relate and predict the effects of thermal history upon the structure of glasses. Galeener and coworkers [7,10,11] have reported extensive studies on changes in structure in amorphous SiO, as a function of fictive temperature. They have also examined fictive temperature [ll] and neutron irradiation [5] effects in amorphous GeO,. These studies have led to assignments of Raman bands to bridging oxygen motion. The effects of T+ (the temperature at which a liquid was equilibrated prior to quenching the liquid to glass) on intrinsic defect concentrations using EPR [12], electrical [14] and optical [15] techniques have been reported. It has been established that T+ has a significant influence upon the electronic structure of these glasses. We report here a Raman and optical study of T+effects on the vibrational spectra of high-purity GeO, glasses. 0022-3093/87/$03.50 0 Elsevier Science Publishers (North-Holland Physics Publishing Division)
B.V.
R. H. Magruder
2. Experimental
et al. / Ge02
gloss prepororion
history
57
procedure
A series of high purity GeO, glasses were melted and equilibrated in platinum crucibles in air. The T,s were 1690, 1650, 1550 and 1450” C. The average cooling rate was 5 o C/s from T+ to 400 o C. Samples were core-drilled from the crucible to yield cylindrical samples approximately 12 mm in diameter and 10 mm in length. Discs approximately 1 mm thick were cut from the cylinders and surfaces were polished using diamond abrasive (6 pm finish) and non-aqueous lubricants. Samples were analyzed for trace level impurities using neutron activation techniques [16] and IR absorption for OH content. The samples examined had sodium contents of lo-12 ppm, chlorine content of 1200-1600 ppm and OH content of 180-210 ppm. No other impurities were detected. Raman measurements as reported herein were repeated on not less than two samples for each T+ except in the case of the single 1690 o C melt. The indices of refraction of these glasses were measured at A = 632.8 nm using the Becke line technique [17] with standard immersion oils which were mixed to achieve the index precision required. The polarized Raman spectra were obtained at room temperature using 90” scattering geometry with a Beckman 700 Raman spectrometer. The source was an argon ion laser operating at 514.5 nm with a 200 mW of power. The spectral slit width was 8 cm-‘. The frequency uncertainty was f 3 cm-‘.
3. Results The Raman spectra of vitreous GeO, previously reported [5,7,12] have been normalized to the 420 cm-’ band. We compare the relative intensities of the
.60L-. z : 2 c
0 520 cm-’ x 55Elcm-’
I 1450
1550
1650
I750
1450
T,+ (“C1
Fig.
1. Normalized intensify as a function T+ for the 862 and 977 cm-’ bands.
15kO T+
of
Fig.
16;O
1750
(“Cl
2. Normalized intensity as a function T+ for the 520 and 558 cm-’ bands.
of
R. H. Magruder
58
et al. / GeO? glass preparation
x
1450
1550
1650 T+
Fig. 3. Normalized
intensity
as a function
history
347 cm-’
1750
(“C)
of T, for the 347 and 278 cm-’
bands.
GeO, Raman bands as a function of T+ after normalization to the 420 cm-’ band. The general form of the Raman spectra which we observe in all cases is similar to those previously reported [5,8,12]. The changes which we observed as a function of T+ include a twofold decrease in the normalized intensity of the 977 and 862 cm-’ band with increasing T+. The intensities of these two bands are plotted as a function of T+ in fig. 1. The 558 cm-’ shoulder, which consists of 556 and 595 cm-’ bands, shows a similar although smaller decrease in intensity with increasing T+ as shown in fig. 2. The intensity of the 520 cm-’ band is independent of T+ within the limits of experimental error as is shown in fig. 2. The intensities of the low frequency bands at 347 and 278 cm-’ shown in fig. 3 are also independent of
Te.
The index of refraction measurements for the same series of glasses is shown in table 1. These measurements indicate that the index is independent of T+ within the limits of the experimental error, RMS deviation of k 0.0025. Consequently, the density change corresponding to these changes is anticipated to be proportional to the index change observed and is constant to within less than 1 part in 400.
Table GeO,
1 glass index
of refraction
summary.
X = 6328 A
T’(“‘J
Index
1450 1550 1650 1690
1.605-1.610 1.605-1.610 1.610-1.615 1.603-1.607
R. H. Magruder
Ed al. / GeO,
glass preparation
history
59
4. Discussion The intensities of all the bands are normalized to the intensity of 420 cm-’ band. This band originates from the symmetric stretching mode of the bridging oxygen. It is not assumed that the intensity of the 420 cm-’ band is invariant with T+. The 977 and 862 cm-i bands have been assigned [l] to the LO and TO antisymmetric stretch of the oxygen between two bridging Ge ions. As T+ increases there is a twofold decrease in intensity of both these bands relative to the 420 cm-’ band. It has been well established that the amount of oxygen in the network decreases with increasing T+. However, a calculation of the amount of oxygen lost based on the intensity of the 245 nm band [15] indicates that the decrease in the number of Ge-0-Ge bonds due to the decrease in the number of oxygen ions is too small to account for the decrease in the 862 and 963 cm-’ bands. We suggest that these intensity changes are related to the manner in which the Ge-0-Ge vibrational modes are coupled to the glassy network. As the 862 and 977 cm-’ bands are weakly allowed in the Raman spectra, changes in the polarizability derivative for this band due to changes in the disorder of the glass will be proportionally larger than for the strongly Raman active 420 cm-’ band. If, as suggested by McMillan in this work [9] on vitreous silica, the glass structure is indicative of the liquid from which it was quenched, then intensity changes may result from changes in the equilibrated liquid structure. It is evident from the above cited works that the liquid structure changes with temperature and those differences originating in the liquid were noted by Seifert et al. [8]. It has been concluded in a number of previous papers [13-151 that those differences persist during cooling and are stable and detectable in the glasses at room temperature. This assertion diverges from “classical” glass theories which argue that the glass liquid is in metastable thermodynamic equilibria as it is cooled from T+ until it diverges from metastable equilibria at Tg. The previous data as well as the current data indicate that the structure characteristic of and derived from the original liquid equilibria is preserved and detectable in glasses quenched from differing equilibrated liquid temperatures. We do not suggest that no structural changes occur during quenching but rather that, for quenching rates employed here, remnants of liquid structure are preserved to room temperature and they are detected in the Raman measurements. We hypothesize, in confirmity with results of studies of liquid structure [8], that the disorder of the liquid increases with T+. This increased disorder is preserved in the glass quenched from the liquid and that the manifested by the reduced intensity of the 862 and 977 cm-’ bands. We interpret this to indicate that the degree of polymerization decreases with increasing T+. Galeener and Geils [12] found the intensity of Raman bands in the 830-1500 cm-’ region to increase with “fictive” temperature although the melt temperatures studied were 1200 and 1550°C with presumably identical quenching rates. Our observations are nor a consequence of fictive tempera-
60
R. H. Magruder
et al. / GeO,
glass preparation
histoy
ture effects since all glasses were cooled at the same rate from differing temperatures above the equilibrium melting temperature (1115 ’ C). Galeener and Geils’ observations also appear to be a consequence of melting conditions and OH content rather than fictive temperature. Another consequence, known for many years, is the decrease in viscosity of the liquid with increasing temperature which has been rationalized by Mackenzie [18] as a consequence of “the decrease of the degree of polymerization (of the liquid) with increasing temperature (1115 to 1550°C)“. We suggest that the decrease in intensity of the 969 and 860 cm-’ bands (corresponding to our 977 and 862 cm-’ bands) reported by Seifert et al. above the liquidus is due to this effect. Seifert et al. [8] have examined the Raman spectra of GeO, at 1250 and 135O“C which is the liquid state (r,,, = 1115°C). The spectra obtained at those two temperatures display a decreasing intensity of the 860 and 969 cm-’ bands with increasing liquid temperature. Our results obtained on liquids quenched from 1690, 1650, 1550, and 1450 o C and measured at 25 o C display a similar decrease in those bands. A similar argument can be applied to the shoulder at 558 cm-’ which contains the 556 cm-’ and 595 cm-’ bands. These bands have been assigned to the TO and LO symmetric stretch of the oxygen ion [l]. Sharma et al. [4] suggest that these bands serve as a “glass envelope” comparable to the 800 cm-’ band in fused silica. The general decrease in intensity in going from 7” of 135O’C to T+ of 1690 o C as seen in fig. 2 is, according to Sharma et al., indicative of depolymerization of the glass structure as suggested above. The trend of these bands agrees with the trend seen for the 862 and 977 cm-’ bands. While the intensity changes are not as pronounced, we note the reason for this may be difficulty in resolving the 558 cm-’ shoulder because it lies on the dominant 420 cm-’ band. One puzzling feature of these results is the lack of frequency shifts in both the 977, 862 and 595, 558 LO-TO pairs with changing T+. A change in frequency for these bands would be indicative of changes in bond angle and/or bond length [1,5]. This lack of frequency shifts is in accordance with our measurements showing no change in density. In the low-frequency region, the band at 278 cm-’ has been assigned [l] to the TO mode of a rocking motion of the bridging oxygen. The 347 cm-’ band has been attributed [4,19] to mostly Ge motion with a small amount of oxygen motion. These bands are difficult to resolve because they reside on the shoulder of the 420 cm-’ band. We do note the intensity of these bands appear to remain constant or decrease slightly for T+ 2 1450 o C. According to Galeener, this decrease may result from Ge-Ge bonds in the more reduced glass. The higher T+ glasses have been shown to be more reduced. These bands are clearly not as sensitive to T+, as the higher frequency bands. The 520 cm-’ band, which has been attributed to several structures, appears to remain constant over the T+ region examined (see fig. 2). At this point, we can offer no insight as to its origin.
R. H. Magruder
et al. / Ge02
glass preparation
hisror?,
61
5. Conclusion Raman measurements can be interpreted to indicate differences in degree of polymerization at room temperature in glasses derived from varying T+. The authors wish to acknowledge the financial support of this study under AROD Contract #DAAG29-84K-0143.
References [l] [2] [3] [4] (51 (61 [7] [8] [9] [lo] [ll] [12]
F.L. Galeener and G. Lucovsky, Phys. Rev. Lett., 37 (1986) 1474. F.L. Galeener, Phys. Rev. B19 (1979) 4294. SK. Sharma, D. Virgo and I. Kushiro, J. Non-Cryst. Solids 33 (1979) 235. SK. Sharma, D.W. Matson, J.A. Philpotts and T.L. Roush, J. Non-Cryst. Solids 68 (1984) 99. F.L. Galeener, J. Non-Cryst. Solids 40 (1980) 527. P. McMillan, B. Piriou and R. County. J. Chem. Phys. 81 (1984) 4234. F.L. Galeener, J. Non-Cryst. Solids 71 (1985) 373. F.A. Seifert, B.O. Mysen and D. Virgo, Geochim Cosmochim. Acta 45 (1981) 1379. P. McMillan, Amer. Mineral. 69 (1984) 622. J.E. Mikkelsen and F.L. Galeener, J. Non-Cryst. Solids 37 (1980) 71. A.E. Geissberger and F.L. Galeener, Phys. Rev. B28 (1983) 3266. F.L. Galeener and R.H. Geils, The Structure of Non-Crystalline Materials, Ed. P.H. Gaskell (Taylor and Francis, London, 1977). [13] G. Kordas, R.A. Weeks and D.L. Kinser. J. Appl. Phys. 54 (1983) 5394. [14] R.H. Magruder, III, D.L. Kinser, R.A. Weeks and J.M. Jackson, J. Appl. Phys. 57 (1985) 345. [15] J.M. Jackson, M.E. Wells, G. Kordas, D.L. Kinser, R.A. Weeks and R.H. Magruder, III, J. Appl. Phys. 58 (1985) 2308. [16] Neutron activation analysis performed at Oak Ridge National Laboratory by J. Emergy. [17] P.F. Kerr, Optical Mineralogy, 4th Ed. (McGraw-Hill, New York, 1977). [18) J.D. MacKenzie, in: Modem Aspects of the Vitreous State. ed. J.D. MacKenzie (Butterworths. London, 1960). [19] F.L. Galeener, A.E. Beissberger, G.W. Ogar, Jr. and R.E. Loehman, Phys. Rev. B 28 (1983) 4768.
Journal
RAMAN
STUDIES
Solids 94 (1987) 56-61 North-Holland. Amsterdam
OF THE GeO, GLASS PREPARATION
R.H. MAGRUDER,
III
Belmonr
TN 37203,
College,
of Non-Crystalline
Nashville,
HISTORY
USA
S. MORGAN Fisk
Universiry.
Nashville,
D.L. KINSER Vanderbilt Received Revised
University,
TN 37203,
USA
and R.A. WEEKS Nashville,
22 December 1986 manuscript received
TN 37235,
20 April
USA
1987
A series of high purity GeO, glasses with T+‘s from 1960 to 1450°C were prepared and the Raman spectra measured. In the normalized spectras the 977 and 862 cm-’ LO and TO pair as well as the 558 cm- ’ shoulder were seen to decrease with increasing T+. The decreases observed are a consequence of the increase of depolymerization of the equilibrated liquid with increasing T+. As the melt liquid is quenched through Tg, remnants of the liquid structure are preserved to room temperature resulting in a decrease in the degree of polymerization of the glass structure.
1. Introduction A number of investigators have established assignments for Raman bands in amorphous SiO, and GeO, based upon oxygen motion in these materials [l-5]. The correlation of oxygen motions with local structural parameters such as bond angle has allowed the use of Raman techniques to study the effect of variables such as pressure [4,6], thermal history [7-91 and irradiation [5] upon these arrangements. Galeener [7] and McMillan [9] have sought to relate and predict the effects of thermal history upon the structure of glasses. Galeener and coworkers [7,10,11] have reported extensive studies on changes in structure in amorphous SiO, as a function of fictive temperature. They have also examined fictive temperature [ll] and neutron irradiation [5] effects in amorphous GeO,. These studies have led to assignments of Raman bands to bridging oxygen motion. The effects of T+ (the temperature at which a liquid was equilibrated prior to quenching the liquid to glass) on intrinsic defect concentrations using EPR [12], electrical [14] and optical [15] techniques have been reported. It has been established that T+ has a significant influence upon the electronic structure of these glasses. We report here a Raman and optical study of T+effects on the vibrational spectra of high-purity GeO, glasses. 0022-3093/87/$03.50 0 Elsevier Science Publishers (North-Holland Physics Publishing Division)
B.V.
R. H. Magruder
2. Experimental
et al. / Ge02
gloss prepororion
history
57
procedure
A series of high purity GeO, glasses were melted and equilibrated in platinum crucibles in air. The T,s were 1690, 1650, 1550 and 1450” C. The average cooling rate was 5 o C/s from T+ to 400 o C. Samples were core-drilled from the crucible to yield cylindrical samples approximately 12 mm in diameter and 10 mm in length. Discs approximately 1 mm thick were cut from the cylinders and surfaces were polished using diamond abrasive (6 pm finish) and non-aqueous lubricants. Samples were analyzed for trace level impurities using neutron activation techniques [16] and IR absorption for OH content. The samples examined had sodium contents of lo-12 ppm, chlorine content of 1200-1600 ppm and OH content of 180-210 ppm. No other impurities were detected. Raman measurements as reported herein were repeated on not less than two samples for each T+ except in the case of the single 1690 o C melt. The indices of refraction of these glasses were measured at A = 632.8 nm using the Becke line technique [17] with standard immersion oils which were mixed to achieve the index precision required. The polarized Raman spectra were obtained at room temperature using 90” scattering geometry with a Beckman 700 Raman spectrometer. The source was an argon ion laser operating at 514.5 nm with a 200 mW of power. The spectral slit width was 8 cm-‘. The frequency uncertainty was f 3 cm-‘.
3. Results The Raman spectra of vitreous GeO, previously reported [5,7,12] have been normalized to the 420 cm-’ band. We compare the relative intensities of the
.60L-. z : 2 c
0 520 cm-’ x 55Elcm-’
I 1450
1550
1650
I750
1450
T,+ (“C1
Fig.
1. Normalized intensify as a function T+ for the 862 and 977 cm-’ bands.
15kO T+
of
Fig.
16;O
1750
(“Cl
2. Normalized intensity as a function T+ for the 520 and 558 cm-’ bands.
of
R. H. Magruder
58
et al. / GeO? glass preparation
x
1450
1550
1650 T+
Fig. 3. Normalized
intensity
as a function
history
347 cm-’
1750
(“C)
of T, for the 347 and 278 cm-’
bands.
GeO, Raman bands as a function of T+ after normalization to the 420 cm-’ band. The general form of the Raman spectra which we observe in all cases is similar to those previously reported [5,8,12]. The changes which we observed as a function of T+ include a twofold decrease in the normalized intensity of the 977 and 862 cm-’ band with increasing T+. The intensities of these two bands are plotted as a function of T+ in fig. 1. The 558 cm-’ shoulder, which consists of 556 and 595 cm-’ bands, shows a similar although smaller decrease in intensity with increasing T+ as shown in fig. 2. The intensity of the 520 cm-’ band is independent of T+ within the limits of experimental error as is shown in fig. 2. The intensities of the low frequency bands at 347 and 278 cm-’ shown in fig. 3 are also independent of
Te.
The index of refraction measurements for the same series of glasses is shown in table 1. These measurements indicate that the index is independent of T+ within the limits of the experimental error, RMS deviation of k 0.0025. Consequently, the density change corresponding to these changes is anticipated to be proportional to the index change observed and is constant to within less than 1 part in 400.
Table GeO,
1 glass index
of refraction
summary.
X = 6328 A
T’(“‘J
Index
1450 1550 1650 1690
1.605-1.610 1.605-1.610 1.610-1.615 1.603-1.607
R. H. Magruder
Ed al. / GeO,
glass preparation
history
59
4. Discussion The intensities of all the bands are normalized to the intensity of 420 cm-’ band. This band originates from the symmetric stretching mode of the bridging oxygen. It is not assumed that the intensity of the 420 cm-’ band is invariant with T+. The 977 and 862 cm-i bands have been assigned [l] to the LO and TO antisymmetric stretch of the oxygen between two bridging Ge ions. As T+ increases there is a twofold decrease in intensity of both these bands relative to the 420 cm-’ band. It has been well established that the amount of oxygen in the network decreases with increasing T+. However, a calculation of the amount of oxygen lost based on the intensity of the 245 nm band [15] indicates that the decrease in the number of Ge-0-Ge bonds due to the decrease in the number of oxygen ions is too small to account for the decrease in the 862 and 963 cm-’ bands. We suggest that these intensity changes are related to the manner in which the Ge-0-Ge vibrational modes are coupled to the glassy network. As the 862 and 977 cm-’ bands are weakly allowed in the Raman spectra, changes in the polarizability derivative for this band due to changes in the disorder of the glass will be proportionally larger than for the strongly Raman active 420 cm-’ band. If, as suggested by McMillan in this work [9] on vitreous silica, the glass structure is indicative of the liquid from which it was quenched, then intensity changes may result from changes in the equilibrated liquid structure. It is evident from the above cited works that the liquid structure changes with temperature and those differences originating in the liquid were noted by Seifert et al. [8]. It has been concluded in a number of previous papers [13-151 that those differences persist during cooling and are stable and detectable in the glasses at room temperature. This assertion diverges from “classical” glass theories which argue that the glass liquid is in metastable thermodynamic equilibria as it is cooled from T+ until it diverges from metastable equilibria at Tg. The previous data as well as the current data indicate that the structure characteristic of and derived from the original liquid equilibria is preserved and detectable in glasses quenched from differing equilibrated liquid temperatures. We do not suggest that no structural changes occur during quenching but rather that, for quenching rates employed here, remnants of liquid structure are preserved to room temperature and they are detected in the Raman measurements. We hypothesize, in confirmity with results of studies of liquid structure [8], that the disorder of the liquid increases with T+. This increased disorder is preserved in the glass quenched from the liquid and that the manifested by the reduced intensity of the 862 and 977 cm-’ bands. We interpret this to indicate that the degree of polymerization decreases with increasing T+. Galeener and Geils [12] found the intensity of Raman bands in the 830-1500 cm-’ region to increase with “fictive” temperature although the melt temperatures studied were 1200 and 1550°C with presumably identical quenching rates. Our observations are nor a consequence of fictive tempera-
60
R. H. Magruder
et al. / GeO,
glass preparation
histoy
ture effects since all glasses were cooled at the same rate from differing temperatures above the equilibrium melting temperature (1115 ’ C). Galeener and Geils’ observations also appear to be a consequence of melting conditions and OH content rather than fictive temperature. Another consequence, known for many years, is the decrease in viscosity of the liquid with increasing temperature which has been rationalized by Mackenzie [18] as a consequence of “the decrease of the degree of polymerization (of the liquid) with increasing temperature (1115 to 1550°C)“. We suggest that the decrease in intensity of the 969 and 860 cm-’ bands (corresponding to our 977 and 862 cm-’ bands) reported by Seifert et al. above the liquidus is due to this effect. Seifert et al. [8] have examined the Raman spectra of GeO, at 1250 and 135O“C which is the liquid state (r,,, = 1115°C). The spectra obtained at those two temperatures display a decreasing intensity of the 860 and 969 cm-’ bands with increasing liquid temperature. Our results obtained on liquids quenched from 1690, 1650, 1550, and 1450 o C and measured at 25 o C display a similar decrease in those bands. A similar argument can be applied to the shoulder at 558 cm-’ which contains the 556 cm-’ and 595 cm-’ bands. These bands have been assigned to the TO and LO symmetric stretch of the oxygen ion [l]. Sharma et al. [4] suggest that these bands serve as a “glass envelope” comparable to the 800 cm-’ band in fused silica. The general decrease in intensity in going from 7” of 135O’C to T+ of 1690 o C as seen in fig. 2 is, according to Sharma et al., indicative of depolymerization of the glass structure as suggested above. The trend of these bands agrees with the trend seen for the 862 and 977 cm-’ bands. While the intensity changes are not as pronounced, we note the reason for this may be difficulty in resolving the 558 cm-’ shoulder because it lies on the dominant 420 cm-’ band. One puzzling feature of these results is the lack of frequency shifts in both the 977, 862 and 595, 558 LO-TO pairs with changing T+. A change in frequency for these bands would be indicative of changes in bond angle and/or bond length [1,5]. This lack of frequency shifts is in accordance with our measurements showing no change in density. In the low-frequency region, the band at 278 cm-’ has been assigned [l] to the TO mode of a rocking motion of the bridging oxygen. The 347 cm-’ band has been attributed [4,19] to mostly Ge motion with a small amount of oxygen motion. These bands are difficult to resolve because they reside on the shoulder of the 420 cm-’ band. We do note the intensity of these bands appear to remain constant or decrease slightly for T+ 2 1450 o C. According to Galeener, this decrease may result from Ge-Ge bonds in the more reduced glass. The higher T+ glasses have been shown to be more reduced. These bands are clearly not as sensitive to T+, as the higher frequency bands. The 520 cm-’ band, which has been attributed to several structures, appears to remain constant over the T+ region examined (see fig. 2). At this point, we can offer no insight as to its origin.
R. H. Magruder
et al. / Ge02
glass preparation
hisror?,
61
5. Conclusion Raman measurements can be interpreted to indicate differences in degree of polymerization at room temperature in glasses derived from varying T+. The authors wish to acknowledge the financial support of this study under AROD Contract #DAAG29-84K-0143.
References [l] [2] [3] [4] (51 (61 [7] [8] [9] [lo] [ll] [12]
F.L. Galeener and G. Lucovsky, Phys. Rev. Lett., 37 (1986) 1474. F.L. Galeener, Phys. Rev. B19 (1979) 4294. SK. Sharma, D. Virgo and I. Kushiro, J. Non-Cryst. Solids 33 (1979) 235. SK. Sharma, D.W. Matson, J.A. Philpotts and T.L. Roush, J. Non-Cryst. Solids 68 (1984) 99. F.L. Galeener, J. Non-Cryst. Solids 40 (1980) 527. P. McMillan, B. Piriou and R. County. J. Chem. Phys. 81 (1984) 4234. F.L. Galeener, J. Non-Cryst. Solids 71 (1985) 373. F.A. Seifert, B.O. Mysen and D. Virgo, Geochim Cosmochim. Acta 45 (1981) 1379. P. McMillan, Amer. Mineral. 69 (1984) 622. J.E. Mikkelsen and F.L. Galeener, J. Non-Cryst. Solids 37 (1980) 71. A.E. Geissberger and F.L. Galeener, Phys. Rev. B28 (1983) 3266. F.L. Galeener and R.H. Geils, The Structure of Non-Crystalline Materials, Ed. P.H. Gaskell (Taylor and Francis, London, 1977). [13] G. Kordas, R.A. Weeks and D.L. Kinser. J. Appl. Phys. 54 (1983) 5394. [14] R.H. Magruder, III, D.L. Kinser, R.A. Weeks and J.M. Jackson, J. Appl. Phys. 57 (1985) 345. [15] J.M. Jackson, M.E. Wells, G. Kordas, D.L. Kinser, R.A. Weeks and R.H. Magruder, III, J. Appl. Phys. 58 (1985) 2308. [16] Neutron activation analysis performed at Oak Ridge National Laboratory by J. Emergy. [17] P.F. Kerr, Optical Mineralogy, 4th Ed. (McGraw-Hill, New York, 1977). [18) J.D. MacKenzie, in: Modem Aspects of the Vitreous State. ed. J.D. MacKenzie (Butterworths. London, 1960). [19] F.L. Galeener, A.E. Beissberger, G.W. Ogar, Jr. and R.E. Loehman, Phys. Rev. B 28 (1983) 4768.